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## Welcome
I study galaxies, stars, and how stars change galaxies.
I'm a Ph.D. student in the UC Berkeley Department of Astronomy. I use supercomputer simulations and data from big telescopes to better understand how the universe works.
My speciality is galaxy formation, with a focus on low-mass galaxies. I'm also interested in a range of problems in stellar physics and, more generally, in developing new methods to extract information from data. My advisors are Eliot Quataert and Dan Weisz .
I was an undergrad at Yale University, where I worked with Marla Geha. I graduated with a B.S. in astrophysics in 2016.
### Research Interests
I am interested in a broad range of topics at the intersection of cosmology, galaxy formation and evolution, and stellar physics. I try to work at the interface between of theory and observations, emphasizing thorough tests of theoretical predictions with observational data.
Brief summaries of some of my projects are available below.
#### Dynamical effects of stellar feedback on low-mass galaxies
Using galaxy simulations from the Feedback in Realistic Environments (FIRE) project, I have shown that feedback-driven gas outflows can couple energy from stellar feedback to the orbits of stars and dark matter. This causes stars to migrate coherently outward, producing metallicity gradients and apparent outside-in quenching signatures similar to those observed in nearby dwarf galaxies.
Because stellar feedback disrupts star forming gas clouds, the star formation rate of low-mass galaxies varies in concert with the dynamics and spatial distribution of stars and dark matter. I have shown that this leads to observationally testable predicted correlations between galaxies' star formation rates and their sizes, velocity dispersions, and dark matter density profiles.
Feedback-driven outflows are dynamically important when (a) star formation is bursty, (b) the potential is shallow, and (c) the baryon fraction is relatively high. I have shown that these conditions are satisfied not only in dwarf galaxies, but also in the high-redshift progenitors of Milky Way-mass galaxies. As a result, many of the dynamical processes discussed above also apply. In particular, I predict the oldest stars in the Milky Way to have migrated outwards since they formed, so that ancient stars are found primarily in the inner stellar halo at $z=0$.
For details, see the paper Where are the most Ancient Stars in the Milky Way?.
Some popular science coverage related to these papers can be found in this article. A follow-up investigation can be found in this paper.
#### Stellar feedback as a driver of gas kinematics and morphology
Stars inject energy into their host galaxies' gas through supernovae, radiation pressure, and stellar winds. I have shown that, particularly at low masses, the resulting gas outflows dramatically change galaxies' observable properties, heating their gas and preventing the formation of stable disks. This failure of disk formation turns out to be closely related to the stochastic star formation histories our model predicts for low-mass galaxies.
Spatially resolved gas kinematic maps are expensive and observationally in short supply. Using simulated galaxies, I have shown that one can also extract kinematic information from spatially unresolved observations, which have already been obtained for large, morphologically unbiased samples of galaxies in the local Universe. I have then used mock-observations of unresolved HI to compare simulations and data.
#### Globular cluster formation
I have developed a semi-analytic model to predict the globular cluster populations of galaxies based on their assembly histories. One of the lessons of this model is that many properties of globular cluster populations are primarily set during hierarchical assembly and are not sensitive to details of the globular cluster formation process.
#### Stellar multiplicity
On much smaller scales, I have studied how the presence of unrecognized binarity, which affects nearly half of stars targeted by spectroscopic surveys of the Milky Way, can bias stellar parameters and abundances derived from fitting spectra. I have also developed a binary spectral model that corrects these baises.
With a binary spectral model in hand, I analyzed spectra of main-sequence stars from the APOGEE survey in order to find targets whose spectra show evidence of unresolved multiplicity. Our model made it possible to identify 2-3 times more binaries and triples than can be identified by traditional radial velocity methods, which are only sensitive to short-period systems.
More recently, I've studied the occurence rate and separation distribution of very wide binaries, with separations of tens to tens of thousands of AU. Gaia astrometry makes it possible to identify gravitationally bound binaries and eliminate chance alignments with ruthless efficiency, allow us to create a very pure catalog. Using the catalog, we showed that there are fewer-than-expected very wide binaries containing a white dwarf. We proposed that these binaries have been disrupted by velocity kicks during white dwarf formation due to anisotropic mass loss.
Cross-matching the binary catalog with Galactic spectroscopic surveys allows us to measure how the binary fraction varies with metallicity. We find that it becomes strongly anti-correlated with metallicity at separations less than 200 AU, likely corresponding to the separation below which binaries form by disk fragmentation.
#### The initial mass function of low-mass galaxies
Despite 60+ years of research, it remains unclear whether the stellar initial mass function (IMF) is constant or varies with environment. I have carried out statistical tests to determine what observational data is needed to robustly identify IMF variations and have designed an efficient observing strategy to search for IMF variations in nearby dwarf galaxies with JWST.
#### The initial-final mass relation
The recent Gaia data release provided accurate parallaxes for a homogenous sample of tens of thousands of field white dwarfs, revealing never-before-seen substructure in the color magnitude diagram (CMD). I developed a model to predict the white dwarf CMD for a given initial-final mass relation (IFMR) and used it to constrain the IFMR for stars with a wide range of initial masses.
For details, see the paper An Empirical Measurement of the Initial-Final Mass Relation with Gaia White Dwarfs. Here's some popular coverage of the paper (in German).
### Publications and Curriculum Vitae
My CV (current as of June 25, 2019) is available here.
### Public Code and Data
Wide binaries with spectroscopic metallicities
The catalog of wide binaries within 200 pc that were observed by a spectroscopic survey and analyzed in the paper The wide binary fraction of solar-type stars: emergence of metallicity dependence at a < 200 AU is available here .
Gaia wide binary catalog
The catalog of high-confidence wide binaries within 200 pc produced in the paper Imprints of white dwarf recoil in the separation distribution of Gaia wide binaries is available here .
Separation distribution inference
The code used to infer the intrinsic separation distribution of wide binaries (correcting for incompleteness at small separations) in the paper Imprints of white dwarf recoil in the separation distribution of Gaia wide binaries is available here .
Initial-final mass relation
A tabulated version of the IFMR derived in the paper An empirical measurement of the initial-final mass relation with Gaia white dwarfs is available here .
Spectral models
A public version of the code BinSpec, which models and fits spectra of single- and multiple-star systems, is available on available GitHub .
Spectroscopic binary catalogs
Several catalogs accompanying the paper Discovery and Characterization of 3000+ Main-Sequence Binaries from APOGEE Spectra are available here .
FIRE galaxy simulation angular momentum
True and mock-observed baryon angular momenta for simulated galaxies from the paper Gas kinematics, morphology and angular momentum in the FIRE simulations are available here .
### Visualizations
#### LAMOST spectra along the main sequence
The animation below shows how the normalized optical spectrum of main-sequence stars changes with mass along the main sequence, assuming LAMOST-like resolution ($R\sim 2000$) and wavelength coverage. The spectral model uses The Payne, developed by Yuan-Sen Ting, to interpolate between synthetic model spectra.
#### LAMOST binary spectrum
This animation shows how the LAMOST-like spectrum of an unresolved main-sequence binary system with a solar-type primary changes with mass ratio. The bottom-right panel shows that the spectral signature of binarity is maximized at $q\sim 0.8$. For details, see El-Badry et al. 2018. | {} |
re **Puzzle 165** about adjoints for the forgetful functor \$$U : \textbf{Grp} \rightarrow \textbf{Mon}\$$:
I think people are on the right track in trying to construct a left adjoint as the free group on a monoid \$$M\$$ but the construction is trickier and involves words/quotients.
Specifically, we take words (ie finite sequences) comprising elements of \$$M\$$ and their formal inverses (ie tokens of the form \$$x^{-1}\$$ where \$$x \in M\$$).
We "reduce" these words as far as possible using these following rules:
• multiply together any adjacent "plain" elements – so \$$[x, y]\$$ becomes \$$[xy]\$$
• multiply together any adjacent "inverse" elements – so \$$[y^{-1}, x^{-1}]\$$ becomes \$$[(xy)^{-1}]\$$
• remove any adjacent pairs of elements and their inverses – so \$$[x, x^{-1}]\$$ becomes \$$[\ ]\$$
• remove any adjacent pairs of inverses and plain elements – so \$$[y^{-1}, y]\$$ becomes \$$[\ ]\$$
• remove any units or inverses of units – so \$$[1]\$$ becomes \$$[\ ]\$$, as does \$$[1^{-1}]\$$
To multiply two reduced words we concatenate them and reduce. The empty word is the identity, and every word has an inverse (reverse the order of terms and invert each one, so \$$[x, y^{-1}, z]^{-1} = [z^{-1}, y, x^{-1}]\$$).
So we have a group, which we'll call \$$FM\$$. We can check any monoid homomorphism from \$$M\$$ into the underlying monoid of a group \$$G\$$ can be uniquely extended to a group homomorphism \$$FM \rightarrow G\$$, and any such group homomorphism restricts to a monoid homomorphism \$$M \rightarrow UG\$$. So \$$F\$$ is left adjoint to \$$U\$$.
The right adjoint is simpler to construct – it just sends every monoid \$$M\$$ to its submonoid \$$RM\$$ of invertible elements (considered as a group). Then group homomorphisms \$$G \rightarrow RM\$$ correspond naturally to monoid homomorphisms \$$UG \rightarrow M\$$. | {} |
# American Institute of Mathematical Sciences
February 2005, 12(2): 193-212. doi: 10.3934/dcds.2005.12.193
## Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations
1 Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 117, Taiwan 2 Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan
Received July 2003 Revised October 2003 Published December 2004
We study entire solutions of a scalar reaction-diffusion equation of 1-space dimension. Here the entire solutions are meant by solutions defined for all $(x,t)\in\mathbb R^2$. Assuming that the equation has traveling front solutions and using the comparison argument, we prove the existence of entire solutions which behave as two fronts coming from the both sides of $x$-axis. A key idea for the proof of the main results is to characterize the asymptotic behavior of the solutions as $t\to-\infty$ in terms of appropriate subsolutions and supersolutions. This argument can apply not only to a general bistable reaction-diffusion equation but also to the Fisher-KPP equation. We also extend our argument to the Fisher-KPP equation with discrete diffusion.
Citation: Jong-Shenq Guo, Yoshihisa Morita. Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 193-212. doi: 10.3934/dcds.2005.12.193
[1] Maho Endo, Yuki Kaneko, Yoshio Yamada. Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3375-3394. doi: 10.3934/dcds.2020033 [2] Masaharu Taniguchi. Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3981-3995. doi: 10.3934/dcds.2020126 [3] Patrick Martinez, Judith Vancostenoble. Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 695-721. doi: 10.3934/dcdss.2020362 [4] Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020319 [5] Zhenzhen Wang, Tianshou Zhou. Asymptotic behaviors and stochastic traveling waves in stochastic Fisher-KPP equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020323 [6] Hideki Murakawa. Fast reaction limit of reaction-diffusion systems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1047-1062. doi: 10.3934/dcdss.2020405 [7] Michiel Bertsch, Danielle Hilhorst, Hirofumi Izuhara, Masayasu Mimura, Tohru Wakasa. A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3117-3142. doi: 10.3934/dcds.2019226 [8] Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, , () : -. doi: 10.3934/era.2021003 [9] Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020316 [10] Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020321 [11] Shin-Ichiro Ei, Shyuh-Yaur Tzeng. Spike solutions for a mass conservation reaction-diffusion system. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3357-3374. doi: 10.3934/dcds.2020049 [12] Chihiro Aida, Chao-Nien Chen, Kousuke Kuto, Hirokazu Ninomiya. Bifurcation from infinity with applications to reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3031-3055. doi: 10.3934/dcds.2020053 [13] Raffaele Folino, Ramón G. Plaza, Marta Strani. Long time dynamics of solutions to $p$-Laplacian diffusion problems with bistable reaction terms. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020403 [14] Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, , () : -. doi: 10.3934/era.2020118 [15] Fang-Di Dong, Wan-Tong Li, Shi-Liang Wu, Li Zhang. Entire solutions originating from monotone fronts for nonlocal dispersal equations with bistable nonlinearity. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1031-1060. doi: 10.3934/dcdsb.2020152 [16] H. M. Srivastava, H. I. Abdel-Gawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020433 [17] Lin Shi, Xuemin Wang, Dingshi Li. Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5367-5386. doi: 10.3934/cpaa.2020242 [18] Guillaume Cantin, M. A. Aziz-Alaoui. Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020283 [19] Shin-Ichiro Ei, Hiroshi Ishii. The motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effect. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 173-190. doi: 10.3934/dcdsb.2020329 [20] Nabahats Dib-Baghdadli, Rabah Labbas, Tewfik Mahdjoub, Ahmed Medeghri. On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021004
2019 Impact Factor: 1.338 | {} |
# Driving line input of a speaker from a differential amplifier, why is the output clipped?
I have a differential audio signal which I want to use to drive a single-ended device (in this case, an amplified pc desktop speaker with line level inputs) with 10kohm impedance. I have wired up a TLV2462 op-amp as a differential amplifier:
simulate this circuit – Schematic created using CircuitLab
The opamp power is 5v relative to ground, which is not connected to the amp ground in the circuit above. The input common mode voltage is 0.75v, and the differential signal is about 0.5v p-p, so the inputs should be well within the rails.
If I put a scope between amp input and amp ground with the load disconnected, I see the output signal exactly as I want it (sorry for the bad cellphone pic of a cheap scope):
But if I connect the load/speaker, the output is clipped slightly below 0v:
I see exactly the same output if I just put a 10k resistor in the circuit instead of connecting the speaker.
Edit: In the answers and comments below, several people have commented on ground and amp ground not being connected. If I connect A to ground, then I see basically the same as the second scope image below, but the clipping is actually at ground, not a little below it. If I put a capacitor between amp ground and A (now ground) instead of connecting those directly, I get the output I want. But, I don't really understand why.
Is the ground connection and capacitor I describe above the "right" fix? Why does it work? If not, what should I be doing instead?
Since this is for music, I'd like to keep frequencies above 20 Hz, if that's practical. The impedance of the load is 10k.
• You mention "not connected to ground in the circuit below" yet there is no circuit below and this confuses me. You also say the output is clipped slightly below 0V - an op-amp powered by +V and 0V cannot produce an output less than 0V. Also, where is 0V on the scope shots? – Andy aka Jul 8 '16 at 8:17
• Whoops. I meant above. Edited. – archbishop Jul 8 '16 at 8:18
• The scope ground is connected to the ground in the schematic, not the ground input of the op-amp (and the signal to Vout). 0V on the scope shot is where the yellow indicator on the left is; on the right side of the photo you can see the horizontal line with short marks along it. When I said the input common voltage is 0.75v, that is measured relative to the op-amp ground. – archbishop Jul 8 '16 at 8:24
• Do you provide the op-amp with -5V supply so its output can go negative? Show the op-amp power supply connections in your circuit. – Dmitry Grigoryev Jul 8 '16 at 9:11
• Voting to leave question OPEN for now. OP must show effort at understanding the problem and correcting it. – Sparky256 Jul 8 '16 at 21:54
Step 1:
PC speakers are crappy at best. Who knows what they call ground, how they relate it and where exactly it comes from.
Thus, Step 2:
You need to have ONE ground point in your system.
Which follows to Step 3:
You need AC coupling in your schematic, because you do not know what will be at the output, in terms of power-loops through whatever other connection, such as power-earth.
Gives Step 4:
The same ground loops may be causing your input signal to jump/drop to either power-rail and op-amps only really work with voltages between their power-rails. Many op-amps even only work with a (small) part in the middle of that region.
simulate this circuit – Schematic created using CircuitLab
Where the 5k resistors make a voltage divider to keep your incoming signals on average around 1/2 Vcc, as long as your signal source can cope with 5k/3 =~ 1.6k loading that should be fine. If your signal source is very weak, you may need a balancing resistor coming from a dedicated 1/2Vcc point, like so:
simulate this circuit
Whether your capacitors need to be in the range of single nF, hundreds of nF, or several μF, only someone knowing all the specs of the signal (and allowable star-up behaviour) can tell you.
• I built the upper circuit. Wired up like this, the output is maybe 5mV dc. If I measure the two terminals of R7, I see the input sine wave, about .4v p-p, with about 2v offset at the bottom end, and 3v offset at the top. So, they are kinda near 1/2Vcc, but with the large DC offset between the two inputs, this doesn't really look like a differential signal at all? The specs for the chip driving the input signal say the allowed load is 16 ohm to OC (open circuit, I guess), so 1.6k should be fine. – archbishop Jul 9 '16 at 3:48
The opamp power is 5v relative to its ground, which is not connected to the ground in the circuit above.
Well here's one problem - the negative power rail being 0V does need to connect to the ground points. Not being connected to ground means the signal ground can float off relative to power ground and break rules on input common mode range.
Using an output capacitor will probably achieive what you want but you must have the power rails of your op-amp tied to signal ground: -
Choose C to avoid too much bass cut-off but without knowing what value Rload truly is or your lowest frequency I can't give a value.
• I'm not sure how to use this schematic tool to indicate what I want, which is that the negative power rail connected to ground is not connected to the ground for the single-ended output signal path. – archbishop Jul 8 '16 at 8:26
• So why did you state what I highlighted in my answer? That clearly says that your op-amp power supply is not referenced to ground in the circuit and the only ground in the circuit is at the bottom of R4 and the load. – Andy aka Jul 8 '16 at 8:29
• Let me try again. I have a power supply. gnd and +5 are connected to gnd and Vdd+ on the op-amp. The same supply is powering the signal generator, which has the properties I gave above. the r4 and the "ground" input of the speaker are connected to each other, the ground input to the scope, and nothing else. I grant any of this may be wrong or mislabeled, but I believe it describes my circuit. – archbishop Jul 8 '16 at 8:36
• You cannot have your power rails galvanically isolated from your signal 0V in regular op-amp circuits. Your expectations of your circuit exceed the reality. If you need an AC output that is symmetrical about ground use an output coupling capacitor or an extra negative rail. – Andy aka Jul 8 '16 at 8:46
• Then the 3 dB cut-off point of a series 1uF feeding a 10k resistor is 15.9 Hz i.e. $\dfrac{1}{2\pi RC}$. You can make the capacitor bigger of course. – Andy aka Jul 9 '16 at 10:22 | {} |
Tech Problem Aggregator
# Invalid Configuration Data error
Q: Invalid Configuration Data error
I keep getting this error message at start up. It gives me the option of F1 to resume or F2 to enter set up. When I hit F1 it starts fine enough but I'm concerned about this. Follows is a start up list report and then a hijack this log.
start up list log
StartupList report, 4/15/2006, 8:49:48 PM
StartupList version: 1.52
Started from : C:\Program Files\StartUpList\StartupList.EXE
Detected: Windows XP SP2 (WinNT 5.01.2600)
Detected: Internet Explorer v6.00 SP2 (6.00.2900.2180)
* Using default options
==================================================
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\spoolsv.exe
C:\WINDOWS\Explorer.EXE
C:\WINDOWS\GWHotKey.exe
C:\Program Files\HP\HP Software Update\HPWuSchd2.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgcc.exe
C:\Program Files\Logitech\MouseWare\system\em_exec.exe
C:\Program Files\Zone Labs\ZoneAlarm\zlclient.exe
C:\WINDOWS\system32\ctfmon.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgamsvr.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgupsvc.exe
C:\PROGRA~1\Symantec\NORTON~1\GHOSTS~2.EXE
C:\Program Files\Common Files\Microsoft Shared\VS7DEBUG\MDM.EXE
C:\WINDOWS\system32\nvsvc32.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\ZoneLabs\vsmon.exe
C:\WINDOWS\system32\utilman.exe
C:\Program Files\StartUpList\StartupList.exe
--------------------------------------------------
Listing of startup folders:
Shell folders Common Startup:
Logitech Desktop Messenger.lnk = C:\Program Files\Logitech\Desktop Messenger\8876480\Program\LDMConf.exe
--------------------------------------------------
Checking Windows NT UserInit:
[HKLM\Software\Microsoft\Windows NT\CurrentVersion\Winlogon]
UserInit = C:\WINDOWS\system32\userinit.exe,
--------------------------------------------------
Autorun entries from Registry:
HKLM\Software\Microsoft\Windows\CurrentVersion\Run
MSConfig = C:\WINDOWS\PCHealth\HelpCtr\Binaries\MSConfig.exe /auto
NvCplDaemon = RUNDLL32.EXE NvQTwk,NvCplDaemon initialize
NeroFilterCheck = C:\WINDOWS\system32\NeroCheck.exe
Multi-function Keyboard = GWHotKey.exe
Logitech Utility = Logi_MwX.Exe
KernelFaultCheck = %systemroot%\system32\dumprep 0 -k
HP Software Update = C:\Program Files\HP\HP Software Update\HPWuSchd2.exe
HP Component Manager = "C:\Program Files\HP\hpcoretech\hpcmpmgr.exe"
DXDllRegExe = dxdllreg.exe
AVG7_CC = C:\PROGRA~1\Grisoft\AVGFRE~1\avgcc.exe /STARTUP
Zone Labs Client = C:\Program Files\Zone Labs\ZoneAlarm\zlclient.exe
--------------------------------------------------
Autorun entries from Registry:
HKCU\Software\Microsoft\Windows\CurrentVersion\Run
ctfmon.exe = C:\WINDOWS\system32\ctfmon.exe
--------------------------------------------------
Shell & screensaver key from C:\WINDOWS\SYSTEM.INI:
Shell & screensaver key from Registry:
Shell=Explorer.exe
SCRNSAVE.EXE=C:\WINDOWS\System32\logon.scr
Policies Shell key:
--------------------------------------------------
Enumerating Browser Helper Objects:
(no name) - C:\Program Files\Spybot - Search & Destroy\SDHelper.dll - {53707962-6F74-2D53-2644-206D7942484F}
--------------------------------------------------
HP DArC Task #Hewlett-Packard#hp psc 2400 series#1097730647.job
--------------------------------------------------
[Support.com Configuration Class]
[WUWebControl Class]
InProcServer32 = C:\WINDOWS\system32\wuweb.dll
CODEBASE = http://v5.windowsupdate.microsoft.c...ls/en/x86/client/wuweb_site.cab?1097382015536
[{B9191F79-5613-4C76-AA2A-398534BB8999}]
[PhotosCtrl Class]
InProcServer32 = C:\Program Files\Yahoo!\Common\YPhotos.dll
CODEBASE = http://photos.yahoo.com/ocx/us/yexplorer1_9us.cab
[Shockwave Flash Object]
InProcServer32 = C:\WINDOWS\system32\Macromed\Flash\Flash8.ocx
[MicroX Persistent Mainframe Display Control]
CODEBASE = http://www.workathomeagent.net/walldata/curVersion/hostexpress.cab
[Live Collaboration]
InProcServer32 = C:\WINDOWS\DOWNLO~1\RntX.dll
CODEBASE = http://livenj02.rightnowtech.com/7502-b145h/rnl/java/RntX.cab
--------------------------------------------------
PostBootReminder: C:\WINDOWS\system32\SHELL32.dll
CDBurn: C:\WINDOWS\system32\SHELL32.dll
WebCheck: C:\WINDOWS\System32\webcheck.dll
SysTray: C:\WINDOWS\System32\stobject.dll
UPnPMonitor: C:\WINDOWS\system32\upnpui.dll
--------------------------------------------------
End of report, 6,256 bytes
Report generated in 0.210 seconds
Command line options:
/complete - to include empty sections and unsuspicious data
/full - to include several rarely-important sections
/force9x - to include Win9x-only startups even if running on WinNT
/forcent - to include WinNT-only startups even if running on Win9x
/forceall - to include all Win9x and WinNT startups, regardless of platform
/history - to list version history only
hijack this log
Logfile of HijackThis v1.96.1
Scan saved at 8:53:07 PM, on 4/15/2006
Platform: Windows XP SP2 (WinNT 5.01.2600)
MSIE: Internet Explorer v6.00 SP2 (6.00.2900.2180)
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\spoolsv.exe
C:\WINDOWS\Explorer.EXE
C:\WINDOWS\GWHotKey.exe
C:\Program Files\HP\HP Software Update\HPWuSchd2.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgcc.exe
C:\Program Files\Logitech\MouseWare\system\em_exec.exe
C:\Program Files\Zone Labs\ZoneAlarm\zlclient.exe
C:\WINDOWS\system32\ctfmon.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgamsvr.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgupsvc.exe
C:\PROGRA~1\Symantec\NORTON~1\GHOSTS~2.EXE
C:\Program Files\Common Files\Microsoft Shared\VS7DEBUG\MDM.EXE
C:\WINDOWS\system32\nvsvc32.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\ZoneLabs\vsmon.exe
C:\WINDOWS\system32\utilman.exe
C:\Program Files\HiJackThis\HijackThis.exe
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Bar = http://red.clientapps.yahoo.com/cus...sbcydial/*http://www.yahoo.com/search/ie.html
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Page = http://red.clientapps.yahoo.com/customize/ie/defaults/sp/sbcydial/*http://www.yahoo.com
R0 - HKLM\Software\Microsoft\Internet Explorer\Main,Start Page = http://yahoo.sbc.com/dial
R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Search Bar = http://red.clientapps.yahoo.com/cus...sbcydial/*http://www.yahoo.com/search/ie.html
R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Search Page = http://red.clientapps.yahoo.com/customize/ie/defaults/sp/sbcydial/*http://www.yahoo.com
R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = http://yahoo.sbc.com/dial
R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Search_URL = http://red.clientapps.yahoo.com/customize/ie/defaults/su/sbcydial/*http://www.yahoo.com
R1 - HKCU\Software\Microsoft\Internet Explorer\SearchURL,(Default) = http://red.clientapps.yahoo.com/customize/ie/defaults/su/sbcydial/*http://www.yahoo.com
O2 - BHO: (no name) - {53707962-6F74-2D53-2644-206D7942484F} - C:\Program Files\Spybot - Search & Destroy\SDHelper.dll
O3 - Toolbar: Sage Web Accelerator - {8B79EE88-E62D-4AA8-B530-CC357BA112B7} - C:\Program Files\Accelerator\Toolband.dll (file missing)
O4 - HKLM\..\Run: [MSConfig] C:\WINDOWS\PCHealth\HelpCtr\Binaries\MSConfig.exe /auto
O4 - HKLM\..\Run: [NvCplDaemon] RUNDLL32.EXE NvQTwk,NvCplDaemon initialize
O4 - HKLM\..\Run: [NeroFilterCheck] C:\WINDOWS\system32\NeroCheck.exe
O4 - HKLM\..\Run: [Multi-function Keyboard] GWHotKey.exe
O4 - HKLM\..\Run: [Logitech Utility] Logi_MwX.Exe
O4 - HKLM\..\Run: [KernelFaultCheck] %systemroot%\system32\dumprep 0 -k
O4 - HKLM\..\Run: [HP Software Update] C:\Program Files\HP\HP Software Update\HPWuSchd2.exe
O4 - HKLM\..\Run: [HP Component Manager] "C:\Program Files\HP\hpcoretech\hpcmpmgr.exe"
O4 - HKLM\..\Run: [DXDllRegExe] dxdllreg.exe
O4 - HKLM\..\Run: [AVG7_CC] C:\PROGRA~1\Grisoft\AVGFRE~1\avgcc.exe /STARTUP
O4 - HKLM\..\Run: [Zone Labs Client] C:\Program Files\Zone Labs\ZoneAlarm\zlclient.exe
O4 - HKCU\..\Run: [ctfmon.exe] C:\WINDOWS\system32\ctfmon.exe
O4 - Global Startup: Logitech Desktop Messenger.lnk = C:\Program Files\Logitech\Desktop Messenger\8876480\Program\LDMConf.exe
O8 - Extra context menu item: &AOL Toolbar search - res://C:\Program Files\AOL Toolbar\toolbar.dll/SEARCH.HTML
O8 - Extra context menu item: E&xport to Microsoft Excel - res://C:\PROGRA~1\MICROS~2\OFFICE11\EXCEL.EXE/3000
O8 - Extra context menu item: Yahoo! Dictionary - file:///C:\Program Files\Yahoo!\Common/ycdict.htm
O8 - Extra context menu item: Yahoo! Search - file:///C:\Program Files\Yahoo!\Common/ycsrch.htm
O9 - Extra 'Tools' menuitem: Sun Java Console (HKLM)
O9 - Extra button: Research (HKLM)
O9 - Extra button: AIM (HKLM)
O9 - Extra button: Real.com (HKLM)
O9 - Extra button: Messenger (HKLM)
O9 - Extra 'Tools' menuitem: Windows Messenger (HKLM)
O16 - DPF: {6414512B-B978-451D-A0D8-FCFDF33E833C} (WUWebControl Class) - http://v5.windowsupdate.microsoft.c...ls/en/x86/client/wuweb_site.cab?1097382015536
O16 - DPF: {D18F962A-3722-4B59-B08D-28BB9EB2281E} (PhotosCtrl Class) - http://photos.yahoo.com/ocx/us/yexplorer1_9us.cab
O16 - DPF: {D8EE8DC0-F193-11D0-B1E5-08005A885319} (MicroX Persistent Mainframe Display Control) - http://www.workathomeagent.net/walldata/curVersion/hostexpress.cab
O16 - DPF: {E7D2588A-7FB5-47DC-8830-832605661009} (Live Collaboration) - http://livenj02.rightnowtech.com/7502-b145h/rnl/java/RntX.cab
Can you tell me what's up with this error message?
Jen
More replies
I was trying to repair a software installation (Iomegatools) by removing and reinstalling this software. My system froze after the installation and I shut down the computer and tried to restart Windows XP. On restart, I get a black screen with white type indicating I have an invalid system configuration. It suggests I run Setup to input the correct date and time. When I get past that it starts to load windows XP but freezes on a blue screen with the Windows XP logo but no User logon information. Any suggestions?
Thanks,
Jon B
A:Invalid System Configuration Error
Have you tried to start the machine in safe mode and use XP system restore yet?
7 more replies
Hy!
I am using Windows 7 and Ubuntu 10.10 alongside on my notebook. They both have separate partitions, Windows 7 has an NTFS and Linux have az EXT4 one.
My music files are on the NTFS one, with the Windows 7.
When I use EasyTag on Ubuntu to edit the tags of the music files (.mp3 ones), than I can't see the tags in Windows 7, all fields are blank and if I try to edit any of the fields, I get the following errorcode when trying to apply the changes:
A:Error 8x8007000D: The data is invalid
I have only seen that error code once before, it had to do with the windows not being legitimate though. That doesn't seem to be the case here. It looks like for some reason Windows 7 will not read the data that was altered using ubuntu.
I think windows is throwing up that error code simply because it has no idea how to deal with it. The only thing I can think of is to go back into ubuntu use easytag to try and blank the fields, then see if windows will read them.
Support back and forth between linux and windows has always been a tad problematic.
4 more replies
After installing my BenQ network card into my pc i tried to install the ethernet controller asked by windows but when i try to install this i get an error saying "the data is invalid" and i cannot go any further.
I have tried using different drivers but i still get the same error.
I am running Windows 2000 pro and have had a look at a simliar problem on another thread, but cannot find the permissions tab they used in Regedit.
What should i do?
Thanks
A:network card invalid data error
ive sorted it using Regedt32
1 more replies
Hi,
I am unable to install the drivers for my NIC's getting the error 'Invalid data as shown in the images below'.
It has previously been working fine on all adapters but I needed to uninstall the network cards as HyperV was throwing up an error when creating virtual switches which may have caused this?
---- -------------------- ------- ------ ---------- ---------
Ethernet 40 Intel(R) PRO/1000 PT Dual Port Netwo... 117 Not Present 0 bps
Ethernet 39 Broadcom BCM5709C NetXtreme II Gig...#2 132 Not Present 0 bps
Ethernet 38 Intel(R) PRO/1000 PT Dual Port Net...#2 131 Not Present 0 bps
Ethernet 37 Broadcom BCM5709C NetXtreme II Gi...#50 130 00-26-55-1A-A8-4A 0 bps
Ethernet 34 Intel(R) PRO/1000 PT Dual Port Net...#3 127 00-1F-29-56-C2-51 0 bps
Ethernet 33 Intel(R) PRO/1000 PT Dual Port Net...#4 126 00-1F-29-56-C2-50 0 bps
vEthernet (VLAN3 (Desk... Hyper-V Virtual Ethernet Adapter #3 71 Not Present 00-1F-29-56-C2-51 0 bps
vEthernet (VLAN2 (Serv... Hyper-V Virtual Ethernet Adapter #2 64 Up ... Read more
A:Unable to install NIC's - Invalid data error
It helps to know if you are using some kind of Virtual Machine software.
10 more replies
I recently booted up my Gateway notebook only to find the "blue screen of death"
I rebooted and it came up to a windows boot manager screen which says windows failed to start..insert installation disc and click repair to fix...blah blah...i'm sure you know the story...
My question is, I booted the Vista disc and when I click repair it doesn't even find the C: drive...when I try and run the BCD fix from the command prompt screen, it says it found 0 Windows installations...would this indicate a faulty hard drive?? If so, I dont mind replacing the drive, I just wanna make sure this is the issue before I spend the money to replace it...
Much thanks for any help anyone can offer!
A:Boot Configuration Data Error
I'm not sure what BCD fix you tried, but see if it is this one and if not, try this one.
To run the Bootrec.exe tool, you must start Windows RE. To do this, follow these steps: (you need a Vista Installation Disk to do this)
1. Put the Windows Vista installation disc in the disc drive, and then start the computer.
2. Press a key when you are prompted.
3. Select a language, a time, a currency, a keyboard or an input method, and then click Next.
5. Click the operating system that you want to repair, and then click Next.
6. In the System Recovery Options dialog box, click Command Prompt.
7. Type Bootrec.exe, and then press ENTER.
Note If rebuilding the BCD does not resolve the startup issue, you can export and delete the BCD, and then run this option again. By doing this, you make sure that the BCD is completely rebuilt. To do this, type the following commands at the Windows RE command prompt:
bcdedit /export C:\BCD_Backup
c:
cd boot
attrib bcd -s -h -r
ren c:\boot\bcd bcd.old
bootrec /RebuildBcd
See if that works.
If you don't have the disk (or that didn't work), try EasyBCD http://neosmart.net/dl.php?id=1 and see if that helps resolve the problem.
If that doesn't work, you probably have some type of hardware problem - but it's hard to tell. It may be as simple as the hard drive cable got disconnected a... Read more
3 more replies
Hello all,
I am trying to install some software, and the installer barely gets started then stops and gives me this error:
Error 1324 The path My Data contains an invalid character.
I am trying to install Call of Duty 5 World at War onto Windows 64 bit Ultimate.
Does anyone have any ideas on fixing this error?
A:Error 1324 The path My Data contains an invalid character.
Hi,
Try to enter the path you want to install to manually i.e: (probably)
C:\Program Files\Microsoft Games\Microsoft Flight Simulator X\ in the setup wizard
DO NOT use the %Program Files% tag.
It sounds like this will not work, however.
If it does or does not:
Back up your registry: (here's how if you don't know how: Back up the registry)
Click Start, and type regedit. Press enter and enter administrator password if necessary.
Navigate to: Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Current Version
Make sure the Current Version folder looks as it should. Here is an image of a working Current Version folder:
If your ProgramFilesDir, ProgramFilesPath or CommonFilesDir is different, correct it or if unsure, post back. In particular the ProgramFilesPath SHOULD BE REG_EXPAND_SZ. If your ProgramFilesPath is REG_SZ, change this to REG_EXPAND_SZ. This corruption is quite common. If necessary, make these registry entries.
Try your FSX installation again. If it still does not work, try copying your entire DVD to your desktop (or wherever) and have a look through the directories for strange symbols, signs of a corrupt disk. This will take a while to copy.
If you can and these steps do not work, please can you post the FSX install log file and messages in event viewer. Post back if these steps do not work or you don't know how to do any of the above.
Hope this helps.
Richard
1 more replies
I did a search for this and it seems a few people have had the same problem. I bought the oblivion expansion pack for download on direct2drive.com and when the zip file is all done it gets an error trying to download data2.cab and data3.cab (the two biggest files). The error is "Error: invalid compressed data to inflate" for both.
All of the other files within the zip come out just fine, it just seems to be the two important ones of course. This is the second time i have downloaded it, and it takes about 2 hours. I tried using Alzip and that says the two suspect files are corrupt.
More replies
I upgraded my mainboard from an ASUS A7M266 to a Soyo K7Dragon+ and found that XP would not let me load the mainboard drivers. So I wiped my drive and started over without any pci cards installed. After XP was installed I tried to install my Soundblaster Live Card. Windows told me that the data was invalid so it could not load the drivers. Son of a... I tried moving the card to a different slot, and also tried removing it and using the onboard audio. Both solutions ended up with the same answer, the data invalid error. I looked into the problem and found out that it is a problem in windows xp with pci cards and scsi device pci cards. Here is the solution for those of you that may experience that. The fix works, I know as I am living proof!
Why do I get the message "data is invalid" when installing a device driver under WindowsXP?
This error appears to be due to a protection problem in the Windows registry and can occur with a variety of drivers (sound cards and SCSI drivers have been reported). To fix this problem, go to Start, Run... and type "regedit" without the quotes to run the Registry Editor. Navigate to
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\ENUM\PCI
and you will see a number of keys of the form "VEN_xxxx", where xxxx are strings like "1102&DEV_0004&SUBSYS_00011103&REV_04". Under each of these folders will be another folder with a long numerical name. Open each folder and look for the "... Read more
A:Installing PCI card..drivers: data invalid error
the data is invalid windows2000 smc fast ethernet network card - no permission button
sir, regarding the very same problem as mentioned in the thread. Yes, i heard lot of website providing the same method of solution, but when i use regedit, there is not "permission" button in it. Hence the solution is not workable for me althought i am facing the same problem as mentioned.
i am using windows 2000 pro
amd xp athlon 2000
:giddy:
thank you,
andrew
24 more replies
I upgraded my mainboard from an ASUS A7M266 to a Soyo K7Dragon+ and found that XP would not let me load the mainboard drivers. So I wiped my drive and started over without any pci cards installed. After XP was installed I tried to install my Soundblaster Live Card. Windows told me that the data was invalid so it could not load the drivers. Son of a... I tried moving the card to a different slot, and also tried removing it and using the onboard audio. Both solutions ended up with the same answer, the data invalid error. I looked into the problem and found out that it is a problem in windows xp with pci cards and scsi device pci cards. Here is the solution for those of you that may experience that. The fix works, I know as I am living proof!
Why do I get the message "data is invalid" when installing a device driver under WindowsXP?
This error appears to be due to a protection problem in the Windows registry and can occur with a variety of drivers (sound cards and SCSI drivers have been reported). To fix this problem, go to Start, Run... and type "regedit" without the quotes to run the Registry Editor. Navigate to
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\ENUM\PCI
and you will see a number of keys of the form "VEN_xxxx", where xxxx are strings like "1102&DEV_0004&SUBSYS_00011103&REV_04". Under each of these folders will be another folder with a long numerical name. Open each folder and look for the "DeviceDes... Read more
A:Installing PCI card drivers - data invalid error
1 more replies
Several times, and only from a cold boot, I get a pop-up stating "Boot Configuration Editor Has Stopped Working" However everything loads okay and functions. What might be causing this and what does it mean. IE: What function does this editor serve?
SYSTEM SPECS
INTEL I7-920 PROCESSOR
WINDOWS 7 HOME PREMIUM 64 BIT
12 GB TRI CHANNEL DDR3 SDRAM AT 1333 MHZ
1 TB 7200 SATA 3.9 GBS 16 MB CACHE
CREATIVE SOUNDBLASTER X-FI
DELL WIRELESS KEYBOARD AND MOUS
Dave K.
A:Boot configuration data editor error win 7
Run Startup Repair on a cold boot.
5 more replies
Does anyone no how to fix this? Yesterday I got a UAC Zero Access Virus and tried using windows repair disc to go back to a restore point. That just made everything worse and now I can't boot into windows at all. I have a multiboot PC (its set to just windows 8 and windows 7 right now, windows 7 being the biggest partition on the drive).
Recovery
Your PC needs to be repaired
The boot configuration data for your pc is missing or contains errors.
File:\Boot\BCD
Error code: 0xc000000f
A:The Boot Configuration Data For Your PC Is Missing or Contains Error
Can you boot into either of the two operating systems?
15 more replies
Have a HP compaq 6300 pro running windows 7 pro. today computer would not boot,
black screen came up it asks me to insert installation disc
scrolling down it lists the following
file \boot\BCD
Status: 0xc000000f
info: an error occurred while attempting to read the boot configuration data.
unfortunately since windows came preinstalled there was no installation disc
it said since it was preinstalled to contact manufacturer.
my support/ waranty with HP for this computer has ended
Thanks in advance for any assistance in this matter
Bob J
If you have access to another Windows 7 computer create a System Repair Disk. Boot it and do a Startup Repair. It may take up to three attempts to fully do the repair. If you have 64bit then you would need to find a Windows 7 64bit computer.
2 more replies
I have a Netgear WN121T Wireless USB adaptor but it won't install. I have downloaded the latest firmware (version 5) and tried to install it but I get an error message saying 'Data is inavlid'. After searching forums I have attempted to change the permissions in the device manager and I have aldo deleted the contents of teh driver cache. Neither solutions have worked for me and I was wondering if anyone had any other suggestions?
A:'Data Is Invalid' Error message when installing wireless USB adaptor
general rule of thumb - if it ain't broke, don't fix it. If it was working fine prior to the firmware update, then you shouldn't have messed with it. I would try to go back to the defaults.
3 more replies
Hi, I was running Windows 7 on a Dell Vostro 3700 Laptop..After doing a spyware scan and finding and deleting all the entries I found, the next time I turned it on I get the error: oxc000000f "An error occured while attmepting to read the boot configuration data File: \Boot\BCD"
I have looked online for solutions and tried using the Windows 7 disc (a copy) and also tried using 3 recovery disks, these all fail because it just stays completely black with a cursor (left for hours even) or I get a error message something around the lines of "insert correct boot media into the correct boot device" and I have no idea what this means. I cannot do a repair because I can only get the Windows disc to load if I remove the hard drive?? this is the only way I have got it past the green loading bar, so I am stuck and have no idea what to do..it only seems to respond to cds if the hard drive is removed?.. this all happened very suddenly and now I have a very expensive ?800 paperweight.. Any help massively appreciated!
To add to this - I also tried the command prompt typing the bootrec.exe code that I found on the internet..selecting command prompt from the option when the Windows 7 disc was loaded, but basically it came up with an error of some sort and it had a drive letter of X:/ on the command prompt ?? ..Also to get to this the hard drive was removed because like I said I cannot get the discs working with it in.. I'm guessing this means the hard drive is screw... Read more
A:Error oxc000000f Need help repairing Boot Configuration Data??
Are selecting the optical drive as your boot device for the windows install disk? sounds like maybe with the hard drive removed its defaulting to the optical drive and booting correctly. Also, make sure you have a good copy of the windows disk.
8 more replies
Hi, thank you. glad to be the newest member here. I have an Aspire S3 laptop Windpows 8 to 8.1 - that now has a BCD error blue screen upon start up that is error OXCOOOO0D - boot configuration data Recovery
Your PC needs to be repaired.
The BCD is missing some required info.
File:\BCD
you'll need to use recovery tools...
I don't have an install/repair cd/dvd, and I don't have my product key - since its on the BIOS and is unretrievable. I want to save ALL my files so, please, if someone can help, thak you! All I tried so far is to get into the BOOT by pressing F2 and switched it from UEFI to Legacy only it asks for BOOT disk...
A:windows 8.1 error 0xc00000d boot configuration data
Bump.........
9 more replies
I have a Dell and won't boot giving a black screen but will boot after about 10 turn on and offs. It is very annoying and have uploaded the latest drivers for the system. Since installing Windows 7 there seems to be this erratic problem with the Dell XP. Anyone have an idea about how to fix this problem?
A:[MOVED]Re: Boot configuration data editor error win 7
Moved from this topic: http://www.techsupportforum.com/f217...ml#post2898619
1 more replies
My Dell Insperion 15 now has this boot error. I tried using the recovery USB from my HP. It is smart enough to know that I'm not trying to reboot the HP computer so it doesn't work. This is so frustrating. What to do?
A:windows 8.1 error 0xc00000d boot configuration data
Check HDD with this: Hard Drive Diagnostics Tools and Utilities (Storage) - TACKtech Corp.
Test your RAM: RAM - Test with Memtest86+ - Windows 7 Help Forums
one stick at a time eight passes per stick
Drive letters in WinPe will probably be different from what you see in windows - that is normal.
I would delete the bcd store and run the commands again. You should be pointing them at the reserved system partition .
Otherwise, at cmd prompt, type:
diskpart
lis vol
( Look to see the drive letter for your main windows partition - if it is D then type as below, otherwise replace D with the letter diskpart gives for the main windows partition)
sel vol d
act
exi
bcdboot d:\windows /s d:
bootsect /nt60 all /mbr
restart the pc - you're good.
7 more replies
Help I can't get past the booting error and there is no way for me to pass this? I've tried many things and can't get past it
File: \Boot\BCD
Status: 0xc000000f
Info: An error occurred while attempting to read the boot configuration data.
OS: Vista x64 Bit
A:Error while attempting to read boot configuration data?
1 more replies
Hi everyone,
I tried to install new updates of Ableton live and the machine crashed badly... and since them it has really gone a bit wonky.
When I press the on button to boot up the laptop I get the following message.
The Windows Boot Configuration Data (BCD) Store file contains some invalid information.
Object : GUID : (8cb2db4-7co5-11de842e-bt611d44fefa)
Description: Windows recovery format.
Status: oxcoooooo24
Info: The configuation for an element within the object is invalid in the boot configuation store.
The assiocated windows boot loader entry may not be available for selection until the problem is rectified by an administrator.
Enter= continue.
So then I press enter... it boots up. (in about 5 seconds as it is a ssd...)
When I do this action: to see if I can do a restore etc...
Start-Control Panel- the progress bar at the top of the expoler window freezes half way and I cannot access any of the menu Items.
Also I canot move this panel or close the window.
I have a back up on another external drive ..... plus I have made a repair disk and so on when I first got the machine.
I would be stoked if you could provide me with the next steps so I can resolve this situation.
Thanks for your time, now lets party on and delve deep into the abyss
A:Windows Boot Configuration Data (BCD) store file error.
Hallo,
hatte auch einen 0x0000024 BCD Fehler. Hatte vor einer Installation die alte Partition auf "VERSTECKT / HIDDEN" gesetzt und nach der Installation vergessen die Partition wieder auf "Partition anzeigen / Show partition" zu setzen und erhielt so bei Bootversuch einige Tage sp?ter den x24 Fehler. Nach dem "ANZEIGEN" funktionierte der Boot wieder.
2 more replies
Hi everyone,
I have windows 8.1 and Lenovo y510. After upgrading from 8.0 to 8.1 a have several problems with my PC. Right now suddenly i cant start my PC.
I have BSOD
Recovery
Your PC needs to be repaired.
The boot configuration data file is missing some required inforamtion.
File\BSD
Error Code:0x0000034
Need to use recovery tools on your instalation media. If you dont have any contact your system administrator or PC manufacturer.
ESC for UEFI firmware setting.
I try different setting in setting utilty (after pressing ESC) and nothing changed.
I dont have any USB or Disc with windows. (but i do have legal copy - it was already installed in my PC) so i cant use any of help with restoring pc from instalation media.
Do you have any idea what to do ?
Thank you very much. A need it pretty serious that pc because of school
A:Error 0x0000034 - Boot Configuration Data File is Missing
From the Repair CD/USB:
How to do a Auto Repair:
Automatic Repair - Run in Windows 8
Note: You may need to do startup repair 3 to 4 times.
Startup Repair - Run 3 Separate Times - Windows 7 Help Forums
Have you made the OEM manufacturer's Recovery Disks?
Information
We always assume you have made your Recovery Disks using the OEM manufacturer's Recovery Media Creator app the first day you had your new PC.
& made the Startup Repair CD. (Windows 8 only)
Recovery Drive - Create with USB Flash Drive in Windows 8
System Repair Disc - Create in Windows 8 (Windows 8 only)
I would recommend you making the OEM manufacturer's Recovery DVD's or USB drive.
or
You can order the Microsoft official OEM Recovery disks from the OEM manufacturer's website.
From the manual for Lenovo G480.
Originally Posted by Lenovo
When the hard disk drive or solid state drive is replaced because of a failure, no
product recovery program is on the new drive. In this case, you must use the
Recovery Disc Set for the computer. Order the Recovery Disc Set and the drive at
the same time so that you can recover the new drive with the pre-installed
software when they arrive.
You can Order Lenovo Recovery Disks from here:
Lenovo Support - Home (US)
Click on Parts & Accessories.
2 more replies
Hi all, im getting that message upon startup. Im running windows 7.
It requests for the windows recovery CD to be inserted, so when I put the CD in to boot I get a "windows is loading files" then a starting windows with the windows logo then just a black screen with a cursor, I left it like this several times for at least an hour an nothing happened.
I can't press F8 to access safe mode etc, nothing will happen.
Pressing F12 to boot from CD just does the same thing as putting the CD in normally.
A:An error occurred while attempting to read the boot configuration data
It seems the CD is damaged.
Burn a new Windows 7 Recovery CD on another computer.
You can download the image or make a copy of a functional Windows 7 Recovery CD.
Boot the new Recovery CD and run automatic StartUp Repair up to three times as sugested in the forum manuals !
Good luck!
1 more replies
Hi, I was running Windows 7 on a Dell Vostro 3700 Laptop..After doing a spyware scan and finding and deleting all the entries I found, the next time I turned it on I get the error: oxc000000f "An error occured while attmepting to read the boot configuration data File: \Boot\BCD"
I have looked online for solutions and tried using the Windows 7 disc (a copy) and also tried using 3 recovery disks, these all fail because it just stays completely black with a cursor (left for hours even) or I get a error message something around the lines of "insert correct boot media into the correct boot device" and I have no idea what this means. I cannot do a repair because I can only get the Windows disc to load if I remove the hard drive?? this is the only way I have got it past the green loading bar, so I am stuck and have no idea what to do..it only seems to respond to cds if the hard drive is removed?.. this all happened very suddenly and now I have a very expensive ?800 paperweight.. Any help massively appreciated!
To add to this - I also tried the command prompt typing the bootrec.exe code that I found on the internet..selecting command prompt from the option when the Windows 7 disc was loaded, but basically it came up with an error of some sort and it had a drive letter of X:/ on the command prompt ?? ..Also to get to this the hard drive was removed because like I said I cannot get the discs working with it in.. I'm guessing this means the ha... Read more
A:An error occured while attempting to read the boot configuration data!
Go to your BIOS and set the CD as the first boot device, your hard drive as second.
If this lets you boot from the Win7 CD with the HDD installed run Startup Repair - Run 3 Separate Times.
7 more replies
This is the error message that my computer had:
"Recovery
Your PC/Device needs to be repaired
The Boot Configuration Data for your PC is missing or contains errors
File:\EFI\Microsoft\Boot\BCD
Error code: 0xc0000185
You'll need to use recovery tools. If you dont have any installation media (like a disc or USB device), contact your PC administrator or PC/Device manufacturer.
Press Esc for UEFI Firmware Settings"
I made a recovery drive and set the UEFI to a USB boot, and when I tried to boot it with a blank USB it didnt recognize it, but when I used the recovery usb it recognized it. I did that to check and see if it actually recognized the recovery data.
Now when I boot it just has the Lenovo screen and the swirling dots. it's been doing this for about a half hour. Is this normal or is there an issued with the hatdware?
A:Boot Configuration Data is missing, Error Code 0xc0000185
The Error code: 0xc0000185 is an I/O error.
This can be a hardware problem or a software problem.
So the first thing to do is to run diagnostics on the hard drive ( http://www.carrona.org/hddiag.html )
If you have difficulties booting to the disk/drive, post back and we'll see about changing some settings in the UEFI to allow the boot.
I'm working on a drive that will do this for you, but it's still in the testing phase (and it's a 700+ mB download).
If the drive is dead/dying, you may have problems trying to recover your data.
Do you have a recent backup? If not, post back for suggestions on how to best backup your information.
FYI - if it is dying, then it's best not to use the drive at all until you've done the backup.
If the drive does die fully, then data recovery gets very expensive (up to $2000 (US)) if it's even possible. 0 more replies Answer Match 60.48% Hi This is the full error message I encountered--> An error occurred while attempting to read the boot configuration data File: \Boot\BCD 1) I have an old Dell Vostro 410, Windows Vista, configured to RAID 1 the whole time. 2) I wasn't able to boot it up one day, pressing the on button only got an amber light momentarily. From the symptom, I replaced the CMOS battery as suggested by someone online and the PC was able to be powered up but it got to a blue screen--> https://www.dropbox.com/s/nyeoq0gwz4i3f2b/2013-12-21%2000.44.17.jpg 3) I realized that's because all the settings on BIOS has been wiped out after I took out the old battery, the "SATA mode" in BIOS was set to IDE instead of RAID, so I set it back to RAID as shown--> https://www.dropbox.com/s/u6oxdg8m092v0vr/2013-12-23%2000.01.31.jpg 4) I tried rebooting the the system again, this time I can see that RAID has been setup accordingly--> https://www.dropbox.com/s/a708qln2oehrm75/2013-12-23%2000.03.57.jpg and https://www.dropbox.com/s/1sfrpfrxtkgke2n/2013-12-22%2023.58.37.jpg 5) But the rebooting was terminated with the message "an error occurred while attempting to read the boot configuration data" --> https://www.dropbox.com/s/orgkn29qaj0nxsb/2013-12-22%2017.48.20.jpg 6) Following the on screen instruction, I tried booting from "Windows installation" CD to repair it, however after pressing a key on the following screen,... Read more A:An error occurred while attempting to read the boot configuration data When you removed the CMOS battery it set the BIOS to the default settings. I suspect you will have to rebuild your RAID configuration. 3 more replies Answer Match 60.48% system configuration data updated ERROR,--Need a solution I have a fairly new Gateway M-1625 laptop running windows vista 32 bit, sp1. I turned it on and beeped twice (beep, beep) and gave me an error message that reads "system configuration data updated ERROR, system configuration data read error" Press f1 to continue f2 to enter set up. I pressed f1 and it sent me to another blank page that reads. Windows failed to start. A resent hardware or software change might be the cause. To fix the problem: 1. Insert your windows installation disc and restart computer 2. Choose your language settings and click next, 3. Click ?repair your computer.? If you do not have the disk, contact your system admin. Etc Tried the repair disc, tried reinstall from Restore DVD still get the same message. Tried the bootrec.exe/fixmbr (worked) Tried the bootrec.exe/fifixboot (Worked) Tried the bootrec.exe/Rebuildbcd Tried reseating the memory and hard drive. Still at the same point. Even tried to install XP over it but never could get it to go. Now I am back to where I started. I already replace the hard drive so i know is no that I think this is a boot problem. what can I do??? More replies Answer Match 60.48% ok i had some recent windows updates succesfuly and rebooted, since that at start up im getting "Error msg : Boot configuration data editor has stopped working" any way to sort this ? what cause it ? Have tryed system restore several diffirent restore dates but still the same. Using a Dell studio xps 8100 win7 home edition 64 bit . A:Error msg : Boot configuration data editor has stopped working Try running system file check . SFC /SCANNOW Command - System File Checker 4 more replies Answer Match 60.48% Hi all, I have a problem with my internet connection on my PC. The internet connection works fine, until I let my PC idle for about an hour or so. The connection then dies, but can be repaired by the Windows Troubleshooter which fixes the error message about the invalid IP configuration. I've reset the modem and the router many times. Did not help. Any (more) ideas? Windows 7 | PC connected with wire and wireless from router | Wireless keeps working to other devices, but not to PC A:How to avoid "invalid IP configuration" connection error? There is a setting in the properties of the network card to Power it down when idle. Turn that off and see what happens. You have to go to Device Manager to get to that setting. 3 more replies Answer Match 60.48% Hi Please Fellas I need a help........I appriciate any help. Thank you When I attending to share folder on my desktop computer ( win xp pro sp2 ) I got following Sharing Error Message. > In Shared Documents Properties >> Sharing - Network Sharing and security I select " Share this folder on the network " Click apply & I get following Error message : " An error occured while trying to share Documents. The data is invalid. The shared resource was not created at this time. " ................................................................................................. Please if you know anything about this problem let me know. Thank you Igi A:Sharing doc error in winxp-sp2: The data is invalid.The shared resources wasn't creat 6 more replies Answer Match 60.06% Help !! I had to clean up my system, reapplying SP2. I tried to reinstall Nero 7 using same installation package that worked previously. I get this error: "the configuration data for this product is corrupt, contact support personnel" I installed Windows Installer 3.1 and still have this problem. I cleaned out all references to Nero in the registry... no luck. A:Error 1610 ? Configuration data for this product is corrupt (Nero install) Start button, Run, regedit Navigate to: HKEY_LOCAL_MACHINE\SOFTWARE\CLASSES\INSTALLER You need to look under the key Features. By examing each of the keys found here you will eventually find one that very clearly states it is for Nero and state the version. Nero will have two entries. One under Features, and one under Products. For example, my Nero 7 UltraEdition used these two keys to store its configuration information: HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Features\62E2F0A3CB0C8B04495AA6AF7BBA0133 HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products\62E2F0A3CB0C8B04495AA6AF7BBA0133 Your results are likely different only in the long number string portion at the end. Delete the key under Features and under Products by right-cliking and choosing delete. Reboot. Try the installation again. 1 more replies Answer Match 60.06% Hi All, I have read most of the messages related to this. Unfortunately ASUS doesn't ship with a Vista disk and the Recovery DVD doesn't boot. Details shown are File: \Boot\BCD Status: 0xc000000f Info: "an error occurred while attempting to read the boot configuration data" Operating medium - Windows Vista Any suggestions, Pls? I may have to return to Techs who MAY have a Vista disk. Cheers A:an error occurred while attempting to read the boot configuration data (Vista) Hi Wawny, Thank you for the post. The error message usually indicates that the boot sector is damaged or missing. We can try to use the following methods to troubleshoot the issue. However, performing the following steps requires a Windows Vista installation disk. If you do not have a disk, please contact your computer manufacturer or Microsoft Customer Service or to obtain one. Microsoft Customer Service: (800) 426-9400, available Monday through Friday, from 6:30 A.M. to 5:30 P.M. Pacific Time. Note: Microsoft Customer Service mainly handles issues regarding replacement manuals, disks, drivers and service packs, product IDs, lost CD keys, product orders, policies related to copying software on additional computers, licensing, and product registration. Method 1: Startup Repair from the Windows Recovery Environment (WinRE) ============================================ 1. Insert the Windows Vista installation disc into the disc drive, and then start the computer. 2. Press a key when the message indicating "Press any key to boot from CD or DVD ?". appears. 3. Select a language, a time and currency, and a keyboard or input method, and then click Next. 4. Click Repair your computer. 5. In the System Recovery Options dialog box, choose the drive of your Windows installation and click Next. 6. At the System Recovery Options Dialog Box, click on Repair your computer. 7. Click the operating system that you want to repai... Read more 15 more replies Answer Match 59.22% Hi, I have exactly the same issue as the person on this page, however I have already tried the three solutions and neither work, further explanation below. http://social.technet.microsoft.com.../thread/022386ba-a445-44ba-97f7-d8ba4b6cc54b/ I was watching a DVD on my PC last night when it began to stutter and finally the system completely froze. I would like it 5 min and then the PC would work again for roughly 5 sec before crashing again, I let this go on for about 20mins but the PC never fixed itself so I rebooted. On rebooting I got the above message. 1. My first attempt to fix it was using safemode, this however didn't work and it prompted me to use the repair progam on the Vista installation disk . 2. I booted from the vista disk and tried a start-up repair. This ran, said something was fixed and asked me to reboot. I did this but to no avail therefore I went back to the repair centre. 3. I did not have system restore turned on so this option was not useful to me. 4. I then read something suggesting I use Bootrec. However I tried running bootrec /RebuildBcd but it could not find my OS, instead I used the following commands; * bcdedit /export C:\BCD_Backup * c: * cd boot * attrib bcd -s -h -r * ren c:\boot\bcd bcd.old * bootrec /RebuildBcd This however didn't work either. 5. I left the PC overnight and now things seem to be worse. When I try and use repair centre it does not actually detect a HDD with Vista installed, it does however still let me p... Read more A:Answer an error occurred while attempting to read the boot configuration data (Vista) If you can take the HD out and put it into another PC as Slave and see if your data is still readable. 1 more replies Answer Match 57.54% I am running into an issue with users renaming files on a shared drive. When the users try to rename, they get the error "A file name can't contain any of the following characters: \ / : * ? < > |". However, neither the new or old filename contains any of these characters, or any other invalid characters as far as I can determine, just alphanumeric characters and spaces.When they try to rename it again, it works without an issue. I have found reports of this error being generated if the file path is too long, but all users are accessing this from a shared drive, and even if the share name is taken into account the file path and name are easily under 100 characters. I have 3 users on 3 different systems reporting this issue, so I don't think it is user error. The workstations are running Windows 7 Pro, SP1. The server is Windows Server 2003 R2 Enterprise, Service Pack 2. The users are located at a remote site, and accessing the share over a site to site VPN. There are XP workstations at the site as well, that do not appear to be having the issue. Any help, suggestions, or guidance is greatly appreciated! More replies Answer Match 56.7% I don't know what happened but since Monday, I can't connect to our workplace's WiFi.. I don't know what to do.. Please help.. Network Connection Details: Also, there was a time that I tried to connect and it said that another computer is using the same IP Address.. (something like that).. I hope someone can help me! Thanks! -G A:Invalid IP Configuration It appears that your wifi's dhcp is down (or turned off). You may have to assign the IP info manually or find out why your wifi dhcp is not working. Is there someone at work that manages the wifi? 3 more replies Answer Match 56.7% I had Win 7 working fine on my other laptop. It has started giving me trouble connecting to the internet. The troubleshooting completes. Tells me its resolved and I continuously get a "Local Area Connection doesnt have a valid IP configuration". The wireless network says "Unidentified Network" No Internet Access. I tried uninstalling and reistalling the drivers and it didnt work. It started happening after I uninstalled Jetico Personal Firewall. A:Invalid IP Configuration See if flushing the DNS cache works to solve the problem.Open a command prompt....from the Start menu, select Run > In the box/"open field", enter cmd.exe enter ipconfig /flushdns press 'enter' 4 more replies Answer Match 56.7% A couple Months ago I went to get on my Computer "Dell Inspiron 531 with Windows 7" and well Yellow Triangle saying "no Internet Access" now tonight same thing 2 Months later I was gonna go on the Internet. Same BULLSHIT. I use that PC everyday. No it is not our Modem, all other PC's work fin and Wi-Fi works great as well. I have tried the same PC on another cord nothing still same stupid BS. No I never updated anything, all stuff is up to date already anyways. Last time this issue happened exactly "one Week later the Internet started working again on it's own after I Unplugged then Replugged the Ethernet Cable" in and been fine till tonight again. I am at my Wits end with this Effing thing! More replies Answer Match 56.7% error: "local area network doesn't have a valid ip configuration" Problem on another machine: aCER aSPIRE w/ windows 7 Had internet previously; no changes made to machine EXCEPT swapped hardwire internet connection from Linksys router to a temp set up on a laptop. Couldn't get laptop to connect via hardwire - went wireless instead Upon return of cable to ASPIRE, got above error message Running connection Wizard doesn't do it! A:invalid IP configuration 9 more replies Answer Match 56.7% i have a wireless modem. unfortunately, i can't connect to the internet unless i'm using the LAN cable connecting from the modem to my laptop. i have run the troubleshooter and it says "invalid ip configuration" or something like that. i've also run ipconfig/all in command prompt (i'm not an expert in this but i go through some forum and they say try like this). without the cable: C:\Users\AP>ipconfig/all Windows IP Configuration Host Name . . . . . . . . . . . . : AP-PC Primary Dns Suffix . . . . . . . : Node Type . . . . . . . . . . . . : Hybrid IP Routing Enabled. . . . . . . . : No WINS Proxy Enabled. . . . . . . . : No Ethernet adapter Local Area Connection: Media State . . . . . . . . . . . : Media disconnected Connection-specific DNS Suffix . : Description . . . . . . . . . . . : JMicron PCI Express Gigabit Ethernet Adap ter Physical Address. . . . . . . . . : 20-CF-30-64-F8-A4 DHCP Enabled. . . . . . . . . . . : Yes Autoconfiguration Enabled . . . . : Yes Wireless LAN adapter Wireless Network Connection: Media State . . . . . . . . . . . : Media disconnected Connection-specific DNS Suffix . : Description . . . . . . . . . . . : Atheros AR9285 Wireless Network Adapter Physical Address. . . . . . . . . : 48-5D-60-38-29-9A DHCP Enabled. . . . . . . . . . . : Yes Autoconfiguration Enabled . . . . : Yes Tunnel adapter isatap.{8BFF2FC5-0B0C-4FDD-A... Read more A:Invalid IP configuration Link-local IPv6 Address . . . . . : fe80::cd8f:b300:edba:9ec0%14(Preferred)Click to expand... Most of our routers do not support IPv6 well (if at all). Google for how to disable IPv6 3 more replies Answer Match 56.28% Hello, I am having intermittent connection issues to the Internet when connecting via my ethernet adapter. My modem connects to my router (D-Link DIR-825) which connects to a Sling Media Powerline kit (see here) via my electrical system which then connects to my ethernet adapter (nVidia nForce network adapter). I can connect to my router wirelessly perfectly fine. However, when using my ethernet adapter, it will intermittently stop working every ~10-20 minutes or so for a period of ~10-20 minutes. If I run the Windows 7 network troubleshooter it informs that my connection does not have a valid IP configuration and that the default gateway is not available, but it cannot fix either of these problems. Eventually it seems to sort itself out, but it is only temporary. Previously, this network configuration had been working perfectly fine for nearly a year. When I run ipconfig /all in the command prompt, I get the following relevant portions when it is not working: Code: Microsoft Windows [Version 6.1.7601] Copyright (c) 2009 Microsoft Corporation. All rights reserved. C:\Windows\system32>ipconfig /all Windows IP Configuration Host Name . . . . . . . . . . . . : Frank-PC Primary Dns Suffix . . . . . . . : Node Type . . . . . . . . . . . . : Broadcast IP Routing Enabled. . . . . . . . : No WINS Proxy Enabled. . . . . . . . : No DNS Suffix Search List. . . . . . : cinci.rr.com Wireless LAN adapter Wireless Network Connection: Connection-specific... Read more A:Intermittent invalid IP configuration To confirm, the computer did not work with a static IP? 3 more replies Answer Match 56.28% Hello, I am having intermittent connection issues to the Internet when connecting via my ethernet adapter. My modem connects to my router (D-Link DIR-825) which connects to a Sling Media Powerline kit (see here) via my electrical system which then connects to my ethernet adapter (nVidia nForce network adapter). I can connect to my router wirelessly perfectly fine. However, when using my ethernet adapter, it will intermittently stop working every ~10-20 minutes or so for a period of ~10-20 minutes. If I run the Windows 7 network troubleshooter it informs that my connection does not have a valid IP configuration and that the default gateway is not available, but it cannot fix either of these problems. Eventually it seems to sort itself out, but it is only temporary. Previously, this network configuration had been working perfectly fine for nearly a year. When I run ipconfig /all in the command prompt, I get the following relevant portions when it is not working: Code: Microsoft Windows [Version 6.1.7601] Copyright (c) 2009 Microsoft Corporation. All rights reserved. C:\Windows\system32>ipconfig /all Windows IP Configuration Host Name . . . . . . . . . . . . : Frank-PC Primary Dns Suffix . . . . . . . : Node Type . . . . . . . . . . . . : Broadcast IP Routing Enabled. . . . . . . . : No WINS Proxy Enabled. . . . . . . . : No DNS Suffix Search List. . . . . . : cinci.rr.com Wireless LAN adapter Wireless Network Connection: ... Read more A:Intermittent invalid IP configuration It looks like you want to use your lan connection so I would disable your wifi and if that fixes your problem search this site for how to change the metric of your lan just in case you want to enable your wifi for some reason set your lan to metric 1 and your wifi to something higher like 10 3 more replies Answer Match 56.28% When I bootup the message reads "Invalid system configuration" - run configuration utilty,press 1 to resume or f2 to enter setup. Pressing 1 takes you into windows. Everything is fine except I can't dial out.Larry I read your advice in the archives.It helped now I can dial out. However the Invalid system configuration message still appears when I bootup.Any suggestions? A:Invalid system configuration This can mean a few things. There is a resource conflict of some sort, but the exact sort... Press F2 to enter setup. Many systems will pop a message up right there telling you what is wrong. There isn't another message is there? Like 3F8 resource conflict, invalid configuration, press F2? You said you couldn't dial - so, in Windows Device Manager check what IO and IRQ your Modem and COM ports are set to. When you go into setup with F2 make sure none of the COM ports in there are set to the same numbers. ------------------ Get free stuff and help out a poor computer tech: LarryCore begs for money Vote for the best Tech Support site: VOTE for Helponthe.net! 1 more replies Answer Match 56.28% Network: Verison Router w/ DHCP 192.168.1.X DLINK access point using DLINK router w/ DHCP 192.168.0.X Cisco access point using DLINK router w/ DHCP 192.168.0.X Problem: New Toshiba notebook connects to Verizon router without difficulty, but cannot connect to DLINK or CISCO without "LIMITED" usage (IP configuration error) [With a lot of reset, renew and Win8 troubleshooting it will connect to the DLINK for about an hour, but the magic must be repeated after an hour or so] History: 4 other Notebooks connect succesfully to any of the 3 access points 3 Phones connect succesfully to any of the 3 access points 2 Tablets connect succesfully to any of the 3 access points Reason for DLINK or Cisco Connection: Verizon router is outside of the local network containing shared drives. More details: available to serious responders A:Invalid IP configuration with a different twist It may help to add the secondary subnet, IP, etc. to the advanced IPv4 TCP/Ip settings of which ever NIC you are using on the Toshiba, this is sometimes required when connecting to different subnets with the same NIC, although I'm not completely sure why it's not connecting to the other access points like the other notebooks. The Toshiba may have one of those so called trial anti virus software's creating problems or some of the preinstalled Toshiba bloatware may be causing problems here. Those other two routers may require a firmware update to work with Windows 8. You might try setting up a single subnet through the Verizon router, turning off DHCP on the other routers so they can pick up an IP from the Verizon routers DHCP, though this doesn't suit your needs it may help to narrow down the problem. 3 more replies Answer Match 56.28% Hello, I recently built two PCs. The master uses an ASUS p9x79 Deluxe mobo; the slave uses an ASUS p9x79 mobo. Both have an Intel 82579V Gigabit LAN Controller. I connected the two with a crossover cable and was able to share data via Remote Desktop, but I was unable to identify the "unidentified network". I have tried changing the network location to both a work location and a home location, but neither attempt successfully allowed me to properly identify the network (i.e. change the name, change the icon, etc.) Then, I had a so-called IT specialist come over. He scratched his head for an hour and couldn't figure out the problem either. He suggested that I buy a switch, which I did. I bought a Cisco five-port Gigabit switch. Each computer connects to the switch with a CAT 6 patch cable. Unfortunately, this did not resolve the issue. I am only trying to connect these two PCs to each other; not to the internet, and not to anything else. When I use the Win7 troubleshooter it has informed me that there is an "invalid IP configuration". An automatic IP assignment as well as a static IP assignment has yielded the same result (i.e. an "unidentified network") The static IP addresses that I used are as follows: Master = 192.168.5.10; Slave = 192.168.5.11; both have a subnet of 255.255.255.0. The firewall has been turned off on both computers, and I do not have the Bonjour software installed. Could it have to do with the slave computers certification? ... Read more A:Troubleshooting Invalid IP Configuration Welcome to the Seven Forums. Since no one has answered your post - I'll take a stable at it. It seems that W7 wants to see (communicate with) a gateway IP address. I've not actually tried this (hence my hesitation to post in your thread) but you can try this: Master = 192.168.5.10 and a gateway of 192.168.5.11 Slave = 192.168.5.11 and a gateway of 192.168.5.10 That might let you change some of the things you want to change - or maybe not. 4 more replies Answer Match 56.28% Hi all, So I walked in to my office one day and found that I could not connect to my work network. I work for a small company, and we've got 3 computers and a printer hard-wire networked through one router. I can currently connect wirelessly, but we'd like to be hard-wired. I've tried setting a static IP, disabling IPv6, disabling IPv6 and IPv4 firewalls on the router, disabling the computer's firewall, replacing the physical cable, tried a tcp/ip reset and even bought and installed a new network adapter. Nothing has worked. I know the drill, so I've attached my IPCONFIG print-out and a screen shot of my router's DCHP Client list. My computer is Geomancer. I'm running Windows 7 Ultimate, SP 1. Thanks! Below are the results of the ping test with the wireless adapter disabled. ECHO is on. Pinging 192.168.1.1 with 32 bytes of data: Request timed out. Reply from 192.168.1.137: Destination host unreachable. Request timed out. Request timed out. Ping statistics for 192.168.1.1: Packets: Sent = 4, Received = 1, Lost = 3 (75% loss), Pinging 46.228.47.115 with 32 bytes of data: Request timed out. Request timed out. Reply from 192.168.1.137: Destination host unreachable. Request timed out. Ping statistics for 46.228.47.115: Packets: Sent = 4, Received = 1, Lost = 3 (75% loss), Ping request could not find host google.com. Please check the name and try again. Unable to resolve target system name google.com. [/php] More replies Answer Match 56.28% Hi, newbie here - first post, hope it's not a duplicate and is in the right place!! I have a Dell 4550, when I boot it up it comes to a screen saying "Invalid configuration information - please run setup program" I then get the option to hit F1 to continue or F2 to run setup utility. Ususally, I will go into the setup utility and make the date and time correct and then carry on. This will fix the problem for that day but then the same thing will happen the next day. Can anyone shed any light on a possible long term solution please? Thanks in advance A:Invalid Configuration Information Your CMOS battery may have reached the end of useful product life.$3.50 at Wal-Mart. Or it may merely be loose.
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I did the paperclip trick and now instead of the password prompt it says this on my dell d600 any help would be great
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When i try to install xp sp2, I keep getting "the data is invalid. xp sp2 could not be installed" error message.
I have re-installed windows and tried installing sp2 from CD, and tried the downlooad from the microsoft website, both with the same result.
Can anybody make any suggestion on what i can try next.
Many thank's Brian.j
[email protected]
A:Installing xp sp2, I keep getting "the data is invalid" error message.
Brian.j said:
When i try to install xp sp2, I keep getting "the data is invalid. xp sp2 could not be installed error message".
I have re-installed windows and tried installing sp2 from CD, and tried the downlooad from the microsoft website, both with the same result.
Can anybody make any suggestion on what i can try next.
Many thank's Brian.j
[email protected]Click to expand...
Welcome to the forums
http://support.microsoft.com/xpsp2getinstall
did you read the above? That looks like a good starting point...doc
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Can't seem to get rid of this error which prevents using USB, tried regcure software but didn't work.
Have service pack 3 installed
Does any one have a solution?
A:"Data is invalid" error on Sony Vaio
Does the usb device(s) work on other computers?
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Hello everyone! This is an issue that has been annoying me for a LONG time and I'd just be ecstatic if you guys could help me somehow.
My Internet works pretty well, except that around 3 times a day or so, it drops. I run the Windows 7 troubleshooter to fix it. Every time, it says "wireless network connection doesn't have a valid ip configuration" and then "fixed" and the Internet resumes working properly. Although it's easy to fix, I wish this problem didn't happen at all in the first place because it can be frustrating if I'm in the middle of a skype call or game.
Any ideas? Also the Internet stops working randomly like this for all devices in the house, not just my computer, so I know it's not my PC.
A:Internet drops because of invalid IP configuration?
do you still have a problem
you say it stops for all devices - any device connected by cable to the router - and does that stop working
if you do not have any devices connected by cable
I would suggest you connect by cable and see if this is an issue as well
if the cable connection does not disconnect - then its a wireless issue and post an xirrus screen shot please
Please make a note of the status of the lights on the modem and on the router when working normally - post that light status here.
Now when the internet disconnects make a note of the status of the lights for the modem and router here again. also note which have changed.
Please post back here the make and exact model of the router and if you have a separate modem, the make and exact model of the modem.
------------------------------------------------------------------------
Run Xirrus Wi-Fi Inspector
If you cannot access the internet with this PC, then you will need to copy the program across to the faulty PC
Save the file to a USB flash drive or other removable media. Plug it into the working computer with internet access and copy the file and install the program.
You will now need to take a screen shot and copy that back to the working PC and attach the screen shot in a reply on the forum here.
If you do not have another PC - do you have a phone connected to the internet - can you photograph the result and post the image in a reply
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As per a lot of other people on here, I'm having issues with connecting my desktop PC to my BigPond router. It will connect via wireless (have an installed D-Link DWA525 wireless card) but will not connect via LAN.
I've changed the IP, DNS and Default gateways to the same as the other working PC's in the house, but still no luck. The mobo uses Realtek GBE Family PCI-E controllers, but for some reason it won't move off 10Mbps (even when I try to tell it to change this).
I have tried new drivers, and have tried uninstalling drivers and letting windows install its own. None have worked. I've disabled V6, didn't work.
My IPCONFIG ALL shows up the following:
Microsoft Windows [Version 6.1.7600]
C:\Users\CJHBeast>IPCONFIG/ALL
Windows IP Configuration
Host Name . . . . . . . . . . . . : CJHBeast-PC
Primary Dns Suffix . . . . . . . :
Node Type . . . . . . . . . . . . : Hybrid
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No
DNS Suffix Search List. . . . . . : BigPond
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Realtek PCIe GBE Family Controller
Physical Address. . . . . . . . . : 1C-6F-65-3D-7A-18
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes
A:Unidentified network - invalid IP configuration
Quote: Originally Posted by cjhod
As per a lot of other people on here, I'm having issues with connecting my desktop PC to my BigPond router. It will connect via wireless (have an installed D-Link DWA525 wireless card) but will not connect via LAN.
I've changed the IP, DNS and Default gateways to the same as the other working PC's in the house, but still no luck. The mobo uses Realtek GBE Family PCI-E controllers, but for some reason it won't move off 10Mbps (even when I try to tell it to change this).
I have tried new drivers, and have tried uninstalling drivers and letting windows install its own. None have worked. I've disabled V6, didn't work.
My IPCONFIG ALL shows up the following:
Microsoft Windows [Version 6.1.7600]
C:\Users\CJHBeast>IPCONFIG/ALL
Windows IP Configuration
Host Name . . . . . . . . . . . . : CJHBeast-PC
Primary Dns Suffix . . . . . . . :
Node Type . . . . . . . . . . . . : Hybrid
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No
DNS Suffix Search List. . . . . . : BigPond
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Realtek PCIe GBE Family Controller
Physical Address. . . . . . . . . : 1C-6F-65-3D-7A-18
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes
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On boot up the laptop beeps twice and the message "system configuration data read error" appears with F1 to resume or F2 to setup. If I hit F! it boots up as normal. When I switch off and reboot the same ting happens every time...help its driving me crazy !!
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I run with a Dell Dimension 4600C, with Windows XP version 5.1.2600. Lately, my computer has taken to shutting down. But it doesn't shut down and start up again. The computer turns itself off, but the computer indicates that power is still going to the machine. I can't start the computer up without unplugging the CPU from its power source (an APC SurgeArrest outlet bank) and waiting for at least a minute so it won't shut down on me again.
Usually the computer will shut down as soon as it's rebooted once I've done this. I've taken to restarting the computer normally to prevent it from shutting down for at least twenty to thirty minutes.
Most of the time the computer will just run normally after the shut down (until it shuts down again). At other times it gives me a DOS message saying there's 'invalid configuration information' and it gives me the chance to run setup. I ran setup once, but didn't change anything.
Is this a RAM problem or a hardware problem? I'm inclined to say it's XP doing this, but I'm computer illiterate and have absolutely no idea what to do about this.
A:Pc Randomly Shuts Down, Says Invalid Configuration Information (sometimes)
this could be an overheating prob, how long does your computer run from cold till it shuts down? can you monitor the cpu, case temps?also, to check your ram try this?http://www.softpedia.com/get/Tweak/Memory-...iagnostic.shtmlgood luck
4 more replies
hi,,, i have dell inspiron 6400 laptop and when i turn it on it shows invalid configuration information- please run setup program and it directly goes to setup and i do not remember the password aswell .. now i have noway to boot.. please tell me what to do ... thanks...
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Hi I have a dell xps m1210 that show a message "invalid configuration information - please run setup program", i can not even enter the setup, when i press de F2 to enter setup it says "preparing to enter setup", but instead entering the setup it gives me the "invalid configuration information - please run setup program"
Can anyone help me
A:Invalid configuration information - please run setup program
How old is it. Could be a hard drive failure... can you give us the service Tag from the back of the machine?
5 more replies
I have tried everything that I could find on this forum as well as myriad others. I even went so far as to backup my computer and reinstall Windows 8. Still, I cannot connect to the internet. When I first bought the pc, I had no problems connecting. Any help would be greatly appreciated.
Here are my ipconfig /all results:
Microsoft Windows [Version 6.2.9200]
C:\Windows\system32>ipconfig /all
Windows IP Configuration
Host Name . . . . . . . . . . . . : Khaleesi
Primary Dns Suffix . . . . . . . :
Node Type . . . . . . . . . . . . : Hybrid
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No
Wireless LAN adapter Local Area Connection* 11:
Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Microsoft Wi-Fi Direct Virtual Adapter
Physical Address. . . . . . . . . : 1E-D0-5A-15-06-24
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Qualcomm Atheros AR9485 802.11b/g/n WiFi
Physical Address. . . . . . . . . : 2C-D0-5A-15-06-24
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
A:Invalid IP Configuration - Limited Internet Access
169.254.XXX.XXX is an Autoconfiguration IP address. Can you first try and temporarily disable your firewall and Anti-virus program.
Then can you boot your machine into safe mode with networking and test connectivity.
Follow this tutorial (OPTION THREE ONLY) - Safe Mode - Start Windows 8 in
Note
Please replace all references of 'Safe Mode' with 'Safe Mode with Networking'
Please post back your results and then we can troubleshoot from there
Lastly, Do any other machines experience this issue?
Many Thanks,
Josh
6 more replies
Anyone with a clue on how to solve this problem
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I have Windows XP SP2 and it is suddenly not booting up. I get a message that says Invalid Configuration Information, Please Run Setup Program, Floppy Diskette Seek Failure, Performing IDE Configuration, Strike F1 to continue and F2 to run Setup Utility. I press F1 to continue and then Windows loads and all is fine. I have a Dell computer model E310, which doesn't have a floppy disk drive. The computer is two years old. How can I eliminate this message and get Windows to load normally?
A:Invalid Configuration Floppy Diskette Seek Failure
Make sure there isn't a floppy left in the drive.
Change the first device in the boot order to the hard drive in the BIOS
Replace the motherboard battery
1 more replies
Issues found
"Wireless Connection 2" doesn't have a valid IP configuration
"Wireless Connection 2" doesn't have a valid IP configuration Detected
Reset the "Wireless Connection 2" adapter Completed
Investigate router or broadband modem issues Not run
Issues found Detection details
6 "Wireless Connection 2" doesn't have a valid IP configuration Detected
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Computer: Dell Inspiron 1525, 320 GB HD with about 2 GB of free space left, 4 MB memory, running Vista Home Premium 32-Bit, SP1, updates current. Just lately, booting from off, Windows will not load, but instead gives me a \Boot\BCD error (0xc00000f)--an error occurred while attempting to read the boot configuration data. I have repaired this error with my Dell-supplied OS disc repeatedly, and each time I turn off the computer it has the same error at startup. I have read that I may have to rebuild the BCD, but I don't know how to do that. Before I check with Dell, who I suspect will just tell me to reload Windows, I need to know how approach fixing my boot configuration data. The computer has had no new software installations, just routine Windows and Trend Micro Internet Security updates, I checked the disc for errors, and a few files were missing or incorrect, and defragmentation has also been performed routinely. Dell PC checkup finds no issues. How should I proceed?
A:Boot\BCD error reading boot configuration data when starting from cold boot
Try this hard drive diagnostic procedure: http://usasma.vox.com/library/post/b...agnostics.html
Repeated errors on a hard drive usually indicate an impending failure. I'd backup your stuff as soon as possible.
5 more replies
We are getting the above error randomly on some of the laptops we have deployed. The error comes right after you boot or when the windows 7 is left running. There are no special software running. The error in details is below.
"The boot configuration Data (BCD) settings for the following boot application have changed since Bitlocker was enabled
change settings: 0x26000090
You must supply a bitlocker recovery key to start this system.
Confirm that the changes to the BCD settings are trusted.
If the changes are trusted then suspend and resume bitlocker. This will reset bitlocker to use the new BCD settings.
Otherwise restore the original BCD settings"
Can anyone please explain on how to correct this error. As before this is happening on few of the machines and we are seeing more as we go. Any tips would be nice...Thanks
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Guys,
Please help. Every time I plug something into the USB ports I get Window recognise it then try to down load the drivers and come up DATA INVALID then shut it down. It dosn't matter if I have the disk or not the same problem comes up. This includes things that I have previously used fine on the PC. I'm not a guru so any help would be appreciated.
Thanks
A:Data Invalid WTF
Open Device manager from Start Menu > Run and typing devmgmt.msc and pressing EnterIn Device Manager select USB ControllersRight click on each one and choose Uninstall.Restart and let Windows reinstall them.
1 more replies
Hello there everyone
This is my first post so please be gentle.
We are currently using Windows XP and SP3 and we have suddenly come across a problem when trying to create shares on new laptops to copy over peoples old data. We can create the folder fine and and users and permissions but as soon as i click on accept i get the following message
An Error occured with trying to create share - the data is invalid
I have tried everything, removing SP3, modify the GPEDIT and giving all users full control yet still nothing. Does anyone have a ideas - ITS DRIVING ME NUTS
A:The data is invalid
7 more replies
Hi, I am not a whiz on computers so please excuse any mistakes, I am having problems connecting a samsung E840 to my pc a new hardware wizard comes up then it finishes with data invalid, any help would be most apreciated.
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i have this virus on my computer with threat name Win32/Cryptor
the file name is C:\WINDOWS\system32\igctpuo.dll
it shows up in a resident shield alert every time i click the my computer icon.
and when i click heal is says some files cannot be healed, the data is invalid.
does anyone know how i can get rid of the virus?
A:AVG can't heal because of invalid data
Hello and welcome to TSF.
We want all our members to perform the steps outlined in the link given below, before posting for assistance. There's a sticky at the top of this forum, and a
Quote:
Having problems with spyware and pop-ups? First Steps
link at the top of each page.
http://www.techsupportforum.com/f50/...lp-305963.html
After running through all the steps, you shall have a proper set of logs. Please post them in a new topic, as this one shall be closed.
If you have trouble with one of the steps, simply move on to the next one, and make note of it in your reply.
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i get " data is invalid " whenever i try to install devices like drives or usb phones etc . device manager lists the items but cannot install . what do i do to solve this . cheers peterlakey .
A:data is invalid message - help please !
Backup registry before operations(see http://support.microsoft.com/kb/322756)
Load the regedit.exe program by going to the Start Menu and selecting ‘Run’. Enter regedit.exein the text box. Click the ‘OK’ button.
2. In the registry there is a folder called PCI located at:HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Enum\PCI\
3. Inside there are folders that look something like this:VEN_14F1&DEV_1053&SUBSYS_1047144F&REV_08
4. Each of these folders represent a PCI device located on your motherboard. By default youradministrative privileges DO NOT give you "Full Control" over these keys in Windows XP, only"Read" permissions arein place.
5. Search through all of these "VEN..." folders and look for a key inside each folder labelled"DeviceDesc". This key indicates what the device actually is.
6. Right click on the folder that contains the DeviceDesc key value of "(your drive)" andselect “Permissions”.(in 'Edit' menu)
7. Click Full Control - Allow.
8. Close all programs and restart the computer. Now that you have full control of that PCI folder,reinstall the driver. It should now install correctly.
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Hi, I really hope you can help me, this is driving me nuts!
I cannot install *any* new USB devices. I have tried several memory stick type devices and a 3g modem card. They all work on other peoples laptops fine.
In all cases my Dell laptop (Latitude D600) finds the hardware and the Add new hardware wizard pops up as expected. I click ok to install the driver and after a short while it fails with the message "data is invalid" ...and no clues as to what this means.
USB devices (a webcam, camera and 2 memory sticks) that were installed many months ago are all ok and still work fine.
So... it isn't a hardware problem, it must be something Windows does when installing a new device.
Any ideas how I can fix it?
Thanks!
Marco
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I recently did a Vista Premium reinstall. I downloaded and installed SP1 for Vista without any problems. Then I went to the Microsoft site again and downloaded Sp2 for Vista. When I tried to install it, I got an error 'The data is invalid'. I kept the SP2 executable from the last time I did a reinstall. It worked fine then. With that, I now get the same error. What gives? I can't understand why an executable that worked earlier, wont work now.
I thought of trying another site, but most of these places want you to install an installer before you can download the file.
Where or how do I get a proper file, now?
Thanks
A:[SOLVED] The Data Is Invalid
The best way to do it would be to use windows update.
I could go on asking if you have 32bit or 64bit? did you download the right one?... but i belive that using windows update might be your first/best option.
if windows update does not work or you do not wish to using windows update we are here to help
7 more replies
Hey guys,
I am absoultely stumped with this problem. I cannot get any USB ports to work on my computer. Whenever I try to install drivers in device manager it stops halfway through and I get the message "the device is not valid" and it then stops. I have tried taking out the power cable and then restarting the machine again but that didn't work. I have also edited the registry as a lot of posts online suggest that this problem is to do with the issues with permissions in xp and you can go into the registry and enable devices that way. Still no luck though. I have also tried to reset the registry to default settings but that also does not work. Anyone got any idea how to fix this problem?
A:I keep getting 'the data is invalid' when installing drivers in xp
Hi jonesma1 and welcome to TSF.
Can you tell me what Service Pack you currently have installed. Also, do you have your Windows XP Disk with you?
6 more replies
I have data validation on a column which prevents users from entering a numerical code which is not contained within a standard list. When they copy a row and then insert it, they are able to fill down (copy) the formatting. When doing so, the number code in column A automatically increases the code by 1, which makes it invalid.
Am I able to prevent invalid data from being copied into those cells?
The workbook is macro free, so I am trying to do it without data validation.
A:Invalid Data Allowed with Fill Down
To 'pull down'\auto fill a number without it incrementing you need to grab two cells (with the same number in it) and pull down.
1 more replies
Biostart M7NCG 400 Athlon 2400 CPU Fresh install of XP HOME
Problem I am having is that no matter what I do I get an invalid data message whenever i plug in any usb devices.........
I even tried to change permissions of the devices in the registry.....
A:Invalid Data when installing any usb devices
in the device manager,uninstall all instances of usb
then right click and choose
scan for hardware changes and windows will reinstall
see if this cures it
2 more replies
I was on my gf's computer on the control panel trying to clear unnecessary programs and I thought i was being careful enough... Well i fear i deleted an essential program on the computer and may have ruined it. I removed the Java runtime environment and each of the updates thinking it wasnt necissary. Is this a critical program? The weird thing is as i was removing parts of it it just kept saying computer must restart to complete the removal of the program, and i selected no each time.. all of the sudden the computer turned off and when rebooting it said invalid boot.ini booting from c:windows\
I have an old desktop and was able to give them that for a spare. However the desktop only has a IDE hard drive slot and her computer has a SATA Hard drive, so I cannot run it in my computer.
(it may be useful to tell you now that I have looked inside both computers, and had unplugged the connection to the hd (power and motherboard connection) and reconnected them later)
However i am wondering if i can recover the data on the drive. Many assignments my gf has written for school must be printed for a portfolio later in the year. I burned a windows xp professional cd from an .iso file that is bootable (thats the operating system they had). And after several unsucsessful attemps, was finally able to acess the system BIOS on the broken computer and tell it to start from a cd initally and it seemed to work as i recieve the message:
press any key to boot from cd....
i press it and ... Read more
A:invalid boot.ini trying to recover data
12 more replies
Hello everybody,
I wouldlike to know how to enable/disable the BCD.
antivirus is warning about the BCD is allawing non-signed drivers installation.
Would like to fix this.
Is it worth it?
A:Boot configuration data (BCD)
Being worth it or not, really depends on what you want it for, can you give any more info?
9 more replies
I think I may have made a big mistake, I inadvertently manually deleted ACDSee Pro2 and now I keep getting a Windows Installer dialog box that reads: “The configuration data for this product is corrupt. Contact your support personnel” I believe I may have deleted something I should not have. I’ve downloaded Windows Installer 3.1 and that did not help. I can load(install) other programs with no problems, but I can’t reinstall ACDSee Pro2 .I’ve downloaded from different sites and still the same results.
Anybody have any Ideas I can try. Thanks
A:Configuration Data Is Corrupt
hm maybe something in the registry is causing you greif? unfortunatly i dont know much in the feild of registry cleaners, someone else may be able to lend a suggestion or 6 :D otherwise just misc. search for acdse in there?
goodluck
15 more replies
I was on my PC, my dual boot failed, windows boot configuration data is now gone. I don't have a system install disk, don't have an order number the manufacturer needs to send me one, nothing I've tried worked. The status error is 0xc0000098. Is there a way to fix it without the install disk? Some sort of repair tool I can download? If I could even get a command prompt open I could fix it but it won't boot at all.
A:Boot configuration data gone
Downloading Repair ISO which is small size file is illegal as per Microsoft. But you can download the ISO for Windows 8.1 Enterprise Evaluation, burn it to a blank DVD and then use it to repair your system. The file size is more than 3 GB.
http://technet.microsoft.com/en-us/windows/hh771457.aspx
OR Just ask one of your friends for their Windows 8 DVD and repair your system in a few minutes.
This is why you should create a repair disk the first time you boot your Windows computer.
6 more replies
Hi (first post)
I am unable to install an audio driver without getiing the message:
" An error occurred during the istallation of the device
The data is invalid"
I am using a Mercury KOB KT400 FDSX motherboard, Windows XP and trying to install the driver for a Genius Sound Maker Value 5.1 sound card.
Any help will be greatly appreciated!
A:multimedia audio controller - the data is invalid!!!!!!!
6 more replies
Hi there! Can u please help me to figure out this "INVALID IMAGE" problem that i've encountered since a few days ago till now?
By the way, i've used some of the DATA RECOVERY programs to recover some lost files which i've accidently deleted in my handphones's MEMORY CARD and YES the deleted files has been successfully recovered, but only when I tried to open all the image files, there's not even one of them is readable and it only shows a black background with a massage "INVALID IMAGE" or "NO PREVIEW AVAILABLE".....
The DATA RECOVERY programs that i've used were:
• Data Doctor Recovery Pen Drive
• Stellar Phoenix Photo Recovery (Demo)
• Recover My Photos
• DiskInternals Flash Recovery
• Recuva
• UndeletePlus
• JPEG Recovery Pro 5 (Demo)
• Photo Recovery
• Image Fix and Enchance
Hope that u will reply me ASAP!!! I really need your help!!!
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Hay I'm having trouble with activation windows 7 when I want activation windows I have en error 0x8007000D (the data is invalid) Help
Sory for my bed English
A:Windows 7 activation problem (The data is invalid)
Quote: Originally Posted by arminn
Hay I'm having trouble with activation windows 7 when I want activation windows I have en error 0x8007000D (the data is invalid) Help
Sory for my bed English
What version are you trying to activate.?
9 more replies
Hi (first post)
I am unable to install an audio driver without getiing the message:
" An error occurred during the istallation of the device
The data is invalid"
I am using a Mercury KOB KT400 FDSX motherboard, Windows XP and trying to install the driver for a Genius Sound Maker Value 5.1 sound card.
Any help will be greatly appreciated! :)
A:multimedia audio controller - the data is invalid!!!!!!!
go to you computor manufactures website .hp dell etc and download the latest chipset for your computer then check for audio chipsets /drivers at the same site.failing that go to my computer in the control panel run device manager and check for device conflicts indicated by an exclaimation mark.
1 more replies
I have a client running Windows 8.1. The original problem was that he could not install an HP 6700 printer, the installer package failed every time. I got the same error; I attempted to update all his drivers and noticed that all the installers failed. I then attempted to install it manually and I get a failure: Windows found drivers software for your device but encountered an error while attempting to install it. The data is invalid. I receive the same error if I try to install any driver the same way. Any help would be appreciated. Laptop is an Acer Aspire One running 8.1, there were no recovery discs made and all recovery options fail. Not sure where to go with this.
A:Cannot install any driver, failing for invalid data
Any help would be appreciated.
Try DriverMax
I use the paid version.It works good.
1 more replies
The svcpack.log which is in C:\Windows is kind of long but I just want to find out what the last few lines of it mean, here they are (notice the line "UpdSpCommitFileQueue for FileQueue failed 0xd", anyone know what this means?):
389.047: Copied file: C:\WINDOWS\system32\rasauto.dll
389.063: Copied file: C:\WINDOWS\system32\rasapi32.dll
389.250: Copied file: C:\WINDOWS\system32\printui.dll
389.297: Copied file: C:\WINDOWS\system32\perfctrs.dll
389.360: Copied file: C:\WINDOWS\system32\olecnv32.dll
389.656: DoInstllation: UpdSpCommitFileQueue for FileQueue failed: 0xd
391.953: Unregistration of sprecovr successful
392.250: The data is invalid.
420.813: Message displayed to the user: The data is invalid.
420.813: User Input: OK
420.828: Service Pack 3 installation did not complete.
Select 'OK' to undo the changes that have been made.
426.063: Message displayed to the user: Service Pack 3 installation did not complete.
Select 'OK' to undo the
426.063: User Input: OK
426.078: Starting process: C:\WINDOWS\$NtServicePackUninstall$\spuninst\spuninst.exe /~ -u -z
782.906: Software Update Rollback has completed with return code 0xbc2. This rollback requires a reboot.
782.906: Service Pack 3 installation did not complete.
Windows XP has been partially updated and may not work properly.
789.563: Message displayed to the user: Service Pack 3 installation did not complete.
Windows XP has been partially updated a... Read more
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When I try to boot my Lenovo Flex 3-1580, Windows 10-64bit, I get the following BSOD: "The Boot Configuration Data for your PC is missing or contains errors.
File: \EFI\Microsoft\Boot\BCD Error code: 0xc0000034"
I haven't been able to get it to try booting from a USB, but I did try reinstalling Windows. That failed when it told me to restart and it went back this issue.
When I tried to find solutions online, they all assumed the computer could boot, so were useless.
Any help is appreciated! Thank you!
A:Boot Configuration Data got corrupted
Hi toasterbot,
It's not an uncommon issue mate, and not that hard to fix. You will need to boot from your Windows disk to fix it .
Boot your computer using Windows installation media
Select the correct time and Keyboard type.
Click Repair your computer in the lower left corner.
Select Troubleshoot from Choose an option screen.
Click Advanced options in Troubleshoot screen.
Click on command Prompt.
Type these following commands one at a time and hit enter after each line of command:
Bootrec /fixmbr
Bootrec /fixboot
Bootrec /scanos
Bootrec /rebuildbcd
shutdown -s
After about a minute after the last command your machine will shutdown. You can remove the Windows media now.
TsVk!
1 more replies
So I just downloaded adware delete or w.e to remove vosteran search which had bee plaguing me for a while. I delete the files it tells me to and as I restart the computer I get the "Recovery\$ system files are missing error code 0xc0000034 File :\BCD. Now I've done the research and it seems I only have 3 options. Windows 8 DVD, windows 8 drive or booting it to system recovery. I don't have the flash drive OR the windows 8 disc and pressing F11 at boot up doesn't do squat... I'm really terrified. I think my computer is done for? If for some reason I manage to fix
d, the bcd, will that detele all my data? System specs: Lenovo ideapad core i5 windows 8 model name 20191. Any ideas suggestions?
A:Boot configuration data is missing
Windows 8, "Missing File: \BCD Error Code: 0xc0000034"
1 more replies
Hi,
When I start my computer this is the screen it gives me:
I do not have a dvd/cd drive on my laptop and the codes that are on the bottom of the laptop are not readeble anymore. What can I do??
Thanks!
A:Boot configuration data is missing
1. Welcome to Tech Support Guy
2. What is the make and full model of the laptop please
3. What OS was on the laptop originally- was that Windows 8/8.1 or what please
4. Do you have a usb flash pen drive and if so what capacity is it please
1 more replies
so DEP doesn't like my skype and thus won't let it stay open. i had DEP turned off before, but then i had my computer wiped and all this and that, so i had to turn it off again. but the tutorial on here by brink for how to turn it off isn't working this time, and i get a message that says
"boot configuration data store could not be opened.
what can i do to fix this?
A:boot configuration data could not be opened?
my boot configuration data apparently cant be accessed, so this isnt working, and for the life of me i cant find a way to get access to it. i tried looking at the comments a few times and dep closed chrome each time i tried. HELP.
1 more replies
I was attempting to install xp as a dual os system. After setting up my partician vista still would not let me install xp , older version error. I used a program vista bootpro or bootpro and changed my boot configuration trying to get it to allow me to install xp. Now I cant boot up my laptop. Only system info I have is toshiba, 2 years old lots of ram, How can I change my BCD back so that I can boot up vista. I tried from xp cd, safe mode, last known. I don't have the vista disk with me at the moment, Can I get it to boot up with that disk? If not how can I create a emergency boot up disk for vista?
Dean
A:Boot Configuration Data Changed
Hi,
I think you might have to wait until you get the Vista disk back.
That will just repair the boot configuration without any problem.
There are various boot disks HERE and the Ultimate Boot CD
but I`m not sure they would be much use.
There is a very good page HERE for dual booting XP/Vista
3 more replies
When I try to boot my Lenovo Flex 3-1580, Windows 10-64bit, I get the following BSOD:
"The Boot Configuration Data for your PC is missing or contains errors.
File: \EFI\Microsoft\Boot\BCD Error code: 0xc0000034"
I haven't been able to get it to try booting from a USB, but I did try reinstalling Windows. That failed when it told me to restart and it went back this issue.
When I tried to find solutions online, they all assumed the computer could boot, so were useless.
Any help is appreciated! Thank you!
More replies
I'm trying to connect a C# program to an Access database, but the wizard keeps crashing every time... Here's as far as I can get...
Wizard opens up
Click "New Connection"
Click "Change"
Select "Microsoft Access Database File" from combo box.
Click "OK"
Type "PROVIDER=Microsoft.Jet.OLEDB.4.0;DATA SOURCE="C:\\Data\\TimeSheet.mdb;" into the ConnectionString text box (tried leaving it blank as well).
Click "Test Connection"
Receive "Test connection succeeded." message box
Click OK
Click OK to continue wizard
This is where I receive the error message, which is
"Format of the initialization string does not conform to specification starting at index 0."
If I set up the connection, data adapter, and dataset in the program itself, I don't have any problem, just if I try to use the wizard. Also tried to set it up in VB .NET, but have the exact same problem. Thanks in advance.
Try specifying just the folder name and not the filename, you can specify the file later in the code.
2 more replies
I have a problem when I am installing USB devices in that I keep getting an error saying hardware did not install correctly data invalid
I found this microsoft fix for the problem http://support.microsoft.com/default.aspx?scid=kb;en-us;810882
My problem is when I browse to C:/windows/driver cache/ii386 I cannot find a file called driver.cab to rename. Which I guess is what is causing the problem!!!
Also my problem is that my machine is a factory install for windows, and I don't have the disc's. Apparently the driver.cab files would be on the disc's but as I don't have them..!?
Does anyone know what I need to do to sort this problem out, apparently is a classic driver problem. I have a new USB keyboard and I cant get it to install!
Many thanks
nicks
A:Solved: Data invalid...driver installation problem
16 more replies
After a hard, unplanned reformat of my son's Dell Inpiron 1100 I had some problems that I solved with help from here in this forum. Now, there are ten items in the Device Manager all with yellow exclamation points, four of those items listed as unknown devices. I've downloaded all the drivers off the Dell Drivers and Downloads site that are relevant (don't get me started about Dell not including the Drivers and Utilities CD and then not sending me one because the machines are out of warranty!). These items don't match up with anything I've downloaded from Dell's drivers site.
When I do a reinstall through Device Manager all I get is "error, invalid data." Here is the list of the marked items in the Device Manager and which ones are marked on the screen as unknown device (by running the reinstall you get what the item is really called at the end of the wizard):
Microsoft ACPI-Compliant Control Method Battery (listed in Device Manager as unknown device)
Microsoft AC Adapter (listed in Device Manager a unknown device)
Audio Codecs
Legacy Audio Drivers
Legacy Video Capture Devices
Media Control Devices
Microsoft Kernel GS Wavetable Synthesizer (listed in Device Manager as unknown device)
Video Codecs
Microsoft Composite Battery (listed in Device Manager as unknown device)
Now, all the battery items... I am running the computer plugged into the outlet in the wall, but I can also run it by battery power. However, when I try and run the BIOS ... Read more
More replies
Hi,
I have been tasked to sort a a problem with an Access 98 database. When I try to run it I recieve the folllowing message:
"F:\1953sqn\recdata.MDB is not a valid path"
The database currently resides in c:\1953sqn. I understand this database was originally link to the network drive f:\ which no longer exist. How do get access to recognise the new database location c:\1953sqn ?
A:Solved: access mdb returns invalid data path
16 more replies | {} |
### Based in the Seattle Area.
Free study guides and discussions about various topics in Mathematics. Thanks for stopping by!
## Mar 11 An interesting limit involving trigonometry
How do we calculate:
$$\lim_{x\to 0} sin^{-1}\bigg(\frac{tanx}{6x^{2}cot3x}\bigg)$$
Have a look here! | {} |
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# Movie Genre Ratings - Addendum
This article was created with Jupyter. To see the code generating all figures and outputs, click 'Show Code'
# Introduction¶
In a previous post, I looked at trends in critic and audience ratings of movies. One finding was that critics on average rate movies lower than audiences. One potential explanation for this is that there is more selection bias with audience ratings - only people who are an audience likely to enjoy a film will tend to see (and therefore rate) it. In other words, if you asked an audience member or a critic how much enjoyment they would get out of seeing a film they rated a 5, you would get similar responses.
However, an alternative explanation is that when I compare audience and critic responses, I'm comparing apples and oranges. Maybe critics, having made a career of rating things, actually have a better calibrated rating scale. As a population, they use a wider range of values. Under this explanation, a 5 from an audience (around the lowest I saw for any movie) is actually more like a 2 from a critic.
Which interpretation is correct? I originally went with the 'they use the same scale' interpretation, partially because I think it holds merit and partially because it leads to numbers that are easier to digest. A 2 point difference on a 10 point scale is meaningful to most people in a way that 1.5 standard deviations is not. However, it's still interesting to see what happens if we use normalized values.
I executed all of the same code, but with normalized (z-scored) values. For the non-stats savvy people: I've just made it so the range of the ratings are about the same for the audience and critic ratings, and made it so an 'average' rating is a 0. This is easier to see in the first figure (compare to the previous post).
# Visualizing Normalized Movie Ratings ¶
In [1]:
%matplotlib inline
#Import some tools we'll use
import pandas as pd
import numpy as np
from bokeh.palettes import Category20, Category20b
from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource, Range1d, LabelSet, Label, HoverTool
from bokeh.charts.attributes import CatAttr
from bokeh.charts import Bar
from scipy.stats.mstats import zscore
#Only output floats to one decimal place in tables
pd.options.display.float_format = '{:,.1f}'.format
output_notebook(hide_banner=True)
In [2]:
###Just copying and pasting the code from the other notebook and zscoring
##DATA PREP
#Remove columns where data is missing
mov = mov[(mov['rt_score'] != 0) & (mov['rt_audience_score'] != 0) & (~pd.isnull(mov['Genre_1']))]
#rt_score is on a 1 to 10 scale, rt_audience_score is 0.5 to 5. Let's rescale
mov['rt_audience_score'] = mov['rt_audience_score']*2
#Only include those columns we want
mov = mov[['title', 'rt_audience_score','rt_score','Genre_1','Genre_2','Genre_3']]
mov['rt_audience_score'] = zscore(mov['rt_audience_score'])
mov['rt_score'] = zscore(mov['rt_score'])
#Calculate difference between audience and critic scores (to use later)
mov['dif'] = mov['rt_audience_score'] - mov['rt_score']
#Generate a unique color based on whatever the first genre is for each movie, for plotting
cat = Category20[20]
cat.append(Category20b[3][0])
genres = mov['Genre_1'].unique()
mov['colors'] = [cat[np.where(genres == genre)[0][0]] for genre in mov['Genre_1']]
#Generate a genre string based on the three genres (to prevent hover tooltips from displaying nans)
mov['Genre_str'] = (mov['Genre_1'] + ' ' +
mov['Genre_2'].fillna('') + ' ' +
mov['Genre_3'].fillna(''))
In [3]:
#Themes aren't really supported yet in Bokeh, so define a function to do styling
def styleBokeh(p):
#Hide the bokeh toolbar
p.toolbar_location = None
#Format axis label fonts
p.yaxis.axis_label_text_font_size = "12pt"
p.yaxis.axis_label_text_font_style = "normal"
p.xaxis.axis_label_text_font_size = "12pt"
p.xaxis.axis_label_text_font_style = "normal"
p.xaxis.major_label_text_font_size = "10pt"
p.yaxis.major_label_text_font_size = "10pt"
#Change title font size
p.title.text_font_size='14pt'
In [4]:
##SCATTER PLOT ALL MOVIES
#Make a data source for bokeh to use
mov_source = ColumnDataSource(mov)
#We want the axes on the same scale, so figure out min of both and max of both
low = mov[['rt_audience_score','rt_score']].min().min() - 0.2
high = mov[['rt_audience_score','rt_score']].max().max() + 0.2
#Define the hover over tooltips
hover = HoverTool(
tooltips=[("Title", "@title"),
("Audience Score", "@rt_audience_score{0.0}"),
("Critic Score", "@rt_score{0.0}"),
("Genres", "@Genre_str")
]
)
#Make the figure
p = figure(title = "Movie critic and audience ratings",
x_range=Range1d(low, high),
y_range=Range1d(low,high),
tools=[hover])
#We'll put critic ratings on the x-axis and audience on the y-axis
p.xaxis[0].axis_label = 'Critic Rating'
p.yaxis[0].axis_label = 'Audience Rating'
#Add a diagonal line for where audience rating = critic rating
p.line((low,high), (low,high),line_color="red", line_width=5, alpha=0.5)
#Plot the points, coloring by Genre_1
p.scatter(x='rt_score', y='rt_audience_score', source=mov_source, color='colors',
size=8, fill_alpha = 1)
styleBokeh(p)
show(p)
The audience and critic ratings have about the same ranges, and the red line seems to go straight through the center of the movies. Great! Now we can look at how this changes things by genre.
In [5]:
##DATA PREP FOR GENRE PLOTS
#Melt the genre columns so we only have one. This will give multiple entries for movies with more than one genre
melted_mov = pd.melt(
mov.drop(['colors', 'Genre_str'],axis=1),
id_vars=['title',
'rt_audience_score',
'rt_score',
'dif'],
value_name='genre')
#A little bit of clean up
melted_mov = melted_mov.drop('variable',1)
melted_mov = melted_mov.dropna()
#Group by genre
genre_groups = melted_mov.groupby('genre')
#Excluding genres with less than 20 entries
genre_revs = genre_groups.mean()[genre_groups['genre'].count() > 20]
In [6]:
##SCATTER PLOT FOR GENRE SCORES
#Make a data source for bokeh
genre_revs_source = ColumnDataSource(genre_revs)
#Get axes ranges
low = genre_revs[['rt_audience_score','rt_score']].min().min() - 0.05
high = genre_revs[['rt_audience_score','rt_score']].max().max() + 0.05
#Define the hover over tooltisp
hover = HoverTool(
tooltips=[("Genre", "@genre"),
("Audience Score", "@rt_audience_score{0.0}"),
("Critic Score", "@rt_score{0.0}"),
("Difference", "@dif")
]
)
p = figure(title='Audience and critic ratings by genre',
x_range=Range1d(low, high),
y_range=Range1d(low,high),
tools=[hover])
p.xaxis[0].axis_label = 'Critic Rating'
p.yaxis[0].axis_label = 'Audience Rating'
#Add a line for where critic score = audience score
p.line((low,high), (low,high),line_color="red", line_width=5, alpha=0.5)
#Scatter plot the genre scores
p.scatter(x='rt_score', y='rt_audience_score', source=genre_revs_source,
size=6)
labels = LabelSet(x='rt_score', y='rt_audience_score', text='genre', source=genre_revs_source,
x_offset=0, y_offset=5, text_font_size="7.5pt", text_align='center')
#Hide the bokeh toolbar
p.toolbar_location = None
styleBokeh(p)
show(p)
Now we can see what genres audiences like more than average (above 0 on the y-axis), what critics like more than average (to the right of 0 on the x-axis). We can also see where audiences and critics disagree most relative to their normal ratings. So while audience members rate drama movies higher than critics do on average, when you take the audience's tendency to rate everything pretty high into account, critics actually like drama more.
Again this is easier to see if we take the difference.
In [7]:
genre_revs = genre_revs.sort_values('dif', ascending = False)
p = Bar(genre_revs.reset_index(),
values='dif',
label=CatAttr(columns=['genre'], sort=False),
legend=False,
title='Difference between critics and audience ratings by genre',
ylabel='Audience ratings minus critic ratings',
tools=[])
p.toolbar_location = None
styleBokeh(p)
show(p)
Now we see that Fantasy is still the genre audiences disagree with critics most about, but we also get a neat separation - there are genres audiences like relatively more (fantasy, adventure, and action), and those that critics like relatively more (thriller, drama, comedy, crime, romance). Sci-fi, animation, and family is where there is the most agreement.
For completeness, I'm including the top 10 lists I generated for the last post. The lists are notably quite similar.
In [8]:
#Make mov presentable for printing
print_mov = mov.drop(['Genre_1', 'Genre_2', 'Genre_3', 'colors'], axis=1)
print_mov.columns = ['Title', 'Audience Score', 'Critic Score', 'Difference', 'Genres']
# Top 10 Fantasy Movies Audiences Love More Than Critics¶
We still get lots of twilight and superhero movies on this scale.
In [9]:
#Get the titles of the 10 fantasy movies with the greatest difference between audience and critics
fantasy_movie_titles = (melted_mov[melted_mov['genre'] == 'Fantasy'].
sort_values(by='dif', ascending=False)
[0:10]
['title'])
#Make the table pretty and output it
fantasy_table = (print_mov
[print_mov['Title'].isin(fantasy_movie_titles)].
sort_values('Difference', ascending=False)
)
fantasy_table.index = range(1,11)
fantasy_table
Out[9]:
Title Audience Score Critic Score Difference Genres
1 300 1.6 -0.4 2.0 War Fantasy Action
2 The Twilight Saga: Breaking Dawn - Part 2 0.8 -1.1 2.0 Fantasy Drama Adventure
3 The Twilight Saga: New Moon 0.3 -1.5 1.8 Fantasy Drama Adventure
4 Pirates of the Caribbean: At World's End 0.8 -0.9 1.7 Fantasy Adventure Action
5 The Hobbit: An Unexpected Journey 1.6 0.0 1.6 Fantasy Adventure
6 Pirates of the Caribbean: Dead Man's Chest 1.1 -0.5 1.6 Fantasy Adventure Action
7 The Hobbit: The Desolation of Smaug 1.6 0.2 1.5 Fantasy Adventure
8 Man of Steel 1.1 -0.3 1.4 Fantasy Adventure Action
9 Thor: The Dark World 1.1 -0.3 1.4 Fantasy Adventure Action
10 The Hobbit: The Battle of the Five Armies 1.1 -0.2 1.3 Fantasy Adventure
# Top 10 Movies Audiences Love More Than Critics¶
This list has mostly the same movies as the unstandardized version, with some of the ordering slightly different.
In [10]:
top10_table = print_mov.sort_values('Difference', ascending=False)[0:10]
top10_table.index = range(1,11)
top10_table
Out[10]:
Title Audience Score Critic Score Difference Genres
1 Bad Boys II 0.3 -2.0 2.3 Crime Comedy Action
2 Transformers 1.6 -0.6 2.3 Sci-Fi Adventure Action
3 Fast & Furious 6 1.9 -0.3 2.2 Thriller Crime Action
4 Transformers: Revenge of the Fallen 0.1 -2.1 2.2 Sci-Fi Adventure Action
5 300 1.6 -0.4 2.0 War Fantasy Action
6 The Twilight Saga: Breaking Dawn - Part 2 0.8 -1.1 2.0 Fantasy Drama Adventure
7 Despicable Me 2 1.9 0.0 1.9 Family Comedy Animation
8 The Twilight Saga: New Moon 0.3 -1.5 1.8 Fantasy Drama Adventure
9 National Treasure: Book of Secrets 0.3 -1.4 1.7 Mystery Adventure Action
10 Pirates of the Caribbean: At World's End 0.8 -0.9 1.7 Fantasy Adventure Action
# Movies Critics Love More Than Audiences ¶
Again, this mostly looks the same as the unstandardized list.
In [11]:
bot10_table = print_mov.sort_values('Difference', ascending=True)[0:10]
bot10_table.index = range(1,11)
bot10_table
Out[11]:
Title Audience Score Critic Score Difference Genres
1 King Kong -1.8 0.9 -2.7 Drama Adventure Action
2 Rocky -0.7 1.4 -2.1 Sport Drama
3 E.T. the Extra-Terrestrial 0.1 2.0 -1.9 Sci-Fi Family Western
4 War of the Worlds -1.5 0.3 -1.9 Thriller Sci-Fi Adventure
5 Charlie and the Chocolate Factory -1.3 0.5 -1.8 Comedy Adventure Family
6 Titanic -0.5 1.1 -1.6 Romance Drama
7 Back to School -1.3 0.3 -1.6 Sport Romance Comedy
8 The Incredibles -0.2 1.4 -1.6 Animation Adventure Action
9 Shakespeare in Love -0.2 1.4 -1.6 Romance Drama Comedy
10 Toy Story 2 0.1 1.6 -1.5 Comedy Animation Adventure
# Conclusion¶
I think you could spend a lot of time discussing what the best way of interpreting the audience and critic scores - it's a strange case where we have a seemingly intuitive score (a 10-point scale), but we don't know if our populations (critics and audiences) are using them the same. It's nice that for the most part, this difference in interpretation doesn't change much in terms of what genres or movies audiences and critics disagree on most. | {} |
Ashish Kumar - let's learn, implement then understand Maths and Physics
“For Every Reason It’s Not Possible, There Are Hundreds Of People Who Have Faced The Same Circumstances And Succeeded.” – Jack Canfield
Real life examples of parabola, Standard forms of Parabola, Definition and geometric proof for parabola, Derivation for equation of parabola, Way to remember all rules of parabolas, Derivation for length of latus rectum of parabola
NCERT EXERCISE 11.2
In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
Question 1. $$y^2 = 12x$$
Question 2. $$x^2 = 6y$$
Question 3. $$y^2 = -8x$$
Question 4. $$x^2=-16y$$
Question 5. $$y^2 = 10x$$
Question 6. $$x^2=-9y$$
In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions:
Question 7. Focus (6,0); directrix x = – 6
Question 8. Focus (0,–3); directrix y = 3
Question 9. Vertex (0, 0); focus (3, 0)
Question 10. Vertex (0, 0); focus (–2, 0)
Question 11. Vertex (0, 0) passing through (2, 3) and axis is along x-axis. | {} |
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# If a cube is inscribed inside a sphere...
Author Message
Director
Joined: 29 Nov 2012
Posts: 685
If a cube is inscribed inside a sphere... [#permalink]
### Show Tags
23 Jun 2013, 06:04
If a cube is inscribed inside a sphere then the diagonal ( longest side) of the cube is equal to the diameter of the sphere?
the formula for diagonal of a cube is D = $$\sqrt{3}$$a
Is this correct? Can I apply this strategy for such questions?
--== Message from the GMAT Club Team ==--
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This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
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Math Expert
Joined: 02 Sep 2009
Posts: 59590
Re: If a cube is inscribed inside a sphere... [#permalink]
### Show Tags
23 Jun 2013, 06:11
fozzzy wrote:
If a cube is inscribed inside a sphere then the diagonal (longest side) of the cube is equal to the diameter of the sphere?
the formula for diagonal of a cube is D = $$\sqrt{3}$$a
Is this correct? Can I apply this strategy for such questions?
Don't understand what you mean by the red parts: longest side in a cube? Also what do you mean by "such questions"?
Other than that all is correct.
_________________
Director
Joined: 29 Nov 2012
Posts: 685
Re: If a cube is inscribed inside a sphere... [#permalink]
### Show Tags
23 Jun 2013, 06:19
I was referring to the diagonal of the cube as the longest side...
An example of this question would be cube is inscribed inside in a sphere. Volume of sphere is provided and we have to find the surface area of the cube?
Bunuel wrote:
fozzzy wrote:
If a cube is inscribed inside a sphere then the diagonal (longest side) of the cube is equal to the diameter of the sphere?
the formula for diagonal of a cube is D = $$\sqrt{3}$$a
Is this correct? Can I apply this strategy for such questions?
Don't understand what you mean by the red parts: longest side in a cube? Also what do you mean by "such questions"?
Other than that all is correct.
Math Expert
Joined: 02 Sep 2009
Posts: 59590
Re: If a cube is inscribed inside a sphere... [#permalink]
### Show Tags
23 Jun 2013, 06:27
fozzzy wrote:
I was referring to the diagonal of the cube as the longest side...
An example of this question would be cube is inscribed inside in a sphere. Volume of sphere is provided and we have to find the surface area of the cube?
Bunuel wrote:
fozzzy wrote:
If a cube is inscribed inside a sphere then the diagonal (longest side) of the cube is equal to the diameter of the sphere?
the formula for diagonal of a cube is D = $$\sqrt{3}$$a
Is this correct? Can I apply this strategy for such questions?
Don't understand what you mean by the red parts: longest side in a cube? Also what do you mean by "such questions"?
Other than that all is correct.
An edge (side) of a cube is not the same as diagonal.
Questions to practice:
http://gmatclub.com/forum/a-sphere-is-i ... 27461.html
http://gmatclub.com/forum/a-rectangular ... 28483.html
http://gmatclub.com/forum/for-the-cube- ... 13841.html
http://gmatclub.com/forum/a-rectangular ... 44733.html
http://gmatclub.com/forum/if-the-box-sh ... 27463.html
http://gmatclub.com/forum/what-is-the-v ... 03680.html
Hope it helps.
--== Message from the GMAT Club Team ==--
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
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_________________
Re: If a cube is inscribed inside a sphere... [#permalink] 23 Jun 2013, 06:27
Display posts from previous: Sort by | {} |
## CUDA and its questions
There we were some question raised during Rupesh’s GPU class today.
• what is sequence of actions for ‘D[1]=10’ in cuda/thrust
• first the index operator
• in device_vector.h Line 240+290/300
declare these members for the purpose of Doxygenating them. they actually exist in a derived-from class
• then vector_base.h L242 L42
• then contiguous_storage.h
• in thrust::detail::contiguous_storage::reference L36
• then operator[] at line173
CAUTION: Not sure about device_reference is focus!? L290 device_reference.inl L2+42 reference.h L82 reference.inl at operator= L65
• Why is the blockDim.z 64 whereas x and y is 1024
That is how it is designed to be in cuda/GPU.
• Why is gridDim.y or z is not $2^{16}$ but $2^{16}-1$
Good question! unknown! Some curious people 1
Some people 2 Since block IDs begin at zero, shouldn’t the maximum dimension therefore be 65536? Having the limit as 65535 allows for block IDs [0, 65534], so we’re losing one ID.
• Does GTX 680 has limit of 2048 threads per thread block?
I think NO. See this! and table F2 in Guide v4 From CC v2.0+ it is 1024
• Valid limits of kernel launches
There are multiple limits. All must be satisfied.
1. The maximum number of threads in the block is limited to 1024. This is the product of whatever your threadblock dimensions are (xyz).
2. The maximum x-dimension is 1024. (1024,1,1) is legal. (1025,1,1) is not legal.
3. The maximum y-dimension is 1024. (1,1024,1) is legal. (1,1025,1) is not legal.
4. The maximum z-dimension is 64. (1,1,64) is legal. (2,2,64) is also legal. (1,1,65) is not legal. Also, threadblock dimensions of 0 in any position are not legal.
Your choice of threadblock dimensions (x,y,z) must satisfy each of the rules 1-4 above.
Source Devtalk
• dim3 is actually a struct of uint3
int3 make_int3(2,3,4);
★ 2 min read · Rajesh Pandian M · cuda | {} |
# The 35th International Symposium on Lattice Field Theory
18-24 June 2017
Palacio de Congresos
Home > Timetable > Session details > Contribution details
# Contribution Parallel
Andalucía I
Weak Decays and Matrix Elements
# $D \rightarrow Kl\nu$ semileptonic decay in lattice QCD with HISQ
## Speakers
• Dr. Bipasha CHAKRABORTY
## Content
The quark flavor sector of the Standard Model is a fertile ground to test any new physics effect through the Unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix. We present a lattice QCD calculation of the scalar and the vector form factors (over a large $q^2$ region including $q^2=0$) associated with the $D\rightarrow Kl\nu$ semi-leptonic decay. The central CKM matrix element, $V_{cs}$ in the Standard Model, is then calculated by comparing the lattice QCD results for the form factors and the experimental decay rate. This calculation has been performed on the $N_f=2+1+1$ MILC HISQ ensembles with the physical and heavier than physical light quark masses.
## Preferred track (if multiple tracks have been selected)
Weak Decays and Matrix Elements | {} |
# Is there a standard way of expressing matrix row and column operations algebraically?
I've looked hard and failed to find any convincingly standard algebraic notation for such. I have a specific problem in mind. It is the transformation of this matrix:
$\mathrm{W} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0.25 & 0 \\ 0 & 0.75 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}$
into this one:
$\mathrm{A} = \begin{bmatrix} 1 & 0 \\ -0.25 & 0.25 \\ -0.75 & 0.75 \\ 0 &-1 \\ \end{bmatrix}$
It's rather easy to see how to do that column by column, basically:
$a_{i,j} = w_{i,j} - w_{i,j+1}$
and I can write code do that but what I'm look for is a nice algebraic nomenclature for the operation, ideally in a standard matrix notation such that I might write:
$\mathrm{A} = f(\mathrm{W})$
and I could write the function f algebraically somehow. I can invent a notation easily enough, for example:
$\mathrm{A} = \mathrm{W}>>1 - \mathrm{W}<<1$
where:
$>>$ is a right shift operator which shifts each column one to right losing the right most column and reducing the number of columns by 1.
$<<$ is a left shift operation which shifts each column one to the left losing the first column and reducing the number of columns by 1.
But I made that up. And of course we can work on transposes and use row operators if they exist instead. By quest here is for the most standard, widely understood and used algebraic notation if it exists, and ideally a reference I could cite that documents it. I've failed to find any such thing.
• Yes! Note that the function which sends $W\rightarrow A$ is linear. Say you have the equation $WM=A$. What must $M$ be to make this equation true? This would allow you to write the function simply as $f(W)=WM$ – rikhavshah May 29 '18 at 2:50
• Food for thought, thanks. But yes what would $\mathrm{M}$ be? I find it easier to replicate the truncation (shift)/resizing operations I noted above by specifying M: I can replicate left truncation with $\mathrm{M}=\begin{bmatrix} 0 & 0 \\ 1 & 0 \\ 0 & 1 \\ \end{bmatrix}$ and a right truncation with: $\mathrm{M}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \\ \end{bmatrix}$ Which seems like a combination of the identity matrix and a null row. But what’s the nomenclature for that, how do we write $\mathrm{M}$ generically? – Bernd Wechner May 29 '18 at 3:21
One potential answer is to use colon notation $$f(W) = W(:,\text{1:end-1}) - W(:,\text{2:end})$$ It is well-known within the numeric linear algebra community; see for example Golub & Van Loan (2013).
This is simply the linear transformation $$A=WP$$ where $$P = \begin{bmatrix} \,\,\,1 & \,\,\,0 \\ -1 & \,\,\,1 \\ \,\,\,0 & -1 \\ \end{bmatrix}$$
Update
Let's consider the case $m=4$, and the permutation matrix with ones on the first sub-diagonal $$B = \begin{bmatrix} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ \end{bmatrix}\in{\mathbb R}^{m\times m}$$
Then $B^m=I,\,$ and the product $$W(I-B) = \big[\,A\,\,c\,\big]$$ yields the desired $A$ matrix augmented by an extra column $(c)$ which contains the difference of the last & first columns of $W$. This is the circulant extension of your differencing algorithm.
• That great! I love it. But is there a way to express $\mathrm{P}$ in generic terms as I have $\mathrm{L}$ and $\mathrm{R}$? As in can this generalise for any $n \times m$ matrix to convert it to a $n \times m-1$ matrix with columns that are the difference of columns in the first? – Bernd Wechner May 29 '18 at 5:52
• @BerndWechner This answer has been updated to make it more generic, regarding the size of the matrices. – greg May 29 '18 at 7:59
• Interesting. Thanks for your creative thinking. I'll experiment with this tomorrow out of interest. But I'd rather have a way of saying A=f(W) rather than finding it embedded in a larger matrix. I'm on a (re)learning curve, as it's been decades since I did a lot of matrix work (pre PC era) and so am revisiting the algebra of matrices. Matrices are distributive for example and so my answer below may simplify to W(R-L). – Bernd Wechner May 29 '18 at 11:01
• @BerndWechner I think we've both come up with the same solution, since $$W(R-L)=W(I-B)R$$ I just think the definition of $R$ will make it awkward to implement. Whereas most computer languages have a simple syntax for extracting a sub-matrix. – greg May 30 '18 at 16:21
Thanks to rikhavshah's hint I think I've nailed something I'm satisfied with, as follows:
$\mathrm{A} = \mathrm{W}\mathrm{R} - \mathrm{W}\mathrm{L}$
where:
$\mathrm{W}$ is an $n \times m$ matrix
$\mathrm{A}$ is an $n \times m-1$ matrix being the differences between adjacent columns in $\mathrm{W}$
$\mathrm{R} = \begin{bmatrix} \mathrm{I}_{m-1} \\ 0_{1,m-1} \end{bmatrix}$ is an $m \times m-1$ right truncating matrix
$\mathrm{L} = \begin{bmatrix} 0_{1,m-1}\\ \mathrm{I}_{m-1} \end{bmatrix}$ is an $m \times m-1$ left truncating matrix
and so a worked example for the specific matrices in the question:
\begin{align*} \mathrm{A} &= \mathrm{W} \mathrm{R} - \mathrm{W} \mathrm{L} \\&= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0.25 & 0 \\ 0 & 0.75 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{bmatrix} - \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0.25 & 0 \\ 0 & 0.75 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} 0 & 0 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} \\&= \begin{bmatrix} 1 & 0 \\ 0 & 0.25 \\ 0 & 0.75 \\ 0 & 0 \\ \end{bmatrix} - \begin{bmatrix} 0 & 0 \\ 0.25 & 0 \\ 0.75 & 0 \\ 0 & 1 \\ \end{bmatrix} \\&= \begin{bmatrix} 1 & 0 \\ -0.25 & 0.25 \\ -0.75 & 0.75 \\ 0 & -1 \\ \end{bmatrix} \end{align*}
which uses only standard notation from:
which I find standard enough with references available for the naive reader.
If there is a better option I'm all ears but this one seems the best so far!
UPDATE:
This can simplify further to:
$\mathrm{A} = \mathrm{W}\boldsymbol\Delta$
Where: $\boldsymbol\Delta = \begin{bmatrix} \mathrm{I}_{m-1} \\ 0_{1,m-1} \end{bmatrix} - \begin{bmatrix} 0_{1,m-1} \\ \mathrm{I}_{m-1} \end{bmatrix}$
Which is easily the most elegant solution to date. Defining on generic multiplier for the conversion. We can think of $\boldsymbol\Delta$ as a differencing matrix methinks which creates for any matrix a new on which has one fewer columns and each column is the difference between two adjacent columns in the original.
• Can I ask why you need 'standard notation'? Notation varies depending on the field of math you're in; it would be perfectly standard to define your own `column difference' matrix $M$ such that $A=WM$. – rikhavshah May 29 '18 at 6:14
• "need" would be an exaggeration. "desire" is a better word. I desire it simply because I'm not very deeply enmeshed in any field right now and not writing for one, so much as trying to understand something and writing it up for lay readers as well some time, plus I simply prefer standards to document or author specific conventions or even field specific ones. Just a preference is all. The problem space I'm looking at however should take any matrix $W$ to produce $A$, of any dimension and any content - to wit a desire to describe the transformation tersely and in standard notation. – Bernd Wechner May 29 '18 at 6:25 | {} |
# Difference between revisions of "User:IssaRice/Computability and logic/Eliezer Yudkowsky's Löb's theorem puzzle"
## Translating the puzzle using logic notation
Löb's theorem shows that if $\mathsf{PA} \vdash \Box C \to C$, then $\mathsf{PA} \vdash C$.
The deduction theorem says that if $\mathsf{PA} \cup \{H\} \vdash F$, then $\mathsf{PA} \vdash H \to F$.
Applying the deduction theorem to Löb's theorem gives us $\mathsf{PA} \vdash (\Box C \to C) \to C$.
When translating to logic notation, it becomes obvious that the application of the deduction theorem is illegitimate, because we don't actually have $\mathsf{PA} \cup \{\Box C \to C\} \vdash C$. This is the initial answer that Larry D'Anna gives in comments.
But now, suppose we define $\mathsf{PA}' := \mathsf{PA} \cup \{\Box C \to C\}$, and walk through the proof of Löb's theorem for this new theory $\mathsf{PA}'$. Then we would obtain the following implication: if $\mathsf{PA}' \vdash \Box C \to C$, then $\mathsf{PA}' \vdash C$. But clearly, $\mathsf{PA}' \vdash \Box C \to C$ since $\Box C \to C$ is one of the axioms of $\mathsf{PA}'$. Therefore by modus ponens, we have $\mathsf{PA}' \vdash C$, i.e. $\mathsf{PA}\cup\{\Box C \to C\} \vdash C$. Now we can apply the deduction theorem to obtain $\mathsf{PA} \vdash (\Box C \to C) \to C$. This means that our "Löb's theorem" for $\mathsf{PA}'$ must be incorrect, and somewhere in the ten-step proof is an error.
## Translating the Löb's theorem back to logic
Since the solution to the puzzle refers back to the proof of Löb's theorem, we first translate the proof from the cartoon version back to logic:
1. $\mathsf{PA} \vdash \Box L \leftrightarrow \Box(\Box L \to C)$
2. $\mathsf{PA} \vdash \Box C \to C$
3. $\mathsf{PA} \vdash \Box(\Box L \to C) \to (\Box \Box L \to \Box C)$
4. $\mathsf{PA} \vdash \Box L \to (\Box \Box L \to \Box C)$
5. $\mathsf{PA} \vdash \Box L \to \Box \Box L$
6. $\mathsf{PA} \vdash \Box L \to \Box C$
7. $\mathsf{PA} \vdash \Box L \to C$
8. $\mathsf{PA} \vdash \Box(\Box L \to C)$
9. $\mathsf{PA} \vdash \Box L$
10. $\mathsf{PA} \vdash C$
## Repeating the proof of Löb's theorem for modified theory
1. $\mathsf{PA}' \vdash \Box L \leftrightarrow \Box(\Box L \to C)$
2. $\mathsf{PA}' \vdash \Box C \to C$
3. $\mathsf{PA}' \vdash \Box(\Box L \to C) \to (\Box \Box L \to \Box C)$
4. $\mathsf{PA}' \vdash \Box L \to (\Box \Box L \to \Box C)$
5. $\mathsf{PA}' \vdash \Box L \to \Box \Box L$
6. $\mathsf{PA}' \vdash \Box L \to \Box C$
7. $\mathsf{PA}' \vdash \Box L \to C$
8. $\mathsf{PA}' \vdash \Box(\Box L \to C)$
9. $\mathsf{PA}' \vdash \Box L$
10. $\mathsf{PA}' \vdash C$ | {} |
×
# Help with summation
$\large{\displaystyle \sum_{n=1}^{P} \frac{n^2}{2^n} + \displaystyle \sum_{n=1}^{P} \frac{n}{2^n}}$
how am I supposed to express this as an equation?......plz help! :( :(
Note by Asif Hasan
1 year, 10 months ago
Sort by:
My solution uses differential calculus. We start with the formula for an infinite geometric series: $\sum_{n=1}^{\infty} x^n = \dfrac{x}{1-x} = \dfrac{1}{1-x} - 1$ Now if we differentiate this with respect to $$x$$, we get: $\sum_{n=1}^{\infty} n x^{n-1} = \dfrac{1}{(1-x)^2} \to (1)$ Differentiating one more time gives us: $\sum_{n=1}^{\infty} n(n-1)x^{n-2} = \dfrac{2}{(1-x)^3} \to (2)$
Multiplying $$(1)$$ by $$2x$$ gives us: $\sum_{n=1}^{\infty} 2n x^n = \dfrac{2x}{(1-x)^2} \to (3)$
Multiplying $$(2)$$ by $$x^2$$ gives us: $\sum_{n=1}^{\infty} n(n-1)x^n = \dfrac{2x^2}{(1-x)^3} \to (4)$
Now after adding $$(3)$$ and $$(4)$$ we get: $\begin{array}{ccl}\displaystyle\sum_{n=1}^{\infty} (n^2+n) x^n & = & \dfrac{2x^2}{(1-x)^3} + \dfrac{2x}{(1-x)^2} \\ \displaystyle\sum_{n=1}^{\infty} (n^2+n) x^n & = & \dfrac{2x}{(1-x)^3} \to (5) \end{array}$
Of course, this is an infinite series. Let's calculate the formula we need using the formulas above:
$\begin{array}{ccl} \sum_{n=1}^{P} (n^2+n)x^n & = & \sum_{n=1}^{\infty} (n^2+n)x^n - \sum_{n=P+1}^{\infty} (n^2+n)x^n \\ & = & \dfrac{2x}{(1-x)^3} - \sum_{n=1}^{\infty} \left((n+P)^2+(n+P)\right)x^{n+P} \\ & = & \dfrac{2x}{(1-x)^3} - x^P \left[\sum_{n=1}^{\infty} (n^2+n)x^n + P \sum_{n=1}^{\infty} 2nx^n + (P^2+P) \sum_{n=1}^{\infty} x^n \right] \\ & = & \dfrac{2x}{(1-x)^3} - x^P \left[\dfrac{2x}{(1-x)^3} + \dfrac{2Px}{(1-x)^2} + \dfrac{(P^2+P)x}{1-x} \right] \end{array}$
Therefore, substituting $$x = \dfrac{1}{2}$$ gives us:
$\sum_{n=1}^{P} \dfrac{n^2+n}{2^n} = 8 - \dfrac{8 + 5P + P^2}{2^P}$ · 7 months, 1 week ago
hey, a little more help plz!! how are we supposed to handle this type::
$\large{\displaystyle \sum_{n=1}^{\infty} \frac{n}{2^n + 3^n}}$ · 6 months, 2 weeks ago
You're welcome! Oh wow, I don't know... There might not even be a closed form for that sum. · 6 months, 2 weeks ago
ohh :( :( thanks for the reply anyway!! · 6 months, 2 weeks ago
Thanks a lot!! Very elegant solution! :D thanks!! · 6 months, 2 weeks ago
$\large{\displaystyle \sum_{n=1}^{P} \frac{n^2}{2^n} + \displaystyle \sum_{n=1}^{P} \frac{n}{2^n}}$
Hit on your profile picture at the right top corner of the page, then hit "Toggle Latex". Copy the latex code and then do whatever you want to :P · 1 year, 10 months ago | {} |
# Easy way to derive rotation matrix
It is very easy to derive rotation matrix. This method is applied to general cases. Derivation Step1. Calculate rotation of unit vectors Step2. Arrange two vectors Background: Why can we derive? Derivation Step1. Calculate rotation of unit…
# Useful knowledge for calculation
Prefix Pressure Others Density of water: Water pressure: Prefix Name Symbol $10^n$ kilo k $10^3$ hecto h $10^2$ deca da $10^1$ $10^0$ deci d $10^{-1}$ centi c $10^{-2}$ Pressure \begin{align} 1 \mathrm{\,Pa}&=1 \mathrm{\,N/m^2}\\ \text{Atm…
# Contraction of completely anti-symmetric tensor
Contraction formula of the completely antisymmetric tensor (or Levi-Civita symbol) is indispensable for vector calculus.If you think it is hard to remember the formula, it is wrong. Actually, the derivation is very easy.At the end of this … | {} |
# Logarithm Problem
1. Jun 28, 2009
### math4life
1. The problem statement, all variables and given/known data
1) Solve the equation using the exponential form of the equation.
Log2(2-5x)=7
2) Rewrite as a single logarithmic expression:
3log x +(1/2)log z
2. Relevant equations
3. The attempt at a solution
1) I have no idea how to solve this.
2) I know that two logarithms multiply to add, but these have different bases so I do not know what to do.
Thanks.
Last edited: Jun 28, 2009
2. Jun 28, 2009
### rock.freak667
Here is a hint.
$$a^b =c \Rightarrow b= log_a c$$
they are in the same base. Logx usually means log10x.
Use the rule
$$rlog_a x = log_a x^2$$
3. Jun 29, 2009
### Mentallic
I'll just fix up rock.freak667's little typo there.
What was meant to be said is: $$r.log_a(x)=log_a(x^r)$$
Coupled with the rule that $$log_a(b)+log_a(c)=log_a(bc)$$
You should have no problem solving the second one
4. Jun 29, 2009
### Staff: Mentor
I think it might be helpful to add that a logarithm can be thought of as the exponent on the base (the number raised to a power) that results in a particular number. So for example, log10100 means the exponent on 10 that results in 100. In other words, this logarithm is the answer to the question 10? = 100. Pretty clearly, the placeholder represented by ? is 2.
Every equation of the form logbx = y can be rewritten as an equivalent exponential equation by = x, and vice versa, with the only restrictions being that b > 0, and b$\neq$ 1, and x > 0. | {} |
# Tag Info
2
To have the right picture in mind, you need to also take into account the Pauli exclusion between the electrons, being fermions, but also more importantly, do not exclude the nucleus from the picture here! Now, Why rule one holds you may ask? Well it clearly cannot be due to dipole dipole interaction between electrons as it's so insanely small (let's say ...
0
The maximum you can strain silicon, for example, before crystalline defects are introduced is ~1%, at which point the conductivity would go down. In the diamond case, the diagram indicates that you’d have to strain it by 200% (i.e. the atoms would have to be spaced twice as far apart as their equilibrium distance) to have no bandgap. This would be far too ...
0
the Dirac Point on Graphene is protected by hidden symmetry. And it is explained very well in the paper arXiv:1406.3800. It is not that easy to understand the hidden symmetry. Personally speaking, I thought it is combination of inversion, time reversal and reflection symmetry, though the hidden symmetry in that paper has a totally different form with my ...
3
If the valence band maximum and the conduction band minimum are on the same position in k-space, this means that you have a direct gap semiconductor (GaAs, InAs, ...). If the CB minimum is at a finite k-value, it would be an indirect gap semiconductor (like Si, Ge, AlAs, ...) The bands appear as parabolas due to the dispersion of a quasi-free electron/hole ...
0
Consider two models: A wave packet of a free electron with $m_e$ with negligible mean energy relative to rest state A wave packet with same parameters of an electron in crystal with $m^*$ with negligible mean energy relative to band edge Assuming that wave packet is large enough for the effective mass approximation to hold (i.e. its uncertainty of ...
0
Second derivative of kinetic energy with respect to momentum equals inverse mass of a particle. In a metal, you have a band structure defined through the dispersion relation of the form E(k) where k is wave vector of electron. Second derivative of this expression can be also taken to be some sort of inertia of a particle, as you can see by analogy with a ...
0
It implies that the band in question would have a narrower bandwidth than would be expected from an electron with free electron mass. In turn, this also means that the electron finds it harder to hop from site to site meaning that the electron is more localized that would be an electron with free electron mass.
2
Note that Sommerfeld's model simply generalizes Drude's theory of metals by taking into account the fact that electrons are fermions, so Pauli exclusion becomes a very important factor. In Sommerfeld's model, there's no effective mass to talk about, as one basically ignores the atoms(nuclei) in the system and considers free moving fermions. So there, your ...
2
The bigger the crystal is, the closer-together those discrete values of k are. A real crystal might be 1cm long, or 100 million atoms. Then there would be 100 million little dots between the vertical bars on your figure. Those dots would be equally spaced with respect to the horizontal axis. It's too many dots to see, they blend together to look just like a ...
0
Even if it's not really appropriate to derivate quantitative results about electrons properties in solids, Jellium model still have some interesting qualitative features. As you correctly pointed, Jellium still a mean-field theory and so fails about dealing with strongly correlated systems. Lets remind a few about jellium model. The starting point is the ...
0
This structure consists of a series of potential wells at an atomic level: A quasi-free electron can travel trough this structure, where it is attracted or weakly bound by the individual atoms. In this case, a potential well due to an Al atom (or a virtual AlAs atom) is deeper than for Ga (or a virtual GaAs atom). In a picturesque view, the free electron is ...
0
An RTD is a special type of TD, and a double barrier is just one of many possible implementations of resonant tunneling. An RTD is called "resonant" because (under certain conditions) the transmission function is equal to one, i.e. complete transmission. This happens due to wave-like interference between the two barriers. Hence called "resonant": the phase ...
Top 50 recent answers are included | {} |
Motivation behind the definition of flat module
Can someone explain what is the motivation behind the definition of a flat module? I saw the definition but I don't really know why it is important to work with these structures.
-
Tensor products conserve almost every property you could ask for. Tensors with flat modules really preserve almost anything you could want. And it turns out that lots of things are flat - for example, over PIDs, flat and torsion free are the same thing. – mixedmath Mar 22 '12 at 3:08
Are you convinced that tensors products are useful ? If you are, then you might want them to behave nicely. – Joel Cohen Mar 22 '12 at 9:07
@JoelCohen What do you mean by "useful" and behave nicely? – Jr. Mar 23 '12 at 0:27
2 Answers
Flatness in commutative algebra satisfies a geometric condition: the fibers of a morphism between two varieties (schemes) don't vary too wildly. A flat morphism $f \colon X \to Y$ of varieties (schemes) can be thought as a continuous family of varieties (schemes) $\{ f^{-1} (y) \}_{y \in Y}$. An important theorem says that if $f \colon X \to Y$ is a flat morphism between two irreducible varieties then its fibers have dimensions equal to $\dim X - \dim Y$.
For example, fix an algebraically closed field $k$, and consider the morphism $f \colon \mathbb{A}^1 \to \mathbb{A}^1$ defined by $x \mapsto x^2$. It corresponds to the ring homomorphism $k[x^2] \hookrightarrow k[x]$. You should be able to prove that $k[x]$ is a flat $k[x^2]$-algebra (it is also free), hence the morphism $f$ is flat. The fibers are almost always made up of two points.
Consider the morphism $g \colon \mathbb{A}^2 \to \mathbb{A}^2$ defined by $(x,y) \mapsto (x, xy)$ (it is an affine chart of the blowing up of the plane). It corresponds to the ring homomorphism $k[x,xy] \hookrightarrow k[x,y]$. The fiber of the point $(0,0)$ is the line $\{ x= 0 \}$ which has dimension $1$, while the fiber of the other points is empty or made up of a single point. You should be able to check that $k[x,y]$ is not flat as $k[x,xy]$-algebra.
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You could make this more precise: for example, you might mention that "a finitely-generated module over a noetherian integral domain is flat if and only if it is locally free of constant rank". But personally I think flatness is a concept from homological algebra and should be distinguished from local-freeness. – Zhen Lin Apr 22 '12 at 0:10
According to the answers to this MO question, flatness should really be thought of as an algebraic condition rather than a geometric one. Mumford [The red book of varieties and schemes, Ch. III, § 10] writes,
The concept of flatness is a riddle that comes out of algebra, but which technically is the answer to many prayers.
For the purposes of homological algebra, it is incredibly useful for a functor to preserve exact sequences, and flatness of a (right) $R$-module $M$ is precisely what is needed to make the functor $M \otimes_R -$ send exact sequences of (left) $R$-modules to exact sequences of abelian groups. For example, if $I$ is a (left) ideal of $R$, then we have an exact sequence of (left) $R$-modules: $$0 \longrightarrow I \longrightarrow R \longrightarrow R / I \longrightarrow 0$$ In general, the tensored sequence is only right exact: $$M \otimes_R I \longrightarrow M \longrightarrow M \otimes_R R / I \longrightarrow 0$$ It's not hard to see that the image of $M \otimes_R I \to M$ is the abelian group $M I$, so when $M$ is flat, the natural map $M \otimes_R I \to M I$ is an isomorphism. Conversely, if this holds for every (left) ideal $I$, then $M$ is flat. Morally, what this is saying is that a flat $R$-module has no "generalised" $R$-torsion; if $R$ is a principal ideal domain, then an $R$-module is flat if and only if it has no $R$-torsion in the ordinary sense. (Think of $M \otimes_R I$ as being a group of formal linear combinations of formal products; one possible way $M \otimes_R I \to M I$ could fail to be an isomorphism is if $m \cdot a = 0$ for some non-zero $m$ in $M$ and non-zero $a$ in $I$.)
Under certain circumstances, flatness coincides with other conditions which are more geometric in nature. For example, if $R$ is a commutative noetherian ring, then the following are equivalent for a finitely-generated $R$-module $M$:
• $M$ is projective.
• $M$ is flat.
• $M$ is locally free, in the sense that there are $f_1, \ldots, f_n$ in $R$ such that $f_1 + \cdots + f_n = 1$ and each $M \otimes_R R[1 / f_i]$ is free.
Actually, we always have the implication projective $\Rightarrow$ flat, even when $M$ is not finitely generated and $R$ is non-commutative/non-noetherian (just so long as the axiom of choice holds!), but the commutative noetherian case is what is usual in algebraic geometry. Being locally free means that $M$ is the module of global sections of a finite-dimensional vector bundle $\tilde{M}$ over $\operatorname{Spec} R$. It is reasonably clear that the rank of $\tilde{M}$ is locally constant on $\operatorname{Spec} R$. We have a partial converse: if $R$ is a noetherian integral domain and the rank of finitely-generated module $M$ is constant on $\operatorname{Spec} R$, then $M$ is locally free and hence flat.
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Mumford's words are really nice! – Andrea Apr 22 '12 at 9:55 | {} |
# How do you use synthetic division to divide x^4-3x^3+3x^2-2x+3 by x^2-3x+2?
Jul 24, 2015
color(red)((x^4-3x^3+3x^2-2x+3)/(x^2-3x+2) = x^2+1+(x+1)/(x^2-3x+2)
#### Explanation:
Step 1. Write only the coefficients of $x$ in the dividend inside an upside-down division symbol.
Step 2. Negate the coefficients in the divisor and put every coefficient but the first one diagonally at the left.
Step 3. Drop the first coefficient of the dividend below the division symbol.
Step 4. Multiply the drop-down by the divisor, and put the result diagonally in the next columns.
Step 5. Add down the column.
Step 6. Repeat Steps 4 and 5 until you would go past the entries at the top with the next diagonal.
The quotient is ${x}^{2} + 1 + \frac{x + 1}{{x}^{2} - 3 x + 2}$.
Check:
$\left({x}^{2} - 3 x + 2\right) \left({x}^{2} + 1 + \frac{x + 1}{{x}^{2} - 3 x + 2}\right) = \left({x}^{2} - 3 x + 2\right) \left({x}^{2} + 1\right) + x + 1 = {x}^{4} - 3 {x}^{3} + 2 {x}^{2} + {x}^{2} - 3 x + 2 + x + 1 = {x}^{4} - 3 {x}^{3} + 3 {x}^{2} - 2 x + 3$ | {} |
## Calculus 10th Edition
$\frac{768\pi}{7}$
Setup the integration using shell method about the x-axis $2\pi \int_0^8 y(\sqrt[3] y) dy$ $2\pi \int_0^8 y^{\frac{4}{3}} dy$, Integrate $2\pi [\frac{3}{7}y^{\frac{7}{3}}]_0^8$, Take definite integral $\frac{768\pi}{7}$ Simplify | {} |
# Random variables and sums of $k$-sided dice
Consider fair $k$-sided dice with the numbers $1$ through $k$ on their faces.
a. Roll one die. Let the RV $X$ be the number on one die. Compute $E[X]$ and $V[X]$.
b. Roll $n$ dice. Let the RV $Y$ be the sum of numbers on the dice. Compute $E[Y]$.
c. Roll two dice and let the random variable $Z$ be the second die subtracted from the first. What is $E[Z]$?
-
Hints: For (a), do you know formulas for $\sum_{i=1}^k i$ and $\sum_{i=1}^k i^2$?
For (b) and (c), use the linearity property of expected value: for any random variables $X$ and $Y$ whose expected values exist and any constants $a$ and $b$, $E[aX + bY] = a E[X] + b E[Y]$. | {} |
Introduction
Initializing and measuring the wave-function of single freely-propagating particles are challenging but fundamental tasks for applications in quantum information processing and enhanced sensing1,2,3,4,5,6,7,8,9,10. The recent development of semiconductor-based single-electron sources11,12,13 and ways of controlling electron propagation14,15,16 have created a new platform harnessing on-demand electronic excitations in this way. These schemes for single electron quantum optics require techniques to both control and probe the single excitations. Specific properties of the sources and the transmission channels into which excitations are launched give rise to different characteristic excitation energy, ejection dynamics, propagation velocity and interactions. As a result, new methods are demanded for reconstruction of the quantum state in different systems17,18.
The key properties of the emitted electron stream are manifest in the first-order coherence, captured by Wigner quasi-probability function $$W(E,t)$$. The Wigner function $$W(E,t)$$ is not directly measurable, but projections along specific trajectories in the phase space of non-commuting variables (position–momentum, energy–time) can be accessed, enabling a tomographic reconstruction19 somewhat like X-ray tomography. Such measurements require a scheme to create and readout projections at different trajectories or mixing angles, for instance via free space evolution of the transverse wavefunction of atomic beams20,21 or by mixing of photons with a local optical field4,22. In this way continuous-variable quantum tomography techniques, developed for atomic beams20 and photonic modes23, have been successfully adapted for on-demand electronic excitations17,24,25.
In the case of a chiral one-dimensional electronic excitations the Wigner function can be written as
$$W(E,t)\,=\,\frac{1}{h}\int {e}^{it\epsilon /\hslash }\left\langle E\,-\,\epsilon /2\right|\hat{\rho }\left|E\,+\,\epsilon /2\right\rangle d\epsilon$$
(1)
where $$\hat{\rho }$$ is the density matrix of the emitted electrons and the energy eigenstates $$\left|E\right\rangle$$ form a complete basis for the propagating mode. The Wigner function of low energy excitations can be extracted by using two-particle interference of the electron beam with a modulated Fermi sea as a local oscillator17,18. This is only possible in a restricted phase-space volume close to the Fermi energy ($$E\,-\,{E}_{F}\ll 1\ \,\text{meV}\,$$) and is not viable over a wider range of parameters, such as excitations in a higher energy range15. It is also not possible where there is no Fermi sea, as in the case of isolated electrons travelling in a depleted lattice space without conduction-band electrons nearby15,26. However, in these cases it is possible to interrogate the beam with a barrier in the beam path13,15,27, an approach which can enable a different method of tomographic reconstruction of the Wigner function28.
Here, we explore a tomographic technique to image the distribution of Wigner quasiprobability for electrons in phase space reconstructed from a set of projections acquired by energy and time selective transmission. The selective control of transmission is achieved by a dynamic barrier in the beam path synchronised with electron emission. This is a technique that is applicable over a wide range of energy and time scales. We use this approach to perform tomography of electrons emitted by an on-demand single-electron source, enabling us to directly characterise the energy-time distribution of excitations at a particular point in a beam path. Using the phase space density we quantify the quantum mechanical purity of the states. We also demonstrate readout and control of an important signature of ejection dynamics, a chirp due to correlation between arrival energy and time, which illustrates the power of the technique in controlling single electronic excitations.
Results
Electron tomography using time-dependent barriers
Marginal distributions at different projection angles in energy–time space can be measured using interaction with a time-dependent barrier in the beam path28. We measure the transmission probability $${P}_{T}$$ for electrons filtered by a high-pass energy barrier with a linearly driven time-varying transmission threshold $${E}_{T}(t)\,=\,{E}_{T0}\,+\,{\beta }_{E}t$$ as in Fig. 1a. The connection to the Wigner function $$W(E,t)$$ is established via
$${P}_{T}\,=\,\iint W(E,t)\ T\left[E\,-\,{E}_{T}(t)\right]\ dE\ dt\ ,$$
(2)
where $$T\left[E-{E}_{T}(t)\right]$$ can be interpreted as the time- and energy-dependent transmission quasiprobability of the barrier, which masks part of the Wigner distribution as in Fig. 1a.
For an intuitive understanding of our tomography protocol it is convenient to use polar coordinates $$\theta ,S$$ as shown in Fig. 1a and methods. The sweep rate $${\beta }_{E}$$ sets a projection angle $$\theta$$ in the energy time plane via $$\tan \theta ={\beta }_{E}/{\beta }_{0}$$ ($${\beta }_{0}$$ sets the energy/time aspect ratio). For a sharp threshold barrier with $$T(E)\,=\,1$$ or $$0$$ for $$E\ > \ 0$$ or $$E\ <\ 0$$, respectively, the derivative $$d{P}_{T}/dS$$ is proportional to the integral of $$W(E,t)$$ along the line $${E}_{T}(t)$$. The line $$S$$ (indicated in Fig. 1a) is perpendicular to the $${E}_{T}(t)$$ line and is akin to the detector coordinate in an X-ray tomography scheme. By measuring $$d{P}_{T}/dS$$ systematically for various values of $${\beta }_{E}$$ and $${E}_{T0}$$ (to select the position along $$S$$) we obtain the Radon transform (sinogram) of $$W(E,t)$$. Its reconstruction is then possible using filtered back-projection to implement the inverse Radon transform (see methods).
Experimental scheme
Our device components, electron source and energy barrier, are defined by gates on a GaAs-based heterostructure26, as shown in Fig. 1b. A tunable-barrier electron pump29,30 (left hand side) is operated using a periodic voltage $${V}_{{\rm{G1}}}(t)$$ (Fig. 1c, left hand side) applied to the left-most barrier, pumping one electron per cycle through the device at a repetition rate $$f$$ giving a quantised pump current $${I}_{P}\,=\,ef$$29,31,32,33,34. The right hand barrier, controlled by $${V}_{{\rm{G2}}}$$ determines the number of electrons pumped, and linearly controls the ejection energy15 (see Supplementary Fig. 1). After ejection, each electron follows a trajectory along the mesa edge governed by the side-wall potential and Lorentz force due to an externally applied perpendicular magnetic field $$B$$ until it reaches the potential barrier controlled by voltage $${V}_{{\rm{G3}}}(t)$$ (Fig. 1c, right hand side)26. The barrier control voltage $${V}_{{\rm{G3}}}(t)$$ is synchronised to $${V}_{{\rm{G1}}}(t)$$ with adjustable delay $${t}_{d}$$27.
The edge gate (which depletes the region of carriers for negative gate voltages $${V}_{{\rm{G4}}}$$26,35), the injection energy (far above the Fermi energy—see Supplementary Note 1), and the travelling time and operation frequency (transit time much shorter than pumping repeat time) lead to one isolated electron being present in the edge channel at a time26. In our implementation of the tomography scheme, $${V}_{{\rm{G3}}}(t)$$ controls the energy threshold $${E}_{T}(t)$$ and therefore determines what proportion of the pumped current is transmitted $${P}_{T}\,=\,{I}_{T}/{I}_{P}$$ (see methods). We use an arbitrary waveform generator to control the threshold barrier time dependence, which we set to have an adjustable linear ramp rate $${\beta }_{E}\,=\,-{\alpha }_{h}d{V}_{{\rm{G3}}}(t)/dt$$ near the moment of electron arrival, where $${\alpha }_{h}\,=\,(0.61\,\pm\,0.02)$$ meV/mV (see Supplementary Note 1 and Supplementary Fig. 1) and $${\beta }_{0}\,=\,(0.12\,\pm\,0.01)$$ meV/ps (see Supplementary Note 3 and Supplementary Figs. 3, 4). We then shift the transmission mask in increments $$\Delta S$$ along the $$S-$$axis using a combination of time delay $${t}_{d}$$ and DC voltage shift $${V}_{{\rm{G3}}}^{{\rm{DC}}}$$ (which controls $${E}_{T0}$$) for each angle $$\theta$$ and measure the transmission probability changes from the change in transmitted current $$\Delta {P}_{T}\,=\,\Delta {I}_{T}/{I}_{P}$$.
Sinogram and tomographic reconstruction
The numerical derivative $$\Delta {P}_{T}/\Delta S$$ collected at different angles $$\theta$$ (a sinogram) is shown in Fig. 2a. Each cut represents a projection of the distribution at a different angle, as indicated in Fig. 2b–d. At $$\theta\,=\,{0}^{\circ }$$ this shows the distribution along the energy axis (as in Fig. 2c) having a width of order ~2 meV15. At the highest angles $$| \theta | \to 9{0}^{\circ }$$ (notwithstanding some minor bandwidth limitations, see Supplementary Note 3) this maps the time of arrival distribution (Fig. 2b) with a width of order ~10−11 s36. At intermediate angles, for instance at $$\theta\,=\,6{0}^{\circ }$$ in Fig. 2d the cut contains a mixture of energy and time information.
We use filtered back-projection23 to compute the electronic distribution from this sinogram, as shown in Fig. 2e. This method enables reconstruction of the mixed state Wigner distribution of electrons, a combined map of electron energy and arrival time measured relative to the centre coordinates used for the collection of the sinogram data (here aligned to the mean electron energy and arrival time $${E}_{0}$$ and $${t}_{0}$$). As some classical fluctuations are present in our experimental implementation we interpret our results as an effective mixed state Wigner function28. Our results are therefore an ensemble measurement of many pure states, with a lower phase-space density than a pure state (discussed below). We can, however, resolve a feature likely to be common to each pure state, a feature of the distribution that we show can be controlled by electron ejection conditions.
Effect of electron ejection dynamics
We observe that measured phase space distribution Fig. 2e is stretched at a certain angle in the energy–time plane, a feature derived from the sharpening of the projection at the corresponding angle in Fig. 2a. This chirp (i.e. time-varying frequency/energy) of the arriving electron energy distribution is an expected feature of electron ejection from a quantum dot under non-stationary conditions; in this kind of pump the driving barrier forces ejection by raising the dot energy with respect to the exit barrier29,37. Previous experiments showed hints of energy–time correlation36 but this is now directly visible in the measured distribution. Indeed, we can show that the chirp can be controlled by changing the conditions under which the electron is ejected.
The entrance barrier DC control voltage $${V}_{{\rm{G1}}}^{{\rm{DC}}}$$ influences when electrons are ejected within the pump waveform27. For different values of $${V}_{{\rm{G1}}}^{{\rm{DC}}}$$ within the $${I}_{p}\,=\,ef$$ plateau (see operating points in Fig. 3a) the arrival time $${t}_{0}$$ can be adjusted over a range of more than 400 ps (11% of the total pump cycle time), as shown in Fig. 3b (circles). For our sinusoidal pump waveform, the sweep rate near the point of ejection is also tuned over a wide range (Fig. 3b squares). This can be set from a maximum rate of $$| d{V}_{{\rm{G1}}}/dt|\,\simeq$$ 0.5 mV/ps to ejection under almost static conditions $$d{V}_{{\rm{G1}}}/dt\to 0$$. Reconstructions of the Wigner function at these operating points are shown in Fig. 3c. These show that the energy–time correlation is controlled by ejection speed. From fits to the data (see Supplementary Note 5) we find that energy–time trajectory $$d\langle E\rangle /dt$$ (see Fig. 3d) tracks the sweep rate of the pump drive barrier, with an estimated strength of the coupling between the pump drive barrier and the emission energy of $$d\langle E\rangle /d{V}_{{\rm{G1}}}\,\simeq\,0.41\,$$ meV/mV.
Resolution and the quantum limit
Under real experimental conditions, the measured distributions can deviate from that expected of a pure quantum state. Additional broadening is expected if the emitted state is mixed, something that can be quantified using the measured phase space maps. A conservative measure of quantum indistinguishability of our wave-packets, relevant for two particle interference experiments, is the maximal statistical weight of a pure state in the mixture18, $${P}_{1}\,=\,{\max }_{\psi }\langle \psi | \hat{\rho }| \psi \rangle$$. Values of $${P}_{1}$$ can be obtained by numerical diagonalization of $$\hat{\rho }$$ or, for the range of values found here $${P}_{1}\ll 1$$, $${P}_{1}$$ has a simple relationship to peak value of the measured phase-space density $${P}_{1}\approx h{W}_{\max }$$ (see Supplementary Note 6 and Supplementary Table 1 for a comparison). We find $${P}_{1}=0.02$$$$0.07$$ as plotted in Fig. 3e (solid symbols). Similarly, the purity of the effective mixed state, $$\gamma\,=\,{\rm{Tr}}({\hat{\rho }}^{2})$$, is related to the average phase space density of the Wigner representation, $$\gamma\,=\,h\langle W(E,t)\rangle\,=\,h\iint {W}^{2}(E,t)dE\ dt$$. From the data in Fig. 3c we find γ = 0.01–0.04.
Our Wigner function reconstructions may also be influenced by certain experimental limitations, for instance the energy broadening of the barrier transmission. For a monotonic detector barrier transmission function $$T(E)$$ going from $$0$$ to $$1$$ over a finite energy scale $$\Delta E$$ is equivalent to smoothing of the underlying $$W(E,t)$$ by a convolution with $$dT/dE$$ along the energy axis, resulting in a smeared density distribution and reduced values of $${P}_{1}$$ and $$\gamma$$28. A semiclassical model calculation38 using $$\Delta E\,=\,0.8$$ meV, the narrowest energy feature seen experimentally (see Supplementary Note 4), suggests a maximum measurable phase space density $$h{W}_{\max }\ \lesssim \ 0.16$$ (Fig. 3e open symbols). Our ability to rotate the source electronic distribution as in Fig. 3c enables us to further probe temporal and energy resolution limits and combine these in an estimate of our experimental resolution. A conservative estimate of the areal resolution is the product of the minimum projected energy width $${\sigma }_{E,\min }\simeq 0.8$$ meV (under slow ejection conditions) and the minimum projected temporal width (under fast ejection conditions) $${\sigma }_{t,\min }\simeq 5$$ ps, giving $${\sigma }_{E,\min }{\sigma }_{t,\min }\simeq 6.1\hslash$$. While this is larger than the absolute minimal level of quantum uncertainty $$\hslash /2$$, this is an upper limit and is also clearly sufficient to resolve non-trivial properties of the excitations studied here. An estimate of the temporal resolution limit from the maximal barrier sweep rate $${\sigma }_{t}^{^{\prime} }\,=\,{\sigma }_{E,\min }/({\alpha }_{h}d{V}_{{\rm{G3}}}^{AC}/dt)\simeq 0.3$$ ps gives $${\sigma }_{E,\min }{\sigma }_{t}^{^{\prime} }\simeq 0.36\,\hslash$$, suggesting that observation of higher purity states than that seen in this source may be possible in our scheme. How details of exact barrier geometry control this resolution limit, and the correspondence of this to the one-dimensional scattering problem28 are open to further detailed study.
Discussion
The ability to tune and readout the properties of electron sources is a potentially useful tool. For instance, periodic electron sources can act as a sensitive probe of on-chip signals39, with an energy–time resolution set by the electronic phase space distribution. Similar to squeezed states in photonics4, it should now be possible to enhance the resolution of measurements along certain phase-space trajectories. In situ Wigner function read-out will also aid the development of electron quantum optics devices where precise control of the Wigner function is required11. It should also be possible to use this scheme to detect coherences via negative fringes in the Wigner function arising from interference effects28,38; the characteristic oscillation period estimated from the kinetic energy of drift motion26 is 2 ps, close to our accessible bandwidth.
In summary, we have shown a technique of generalised electron quantum tomography using numerical back-projection. Our method can reveal non-trivial emission distributions arising from internal dynamics of the quantum dot. The average and the maximal phase space density are 4 and 7% of the quantum limit, which is partly explained by finite resolution effects, but observation of a quantum-limited Wigner function should be possible.
Methods
Quantum tomography scheme
Our experimental implementation maps closely onto a model of scattering between 1-dimensional chiral edge channels under a dynamic barrier which gives Eq.(2) as a result28. While a similar expression has been derived in the classical limit36, this differs in microscopic approach and in the physical meaning attributed to its components (e.g. a classical joint probability distributions versus the Wigner quasiprobability). The model of ref. 28 includes physical effects that we expect experimentally; modification of electron energy by the barrier itself is explicitly included, and the non-trivial geometry of the barrier edge is considered (experimentally this is not infinitely sharp). The derivation also carries through with no correction in a fully quantum mechanical treatment as we outline here.
Central to the approach is the observation that the transmission probability in the presence of a purely linear-in-time modulated voltage is equivalent (by gauge invariance) to transmission through a static barrier of a wave-packet with an additional quadratic phase factor28. One can choose a gauge, in which the electron energy is measured with respect to the transmission threshold energy, set by a barrier height. The presence of the barrier shifts the incoming energy–time distribution along the energy axis as the electrons lose momentum upon entering the gate-affected region. However, if the gate voltage (and hence the decelerating force) depends on time, then the incurred energy shift will depend on the arrival time too, thus deforming the energy–time distribution as it enters the barrier region. For the special case of linear-in-time modulation of the gate, this has a simple shift-and-skew effect on the distribution, which is then filtered at a constant threshold. This maps exactly to the selective transmission effect of Fig. 1a. It also turns out to be independent of the exact spatial profile of the gate edge potential leading into the scattering region, down to some small constant energy and time offsets that reflect the effective position of the barrier edge28.
More specifically, for a static barrier, the probability of transmission is expressed quantum mechanically as
$${P}_{T}\,=\,\int | {\psi }_{\text{out}}(t){| }^{2}dt\,=\,\iint T(E)W(E,t)dE\ dt\ ,$$
(3)
where $$T(E)\,=\,| \tau (E){| }^{2}$$ is the square of a complex scattering amplitude $$\tau (E)$$ that connects the incoming and the outgoing probability amplitudes, $${\psi }_{\text{out}}(E)\,=\,\tau (E)\ {\psi }_{\text{in}}(E)$$, and $$W(E,t)\,=\,{h}^{-1}\int {\psi }_{\,\text{in}\,}^{* }(E+\epsilon /2){\psi }_{\text{in}}(E-\epsilon /2){e}^{i\epsilon t/\hslash }\ d\epsilon$$ is the Wigner function of the incoming (pure) state. A uniform energy modulation of the whole scattering region, as in the case of the time dependent barrier height, can be expressed as a global energy shift $$E\to E+{E}_{T0}\,+\,{\beta }_{E}t$$, where $${E}_{T0}$$ is an adjustable offset and $${\beta }_{E}$$ controls the ramp speed. This is equivalent to a gauge transformation $$\psi (t)\to \psi (t){e}^{i({E}_{T0}t+{\beta }_{E}{t}^{2}/2)/\hslash }$$ where $$\psi (t)\,=\,{h}^{-1/2}\int \psi (E)\ {e}^{-iEt/\hslash }dE$$, which in turn leads to $$W(E,t)\to W(E\,+\,{E}_{T0}\,+\,{\beta }_{E}t,t)$$ in Eq. 3, and hence to Eq. 2.
Linear-in-time barrier sweeps (as used experimentally) should ensure that the electronic distribution after entering the time-dependent barrier region remains undistorted (down to the energy shifts described above) regardless of the spatial barrier shape (e.g. onset sharpness, overall size) $$V(x,t)$$. See ref. 28 for more detailed discussion of model approximations and practical constraints in the quantum limit. For discussion of the range of experimental applicability of this technique (e.g. energy range, effects of available experimental bandwidth) see Supplementary Note 7.
Device design and operation
Our device is defined by surface gates on a GaAs-based two dimensional electron gas heterostructure 90 nm below the surface26. Distance between the electron pump and energy-selective barrier is ~5 μm, as estimated from lithographic dimensions. The device is operated in a dilution refrigerator with base temperature ~100 mK (with RF drive signals turned on) in a perpendicular magnetic field $$B\,=\,12$$ T. The wafer carrier density is ~$$1.7\times 1{0}^{15}$$ m−2 with mobility 170 m2 V−1 s−1. This carrier density and field places the bulk filling factor $$\nu \ <\ 1$$, but this is of secondary importance here because of the large energy and spatial separation between our excitations and the Fermi sea, due to the high electron energy and the depletion gate $${V}_{{\rm{G4}}}$$ (see below for details). This is the same kind of device as used to measure electron velocity26 and phonon emission35.
DC current measurements
DC current readings are taken with commercial transimpedance amplifiers at $$1{0}^{10}\,$$ V/A gain. Amplifiers are connected on the pump ($${I}_{P}$$) and on the far side of the energy-selective barrier ($${I}_{T}$$) as shown in Fig. 1 b. Although not used in our analysis, we also measure $${I}_{R}$$, the reflected current with a third amplifier to confirm that the pumped current is divided between the two output terminals i.e. $${I}_{P}\,=\,{I}_{T}\,+\,{I}_{R}$$ (for simplicity we consider electron current rather than conventional current). During tomography measurements, each current measurement (lasting 200 ms) corresponds to $$\sim5.5\times 1{0}^{7}$$ pump cycles, while every back-projection map samples a total of $$1.5\times 1{0}^{12}$$ pump cycles.
RF connections
The waveforms are synthesized using two Tektronix 70001A Arbitrary Waveform Generators (AWG) connected via a synchronisation unit to effectively give two outputs, one for the source and the other for the energy selective barrier. Both RF signal paths use low-loss cryogenic coaxial cable (beryllium copper, superconducting) inside the cryostat. Broadband (18 GHz) 3 and 1 dB attenuators are present on both lines inside the dilution refrigerator for thermalisation purposes, in addition to 3 dB at room temperature. Due to the larger amplitude requirements for the pump, this line includes a 15 dB linear amplifier (15 GHz bandwidth). Broadband bias tees (18 GHz bandwidth) are used to add DC voltages at cryogenic temperatures near the sample. A 6 GHz low-pass filter was used on the pump drive signal to prevent weak oscillations creating ejection from a non-monotonic drive signal27.
Pumping
A periodic voltage $${V}_{{\rm{G1}}}(t)\,=\,{V}_{{\rm{G1}}}^{AC}(t)\,+\,{V}_{{\rm{G1}}}^{DC}$$ [Fig. 1b, left] is controlled by one AWG channel and a DC voltage source. $${V}_{{\rm{G1}}}^{AC}(t)$$ and $${V}_{{\rm{G1}}}^{DC}$$ are the ac and dc components. The ac component modulates the G1 barrier, pumping $$n$$ electrons per cycle through the device at a repetition rate $$f\,=\,277$$ MHz, giving $${I}_{P}\,=\,44.4$$ pA for $$n\,=\,1$$. The tunnelling processes which select the number of loaded electrons have been discussed extensively in the context of accurate current standards for metrology30,31,32. Note that in the last panel in Fig. 3(c) the escape rate is reduced such that the electron cannot fully escape within the time permitted by the pump waveform, reducing the pump current by $$\sim$$ 8%.
Waveform synthesis and delay control
Both $${V}_{{\rm{G3}}}(t)$$ and $${V}_{{\rm{G1}}}(t)$$ waveforms are $$N\,=\,180$$ points long, 10-bit vertical resolution and played cyclically at a frequency of $${f}_{0}\,=\,277$$ MHz. The phase $${t}_{d}$$ of the two sources is controlled by phase-shifting their synchronisation clock. The pump drive is a sine wave, while $${V}_{{\rm{G3}}}(t)$$ is of the form $${v}_{k}\,=\,\tanh [{A}_{0}\tan (\theta )\sin (2\pi {f}_{0}{t}_{k})]$$ for each time $${t}_{k}$$. $$\theta$$ is the required projection angle and $${A}_{0}$$ linearly scales the slope. This gives a linear voltage ramp near the zero crossings, while smoothly limiting the signal away from this point (see Supplementary Fig. 3). The actual sweep rate was measured in situ39 (see Supplementary Fig. 4) for different values of $$\theta$$ and $${\beta }_{0}\,=\,0.12$$ meV/ps was empirically found using $$\tan \theta\,=\,{\beta }_{E}/{\beta }_{0}$$ (i.e. $${\beta }_{0}$$ is the sweep rate at $$\theta\,=\,4{5}^{\circ }$$). The zero crossing of $${V}_{{\rm{G3}}}(t)$$ are matched to the electron arrival energy and time using the DC offset $${V}_{{\rm{G3}}}^{{\rm{DC}}}$$ and the time delay $${t}_{d}$$. Precise alignment is possible because the waveform, including the linear ramp region, is apparent in a map of transmitted current as described previously15,39. This accounts for RF cable length, the position of the ejection point in the pump waveform and the time for the electrons to traverse the device. The electron velocity measured in similar devices26 is ~0.5–1.5 × 105 ms−1 giving an expected transit time ~30–100 ps13,15,26,27.
Backprojection
Ideally, data would be collected by controlling the transmission mask via combined shifts in $$\Delta {t}_{d}$$ and $${V}_{{\rm{G3}}}^{{\rm{DC}}}$$ (along the axis $$S$$) while using the angular control of the voltage sweep-rate to define the projection angle $$\theta$$. In practice it is difficult to collect data along arbitrary axis $$S$$ (because of finite resolution in voltage and time delay controls) so we measure along a convenient $$S^{\prime}$$ and project this onto the $$S$$ axis (see Supplementary Note 2 and Supplementary Fig. 4). We use a standard procedure for the inverse Radon transform23 with a ramp (high-pass) filter before numerical back projection (we also include a Hann low-pass filter for some noise rejection) (see Supplementary Note 2 and Supplementary Fig. 2). | {} |
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Develop the trinomi equation. solve the product of two consecutive odd integers is 143_ 63) The integers? equation, and find the two consecutive c) 12.12 -1,-13 a) -13 u1 b) -1, 13 of 2 times the first and the second is 364? Find two consecutive integers such that the eoodtion and find the two conse...
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# Changeset 3297 for Deliverables/Dissemination
Ignore:
Timestamp:
May 15, 2013, 10:51:15 PM (7 years ago)
Message:
final version
File:
1 edited
### Legend:
Unmodified
r3287 \hskip -42.5pt\overbrace{\hskip 42.5pt\s{LIN}}^{\text{linearisation}}}^{\texttt{joint}\text{ languages}}\longrightarrow \hskip -42.5pt\underbrace{\hskip 42.5pt\s{ASM}}_{\text{linear map}}}^{\texttt{abstract\_status}\text{ (structured traces)}}$$\vskip 20pt In the process a \structure{stack model} is produced: each function is assigned its stack cost \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %[] \frametitle{Back-end correctness} \begin{theorem} \structure{Hypotheses} \begin{itemize} \item A \structure{RTLabs program} compiling to an \structure{ASM program} and a \structure{stack model} \item A prefix \structure{unstructured trace} followed by a \structure{structured one} of the RTLabs program, \structure{respecting the stack bounds } imposed by the stack model \end{itemize} \structure{Result} \begin{itemize} \item A prefix \structure{unstructured trace} followed by a \structure{structured one} of the ASM output, \structure{with the same observables} (denoted by \approx) \end{itemize}$$ \begin{tikzpicture} \node (s1) [is other, label=above:$s_1$] {}; \end{tikzpicture} $$\begin{itemize} \item \approx denotes having the same \structure{observables} (labels, calls, returns) \item The RTLabs traces respect stack bounds \end{itemize} \end{theorem} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}% [label=assembler] \frametitle{Assembler correctness} \structure{Hypotheses} \begin{itemize} \item An \structure{ASM program} successfully assembling to \structure{labelled object code} with attached \structure{cost map} \item A prefix \structure{unstructured trace} followed by a \structure{structured one} of the ASM program \end{itemize} \structure{Result} \begin{itemize} \item A prefix \structure{unstructured trace} followed by a \structure{structured one} of the ASM output, \structure{with the same observables} \end{itemize}$$ \begin{gathered} \begin{tikzpicture} \node (s1) [is other, label=above:$s_1$] {}; \node (m1) [is other, label=above:$m_1$, right=4cm of s1] {}; \node (t1) [is other, label=above:$t_1$, right=4cm of m1] {}; \draw [-stealth] (s1) -- node [above] {unstructured trace} (m1); \draw [-stealth] (m1) -- node [above] {structured trace} (t1); \begin{scope}[blue] \node (s2) [is other, label=below:$s_2$, below=1cm of s1] {}; \node (m2) [is other, label=below:$m_2$, right=4cm of s2] {}; \node (t2) [is other, label=below:$t_2$, right=4cm of m2] {}; \draw [-stealth] (s2) -- node [below] {unstructured trace} (m2); \draw [-stealth] (m2) -- node [below] {structured trace} (t2); \path ($(s1)!.5!(m1)$) -- node [sloped] {\LARGE$\approx$} ($(s2)!.5!(m2)$); \path ($(m1)!.5!(t1)$) -- node [sloped] {\LARGE$\approx$} ($(m2)!.5!(t2)$); \end{scope} \node (l1) [left=of s1] {ASM:}; \node (l2) [left=of s2] {LOC:}; \node [rotate=-90, blue] at ($(l1)!.5!(l2)$) {$\Rightarrow$}; \end{tikzpicture} \end{gathered} $$\vskip -5pt \begin{itemize} \item The machine cost \structure{equals} the cost according to the cost map: \sum_{\alpha\in m_2\to t_2}\costmap(\alpha) = \clock(t_2) - \clock(m_2) \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}% %[] \frametitle{Extensional simulation} \frametitle{From extensional to intensional simulation} \begin{itemize} \item Usual \structure{extensional} simulation (S for semantical relation): \frametitle{Preserving calls} \begin{itemize} \item If we want to localise simulation result, we need need something to preserve \item If we want to localise simulation result, we need some global info to preserve the \tikz{\node (a) [is call] {}; \node [right=of a, is other] (b) {}; \draw [densely dashed, thick] (a) -- (b);} relation \item We use a \structure{call relation} C (based on program counters) \item We use a \structure{call relation} C, relating call locations in the code \item For call states, we finally ask$$ \begin{tikzpicture}[every join/.style={ar}, join all, thick] \begin{itemize} \item How do we put to use the $C$ relation? \item Define relation $R$ as \item Define \structure{return relation} $R$ as $$\tikz[vcenter, start chain=going below, node distance=8mm] { \node [on, is other, label=right:s_1] {}; \node [on, is other, label=right:s_2] {}; \frametitle{Back to back-end correctness} \begin{theorem} Provided the RTLabs traces respect stack bounds we have$$ \begin{tikzpicture} \node (s1) [is other, label=above:$s_1$] {}; \item We use stack usage hypothesis (coming from front-end correctness) to ensure error does not occur \item States need not be remapped \item States need not be remapped, 1-1 simulation \end{itemize} \item \structure{Unique bounded stack space} \begin{itemize} \item Remap states, absence of stack overflow errors ensures this can be done correctly correctly, 1-1 simulation \end{itemize} \end{enumerate} function bodies have preambles \item Status: the scaffolding underlying all graph passes is done. The proof obligations regarding this particular pass are open is done. The (extensional) proof obligations regarding this particular pass are open \end{itemize} \end{frame} function bodies have preambles \item Status: the scaffolding underlying all graph passes is done. The proof obligations regarding this particular pass are almost finished is done. The (extensional) proof obligations regarding this particular pass are almost finished \end{itemize} \end{frame} \item From the intensional point of view, calls can have suffixes (GOTOs) \item Status: the generic linearisation scaffolding is complete. The proof obligations regarding this particular pass are open (but easy) The lacking proof obligations regard only the easy (extensional) fact that the common LTL/LIN semantics is oblivious to program counter remapping \end{itemize} \section{Assembler correctness} \begin{frame}% %[] \frametitle{Assembler correctness} Assembler outputs \structure{labelled} object code and the \structure{cost map} \begin{theorem} $$\begin{tikzpicture} \node (s1) [is other, label=above:s_1] {}; \node (m1) [is other, label=above:m_1, right=4cm of s1] {}; \node (t1) [is other, label=above:t_1, right=4cm of m1] {}; \draw [-stealth] (s1) -- node [above] {unstructured trace} (m1); \draw [-stealth] (m1) -- node [above] {structured trace} (t1); \begin{scope}[blue] \node (s2) [is other, label=below:s_2, below=1cm of s1] {}; \node (m2) [is other, label=below:m_2, right=4cm of s2] {}; \node (t2) [is other, label=below:t_2, right=4cm of m2] {}; \draw [-stealth] (s2) -- node [below] {unstructured trace} (m2); \draw [-stealth] (m2) -- node [below] {structured trace} (t2); \path ((s1)!.5!(m1)) -- node [sloped] {\LARGE\approx} ((s2)!.5!(m2)); \path ((m1)!.5!(t1)) -- node [sloped] {\LARGE\approx} ((m2)!.5!(t2)); \end{scope} \node (l1) [left=of s1] {ASM:}; \node (l2) [left=of s2] {LOC:}; \node [rotate=-90, blue] at ((l1)!.5!(l2)) {\Rightarrow}; \end{tikzpicture}$$ and $$\sum_{\mathclap{l\in\text{ASM structured trace}}}\costmap(l) = \clock(t_2) - \clock(m_2)$$ \end{theorem} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}% %[] \frametitle{Preserving the traces} \begin{itemize} \item The preservation of structured traces part is as in the back-end \againframe{assembler} \begin{frame}% %[] \frametitle{ASM $\to$ labelled object code} \begin{itemize} \item The preservation of structured traces part is as in the back-end: find $S$ relation, define $C$ relation \item A novelty in the extensional part is our proof of the correctness of a branch displacement algorithm of a branch displacement algorithm (done) \end{itemize} \end{frame} \item When returning from a call, we land at the correct point in the block whose cost was already paid by a label \item Status: done \end{itemize} \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}% %[] \frametitle{Conclusion} \begin{itemize} \item The executable compiler is complete \item Much effort has gone in providing generic scaffolding: structured traces preservation, graph translations and linearisation, all complete \item The scaffolding will scale to any change in the back-end (different architecture, possible different linearisation passes) \item Correctness of the cost static analysis \item \structure{Intensional} parts complete, up to \structure{extensional} holes in the proofs \end{itemize} \end{frame} \end{document} | {} |
Why the sample mean is not a good (sufficient) statistic?
Consider a simple example of $X_{i}$ be i.i.d uniform distribution on the interval $[\theta,\theta+1]$. By strong low of large numbers, I may conclude that $$\overline{X}\rightarrow_{P} \theta+\frac{1}{2}$$ However, it is not so clear what is the pdf or cdf of $\overline{X}$ as I would have to do an $n$-dimensional integral to get the cdf as $F_{\overline{X}}(t)=P(\sum X_{i}<nt,\theta\le X_{i}<\theta+1)$. Nevertheless it seems "intuitive" that $\overline{X}$ should be a good statistic. But practice one soon learns that the real sufficient statistic is $(X_{(1)},X_{(n)})$, and proving this via the factorization theorem is not difficult.
I decided to ask the professor about this after the class. He told me that $\overline{X}$ is not a good statistic because it is not close enough to $\theta$, and as statisticans one has to consider real life applications. But this explanation is not persuasive, since I can use $\overline{X}-\frac{1}{2}$ for the same purpose. I want to ask if $\overline{X}$ is really a bad statistic for this example, and if yes for what reason. Also I want to know if $\overline{X}$ is a sufficient statistic.
-
"the expectation" is not a statistic at all: $\bar X$ is a sample mean, not an expectation. Do you know the definition of a sufficient statistic, and any ways to check for sufficiency? You may find this discussion of the more general case of some help. (The short answer is '$\bar X$ is not sufficient'.) – Glen_b Feb 17 at 4:37
@Glen_b: Yes, thanks for the reminder for correction. I do not know how to use it in $\overline{X}$ case as I did not see $\overline{X}$ appeared in the pdf $1_{X_{(1)}}1_{X_{(n)}}$. – Bombyx mori Feb 17 at 4:42
I'm not sure what 'it' refers to in your second sentence. If you are referring to my link, the idea is to try to follow what's going on in the general case in order to understand in general terms how to apply the factorization theorem to uniform cases. – Glen_b Feb 17 at 4:43
@Glen_b: I mean by the definition of a sufficient statistic or the factorization theorem. Thanks for the short answer - but how to show it? Should not SLLN imply it is a good statistic? – Bombyx mori Feb 17 at 4:45
Here's something for you to ponder: consider random samples from a normal distribution where we average all of the data and where we average the first $\lceil{\sqrt n}\rceil$ observations. As $n\rightarrow\infty$, do both have almost sure convergence? – Glen_b Feb 17 at 5:37
As for your specific example, a simple way to understand why $\bar X$ is not a sufficient statistic for $\theta$ is to consider the following experiment: suppose I tell you $\bar X = 10$. Is this equivalent to all the information pertaining to $\theta$ that we can get from the sample? Of course not: for instance, $X_1 = 9.5, X_2 = 10.4, X_3 = 10.1$ could give us $10$, but so could $X_1 = X_2 = 9.75, X_3 = 10.5$. If you only have knowledge of $\bar X$, you have lost information about $\theta$ that was available in the original sample: namely, that in the first case, we must have $\theta \in [9.4,9.5]$, and in the second, $\theta \in [9.5,9.75]$. Notice those intervals are nearly disjoint. This is why $\bar X$ is insufficient for $\theta$. You may be able to use it to estimate $\theta$ when $n$ is large, but as I have pointed out, sufficiency has to do with data reduction, not estimation. | {} |
# A variable plane is at a distance $k$ from origin and meets the coordinate axes at the points $A,B,C$ respectively. then the locus of centroid of the $\Delta\:ABC$ is ?
$(a)\:\large\frac{1}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\:\:\qquad\:(b)\:\large\frac{3}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\:\:\qquad\:(c)\:\large\frac{4}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\:\:\qquad\:(d)\:\large\frac{9}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$ | {} |
dc.creator Bagnato, V. S. en_US dc.creator Marcassa, L. G. en_US dc.creator Telles, G. D. en_US dc.creator Muniz, S. R. en_US dc.creator Pereira, A. A. en_US dc.date.accessioned 2006-06-15T19:02:50Z dc.date.available 2006-06-15T19:02:50Z dc.date.issued 1998 en_US dc.identifier 1998-RC-07 en_US dc.identifier.uri http://hdl.handle.net/1811/18883 dc.description Author Institution: Instituto de Fisica de S\^{a}o Carlos, Universidade de S\~{a}o Paulo - Caixa Postal 369 en_US dc.description.abstract Using magneto optical trapping that simultaneously trap two different atomic species, we have performed experiments where trap loss due to the crossed specie effects are investigated. Our MOT operates in a room temperature vapor cell which can produce traps with spatial overlapping of two of any of the alkalis Na, K, Rb, Cs. To investigate the cross species cold collisions we use the traditional transient behaviour technique where either the loading or unloading of the MOT is observed for a simple or double specic trap. Measurements of the trap loss rate as a function of intensity show the existence of alternative mechanisms for the exocrgic collisions. A catalysis experiment was also performed two complement the understanding of the observed trap loss rates. Defining $\beta$ as the trap loss rate for Na alone and $\beta^{\prime}$ the loss rate for Na due to collisions with Rb, the behavior of $\beta$ and $\beta^{\prime}$ as a function of Na trap laser intensity is shown in fig.1. As the laser intensity decreases (so does the trap depth), $\beta$ decreases while $\beta^{\prime}$ increases. This behavior is consistent with the fact that the main contribution to $\beta^{\prime}$ are collisions of the type $Na - Rb^{+}$. This behavior is confirmed by the catalysis data where the dependence of $\beta^{\prime}$ with intensity is very gentle. Other combinations of atoms indicate peculiar behavior inherent to each individual systems. Most the observation involving cross species exoergic collisions can not be explained using simple models. Studies involving mixed species cold collisions may find important applications towards the production of mixed Bose-Einstein Condensation. [FIGURE] en_US dc.format.extent 177008 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title INVESTIGATION OF EXOERGIC COLLISIONS IN MIXED SPECIES TRAP: Na/Rb, Na/K, Rb/K en_US dc.type article en_US
| {} |
# It would take a computer bigger than the universe to solve 11 electron
1. Mar 20, 2013
### maverick_starstrider
Hi,
I've seen quite a few textbooks and lectures start by saying something like "to solve a quantum system of N particles would take the best computer in the world, to solve a quantum system of (N+a small number) of particles would take a computer bigger than the universe..", where they give specific numbers. An example of this is Wen's book. My question is which SPECIFIC back of the envelope calculations are they using to get these numbers? It's not something as simple as the Hilbert space for spin growing like 2^N or something so what are the specific assumptions that are made when coming up with these numbers? Anyone know?
2. Mar 20, 2013
### bahamagreen
Probably in reference to what are called P vs NP problems...
3. Mar 20, 2013
### maverick_starstrider
I'm not asking why quantum systems are not computable on classical computers I'm asking what set of assumptions go in to a statement like "To computer a system of blah electrons would require 2^blah bits" or what have you. What is the Hilbert space, what are the assumptions? What is the EXACT calculation that produced those EXACT numbers.
4. Mar 20, 2013
### maverick_starstrider
By way of an example here is one of the opening paragraphs from Wen's book:
"However, in practice, the required computing power is immense. In the 1980s, a workstation with 32 Mbyte RAM could solve a system of eleven interacting electrons. After twenty years the computing power has increased by 100-fold, which allows us to solve a system with merely two more electrons. The computing power required to solve a typical system of 10^23 interacting electrons is beyond the imagination of the human brain. A classical computer made by all of the atoms in our universe would not be powerful enough to handle the problem/' Such an impossible computer could only solve the Schrodinger equation for merely about 100"
Where is he getting the numbers he's quoting? (he doesn't say)
5. Mar 21, 2013
### atyy
Brian Swingle fills in some details in his essay. Basically, the size of the Hilbert space gets very large. He also points out that very good approximations can be obtained if you know which part of Hilbert space to hunt in for your particular application.
http://fqxi.org/community/forum/topic/1559
"More generally, the ground state of the Hamiltonian HN(g1, ..., gk) depends on these k parameters, but the state is a 2N component vector and hence all 2N components are determined by just a few numbers! Even if N is merely 100 and k = 2 we are talking about a two dimensional subset of a 2100 dimensional space! ...
"So what, after all, are all those complex numbers really telling us? Do we need them to predict the results of physical measurements? If so, we’re in trouble. Ignoring causality and the lack of materials, even if we filled up our entire Hubble volume, the whole visible universe, with our best classical storage device, we could only store the quantum state of a few hundred spins using this huge classical memory. Suddenly the illusory nature of Hilbert space is brought into focus."
Last edited: Mar 21, 2013
6. Mar 21, 2013
### cgk
OP, these statements come from arguments which assume that you intent to represent the wave function in an exponential fashion, with N^M numbers, where N is the number of one-particle states and M the number of electrons. If you then go on and formulate a particularly bad representation of the 1-particle space (e.g., a uniform 3d grid of 100 points in 3 dimensions for a molecule) you get those estimates.
What such estimates really show is the ignorance of the people providing them. For example, it is really not hard to find out that the electronic structure of molecules is routinely calculated by tens of thousands of theoretical chemists daily. You could do it on the computers your local super market sells. For friendly small molecules (say, <40 electrons) one can effectively get converged results to a few meV. These techniques of course require some information about the physical systems involved, *but this information is generally available* and can be checked in controlled approximations.
In short: If you read such a statement in a book, you can safely assume that you do not want to learn many-body theory from that book.
7. Mar 21, 2013
### Fightfish
@cgk, those approximation methods require quite a number of assumptions though, in particular they do not work well for strongly-correlated systems, which are important in contemporary condensed matter.
This report provides some examples of the computing power required for classical simulation:
http://sc05.supercomputing.org/schedule/pdf/pap188.pdf
8. Mar 21, 2013
### f95toli
A good example would be high-temperature superconductivity. We have a very good understanding of what goes on in metallic superconductors, including binary systems such as MgB2 and we can calculate all properties more or less from first principles; but no computer in the world is powerfull enough to fully simulate e.g a reasonably large YBCO lattice; which is what you would need in order to e.g. calculate Tc without any assumptions.
Note that this hasn't stopped people from trying; there are a bunch of papers out there where people have tried various "short-cuts" but with limited success. Perhaps if we extended the lattice 10 times in each direction (x,y and z) it would work; but that would require 10^3=1000 faster computers than what we have now...
9. Mar 22, 2013
### cgk
I recognize the fact that there are systems for which those approximation methods will not work well/at all. But just saying that it is impossible to calculate wave functions for any meaningful systems, as the kinds of statements cited by the OP often imply, is still utterly wrong (this is particularly ridiculous if these statements are used to introduce density functional theory).
Even just saying for strongly correlated systems it cannot be done'' is not enough: For example, a vast array of strongly correlated molecular systems are accessible to MCSCF+MRCI (multiconfiguration self-consistent field/multiconfiguration configuration interaction). Also when the strong correlation extents only across one direction, there are methods like DMRG (density matrix renormalization group) which can in principle (and sometimes in practice) handle them. There are even infinite strongly correlated lattice models (like the 1D Hubbard model) for which some ground state wave functions can be calculated analytically with pen and paper with various variations of the Bethe Ansatz.
I would be okay with those statements if they came with some restrictions in scope. For example, by saying that in the very worst case, for a random Hamiltonian with N-body terms and on which we have no further information, the wave function most likely cannot be represented without exponential cost (just like the Hamiltonian itself!). But that is often not the case; the authors make it sound like it is impossible to calculate wave functions of *any* interesting systems. And this is not true. | {} |
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### What are the characteristics of light entering a medium traveling at relativistic speeds?
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### Resources for theory of distributions (generalized functions) for physicists
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### Klein-Gordon Field Angular Momentum Operator in Terms of Creation and Annihilation Operators
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# Math Help - Piecewise function with Taylor's Theorem
1. ## Piecewise function with Taylor's Theorem
Let $U$ be a neighborhood of 0 in $\mathbb {R}$.
Suppose that $f:U \rightarrow \mathbb {R}$ is twice differentiable , f' and f'' are continuous, and $f(0)=0$.
Define $g: U \rightarrow \mathbb {R}$ by $g(x)= \frac {f(x)}{x}$ if $x \neq 0$ and $\lim _{ h \rightarrow 0 } \frac {f(h)}{h}$ if $x = 0$
Show that $g(0)$ exists and that g' exist and is continuous on U. Find $g(0),g'(0)$
Proof so far.
Find $g(0)$:
By the Taylor's Theorem, I can write $f(x)=f(0)+f'(0)x+f''(t)x^2=f'(0)x+f''(t)x^2$
Now, $g(0)= \lim _{h \rightarrow 0 } \frac {f(h)}{h} = \lim _{h \rightarrow 0 } \frac {f(h)-f(0)}{h} = f'(0)$
Is that right so far?
And how do I find g'(0)? Thank you.
Let $U$ be a neighborhood of 0 in $\mathbb {R}$.
Suppose that $f:U \rightarrow \mathbb {R}$ is twice differentiable , f' and f'' are continuous, and $f(0)=0$.
Define $g: U \rightarrow \mathbb {R}$ by $g(x)= \frac {f(x)}{x}$ if $x \neq 0$ and $\lim _{ h \rightarrow 0 } \frac {f(h)}{h}$ if $x = 0$
Show that $g(0)$ exists and that g' exist and is continuous on U. Find $g(0),g'(0)$
Proof so far.
Find $g(0)$:
By the Taylor's Theorem, I can write $f(x)=f(0)+f'(0)x+f''(t)x^2=f'(0)x+f''(t)x^2$
No you can't, there has to be a remainder term.
Now, $g(0)= \lim _{h \rightarrow 0 } \frac {f(h)}{h} = \lim _{h \rightarrow 0 } \frac {f(h)-f(0)}{h} = f'(0)$
Is that right so far?
Since $f(0)=0$:
$
g(0)=\lim_{h \to 0} \frac{f(h)}{h}=\lim_{h \to 0} \frac{f(h)-f(0)}{h}=f'(0)
$
CB
3. Do I find g'(0) the same way then?
$g'(0) = \lim _{h \rightarrow 0 } \frac {g(h)-g(0)}{h} = \lim _{h \rightarrow 0 } \frac { \frac {f(h)}{h}-f'(0)}{h} = \frac {g(0)-g(0)}{h} = 0$
Is this right? | {} |
# The zoo of multivariable functions
In calculus, going from a single variable to millions of variables is hard.
Understanding the three main types of functions helps make sense of multivariable calculus. They all share a deep connection. Let's see why!
In general, a function assigns elements of one set to another.
This is too abstract for most engineering applications. Let's zoom in a little!
As our measurements are often real numbers, we prefer functions that operate on real vectors or scalars. There are three categories:
1. vector-scalar,
2. vector-vector,
3. and scalar-vector.
When speaking about multivariable calculus, vector-scalar functions come to mind first.
Instead of a graph (like their single-variable counterparts), they define surfaces. You can think about a vector-scalar function as a topographic map.
(Image source: Wikipedia, https://en.wikipedia.org/wiki/Terrain_cartography)
Although often not denoted, the argument of a vector-scalar function is always a vector. Most frequently, we write out the components - a.k.a. the variables - explicitly.
Want a practical example of a vector-scalar function? The loss of a predictive model maps the vector of parameters to a single scalar.
Below, you can see the mean-squared error of a simple linear regression model.
Next up, we have the vector-vector functions.
You can imagine them as a force field, putting a vector to each point.
The most important example of vector-vector functions is the gradient.
We call this a gradient field. Let's visualize an example! This is how the vector field given by the gradient of $f(x, y) = x^2 + y^2$ looks.
It is important to note that not all vector-vector functions are gradient fields! For instance, $f(x, y) = (x - xy, xy - y)$ cannot be a gradient.
Can you figure out the reason why? (Hint: take a look at the partial derivatives of $f(x, y)$.)
Next up, we have scalar-vector functions, that is, curves.
Think about the scalar-vector function $f(t)$ as the trajectory of a particle at time $t$.
Technically, there is only a single variable involved. Yet, curves play an essential role in multivariable calculus.
Remember how vector-vector functions define force fields? Scalar-vector functions describe the trajectories of particles moving through them. | {} |
# Big O Calculating Runtime [duplicate]
My question is regarding the last paragraph of this excerpt from "Cracking the Coding Interview."
What's the runtime of this code?
int f(int n) {
if (n <= 1) {
return 1;
}
return f(n -1) + f(n -1);
}
The tree will have depth N. Each node (i.e., function call) has two children. Therefore, each level will have twice as many calls as the one above it. The number of nodes on each level is:
Level #Nodes Also expressed as… Or… 0 1 20 1 2 2 * previous level = 2 2^1 2 4 2 * previous level = 2 * 2^1 = 2^2 2^2 3 8 2 * previous level = 2 * 2^2 = 2^3 2^3 4 16 2 * previous level = 2 * 2^3 = 2^4 2^4
Therefore, there are 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^N (which is 2^n+1 - 1) nodes. (see "Sum of powers of 2 on page 630.)
Try to remember this pattern. When you have a recursive function that makes multiple calls, the runtime will often (but not always) look like O(branches^depth), where branches is the number of times each recursive call branches. In this case 2, so O(2^n).
As you may recall, the base of a log doesn't matter for big O since logs of different bases are only different by a constant factor. Howerver, this does not apply to exponents. The base of an exponent does matter. Compare 2^n and 8^n. If you expant 8^n, you get (2^3)^n, which equals 2^3n, which equals 2^3n * 2^n. As you can see, 8^n and 2^n are different by a factor of 2^2n. That is very much not a constant factor.
I do not understand the last paragraph. What base of a log? What is that and why do they say this here? What do they mean? | {} |
# Synopsis: Bouncing in a Spacetime Ripple
Microparticles suspended in an optical cavity may be a new way to detect gravity waves.
Everything tells us that moving masses should emit gravitational waves, but despite strong indirect evidence, there have been no direct detections. Large international collaborations are now using highly sensitive laser interferometers to look for gravity waves, requiring heroic measures to reduce noise and raise sensitivity. These detectors, however, are optimized for wave frequencies below $10$ kilohertz, causing them to miss potentially important events. In a paper in Physical Review Letters, Asimina Arvanitaki at Stanford University, California, and Andrew Geraci at the University of Nevada in Reno propose using microparticles trapped in an optical cavity as a new kind of high-frequency gravitational wave detector.
The authors consider the theoretical possibility of using a small sphere or disk suspended by radiation forces to detect gravitational waves. They propose trapping this tiny particle in a standing wave produced by an optical cavity and reducing its motion to a minimum with laser cooling. A passing gravitational wave would then produce a small ripple in spacetime causing a change in mirror spacing, shifting the location where the particle is trapped. The altered position of the particle is detected using light reflected from the cavity. For a $75$-micron particle in a $100$-meter-long cavity, Arvanitaki and Geraci estimate that they can exceed the sensitivity of the larger gravitational wave observatories for wave frequencies around $100$ kilohertz.
In their paper, the authors frankly acknowledge that few gravitational wave sources are expected to exist at this frequency, but Arvanitaki and Geraci do consider one exotic possibility. Theoretically predicted particles called axions might form a cloud around a black hole, and these in turn might annihilate to produce gravitons that create gravitational waves at the right frequency for detection by levitating microspheres. – David Voss
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# Appendix - Summary of Sinkage and Shearing Approaches
Bekker for penetration forces:(1)
$p=\left(\frac{{k}_{c}}{b}+{k}_{\phi }\right){D}^{n}-C\stackrel{˙}{D}$
Where:
• D = the sinkage of the track link in the direction perpendicular to the link surface
• p = pressure
• b = track width
• C = damping per unit area coefficient
• kc, kΦ, n = empirically determined constants
Janosi shear force:(2)
$\tau =\left(c+p\mathrm{tan}\phi \right)\left(1-{e}^{-\frac{j}{k}}\right)$
Where:
• τ = shear stress
• j = shear displacement
• c = cohesion
• Φ= angle of internal friction
• k = empirically determined constant
According to the Janosi approach, the shear stress increases while increasing the shear displacement. The maximum shear stress is:(3)
${\tau }_{\mathrm{max}}=c+p\mathrm{tan}\phi$
However, if a value is above a certain value of the shear displacement, then the shear stress is decreased. This is due to the soil failure changing the soil parameters (c and Φ). It's recommended to use a simple approach, where the shear displacement affects the maximum shear stress and not the soil parameter. The term for the proposed approach is a modified Janosi approach.
(4)
${\tau }_{\mathrm{max}}=\left\{\begin{array}{lll}c+p\mathrm{tan}\phi \hfill & \text{ }\text{ }\text{ }\hfill & j<{j}_{\mathrm{max}}\hfill \\ \left(c+p\mathrm{tan}\phi \right){e}^{\frac{{j}_{\mathrm{max}}-j}{{k}_{1}}}\hfill & \hfill & {j}_{\mathrm{max}}\le j\le {j}_{u}\hfill \\ \left(c+p\mathrm{tan}\phi \right)\text{\hspace{0.17em}}r\hfill & \hfill & j>{j}_{u}\hfill \end{array}$
where:
• jmax = the maximum shear displacement which affects increasing the shear stress
• ju = the ultimate shear displacement
• there is no effect on the shear stress while increasing the shear displacement above this point, ju>jmax
• k1 = constant; r = the maximum shear ratio, 1>r>0
For τmax to be a continuous function, the following relationship should be maintained:
(5)
$r={e}^{\frac{{j}_{\mathrm{max}}-{j}_{u}}{{k}_{1}}}$
Thus:
(6)
${k}_{1}=\frac{{j}_{\mathrm{max}}-{j}_{u}}{ln\text{\hspace{0.17em}}\text{\hspace{0.17em}}r}$
A plot of non-dimensional shear stress τ* versus non-dimensional shear displacement j* is provided in the following figure.
Where:
(7)
$\tau *=\frac{\tau }{c+p\mathrm{tan}\phi }\text{ };\text{ }j*=\frac{j}{k}\text{ };\text{ }{j}_{\mathrm{max}}^{*}=\frac{{j}_{\mathrm{max}}}{k}=10\text{ };\text{ }{j}_{u}^{*}=\frac{{j}_{u}}{k}=17\text{ };\text{ }r=0.5$ | {} |
# Listing order of all the elements in multiplicative group and all of its generators
First I want to say that I am new and therefore not that skilled when it comes to problems in abstract algebra. I have this problem which reads:
Let $$p = 19$$ and consider the finite group $$\mathbb{Z}^{*}_{p}$$. Determine the order of every element in $$\mathbb{Z}^{*}_{p}$$, and list all the generators of $$\mathbb{Z}^{*}_{p}$$
I am not sure how to go about this problem, where to start and how would one write this down. My first impulse was to multiply each element in group and then determine it's order and if it is a generator or not, but that seems like an extremely long and painful process. I was wondering if someone has any hint or suggestion as to how I should start tackling this problem?
• You could start by figuring out the order of $2$, and then figure out the orders of powers of $2$ – J. W. Tanner Sep 4 at 20:01
• The group has order $18$. By a theorem in number theory it is cyclic. So first try to find a generator, then all the other elements are its powers and it will become easier. Remember that the order of each element must divide $18$ by Lagrange's theorem. Thus if you want, for example, to find the order of $2$, you don't need to compute all its powers up to $18$, but only the powers which divide $18$. – Mark Sep 4 at 20:04
These exercises are easy and usually very short. I explain with words how to go around these types of problems. Note however that finding generators is non-trivial in general.
Finding generators is not easy and usually for those kind of exercises the only strategy is to guess. However, it is not in general extremely long and painful as you say, because as stated in the comments, a well-known fact is that $$\mathbb{Z}_p^*$$ is cyclic whenever $$p$$ is prime, so if you know about this result, you also know the probability of finding a generator by picking an element at random. It is $$\frac{\text{number of generators}}{|\mathbb{Z}_p^*|}=\frac{\varphi(\varphi(p))}{\varphi(p)}=\frac{\varphi(p-1)}{p-1}$$. The good news is that when $$p=19$$, this ratio equals $$\frac{6}{18}=\frac{1}{3}$$, so it shouldn't take much more than $$3$$ tries to find the generator. Add also the fact that this is a man-made exercise and chances are, we'll need even fewer trials! Actually I could find one in my head before writing this.
Obviously a good idea is not to pick an element at random but one that is easy to compute, say $$2$$. Since the divisors of $$18$$ are $$1,2,3,6,9,18$$, to check whether $$2$$ is a generator, note we need only check that $$2^6 \not\equiv 1 \pmod{19}$$ and $$2^{9}\not\equiv1 \pmod{19}$$ (the first inequality shows $$2$$ isn't of order $$1,2,3$$ or $$6$$, and the second shows it isn't of order $$1,3$$ or $$9$$, so if these are satisfied it must be of order $$18$$, i.e. it has to be a generator). For small numbers, this is easy to check. $$2^6=64\equiv7\pmod{19}$$ and $$2^9=8\times7=56\equiv-1 \pmod{19}$$, so $$2$$ has order $$18$$.
Now, if $$k \in \{1,2,3,6,9,18\}$$, it is easy to see that the elements of order $$k$$ are $$\{2^{18j/k},\gcd(j,k)=1\}$$
Therefore, according to this rule,
the elements of order $$1$$ are $$\{2^{18}\}=\{1\}$$
the elements of order $$2$$ are $$\{2^9\}=\{18\}$$
the elements of order $$3$$ are $$\{2^6,2^{12}\}=\{7,11\}$$
the elements of order $$6$$ are $$\{2^3,2^{15}\}=\{8,12\}$$
the elements of order $$9$$ are $$\{2^2,2^4,2^8,2^{10},2^{14},2^{16}\}=\{4,16,9,17,6,5\}=\{4,5,6,9,16,17\}$$
the elements of order $$18$$ are $$\{2,2^5,2^7,2^{11},2^{13},2^{17}\}=\{2,13,14,15,3,10\}=\{2,3,10,13,14,15\}$$
A quick reality-check for computations at the end is to note that there are $$\varphi(k)$$ elements of order $$k$$ (since there is a single cyclic subgroup of order $$k$$ and its number of generators is $$\varphi(k)$$), and that elements don't appear twice!
• Thank you for the very comprehensive answer! – Rebronja Sep 5 at 7:56
Every element in $$\Bbb Z_{19}^*\cong \Bbb Z_{18}$$ has order dividing $$18$$. There are $$\varphi(2)=1$$ element of order $$2$$, $$\varphi(3)=2$$ elements of order $$3$$, $$\varphi(6)=2$$ elements of order $$6$$, $$\varphi(9)=6$$ elements of order $$9$$, and $$\varphi(18)=6$$ of order $$18$$.
Let's try $$2$$, as per the comments.
$$2^2=4, 2^3=8,2^6=7$$ and $$2^9=512\cong-1\pmod{19}$$, indicating that $$2$$ has order $$18$$ and is a primitive.
Now the other five primitives will be $$2$$ raised to the powers $$5,7,11,13,17$$, which are relatively prime to $$18$$. Thus we get $$2^5=32\cong13\pmod{19}\,,2^7\cong14\pmod{19},2^{11}\cong15\pmod{19}\,,2^{13}\cong3\pmod{19}$$ and finally $$2^{17}\cong{10}\pmod{19}$$ as our primitives.
• I think some of your computations are off in the end (though the reasoning is correct) – Evariste Sep 5 at 2:46
• You're probably right. This happens when I try to do the computations mentally. @Evariste – Chris Custer Sep 5 at 2:55
• Thanks @Evariste I think I got it now. – Chris Custer Sep 5 at 3:01 | {} |
# TRUTHn
TRUTHn
0x0B + n*0x04 [n=0..3] 8 Enable-Protected 0x00 4 4 0,1,2,3,4,5,6,7 n
## TRUTHn
Bit 7 6 5 4 3 2 1 0 TRUTHn[7:0] Access R/W R/W R/W R/W R/W R/W R/W R/W Reset 0 0 0 0 0 0 0 0
## Bits 7:0 – TRUTHn: Truth Table
Truth Table
These bits determine the output of LUTn according to the LUTn-TRUTHSEL[2:0] inputs.
Bit Name Value Description
TRUTHn[0] 0 The output of LUTn is 0 when the inputs are ‘b000
1 The output of LUTn is 1 when the inputs are ‘b000
TRUTHn[1] 0 The output of LUTn is 0 when the inputs are ‘b001
1 The output of LUTn is 1 when the inputs are ‘b001
TRUTHn[2] 0 The output of LUTn is 0 when the inputs are ‘b010
1 The output of LUTn is 1 when the inputs are ‘b010
TRUTHn[3] 0 The output of LUTn is 0 when the inputs are ‘b011
1 The output of LUTn is 1 when the inputs are ‘b011
TRUTHn[4] 0 The output of LUTn is 0 when the inputs are ‘b100
1 The output of LUTn is 1 when the inputs are ‘b100
TRUTHn[5] 0 The output of LUTn is 0 when the inputs are ‘b101
1 The output of LUTn is 1 when the inputs are ‘b101
TRUTHn[6] 0 The output of LUTn is 0 when the inputs are ‘b110
1 The output of LUTn is 1 when the inputs are ‘b110
TRUTHn[7] 0 The output of LUTn is 0 when the inputs are ‘b111
1 The output of LUTn is 1 when the inputs are ‘b111 | {} |
Paul's Online Notes
Home / Calculus I / Integrals / More Substitution Rule
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### Section 5.4 : More Substitution Rule
10. Evaluate $$\displaystyle \int{{{{\sec }^2}\left( {2t} \right)\left[ {9 + 7\tan \left( {2t} \right) - {{\tan }^2}\left( {2t} \right)} \right]\,dt}}$$.
Show All Steps Hide All Steps
Hint : Don’t let this one fool you. This is simply an integral that requires you to use the same substitution more than once.
Start Solution
This integral can be a little daunting at first glance. To do it all we need to notice is that the derivative of $$\tan \left( x \right)$$ is $${\sec ^2}\left( x \right)$$ and we can notice that there is a $${\sec ^2}\left( {2t} \right)$$ times the remaining portion of the integrand and that portion only contains constants and tangents.
So, it looks like the substitution is then,
$u = \tan \left( {2t} \right)$
If you aren’t comfortable with the basic substitution mechanics you should work some problems in the previous section as we’ll not be putting in as much detail with regards to the basics in this section. The problems in this section are intended for those that are fairly comfortable with the basic mechanics of substitutions and will involve some more “advanced” substitutions.
Show Step 2
Here is the differential work for the substitution.
$du = 2{\sec ^2}\left( {2t} \right)dt\hspace{0.25in} \to \hspace{0.25in}\,\,\,\,\,{\sec ^2}\left( {2t} \right)dt = \frac{1}{2}du$
Now, doing the substitution and evaluating the integrals gives,
\begin{align*}\int{{{{\sec }^2}\left( {2t} \right)\left[ {9 + 7\tan \left( {2t} \right) - {{\tan }^2}\left( {2t} \right)} \right]\,dt}} & = \frac{1}{2}\int{{9 + 7u - {u^2}du}} = \frac{1}{2}\left( {9u + \frac{7}{2}{u^2} - \frac{1}{3}{u^3}} \right) + c\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{2}\left( {9\tan \left( {2t} \right) + \frac{7}{2}{{\tan }^2}\left( {2t} \right) - \frac{1}{3}{{\tan }^3}\left( {2t} \right)} \right) + c}}\end{align*}
Do not forget to go back to the original variable after evaluating the integral! | {} |
# vertical alignment of a turned cell
I know using turn command and a sample code like this:
\usepackage{rotating}
\begin{turn}{90} Supervised Learning \end{turn}}
we can rotate a text inside a cell, however, I couldn't find a way to vertically center this rotated text. Any suggestions is appreciated.
Here is the sample MWE:
\begin{table}[]
\centering
\begin{tabular}{|>{\centering\arraybackslash}m{0.5cm}|c|>{\centering\arraybackslash}m{8cm}|}
\hline
\multicolumn{2}{|c|}{Classification} & References \\ \hline
%\multirow{2}{*}{{\begin{turn}{90}Supervised Learning\end{turn}}}
\multirow{2}{*}{\rotatebox[origin=c]{90}{Supervised Learning}}
\end{tabular}
\caption{A Classification}
\label{tab:Machine_Learning_models}
\end{table}
• Maybe some here know this package ... however, to other will help a MWE (small complete document, which we can compile), which will show your problem. – Zarko Aug 28 '16 at 18:57
• my bad, it was called rotating – Amir Aug 28 '16 at 19:16
• I have updated the question with a MWE – Amir Aug 28 '16 at 19:36
• Your subject and objective of your updated question is radically different from what you asked originally. Instead of editing an existing question and changing its content dramatically, you should consider leaving the original query unchanged and posting a second, new query to address the new subject material. If nothing else, this approach would avoid rendering the answer that was addressed the initial version of your query meaningless and inapplicable. – Mico Aug 28 '16 at 19:47
• My question was on how to vertically center a rotated text and my question is still that one. – Amir Aug 28 '16 at 19:56
since your question seems to be unstable system ... i'm afraid that my answer will miss your point as it was Mico answer (which finish with deletion) :-( )
anyway, for exercise:
• your rotated text is taller than rest of table, so it can not bo properly centered
• easier way to rotate cell content is use \rothead macro from makecell package (for which you need to define cell height)
• vertically centering in multirow cell needs some manual tweaking
with this (and expand the table) I obtain the following result:
MWE:
\documentclass{article}
\usepackage{rotating}
\usepackage{array,makecell,multirow}
\begin{document}
\begin{table}[htb]
\centering
\begin{tabular}{| l | c |
>{\centering\arraybackslash}p{8cm}|}
\hline
\multicolumn{2}{|c|}{Classification} & References \\ \hline
& & 1 \\ \cline{2-3}
& & 2 \\ \cline{2-3}
& & 3 \\ \cline{2-3}
& & 4 \\ \cline{2-3}
& & 5 \\ \cline{2-3}
& & 6 \\ \cline{2-3}
& & 7 \\ \cline{2-3}
& & 8 \\ \hline \end{tabular}
\caption{A Classification}
\label{tab:Machine_Learning_models}
\end{table}
\end{document}
Addendum: Font size of text in \rothead is determined by \headfont macro. Default value is \footnotesize. It can be changed by
\renewcommand\theadfont{\normalsize}
(or whatever size, font family and shape you like). Considering above change of font size, the relvant part of MWE become:
\documentclass{article}
\usepackage{rotating}
\usepackage{array,makecell,multirow}
\begin{document}
\begin{table}[htb]
\centering
\begin{tabular}{| l | c |
>{\centering\arraybackslash}p{8cm}|}
\hline
\multicolumn{2}{|c|}{Classification} & References \\ \hline
• Thanks for suggesting makecell package. Could you ellaborate more on the \settowidth\rotheadsize{Supervised Learning} and that [1.5ex] in the command. – Amir Aug 28 '16 at 20:51
• all is explained in answer ...\settowidth\rotheadsize{Supervised Learning} determine the length of text, which rotated should fit into cell. i.e. determine cell height. [1.ex] in multirow is manual adjustment of vertical position of cell content. sorry, i do not understand the second comment. which size is reduced? if you like to have table width equal to text width (i guessing) than the best way to achieve this is use of tabularx instead of table where instead p{...} you use X column type. – Zarko Aug 28 '16 at 21:06
• Thanks @Zarko. My 2nd question was about the text of the {Supervised Learning} is now being reduced in font size despite having enough of space in the column. The vertical alignment is OK now after manually setting [1.ex] – Amir Aug 29 '16 at 13:00
• Indeed, the fonts for vertical text is smaller. It is defined by \theadfont which default size is \footnotesize. to increase it you need to add \renewcommand\theadfont{\normalsize}( or whatever size, font family and shape you like). I will edit my answer. – Zarko Aug 29 '16 at 13:52 | {} |
PDA
itsmillertime
12-01-2014, 11:49 PM
Hi Guys I was hoping that you could help me track down the problem behind why my CNC 6040 router now and then (but pretty much most jobs) it will happily be machining away. When at some point the machine will make a louder 'jarring' kind of noise and it appears to be along the Y axis by what it does to my work pieces (the longest axis which the gantry moves across). The machine doesn't appear to stop but it looks as though it jumps by about 10mm. I haven't been able to physically see this by eye as everything is always too quick and it's not spectacular enough. But I can see it jumps on my work.
You can see from the photos attached what it is doing.
The machine appears to be operating just fine until this happens i.e circles are all correct as are square shapes.
I know that they have lots of quality issues, but I would be really grateful to you guys for advice on how to diagnose this.
Upon starting up the CNC router and running mach3 on my desktop all 3 stepper motors lock as they should and the router happily runs/jogs along all axis. I can turn the stepper knobs by hand freely and cannot feel any rough parts of travel in the ballthreads.
Please help me diagnose this with simple steps. Is it more likely that it's wiring or a stepper motor or driver?
Just guessing possible Y axis wiring issue. But would love to see what you all think.
As you can see this error has made it into all 3 jobs below. Looking forward to hearing what you guys think.
Cheers andy
112671126811269
EddyCurrent
13-01-2014, 12:05 AM
On the second photo it looks like it jumped then came back into line again, did it do that itself or did you intervene and correct it ?
Is it direct drive or via toothed belt ?
Jonathan
13-01-2014, 12:29 AM
I think in the second photo it jumped twice by different amounts, as it's not gone perfectly back into line.
It could just be the Y-axis motor is very occasionally stalling. I'd try running this code (http://www.mycncuk.com/forums/gcode/5843-random-g-code-testing-motor-tuning.html) to test it more thoroughly and report back.
Washout
13-01-2014, 12:32 AM
There are way better guys on here than me to advise, but here goes....
.
What you are describing sounds like a motor stall on the y-axis, which is likely due to 2 causes:
.
1. You have a mechanical problem, such as the rails, ball or lead screw(s) or bearings being out of true and causing binding i.e. a resistance the stepper motor is having difficulty overcoming or;
.
2. You have an electronics issue where data or pulses are getting lost and the steppers are not moving when they are supposed to be.
.
For 1. I would see if you can first disengage the ballscrew/leadscrew and see if the gantry can be moved across its full range of travel with only a little pressure by hand - my own gantry weighs a fair amount but I can push it easily with a finger. Or failing that see if there is any adjustment possible on the ball/leadscrew alignment and redo that - not sure how your ballscrews/motors etc. are attached, so can't really advise on the method of doing this.
.
For 2. Only advise I can give at this stage is if your wiring is not using shielded cable, then replace that with shielded CY cable and ground the shield at the control box end only and to the same ground point all the other earths on your machine should be going to, which should in turn be wired to mains earth. Make sure the ends of the shielding at the stepper motors are isolated i.e. not contacting anything. Other than that you are looking at driver, control board/BoB replacements, but I can't advise on diagnosing your existing components. Also I have seen some stories of inadequate grounding within the control box itself, so check that out.
.
Oh also if the machine came with a cheapo parallel cable for connection to your PC then try another one. I had a problem with my machine getting spurious e-stops that turned out to be a shoddy parallel cable. Replaced it with a chunky shielded one and that problem went away.
.
There'll likely be other guys that can advise further, but having tripped over most of the pitfalls in building reliability into my own machine that's where I would start.
.
Hope that helps.
JAZZCNC
13-01-2014, 12:57 AM
If it's a sudden jump straight after the Jarring noise and it's just on the Long axis then I suspect it's the ballscrew end bearings floating.?
Grab the gantry firmly at both sides and try to move back n forth. If you have end float you'll feel it clunck.
If it's losing position over time then I'd suspect a lose coupling first, after that then I'd look at the wiring. These cheap machines come with crap wire on the motors which gets brittle and breaks internally but still works and causes all sorts of strange things like this. Same with the connectors there rubbish and need replacing.
From you saying it works fine then does this then I don't think you will have it over tuned or anything so wouldn't go messing in that direction just yet.
With the noise your saying it's making then 90% chance it will be mechanical 10% wiring or electrical.
GEOFFREY
13-01-2014, 01:20 AM
It would appear to me that the problem occurs during rapid moves and not whilst cutting. if this is the case you may be able to work around the problem by changing G0 to G1 as a short term fix until you are able to resolve the problem. G.
itsmillertime
13-01-2014, 08:18 AM
Thanks guys loads of ideas to look at here! eddy its a direct drive stepper motor without any drive belts. As for the photo and it correcting itself. I think it did the top text line in a different order I.e do a few letters and go do something else then come back. I haven't corrected anything in any of the pics.. hope that helps?
I think it is most likely a mechanical issue as is suggested. so I'm going to take a few videos while its cutting to see if I can narrow it down further.
@ Jonathan I think you are correct about it having jumped different amounts, it looks like that to me too. I will run the code tonight when I get in from work. thank you!
@ washout and jazz cheers guys I will look into your suggestions after I can nail this this down on video.
and Geoffrey I shall indeed try changing those settings as it does look like its only doing this whilst moving fast and not actually cutting. cheers guys I will report back. hope I haven't missed anyone out trying to type this from my mobile!
cheers andy
richie00boy
13-01-2014, 09:25 PM
Check your pulse train speed as I had a sort of similar issue and found I was running too fast. If you want to post up your axis settings I'll check them against mine. I've got a 3020, but I think the settings should be similar?
itsmillertime
13-01-2014, 11:38 PM
Thanks Richie I will post up some screenshots of my settings tomorrow it could be that the stepper motor is running to fast in one direction and trying to reverse too quickly (if this makes sense?) I have managed to capture it doing this on video twice and have attached a youtube video. You will be able to hear the 'jarring/grinding noise' briefly. Sorry for the crappy fastening down I did the first clip without the spindle running. The second part of the video is just to highlight that it's doing the same thing with the spindle running too.
I am a beginner to all of this and appreciate all of the help you guys have offered. I tried rocking the gantry back and forth and left and right and I was unable to find anything loose as such.. no real obvious play. I will look into this more tomorrow night.
http://youtu.be/hqf3sHZVPjE
Any more thoughts welcome? does this rule anything out or more clearly point to any of the above suggestions?
Thanks again Andy
JAZZCNC
13-01-2014, 11:58 PM
100% the noise is motors stalling from being over tuned and trying to cut too fast.
Looking at the speed you where cutting at I think your being too ambitous on the Feed n speeds for this little machine and the motors are running out of torque and thats why your getting stalling motors.
Drop the feed rates down and try again and I think you'll find it works fine.
You could play with motor tuning which would help but I think your just pushing the little thing too hard.!! . . .. Try lowering the Accel first if you adjust motor tuning has that will have the biggest affect and would cause this kind of stalling/missed steps.
itsmillertime
14-01-2014, 12:22 AM
phew! I'm pleased to hear you say that jazz! Is just me being far too ambitious with it. I will have another play tomorrow night and get those speeds down. what kind of speed would be a conservative setting? also this may sound stupid. I can change the feed speed whilst cutting in vectric whilst setting up my toolpath. Is there a separate option in maxh to adjust the rapid movements in between cuts? or is this dictated purely by feed settings? guessing there's something in mach3 for this?
Thanks again and appreciate your opinion jazz. was beginning to feel open wallet surgery about to take place ;-) .
thank you
JAZZCNC
14-01-2014, 12:36 AM
Rapid speed is the Velocity setting in Motor tuning.
If you watch the video it stalls while cutting not rapiding between moves so I think if you tweak the Accel first and lower the feed while cutting then you'll be ok.
Basically it's stalling under the cutting load which isn't much at this depth but your feed rate is so fast your at the limits of the motors torque so it doesn't take much to make stall.
Just drop the Accel by 10% and try again.
What feed rate was it set at while cutting.?
Edit: If you want to test and see the affects of lowering feedrate without altering anything, machine or G-code, then just lower the feed rate over ride to 75% and try it again.!
Clive S
14-01-2014, 10:40 AM
phew! I'm pleased to hear you say that jazz! Is just me being far too ambitious with it. I will have another play tomorrow night and get those speeds down. what kind of speed would be a conservative setting? also this may sound stupid. I can change the feed speed whilst cutting in vectric whilst setting up my toolpath. Is there a separate option in maxh to adjust the rapid movements in between cuts? or is this dictated purely by feed settings? guessing there's something in mach3 for this?
Just for the sake of clarity Velocity and Accel are two different settings in Mach they are in config\motor tuning. Not to be confused with each other Jazz is referring to the Accel setting that might be a bit too high. Good luck I am sure you will get this sorted. ..Clive
kingcreaky
15-01-2014, 09:28 AM
The way i think of it is, the Acceleration and Velocity settings in Mach act like your speed limiter, they over-ride whatever settings the CAM software specifies in the job.
Its also critical (although I cannot explain why) to ensure the Acceleration and Velocity settings are the same for both your Y axis and X axis. (Z can be different) Otherwise (I found) it effects 90deg corners. Where (I think) the machine is still decelerating (moving) when the next move starts
Personally (others will disagree, I set the accelleration very low (often 100), and the velocity to a comfortable speed for the machine as Im far more interested in quality, than speed) I also find having acceleration set so low helps when jogging your machine manually into a start position and also makes a nice smooth start and stop to each move.
As mentioned above, Mach is your speed limit. So if you have set your velocity to 6000mm/min in mach, and your tool to 8000mm/min in vectric (or your cam software) mach wont let the machine exceed 6000.
The machine jogs (ie with the arrow keys, at the maximum speed stated in mach)
The machine moves (between cuts, at whatever speed the Gcode outputted by your cam software) -- but limited by mach.
The above is just my opinion.
Jonathan
15-01-2014, 09:35 AM
You're noticing the variable corner rounding effect because the acceleration is too low. You should be aiming for around 1000mm/s^2 for the acceleration - certainly at least 500... otherwise in some circumstances your parts wont be as accurate.
Neale
15-01-2014, 09:42 AM
Isn't there also a gcode parameter which affects accuracy at corners? You can either specify stop/start for maximum accuracy but lose feed rate at corners, or give a maximum error value so that Mach or LinuxCNC can approximate the corner to maintain cutting speed. Coupled with a max acceleration figure, it can all start getting a bit complicated.
kingcreaky
15-01-2014, 10:02 AM
thanks for this boys....although since I have set the two the same this no longer happens... not to cloud the issue... its still good practise to ensure the acceleration and velocity values for both the X & Y are the same right or wrong?
JAZZCNC
15-01-2014, 10:35 AM
Matt just going to make some things a bit clearer for sake of others not picking on you here mate but it's not clear and your Soooooo wrong on some it. .:hysterical:
The way i think of it is, the Acceleration and Velocity settings in Mach act like your speed limiter, they over-ride whatever settings the CAM software specifies in the job.
As mentioned above, Mach is your speed limit. So if you have set your velocity to 6000mm/min in mach, and your tool to 8000mm/min in vectric (or your cam software) mach wont let the machine exceed 6000.
The machine jogs (ie with the arrow keys, at the maximum speed stated in mach)
The machine moves (between cuts, at whatever speed the Gcode outputted by your cam software) -- but limited by mach.
This is true but I'll make it clearer because it does apply here.
In the G-code this will only apply to the G1 moves which have F### feed rate parameter but all G0 moves will be at the Velocity setting in motor tuning. So if your over tuned on velocity then you will still lose position if G0 moves are in the g-code even if you lower the feedrate in Cam software.!
Its also critical (although I cannot explain why) to ensure the Acceleration and Velocity settings are the same for both your Y axis and X axis. (Z can be different) Otherwise (I found) it effects 90deg corners. Where (I think) the machine is still decelerating (moving) when the next move starts
Personally (others will disagree, I set the accelleration very low (often 100), and the velocity to a comfortable speed for the machine as Im far more interested in quality, than speed) I also find having acceleration set so low helps when jogging your machine manually into a start position and also makes a nice smooth start and stop to each move.
This is the bit your Sooooo wrong about matt... .Lol
It's not critical and perfectly fine to have differant setting for each axis, Mach will only go fast has the slowest axis anyway when moving 2 axis at same time. Try it.!! . . Double the Speed of Y axis velocity (if machine can do it) and home the machine and jog away good distance and Type G1 X0 Y0 F ( Feed value abobe X axis velocity or same has Y axis velocity) in the MDI box.
Like Jonathan pointed out most if not all of trouble is coming from having the Accel far far to low.
Molasses moves faster than that so MAch's gets tired of waitng and Knobs off to the pub for a quicky but has few too many so when it gets back it's forgot where it was upto and thinks bollocks to it i'll just carry on from here and that's why your getting square circles.!!. . . . Mach pissed.!! . .Lol . . . . Ok well maybe being bit silly but the point is your messed up on tuning.!
You really want to be within 500-800 just for normal use and 1000 and above this if doing mostly 3D type work.
Just remember the golden rule that you can't have High Accel and High Velocity you need a balance and you won't go wrong.
kingcreaky
15-01-2014, 10:41 AM
removes hat. Thanks for taking the time to clarify.
itsmillertime
15-01-2014, 11:13 AM
wow, thanks guys for all the info. I'm at work at the moment but late last night I had a quick look at the settings and my velocity looks way too high. I have found someone elses motor settings for the 6040 machine and Mine is at least 25‰ greater! no wonder why I'm having issues. I'm going to get in tonight change the settings and report back. Thanks to you all for your input. will be good to see this fixed lol. got my fingers crossed for tonight. I will screenshot the settings for anyone else with a similar machine should this quandry happen for others.
I'm sure I won't be the first ;-) cheers guys
Jonathan
15-01-2014, 12:47 PM
In LinuxCNC you can specify a tolerance on the G64 command, so the controller sacrifices constant speed to maintain the toolpath within the specified tolerance. e.g. put 'G64 P0.05' at the begining of the G-code and the path will not deviate by more than the P from the true value.
It's not critical and perfectly fine to have differant setting for each axis, Mach will only go fast has the slowest axis anyway when moving 2 axis at same time. Try it.!! . . Double the Speed of Y axis velocity (if machine can do it) and home the machine and jog away good distance and Type G1 X0 Y0 F ( Feed value abobe X axis velocity or same has Y axis velocity) in the MDI box.
You've raised a mildly interesting point there, which I think is worth expanding to show why what you've observed occurs. The velocity of each axis cannot exceed the values in the motor tuning, however the speed of the machine (i.e. the feedrate) can, unless the machine is only moving in one axis. This occurs because when two axes are moving at given velocities, the resultant feedrate is the vector sum of these velocities. One way to visualise it is as a right angled triangle, where (for example) the velocities of X and Y are the sides adjacent to the right angle - the length of the hypotenuse will equal the feedrate.
Example 1:
Suppose you set your maximum velocity settings for X and Y both to 1000mm/min, home the machine (so it's at 0,0) then enter 'G0 X100 Y100'. Mach will move both X and Y as fast as it can (as it's a G0 move), so the feedrate you actually get is \sqrt{100^2+100^2}\approx 1414mm/min, assuming the machine can accelerate to that feedrate within the specified distance.
The practical upshot of this is you can specify a feedrate higher than the velocity setting, and get that feedrate in some circumstances.
Example 2:
Same as example 1, except we enter 'G1 X100 Y200 F1100'.
The required speed is 1100mm/min, so the following must hold: 1100=\sqrt{X^2+Y^2} (equ. 1), where X and Y are the X and Y axis velocities.
The Y axis must travel twice as fast as X to go in the correct direction (as 200/100=2), so we have \frac{Y}{X}=2 (equ. 2)
We also have the condition X,Y<1000,due to the motor tuning settings.
From (2), Y=2X, so substitute that into 1:
1100=\sqrt{X^2+(2X)^2}
1100=\sqrt{5X^2}
X=\sqrt{\frac{1100^2}{5}}\approx 492mm/min
Whence,
Y=2*X=2*492\approx 984mm/min
(You can also solve this graphically quite easily - which may be more intuitive.)
So the X and Y velocities do not exceed 1000mm/min, yet the machine can in this example cut at 1100mm/min.
In reality, it's probably not a good idea to use this 'feedrate bonus' as it makes the feedrate a function of the direction in which the machine is travelling, so unless you're cutting a single straight line the feedrate you actually get will vary (continuously if an arc move).
JAZZCNC
16-01-2014, 02:01 AM
From (2), Y=2X, so substitute that into 1:
1100=\sqrt{X^2+(2X)^2}
1100=\sqrt{5X^2}
X=\sqrt{\frac{1100^2}{5}}\approx 492mm/min
Whence,
Y=2*X=2*492\approx 984mm/min
I see you like your new toy. . . . Lol . . .(Shame Nobody got F'#$ing clue what your saying. .:hysterical:) irving2008 16-01-2014, 09:42 AM Some of us do :) but it's true J is playing with it. It's a nice new toy tho if I could make it work for me.. Clive S 16-01-2014, 10:19 AM I see you like your new toy. . . . Lol . . .(Shame Nobody got F'#$ing clue what your saying. .:hysterical:)
Dean: its a recipe for a sponge cake anybody can see that:yahoo: ..Clive
Neale
16-01-2014, 11:13 AM
Dare I ask for a bit more clarification? Dangerous ground, here, perhaps! But here goes...
What I'm not quite sure about here is the difference between G0 and G1. So, a few examples to see if I understand. In all cases, we start at (0,0).
G0 X100 Y100
This is a rapid move at max permitted machine speed. If max X and Y speeds are 1000mm/min, then Mach (or LinuxCNC, I presume) will move each axis at max permitted speed which actually moves the cutter at 1414mm/min across the bed (hypotenuse of right-angled triangle).
G1 X100 Y100 F1000
Mach/LCNC calculates the speed needed for each axis to achieve an actual cutting speed of 1000mm/min along the cutting path, which translates to a speed along each axis of 707mm/min, well within max permitted limits. So you could write G1 X100 Y100 F1400 and actually cut at that speed.
What Jonathan has said is that (using these figures) the max cutting speed along either axis is 1000mm/min, but in principle you could ask for higher cutting speeds and if you are cutting along a diagonal, you might achieve them. What is also relevant, maybe, is that it doesn't matter if you have different max speeds along each axis; Mach/LCNC will do the sums needed to make sure you don't exceed either max although this may mean that rapid moves will achieve different speeds over the bed depending on direction.
That all seems pretty straightforward, but it's the difference between G0 and G1 that I'm not quite clear about. G0 takes max speeds for each axis which you have defined for the machine, and will use them for G0 rapid moves and may even achieve speeds over the bed above the max for an axis if you happen to move along a diagonal. G1 needs a speed defined (either by setting it once in the gcode and using it as a default or by setting it in each G1 command) and will use this to calculate actual cutting speed whether along an axis or at some angle (or even around an arc), as long as max speed per axis is not exceeded. I think this means that if I stick a G0 move in at the top of my gcode file with a ridiculously fast F setting, then LinuxCNC will always give me the fastest rapids that preset max X and Y settings permit, but I should make sure that the F setting for g1 cuts is the actual cutting speed that I want. I use LinuxCNC, by the way, so maybe there is also a slight difference of interpretation compared to Mach 3.
As far as the original question is concerned, all this means is that you can look at max speed and accel along each axis independently in order to avoid missing steps and other nastiness, and actual speeds over the bed are just an accident of geometry and don't affect design and tuning parameters. If you are missing steps along X, say, during rapid feeds you might choose to reduce accel or max speed on that axis but you don't necessarily have to change Y if that is working fine with its current settings. However, if you get skipping during cuts, then it's a bit more complicated and you probably need to reduce the F cutting speed parameter just to reduce load as you can't tune this by axis.
And my apologies, guys - I was desperately trying to find an excuse for using nested integral signs and the odd greek symbol from the LaTeX library but just couldn't find a way to fit them in...
Jonathan
16-01-2014, 11:52 AM
So you could write G1 X100 Y1000 F1400 and actually cut at that speed.
I think you meant Y100 or X1000 there.
Otherwise, nicely summarised.
I think this means that if I stick a G0 move in at the top of my gcode file with a ridiculously fast F setting, then LinuxCNC will always give me the fastest rapids that preset max X and Y settings permit, but I should make sure that the F setting for g1 cuts is the actual cutting speed that I want.
The 'F' command does not affect G0 moves. By definition, G0 moves the machine as fast as permitted by the motor tuning, unless you've overridden it using the feedrate adjustment, in which case the speed would be lower.
As far as the original question is concerned, all this means is that you can look at max speed and accel along each axis independently in order to avoid missing steps and other nastiness, and actual speeds over the bed are just an accident of geometry and don't affect design and tuning parameters. If you are missing steps along X, say, during rapid feeds you might choose to reduce accel or max speed on that axis but you don't necessarily have to change Y if that is working fine with its current settings. However, if you get skipping during cuts, then it's a bit more complicated and you probably need to reduce the F cutting speed parameter just to reduce load as you can't tune this by axis.
Yes, that's correct.
And my apologies, guys - I was desperately trying to find an excuse for using nested integral signs and the odd greek symbol from the LaTeX library but just couldn't find a way to fit them in...
Here's an easy way to get some different symbols in... derive a formula to find the direction (angle) for which the machine can travel at the highest feedrate, for given X and Y rapid speeds.
It's just occurred to me that you could actually do something useful with that formula - potentially surface your bed faster by using a raster pass set to that angle.
Neale
16-01-2014, 12:10 PM
Ooh, an excuse for some calculus! That'll get 'em rolling in the aisles...
Thanks for pointing out typo, Jonathan - correction made.
On the F setting and G0, though - my comment was based on my experience with LinuxCNC, and I wonder if I have misremembered or LCNC works a little differently to Mach 3 (which seems from casual observation on this forum to be much more popular). If I type G0 commands into LCNC to move the machine "manually", my recollection is that it bitches if it has not seen a previous F setting in a G0 context. I tend to have to type something like "G0 X100 Y100 F1200". Once I've done that, I don't need the F parameter for subsequent G0 commands. In other words, it doesn't seem to default to the max machine speeds. The way you describe it makes much more sense and I wish it worked like that on my system but it doesn't seem to. I'll have to experiment - I might have missed something subtle.
Jonathan
16-01-2014, 12:19 PM
If I type G0 commands into LCNC to move the machine "manually", my recollection is that it bitches if it has not seen a previous F setting in a G0 context.
I don't remember... by all means check.
According to the definition here, it shouldn't be a problem:
G Codes (http://linuxcnc.org/docs/html/gcode/gcode.html#sec:G0)
Also notice that they mention what we just discussed - 'The maximum rapid traverse rate can be higher than the individual axes MAX_VELOCITY setting during a coordinated move.'
GEOFFREY
16-01-2014, 07:32 PM
I see you like your new toy. . . . Lol . . .(Shame Nobody got F'#\$ing clue what your saying. .:hysterical:)
Hey Jazz, I was under the impression that you were into latex!!! G.
JAZZCNC
16-01-2014, 09:07 PM
Hey Jazz, I was under the impression that you were into latex!!! G.
Nah but I do have a pallet of Latex I can sell you.???. . . .Gloves. :hysterical: . . .( Also Nitrile and Vinyl if that's your fetish. . Lol)
itsmillertime
17-01-2014, 08:08 PM
Nah but I do have a pallet of Latex I can sell you.???. . . .Gloves. :hysterical: . . .( Also Nitrile and Vinyl if that's your fetish. . Lol)
OMG lol What did I just walk back into? :whistle::beer:
I wanted to update you on my progress with getting this jumping/ noise issue out of the way. Well... I figured that you guys Jazz I think mentioned it first that I was expecting too much and the speeds were too high with the rapid and cutting settings.
Well, Lo and behold after trying lots of different tuning combinations. I discovered setting the speeds too low also made for some horrible sounds. But I came across a another post with some supplier recommended settings. That were indeed a lot slower than what I had been gave.
112971129811299
These settings were actually found to be the best for my 6040 machine. And they are
steps velocity accel' step dir
X 320 2000 200 10 5
Y 320 2000 200 10 5
Z 320 800 150 10 5
My old settings that made the occasional noise and stalled the motors were
steps velocity accel' step dir
X 320 3000 200 3 1
Y 320 3000 200 3 1
Z 320 800 200 3 1
It sounds loads better now and doesn't fly about making my table shake slightly with the speed of movement of the gantry.
I have re-cut a few test pieces and haven't had the horrible sound or any missed steps.... yet ;-) Never say never eh!
I just want to say a really big thanks to all you guys for all of your invaluable advice I really do appreciate it and would have been stuck without all your help. cheers guys
Andy :-)
itsmillertime
18-01-2014, 07:33 PM
Well, Spoke to soon! Although the motor tuning appears to be better and it certainly still sounds better. I have had the same problem come back. The stalling and the engraving being out of line by about 10mm as though the motor stalled again (complete with grinding noise!)
I turned the power off and swapped over the X and Y axis connectors at the 'blue' controller breakout box. Looking to see if the fault would swap over the the X axis (My fault has always shown on the Y axis so far)
Lo and behold I rotate my workpiece by 90 degrees and power up and run the machine again. The error appears again exactly the same (but without any really noticeable grinding on the machines X axis. Apart from the engraved text appearing backwards the error is in the same place on the workpiece. This I think tells me that the problem is in my Y axis driver board? Plus my Z axis (at approx the same time as the initial Y axis error reappeared seemed to plunge deeper by about 2mm after/ same time as the Y axis stalled. Inside the breakout box the driver boards are separate.
Am I right in thinking that it can only be a crappy control box (mixed with maybe crappy unscreened -and not star earthed either..)
I'm now looking at replacing the existing chinese cable in the 6040 router with screened cable is this the best thing to do and any links to the best 4 core stuff to buy for the job please?
Also I am going to need to replace the break out box. What is the best and easiest stepper controller solution in the UK. Balancing cost and quality. I would stick with the stepper motors I have for now but probably need to upgrade this crappy control box.
Would really like to hear your suggestions guys.. :-)
Thanks again Andy
JAZZCNC
18-01-2014, 07:58 PM
Calm down Mr mannering don't go scraping things just yet.!! . . . Still some other things it could be and if you have separate drives there's half a chance it's just a setting or pulse issue.!
Looking at your motor tuning with 320 steps Per setting and presuming a 5mm pitch screw means the drives must or should be set to 1600 micro steps.
This is relatively high for these machines so It could just be your system can't handle that many pulses and your getting missed steps.?
So first we need to confirm this so can you give us a good quality picture of the drives and there wires and Dip switches if any.
Try and find out ther PSU voltage.
Next what is the Kernal speed set at.? You'll find it in ports & pins.
Show us more before spending any money.
itsmillertime
18-01-2014, 08:51 PM
Lol Cheers Jazz ;-)
Just got frustrated with trying to get it running consistently! I have just gone out and taken the case off and had a look inside.
It looks like the switches are set for 1600microsteps. From the PSU I can see on the label (DC output 24v and current 12.5A) outside case says drive voltage 24v DC drive current 3A.
The kernel speed is set at the lowest setting 25khz? I have attached some pics of the controller.113071130811309113101131111312113131131 4
Jonathan
18-01-2014, 08:58 PM
The kernel speed is set at the lowest setting 25khz? I have attached some pics of the controller.
320 step/mm * 2000 mm/min = 640,000 step/min
640,000/60=10.67kHz
10.67kHz is less than 25kHz ... so that shouldn't be a problem.
itsmillertime
18-01-2014, 09:08 PM
Thanks Jonathon for showing the workings of that, makes it a load easier to understand the reasons behind the settings. cheers andy
JAZZCNC
18-01-2014, 10:30 PM
320 step/mm * 2000 mm/min = 640,000 step/min
640,000/60=10.67kHz
10.67kHz is less than 25kHz ... so that shouldn't be a problem.
Jonathan I was more concerned that the Kernal speed was set too high which can cause strange happenings like this.!!. . . Long shot but it happens.
Andy.
First are you 100% sure there's no mechanical issues.? No binding etc. It won't take much stickage at these speeds with such low powered motors/drives to rob torque.
If not then next try cutting the same part but in air without spindle running. This will eliminate VFD/Spindle interference.
After that then carefully inspect wires at the motor connectors and at the BOB/drives for any lose connections.
The drives are better than some of these machines but still cheap low quality drives. That said they should do this job thou with just 24v you can't expect too much.
Again I'm clutching straws here but you could try setting the micro stepping to 400 on drives and see if it changes anything. Just do the problem Axis first to see if it alters any thing.
You'll need to go into Motor tuning and set the Steps Per to 80 and retune the motors. You'll see can get much higher velocity on that axis now but I wouldn't anyhigher than you have it now.
Failing any of this working and machine being mechanicly sound then scrap it all and get this MX3660 - 3-Axis DSP Based Digital Stepper Drive Max 60 VDC / 6.0A (http://www.zappautomation.co.uk/en/digital-stepper-drivers/979-mx3660-3-axis-dsp-based-digital-stepper-drive-max-60-vdc-60a.html) along with 48V PSU.
It will transform the machine and I'm pretty sure it will fit neatly into your existing box with only slight modification. It comes complete with Digital drives, built in BOB and Spindle speed control.
Rated upto 60V 6A and will easily run motors at 50-55Vdc with a unregulated PSU so if you want to upgrade motors to say 3nm at a later date then you can. . . . .Or take it with you to another bigger machine.!!
george uk
18-01-2014, 11:17 PM
Hi
My friend had a similar problem a few years ago, after a lot of messing about, we found a few important but simple things helped out.
1. Check your parallel cable, and both connections, ( someone on here already mentioned it ),
2. Try not to cross any of the cables for the axis, especially with the spindle cable and keep them away from estop cables. but try rout them away from each other, or at least insulate them a bit.
The version of Mach your using, did it come with the machine
3. Some of the Chinese suppliers send out hacked versions of mach ( can not remember the build number ), and its full of bugs,
2 years ago, when dealing with a problem on my friends machine, the hacked version of mach was buggy on the axis drives and spindle speed setup for slow spindle rates.
edit. just looked at your wireing again, you have 3 axis power cables running very close to your other wires, If your Y axis driver is the one on the right side, i would route them power cables elsware, or at least dont let them get close.
itsmillertime
18-01-2014, 11:24 PM
Cheers Jazz,
You have been pretty thorough with your suggestions and I do appreciate you taking time out to give your advice. I will go over the machine tomorrow. take off the suspect axis stepper motor and move the gantry by hand to see if it is binding / any resistance present.
As for possible interference from the spindle? I did think of this before. So I've ran g code with the spindle powered off/and in the air and its still stalled. Its very random when it happens.. but it happens frequently enough to prevent me working on anything expensive or intricate. Possibly happens once on every other job. But its enough to ruin whatever I'm doing!
I will physically swap over the x and y driver boards and see if the fault does indeed transpose to the x axis as I suspect. I can barely live with the one problem. But with the Z axis losing its zero. Its a step too far!! boom tish ;-)
Going to also swap out my parallel desktop cable for another one I have and change/ ensure my desktop is in standard PC mode not acpi..
Then I will try the changing steps as you suggest and if that doesn't work after inspecting all cables etc?
I will replace/upgrade all stepper cables and shield the vfd cables. Earthing all of the screens.
Still not working? I will be delighted in swapping out the controller with the one you suggest.
Having these issues are a great way to get to know my way about the machine so I view it as a learning exercise in getting to understand how it all works.
Will let you know how it goes tomorrow. wish me luck!
thanks again for all the help
andy
itsmillertime
18-01-2014, 11:32 PM
thanks George for your reply too. only noticed your reply after answering jazz so we just cross posted!
Yes the Mach that I have was supplied on a CD and I'm sure its been unlocked as it never asked me for a key. not sure of the version I will have to look that up tomorrow. Going to get a legit version of Mach but need to try and get this machine running first( if possible!) as this could really break my budget the way this is going!
thanks for the cable suggestions I'm going to give that a shot tomorrow.
will let you know if I find anything!
thanks andy
george uk
19-01-2014, 12:02 AM
looking again at your pictures, i would definably suggested routing the wires away from each other, especially the power cables away from the data cables. I would also check that anything supposed to be earthed to the case, is firm
I think mach3 comes in a trial version from there site, ( limited to 500 lines i think ) If your only running at 25kh, the hacked version might not affect you that much, in fact, it was only the spindle controll that we found buggy. Because of all the other things you have tried, its probably interference with the wires, or the driver board ( cheap to replace ) .
Mach3/4 well worth buying a licence for, the support and help you get on there is like the help you get on here, saves you hours of reading and headscratching
JAZZCNC
19-01-2014, 01:01 AM
looking again at your pictures, i would definably suggested routing the wires away from each other, especially the power cables away from the data cables. I would also check that anything supposed to be earthed to the case, is firm
It won't hurt doing this but I would be very surprised if this is anything to do with it has he's only running 24vdc. Only the 240V mains voltage will be worth routing signal wires away from has 24Vdc won't produce much noise.
When it's noise it's often a very slow process of missed steps or the complete opposite and it's tripping drives or E-stops etc. If the VFD isn't affecting it then wires being a little close to each other won't be.!
The Parallel Cable is always worth swapping out for another when having trouble and it will probably been me who you've seen suggest before George has i've seen it many times. Thou I don't think it's that in this case other wise would have siggested it.
Andy george is correct about the Hacked version of Mach3 and now knowing this I wouldn't do anything else untill you have un-installed it and replaced with the genuine and currant lock down version.
To be honest I'm still thinking it's a Mechanical issue with binding that's robbing the low amount of torque that's left at the higher feed rates. These motors are 4 wire motors so can run out of torque very quickly when rpm rises and with only 24V then there won't be very much torque to start with.!
itsmillertime
19-01-2014, 11:58 PM
Ok guys,
I spent a few hours this afternoon stripping down bits and taking the bed off and removing the stepper motors from the router trying to look for any mechanical binding etc along the Y - the gantry driving axis.
It doesn't sound particularly smooth but I dont have much to compare it to. The gantry moves quite freely by turning the leadscrew by hand. I can freely push the gantry across the length of the machine and back with a gentle concerted push by hand. It's definitely less resistive in the middle section and approx the last 4" at either end the resistance increases by about an extra 15% and the noise from the ballscrew is slightly more pronounced and it's just a little more 'jerky' towards the last 4-6 inches of travel.
I checked the travel and the resistance of the x axis and this is noticeably smoother to push but I think thats because it's lighter and better supported on the 2 bars and less to travel. It does make a similar noise to the Y axis it's just less 'clanky' and smoother.
I moved the gantry right up to the ends and looked for gaps/ being square with the frame. At one end of travel (near the stepper motor) it's pretty much bang on. But at the other end of of the router I measured the gap at approx 2mm in one corner with the other corner at 0mm flush with the gantry. 2mm is quite a noticeable gap across the end. I have attached a photo.
So what's the best way to work out if its true? Could this be causing some resistance? I guess measure across rails at one end and do the same at the other? I haven't removed the lead screw or anything yet as I didn't want to really disturb anything else until I asked here!!
Is there any easy way of doing this, maybe loosen up the rails and run the gantry from the one end to the other? Then tighten up the rails? I checked all the allen screws and all are tight.
I may have found a possible cause of the motor stalling. One of the grub screws on the Y axis coupler didnt feel very tight (possibly loose) and maybe causing the coupler to slip when the load got too much? Not 100% certain that is it. But it's the very same axis that has had the problems.
I guess what I'm asking is, is the noise my machine makes when moved by hand (pushed) normal? Should I expect any resistance at extremes of travel. And whats the best way of making sure its square/ true and not a bent ballscrew.
Where should I go from here please guys?
While I have the bed up and I'm looking for biding/mechanical issues I want to rule them out I guess. Also should there be any oil of grease on the ballscrew? No nipple or any obvious lube in place.
http://youtu.be/5mxulmQ8Ivo
Sorry that the video is 3 mins long but it shows the freedom of movement and sound of my y and x axis being moved by hand.
Below is a photo of the gantry with the gap approx 0mm/ flush at one side and 2mm at the other. I took measurements to show the difference in the gap.1132711328
11326
Thanks again for all your advice. Just hoping to rule out any big mechanical issues before going for drivers etc..!
andy
JAZZCNC
20-01-2014, 12:56 AM
Andy wouldn't worry about the 2mm gap it's just the frame thats out of square which doesn't mean a lot. More important that the x axis gantry is square to the Y axis rails and the y axis rails are parallel to each other.
The Y axis doesn't look to be binding too much but it does look and sound very dry so get some grease in the ballnut or at least bit of light lube oil on the screws.! . . . If the coupling was loose then it's 90% chance you've found your problem.
One thing I didn't like the sound of was the rattling when you grabbed the end of the ballscrew. Check if the ballscrew is floating back n forth by grabbing the end, there should be no movement.
If this is ok then I'd just grease and lube everything and put back together. If the ballscrews don't have a small flat on the end then file one on to give the grub screw a flat surface to grip on then Loctite the coupling grub screws.
richie00boy
20-01-2014, 10:54 PM
I had a bit of an issue with getting tighter at one end. I loosened the stepper bolts and coupling screws and bearing block and found the tightest spot then jiggled all the above to try and get it into the best position to bind the least. Seems to have done the job. I also had a slightly less tight coupling screw - wonder if it's a symptom of binding?
itsmillertime
13-02-2014, 11:10 PM
richie - thanks mate for your reply. It could be something like that causing a slight bind but I was unable to replicate any real significant difference in 'feel' during pushing the axis' by hand.
Sooooo, what did I do next? Well after getting really fed up with it all. I decided to take the advice of you guys especially jazz and his recommendations and I went shopping...
I bought MX3660 - 3-Axis DSP Based Digital Stepper Drive Max 60 VDC / 6.0A
SPS487. 48V unregulated power supply
3x SY60STH86-3008B Nema 23 Stepper motors
I also bought the screened cable recommended in another thread and rewired all 3 motors back to the control box. I’ve earthed all cables at the box end and replaced all components. It all fits nicely in my blue box too.
After all of this I have fired her up and she is running perfectly. No more stalling, missed steps, or dodgy inconsistent cuts!!!
Just want to say thanks to all you guys and to Jazz for his kit recommendations. So much smoother, quieter and working well! Now I finally have a machine I am happy to work with at last.
cheers guys. :-)
Got a few questions to ask about my setup to perfect it. But will ask them later. just wanted to let you guys know how it turned out!
thanks andy
JAZZCNC
13-02-2014, 11:41 PM
Great news and happy your sorted. . :yahoo:
Can't beat good electronics they make a world of differance and don't workout that much more expensive in the grand scheme of things when you consider you only spend the money wounce and they work perfectly so No spending weeks pulling hair.!!
itsmillertime
13-02-2014, 11:49 PM
lol ain't that the truth. Sat watching nervously while it did its first test cut after being rebuilt. Phew that was nerve wracking!
Glad I listened to the advice regards new electronics. The bigger motors and the electronics make a HUGE difference with the way its running now.Looking forward to actually making things rather than fixing them lol. Thanks for all the time you guys took for your advice.
andy | {} |
# American Institute of Mathematical Sciences
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July 2018, 14(3): 931-951. doi: 10.3934/jimo.2017083
## Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts
1 School of business administration, Zhongnan university of economics and law, 182 Nanhu Avenue, East Lake High-tech Development Zone, Wuhan 430073, China 2 OASIS -ENIT, University of Tunis El Manar, BP 37, LE BELVEDERE 1002 TUNIS, Tunisia 3 LGI, Centrale Supelec, Paris Saclay University, Grande Voie des Vignes, 92295 CHATNAY-MALABRY CEDEX, France
* Corresponding author: Shouyu Ma
Received March 2016 Revised August 2017 Published September 2017
Fund Project: The first author is supported by the China Scholarship Council.
Existing papers on the Newsboy Problem that deal with price dependent demand and multiple discounts often analyze those two problems separately. This paper considers a setting where price dependence and multiple discounts are observed simultaneously, as is the case of the apparel industry. Henceforth, we analyze the optimal order quantity, initial selling price and discount scheme in the News-Vendor Problem context. The term of discount scheme is often used to specify the number of discounts as well as the discount percentages. We present a solution procedure of the problem with general demand distributions and two types of price-dependent demand: additive case and multiplicative case. We provide interesting insights based on a numerical study. An approximation method is proposed which confirms our numerical results.
Citation: Shouyu Ma, Zied Jemai, Evren Sahin, Yves Dallery. Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts. Journal of Industrial & Management Optimization, 2018, 14 (3) : 931-951. doi: 10.3934/jimo.2017083
##### References:
show all references
##### References:
sequence of events for a selling season
Expected profit $E(\pi(Q^{*}))$, as a function of the discount number, for normally distributed demand
Expected profit $E(\pi(Q^{*}))$, as a function of the intial price
discount schemes
The value of ($E(\pi(Q^{*}))-E_\sigma$), as a function of discount number, with normal distribution
The value of ($E(\pi(Q^{*}))-E_\sigma$), as a function of discount number, with uniform distribution
Expected profit as function of discount number n
Discount percentages at $v_0=6$ for different schemes
Expected profit as function of initial price
Comparison with the work of Khouja(1995, 2000)
parameter price-demand relation demand distribution discount prices [6] fixed general known [8] additive uniform and normal linear our paper additive and multiplicative general all types
parameter price-demand relation demand distribution discount prices [6] fixed general known [8] additive uniform and normal linear our paper additive and multiplicative general all types
The optimal order initial price, order quantity and expected profit for different combinations of n, b, $\sigma_0$ for normally distributed demand
test n b $\sigma_0$ $v^*_{0}$ $Q^*$ $E(\pi(Q^*, v_0^*))$ 1 4 6 2 10.20 55.8 249.0 2 4 6 4 10.18 55.9 246.9 3 4 6 6 10.24 56.1 245.0 4 4 6 8 10.23 56.9 243.4 5 4 8 2 8.54 50.4 153.3 6 4 8 4 8.58 49.8 151.6 7 4 8 6 8.59 49.6 150.2 8 4 8 8 8.57 50.0 148.6 9 4 10 2 6.60 46.3 95.0 10 4 10 4 6.64 44.5 94.3 11 4 10 6 6.64 44.3 93.6 12 4 10 8 6.61 44.6 92.2 13 5 6 2 11.41 56.6 263.9 14 5 6 4 11.51 56.4 262.0 15 5 6 6 11.47 56.7 260.2 16 5 6 8 11.54 57.4 258.2 17 5 8 2 8.81 51.9 159.8 18 5 8 4 8.71 50.9 158.6 19 5 8 6 8.75 50.8 157.4 20 5 8 8 8.81 51.2 155.8 21 5 10 2 7.09 45.7 100.1 22 5 10 4 7.06 45.0 99.8 23 5 10 6 7.01 45.1 98.8 24 5 10 8 7.09 45.3 97.6 25 6 6 2 11.90 57.6 271.5 26 6 6 4 11.90 57.2 270.0 27 6 6 6 11.88 57.5 268.3 28 6 6 8 12.0 58.2 266.3 29 6 8 2 8.91 52.6 164.5 30 6 8 4 8.91 51.5 163.7 31 6 8 6 8.94 51.6 162.6 32 6 8 8 8.91 52.1 161.0 33 6 10 2 7.16 44.8 103.8 34 6 10 4 7.18 45.7 103.3 35 6 10 6 7.19 45.8 102.3 36 6 10 8 7.18 46.1 100.0
test n b $\sigma_0$ $v^*_{0}$ $Q^*$ $E(\pi(Q^*, v_0^*))$ 1 4 6 2 10.20 55.8 249.0 2 4 6 4 10.18 55.9 246.9 3 4 6 6 10.24 56.1 245.0 4 4 6 8 10.23 56.9 243.4 5 4 8 2 8.54 50.4 153.3 6 4 8 4 8.58 49.8 151.6 7 4 8 6 8.59 49.6 150.2 8 4 8 8 8.57 50.0 148.6 9 4 10 2 6.60 46.3 95.0 10 4 10 4 6.64 44.5 94.3 11 4 10 6 6.64 44.3 93.6 12 4 10 8 6.61 44.6 92.2 13 5 6 2 11.41 56.6 263.9 14 5 6 4 11.51 56.4 262.0 15 5 6 6 11.47 56.7 260.2 16 5 6 8 11.54 57.4 258.2 17 5 8 2 8.81 51.9 159.8 18 5 8 4 8.71 50.9 158.6 19 5 8 6 8.75 50.8 157.4 20 5 8 8 8.81 51.2 155.8 21 5 10 2 7.09 45.7 100.1 22 5 10 4 7.06 45.0 99.8 23 5 10 6 7.01 45.1 98.8 24 5 10 8 7.09 45.3 97.6 25 6 6 2 11.90 57.6 271.5 26 6 6 4 11.90 57.2 270.0 27 6 6 6 11.88 57.5 268.3 28 6 6 8 12.0 58.2 266.3 29 6 8 2 8.91 52.6 164.5 30 6 8 4 8.91 51.5 163.7 31 6 8 6 8.94 51.6 162.6 32 6 8 8 8.91 52.1 161.0 33 6 10 2 7.16 44.8 103.8 34 6 10 4 7.18 45.7 103.3 35 6 10 6 7.19 45.8 102.3 36 6 10 8 7.18 46.1 100.0
Optimal epected profit for different discount schemes
scheme coe optimal expected profit linear 0 158.5 1 -0.03 144.9 2 -0.02 151.1 3 -0.01 155.8 4 0.01 159.1 5 0.02 157.8 6 0.03 153.4
scheme coe optimal expected profit linear 0 158.5 1 -0.03 144.9 2 -0.02 151.1 3 -0.01 155.8 4 0.01 159.1 5 0.02 157.8 6 0.03 153.4
Expected profit function for uniform and normal distributions
Distribution $U[\mu_0-\sigma_0, \mu_0+\sigma_0]$ $N(\mu_0, \sigma_0)$ Condition for $\epsilon=0$ $\forall j, \sigma_0\leq \frac{\mu_{j}-\mu_{j-1}}{2}$ $\forall j, \sigma_0\leq \frac{\mu_{j}-\mu_{j-1}}{4}$ $E(\pi(Q^*))$ $E_\sigma+E_v$ $E_\sigma+E_v$ $E(\pi(Q^*))$ for linear case equation 4.11 equation 4.11 $E_v$ equation 4.8 equation 4.8 $E_\sigma$ equation 4.9 equation 4.10
Distribution $U[\mu_0-\sigma_0, \mu_0+\sigma_0]$ $N(\mu_0, \sigma_0)$ Condition for $\epsilon=0$ $\forall j, \sigma_0\leq \frac{\mu_{j}-\mu_{j-1}}{2}$ $\forall j, \sigma_0\leq \frac{\mu_{j}-\mu_{j-1}}{4}$ $E(\pi(Q^*))$ $E_\sigma+E_v$ $E_\sigma+E_v$ $E(\pi(Q^*))$ for linear case equation 4.11 equation 4.11 $E_v$ equation 4.8 equation 4.8 $E_\sigma$ equation 4.9 equation 4.10
Expected profit function for uniform and normal distributions
Distribution $U[\mu_0-\sigma_0, \mu_0+\sigma_0]$ $N(\mu_0, \sigma_0)$ Condition that $\epsilon=0$ $\forall j, \sigma_0\leq\frac{\mu_{j}-\mu_{j-1}}{2}$ $\forall j, \sigma_0\leq\frac{\mu_{j}-\mu_{j-1}}{4}$ $E(\pi(Q^*))$ $E_\sigma+E_v$ $E_\sigma+E_v$ Exponential case equation 5.8 equation 5.8 $E_v$ equation 5.5 equation 5.5 $E_\sigma$ equation 5.6 equation 5.7
Distribution $U[\mu_0-\sigma_0, \mu_0+\sigma_0]$ $N(\mu_0, \sigma_0)$ Condition that $\epsilon=0$ $\forall j, \sigma_0\leq\frac{\mu_{j}-\mu_{j-1}}{2}$ $\forall j, \sigma_0\leq\frac{\mu_{j}-\mu_{j-1}}{4}$ $E(\pi(Q^*))$ $E_\sigma+E_v$ $E_\sigma+E_v$ Exponential case equation 5.8 equation 5.8 $E_v$ equation 5.5 equation 5.5 $E_\sigma$ equation 5.6 equation 5.7
[1] Guiyang Zhu. Optimal pricing and ordering policy for defective items under temporary price reduction with inspection errors and price sensitive demand. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021060 [2] Gaurav Nagpal, Udayan Chanda, Nitant Upasani. Inventory replenishment policies for two successive generations price-sensitive technology products. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021036 [3] Qiang Lin, Yang Xiao, Jingju Zheng. Selecting the supply chain financing mode under price-sensitive demand: Confirmed warehouse financing vs. trade credit. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2031-2049. doi: 10.3934/jimo.2020057 [4] Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 [5] Fabio Camilli, Serikbolsyn Duisembay, Qing Tang. Approximation of an optimal control problem for the time-fractional Fokker-Planck equation. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021013 [6] Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021014 [7] Haripriya Barman, Magfura Pervin, Sankar Kumar Roy, Gerhard-Wilhelm Weber. Back-ordered inventory model with inflation in a cloudy-fuzzy environment. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1913-1941. doi: 10.3934/jimo.2020052 [8] Caichun Chai, Tiaojun Xiao, Zhangwei Feng. Evolution of revenue preference for competing firms with nonlinear inverse demand. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021071 [9] Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021035 [10] Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups. Electronic Research Archive, , () : -. doi: 10.3934/era.2021022 [11] Chong Wang, Xu Chen. Fresh produce price-setting newsvendor with bidirectional option contracts. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021052 [12] Claudianor O. Alves, Giovany M. Figueiredo, Riccardo Molle. Multiple positive bound state solutions for a critical Choquard equation. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021061 [13] Kai Cai, Guangyue Han. An optimization approach to the Langberg-Médard multiple unicast conjecture. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021001 [14] Shoufeng Ji, Jinhuan Tang, Minghe Sun, Rongjuan Luo. Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021051 [15] Ru Li, Guolin Yu. Strict efficiency of a multi-product supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2203-2215. doi: 10.3934/jimo.2020065 [16] Xue Qiao, Zheng Wang, Haoxun Chen. Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021079 [17] Anastasiia Panchuk, Frank Westerhoff. Speculative behavior and chaotic asset price dynamics: On the emergence of a bandcount accretion bifurcation structure. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021117 [18] Guanwei Chen, Martin Schechter. Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021124 [19] Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313 [20] Tobias Geiger, Daniel Wachsmuth, Gerd Wachsmuth. Optimal control of ODEs with state suprema. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021012
2019 Impact Factor: 1.366 | {} |
## Tuesday, December 15, 2009
### Nuts and bolts (15/12/09)
Some interesting items I came across recently worth a look at:
Interstellar Propulsion Research: Realistic Possibilities and Idealistic Dreams by Les Johnson gives an introductory rundown on the current status of possible interstellar missions and propulsion options. Apart from the mentioned warp drive (update: read this and this), all of the options are based on sound physics however all of them have severe technical and engineering difficulties to overcome if they are going to happen one day. Ironically getting the hardware required into orbit for these big spacecraft could be the biggest hurdle to overcome as using chemical rockets is expensive. The above options are based on our current understanding of Physics and we still have a lot to learn how nature really works.
The Final Frontier: The Science of Star Trek, interview with Lawrence Krauss. I read the first version of his book years ago and found it quite stimulating reading should interest all you Star Trek fans out there. I saw the world premiere opening of the movie at the Sydney Opera House and got a few autographs myself from the (new) Spock, Sulu and JJ Abrams, I liked the movie.
A Blueprint for a Quantum Propulsion Machine, here's also a review from Paul Gilster on this paper by Alexander Feigel. It remains to be seen if these so called "magneto-electric particles" do change the momentum of the quantum vacuum and thereby provide a means to change the orientation of a spacecraft without using propellant although many do this already using gyroscopes for eg however the physics if sound would be very interesting as this would provide another avenue to study the Quantum Vacuum. Another paper on this worth reading is here.
Been busy working on Sydney Harbour most days day and night as it is the busy season here. Some recent photos: Nice sailing boat in Farm Cove and checkout this sailing boat skipper going under the Anzac bridge, got his air draft right! Big tow job Bradley's Head outbound (click on photos for larger version).
## Monday, November 30, 2009
### Poem mystery author
Although I can't say I'm a big fan of poetry, I do like a very few which deal with the stars, our Universe and (big surprise here) Man's quest to venture to the stars. When I was a small boy and pointed my telescope to Saturn for the first time, this was one of those moments you never forget for the rest of your life. After countless nights behind the eyepiece (it's quite addictive!), one eventually starts to ponder on thoughts on interstellar travel and watching StarTrek makes it worse ;-) There is one poem which I can't seem to find out who wrote it. I've posted the question to poem newsgroups and contacted various knowledgeable people but to no avail. It's engraved on the back on one of my brass compasses (Dollond London) which I got from a flea market a while ago next the Maritime Museum. Do you know who wrote this poem so I can give this mystery author proper credit?
One of the reasons why I bought this compass was because I liked this poem very much, if I didn't know better my first thoughts were either a Physicist wrote it or an author with deep thoughts on Nature. It talks about time, "a continuum moves and swirls..." (the vacuum?), the celestial sphere and life. Talk about big topics! The vacuum is central to Physics and today is still "beyond my inner sight and imagination" ie Physicists still don't understand it at the quantum level although they are getting better. Actually understanding the vacuum has been central to Physics most of our history, see this very interesting painting.
Some of you who work on Sydney Harbour may have noticed that Thor Gitta was docked in White Bay for quite a while (over a month), the mystery why she was there for all this time has been solved: she was waiting for this barge to unload her big load of cable:
## Tuesday, November 17, 2009
### Cosmology, The Big Bang and Entropy
I went to Sean Carroll's talk yesterday at Sydney University. As many of you are aware, Sean is one of the bloggers on Cosmic Variance and is touring Australia for his talks. He also has an upcoming book titled From Here to Eternity: The Quest for the Ultimate Theory of Time.
Sean talked about all the big ideas that face Cosmologists these days and in particular Entropy and its relation to the evolution of our Universe starting from a state of low entropy / high order progressing towards a state of high entropy / low order. I didn't like his interpretation of time (particularly the "arrow of time") as mentioned in my previous post and as for the state of the Universe, this is ambiguous because we cannot observe the Universe from the outside hence there is no entropy for the Universe either.
Cosmologists have a fairly good idea what the state of the Universe was 1 second after the Big Bang however at "t = 0" (time cannot be defined here as there is no matter at this stage hence no clocks), no one knows as General Relativity breaks down however before the Big Bang? Sean speculated on an idea that our Universe may have begun from a single quantum fluctuation from the inherent energy of the vacuum, ie we live in a baby Universe an offshoot from another Universe. There was quite a good turnup and the lecture theatre was pretty full, all in all enjoyed the talk.
Still experimenting with $\LaTeX$ in Blogger using this script. Testing...
$\tan(2\theta) = {2\tan\theta \over 1-\tan^2\theta}$
$\int \csc^2x\, dx = -\cot x+ C.$
$\ P_{r-j}=\begin{cases} 0& \text{if r-j is odd},\\ r!\,(-1)^{(r-j)/2}& \text{if r-j is even}. \end{cases}$
$\qquad \lim_{\alpha\to \infty} {\sin\alpha \over \alpha} = 0$
$\root n \of {\prod_{i=1}^n X_i} \leq {1 \over n} \sum_{i=1}^n$
$\ \cfrac{1}{\sqrt{2}+\cfrac{1}{\sqrt{2}+\cfrac{1}{\sqrt{2}+\dotsb }}}$
$\ \nabla \cdot \mathbf{D} = \rho_f$
$\ \nabla \cdot \mathbf{B} = 0$
$\ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$
$\ \nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t }$
$\ \boxed{m &= \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}}$
## Sunday, November 15, 2009
### Review: LyX and viXra
Been busy the last few days between work learning about LaTeX. Widely used by the academic and research community to write up high quality documents, scientific papers, books etc and especially useful for writting out mathematical formulae with their many special formatting requirements. The text it produces is beautiful.
I tested out LyX, which is a free Windows based Graphical User Interface (GUI) document processor for LaTeX and automatically will download MiKTeX during installation which is also required for your computer. Seems to work very well on my small laptop. Once you write up your document, you can preview it with Lyx's DVI previewer. Once you're happy with it, export the document in Adobe PDF format and you're done. LaTeX has many formatting tags if you look at the source code and although Lyx has also many GUI buttons, it's useful to sometimes type in the code by hand. There's also an excellent beginer's guide to LaTeX which I found handy called A Gentle Introduction to TEX. Great thing is, MiKTeX and LyX are both free for download! Google Documents also have the ability to insert equations and their online chart rendering feature has LaTeX command options (see links for the following):
A few days ago I also found out about the new viXra.org e-print archive. Unlike arXiv.org, this is open to anyone who wants to publish a paper and you don't need a "sponsor" (which is required by arXiv). This is great for people who aren't affililated with a research institution, university etc or can't find someone to endorse their paper. There are many Physics papers out there that are highly speculative and many academics aren't willing to be affiliated with a paper that at first appearances could be junk. The only problem is this doesn't help scientific progress. Their Why page explains all this in more detail. Because this is open to anyone, many junk papers will be found there however there are some interesting ones as well worth a read, all in all think viXra is a great idea. Worth keeping an eye on.
Attached photos: Students practicing survival at sea skills, liferaft deployment etc at the Qantas training pool, Sydney Airport.
## Wednesday, November 4, 2009
### What exactly is time?
I came across today the following paper reviewed on the arXiv Blog and also on arXiv: Can the Arrow of Time be understood from Quantum Cosmology?
The question itself used as the title is flawed. There is no such thing as the "Arrow of Time" in Nature and after reading the paper suspect this will lead to another Not Even Wrong theory. This is a common misunderstanding in Physics so what exactly is time? It's about time we have a look. There's a wiki article however I prefer the explanation on p40 of the first volume of Motion Mountain:
"Time is what we read from a clock."
That's it! Your first intuition is correct ie you check your clock to find out what time it is. Note that clocks can be the Moon, the Sun, sundials, atomic clocks, Harrison's H1 clock etc.
Schiller goes on:
"Time is a concept introduced specially to describe the flow of events around us; it does not itself flow, it describes flow. Time does not advance. Time is neither linear nor cyclic. The idea that time flows is as hindering to understanding nature as is the idea that mirrors Page 71 exchange right and left. The misleading use of the expression ‘flow of time’, propagated first by some flawed Ref. 36 Greek thinkers and then again by Newton, continues. Aristotle (384/3–322 bce), careful to think logically, pointed out its misconception, and many did so after him. Nevertheless, expressions such as ‘time reversal’, the ‘irreversibility of time’, and the much-abused ‘time’s arrow’ are still common. Just read a popular science magazine chosen at random.
The fact is: time cannot be reversed, only motion can, or more precisely, only velocities of objects; time has no arrow, only motion has; it is not the flow of time that humans are unable to stop, but the motion of all the objects in nature. Incredibly, there are even books written by respected physicists that study different types of ‘time’s arrows’ and compare them with each other. Predictably, no tangible or new result is extracted. Time does not flow."
There you have it, if you were thinking of becoming a time traveller with exotic machinery don't waste your time. However time machines are available for purchase if you want one ;-), they only allow you to see back in time though and we are constrained to seeing the observable Universe.
Because light from the Sun for eg takes just over 8 minutes to reach us here on Earth, astronomical objects you see in the sky are essentially as they were when the light left them and because of the vastness of space and the speed of light, it takes time for the light from these objects to reach us. For eg light from our neighbour the Andromeda Galaxy takes 2.5 million years to reach us so if you look at it with a telescope (or with binoculars), you are seeing the galaxy as it was 2.5 million years ago. The bigger the telescope, the further you can see back:
At time t = 0, current Physics cannot explain what happened as the Physics cube mentioned in the previous post isn't complete. And before that? Roger Penrose gave a good talk in 2007 at Darling Harbour titled: What happened before the Big Bang?
Photos: Claudia I coming into Blackwattle Bay the other day delivering more concrete supplies.
## Thursday, October 29, 2009
### Propulsion Physics and the future ahead
I recently stumbled on a 2004 presentation by Marc Millis while doing some searches and is well put together. Unfortunetly NASA's former Breakthrough Propulsion Physics (BPP) Project (wiki article here) funding got cancelled a few years ago and today I read in Paul Gilster's Centauri Dreams outlining a report which recommends that NASA reinstate the (also cancelled!) NASA Institute for Advanced Concepts in one form or another, no doubt there are many reasons why they both got cancelled (which I think cancelling BPP was a big mistake regardless of NASA's new lunar or otherwise objectives considering the already minimal funding it received and the great job Marc and others put into it) however unfortunetly this means today that there are no substantially funded organisations dedicated to organising and researching advanced concepts or potential physics breakthroughs that could lead to making interstellar travel practical, economical and a viable proposition so we wait and see what mainstream Physics and individual researchers come up next.
Last night I watched the awesome Ares I-X launch and this is only the little puppy version of the big one they'll be using to launch crew to the Moon (however I'm reading in today's paper that the Moon program funding, yes you guessed could be cancelled!). No doubt money's tight for everyone at the moment but when I see how public money is wasted these days on other things with questional benefits to the public, I wonder...
I've outlined in a previous post why it is important for humans to settle on another planet (preferably on another Earth-like planet which means an interstellar journey to other star systems) and rockets just won't do the job (and are expensive, the Ares launch cost \$445m according to the today's paper article).
So it's back to Propulsion Physics and first principles (or revised first principles?). There's no need for me to reiterate on Marc's presentation but the most important points are on p8 and p34:
1. Mass: Discover new propulsion methods that eliminate (or dramatically reduce) the need for propellant.
2. Speed: Discover how to circumvent existing limits (light-speed) to dramatically reduce transit times.
3. Energy: Discover new energy methods to power these propulsion devices.
"These goals are THE breakthroughs needed to conquer the presently impossible ambition of human interstellar exploration."
I'll talk about the Physics of these 3 points in a future post, what striked me in this presentation and what I wanted to mention in this post was on the last page:
"Science community does not address propulsion opportunities, but instead seeks a Theory of Everything. A propulsion focus increases options."
This is a good point, rephrased the Science community seeks to complete the Physics cube below:
Top right corner specifically. This is good as a Relativistic Quantum Theory of Gravity could lead to BPP and answer many unknowns in Physics and the Universe. However only seeking a unified theory of Physics isn't a good approach in my view. String Theorists have spent the last 25 years searching for their unified theory with so far a dead end (Peter Woit's book Not Even Wrong is a good read on this) and makes no new predictions in Physics that are verifiable and testable with the Large Hadron Collider. Even Einstein in his later years searched a unified theory of Physics to no avail. As pointed out earlier the Propulsion focus shouldn't be left out in the mainstream Physics research community. I'm not saying that all research into String Theories for eg should be abandoned (although myself I think it's a dead end) however there needs to be a more balanced focus to propulsion in mainstream Physics research, sometimes approaching a problem from a different angle can lead to productive results and in my view this is why cancelling the BPP Program at NASA was a huge mistake (where they should be leading the world by example). Practical and economical Interstellar flight may turn out to be impossible however while seeking solutions (as history shows in Physics) sometimes people stumble on other unexpected Physics.
What is the current state of affairs? As the BPP site mentions, "No breakthroughs appear imminent." There are many theories floating around however, either the theories haven't stood up to experiment or are inconclusive or there is no funding to test the theories put forth. Out of all the "crackpot theories" submitted each year, if one turns out to be correct, then this could change everything. There needs to be a funded program (like the BPP Project) that investigates and manages all this. For those who wish to dig deeper into all this a very good starting point is the following book: Frontiers of Propulsion Science. For those wondering checkout: What would a relativistic interstellar traveller see? I'll finish this post with a paragraph I like by Walter Drösher and Jochem Hauser in their paper (although I got a bit lost in their Extended Heim Theory and don't quite understand it):
## Wednesday, October 28, 2009
### What cats talk about at the Fish Markets
There are quite a lot of cats at the wharf where the boats are kept and wondered what they sometimes talk about, now I know! :-))
## Tuesday, October 27, 2009
### Who said the sky's the limit and is Physics wrong?
(23/10/09)
I was walking in the city earlier today and saw these ad billboards in the street:
Normally I wouldn't take a second look (I don't even have a credit card myself, think they're a waste of money) but saw a rocket in the stars so had to study it in detail! :-)) These ads actually give sound advice for anyone into Physics&Astronomy! When I looked at the first ad "Who said the sky's the limit?", immediate thoughts were, well Nature says what the limits are and the maximum speed that anything can travel in our Universe is the speed of light, C = 300,000Km/s.This applies not only to light but also matter, radio waves, information transfer etc. Protons, electrons etc are routinely accelerated to 0.99C at particle accelerators but never go over the speed limit.
Einstein's Special Theory of Relativity 101: "The speed of light in vacuum is always C, independent of the motion of thesource or of the observer".
This at first seems counter intuitive after all if you see a car moving at 100Km/h on the freeway then light leaving their headlights should be travelling at 100Km/h + C right? Wrong, light still travels at C! (Don't worry about the air makes very little difference you could do this in space for eg). This makes perfect sense if you think of everything you see around you immersed in the vacuum and this vacuum (which is a complicated "quantum fluctuating soup") doesn't allow light to travel faster then C. Strange things happen as you travel 1/3C or faster (time dilation etc...)
Second ad basically was telling me that although exploring the Universe with telescopes etc is good, get off your butts and build some ships to do some serious exploring beyond the solar system! ;-) Given the distances involved in our Galaxy, the speed limit (C) imposed on us by the vacuum is problematic. Closest star is 4.2 lightyears away for eg however if you're planning your next trip to Alpha Centauri don't despair this isn't the end of the story there are different types of vacuums which are under study... even Roger Penrose (who wrote the masterpiece The Road to Reality) recently mentions that our current theories are "wrong" although some don't agree with all he says it's interesting reading:
http://discovermagazine.com/2009/sep/06-discover-interview-roger-penrose-says-physics-is-wrong-string-theory-quantum-mechanics
Looking forward to some more American Express credit card ads! ;-)
### 50 years of space exploration map
(17/10/09)
Checkout this beautiful map illustrating where our probes have been so far in the solar system:
http://wanderingspace.net/2009/10/50-years-of-space-exploration-map/
There's a zoomable version at:
http://books.nationalgeographic.com/map/map-day/2008/09/18
Very nice. Checkout the scale at the bottom, you'll see Voyager 1 at 10 billion miles (16.5 billion Kms) way past Pluto's orbit heading into interstellar space and this is the first human made object to leave the solar system. It was launched in 1977 and is still transmitting! No batteries onboard, the probe is powered by Radioisotope Thermoelectric Generators (RTGs):
which should generate electricity for the probe till 2025, at this distance from the sun, solar panels don't work. I think if ET finds the onboard golden record they should have a box office sellout at the movies on their planet! ;-)
Attached photo: Suncat getting ready for the Manly fast ferry service.
### Greenwich Longitude turns 125 years old!
(14/10/09)
The Prime Meridian (Longitude 0°) at Greenwich Observatory turned 125 years old! It was born on the 13th October 1884, read about it at:
http://backreaction.blogspot.com/2009/10/125-years-of-greenwich-longitude.html
### Gigagalaxy Zoom project
(12/10/09)
Here's a useful website if you haven't got the time to do some stargazing or just wondered what's at the centre of our galaxy, checkout the recently released:
http://www.gigagalaxyzoom.org/
Has high quality photos of our stellar neighbourhoods and you can zoom in and out from some photos etc. If you don't have the time to visit the centre of our galaxy, here it is:
http://www.eso.org/gallery/v/ESOPIA/Quasars/phot-46-08-fullres.tif.html
Don't get too close though, there's a black hole at the centre ;-)
Attached photo: Steve Irwin leaving Sydney today http://www.seashepherd.org/
### Submarine neutrino communication
(07/10/09)
Here's some interesting reading for you submarine buffs out there:
http://www.technologyreview.com/blog/arxiv/24203/
This Physicist published a paper on how to use neutrinos as a possible effective communication method for submarines underwater to receive messages only. As you know only extra low frequency (ELF-VLF) radio waves can be used for communications by submarines underwater as the higher frequencies get severely attenuated and because of the very low frequency, only very low bit rates can be used. Neutrinos are particles that are created in certain nuclear reactions and radioactive decays, they travel close to the speed of light and interact very rarely with normal matter. Although we don't realise it, right now your body is emitting roughly 400 neutrinos per second due to the naturally occuring radioactive isotopes of Calcium and Potassium in your bones. You are basically neutrino transmitters.
Attached photos:
- Someone who named this barge "Nebula" must be into Astronomy ;-)
- This catamaran had a Compass Adjuster onboard the other morning, heard them call up Harbour Control on Ch13 when they were using transits in the channel. I better finish the course ASAP!
## Monday, October 26, 2009
### Saturn at equinox and the same colour illusion
(04/10/09)
Checkout these interesting Astronomy Picture of the Day photos:
http://antwrp.gsfc.nasa.gov/apod/ap090930.html
http://antwrp.gsfc.nasa.gov/apod/ap091004.html
Goes to show when it comes to Science, appearances can be deceiving, don't always trust your brain ;-) Attached photos: Lithgow today under Anzac bridge (with a nice new Rosman Ferries paint job) and tugboats busy with CSL Pacific a few days ago 6am in White Bay, now this ship definately needs a paint job.
### Internal Combustion Engines MIT OpenCourseWare now online
(24/09/09)
For those interested, MIT has released today free online course notes for internal combustion engines including diesel engines:
http://ocw.mit.edu/OcwWeb/Mechanical-Engineering/2-61Spring-2008/CourseHome/
Click on "Lectures notes" on the sidebar to donwload individual lecture notes or you can download the lot. Last lecture explains hydrogen fuel cells and other techonlogies. Attached today's harbour photos.
### New rocky exoplanet found and first detailed photos of an atom!
(18/09/09)
Lots of good things happening in Physics & Astronomy this week! I read an article in today's MX newspaper but check the articles below for more info:
http://www.eso.org/public/outreach/press-rel/pr-2009/pr-33-09.html
http://www.centauri-dreams.org/?p=9451
The Astronomers did a good job and confirmed that a planet outside our solar system (500 lightyears away) is rocky (not like Jupiter size planets for eg made of gas). Might be a bit too hot for your comfort though so lets hope the Astronomers get lucky and find another Earth-like planet soon because this one is starting to get too crowded ;-) Have a look at these first detailed photos of the electron clouds of carbon atoms:
http://www.insidescience.org/research/first_detailed_photos_of_atoms
The nucleus itself (protons and neutrons) is too small to be seen, between the electrons and the nucleaus itself it's empty space.
Attached photos: ships docked in White Bay last Saturday night. Reef Endeavour has been there for months and Golden Mermaid with the red flashing light on top stank like fertiliser or nitrates, busy discharging into lots of tankers waiting at the wharf.
### Lucas Heights nuclear reactor open day
(13/09/09)
In case you didn't know the Lucas Heights nuclear reactor is having an open day for the public on Saturday 19th September (thanks to Tony for the info):
http://www.ansto.gov.au/
Not sure if I can make it that day but if I'm free I'll be bringingwith me my specially modified geiger counter
:-) I checked again tonight (Sunday) how many ships there are anchored off Newcastle on http://marinetraffic.com/ and I counted over 40 ships!!!?! Talk about busy little Harbour!
### Live Ships AIS Map online
(10/09/09)
Checkout this website:
http://marinetraffic.com/
Shows on the map live AIS information of vessels around the world including Sydney. Checkout how many ships there are outside Newcastle waiting for coal!! You'll see some of the Sydney Ferries for eg also have AIS and you can click on the icons to get a photo of the boat and other info if available. Attached photos: Cronulla Ferries.
### Degaussing range and nuclear powered ships
(07/09/09)
For those who have to sometimes give commentary during the cruise, here's your big chance to impress your passengers by telling them about the degaussing range at Steele Point, Rose Bay where you sometimes see Navy ships hanging around, find out what's going on:
http://www.brighthub.com/engineering/marine/articles/43712.aspx
http://www.brighthub.com/engineering/marine/articles/43714.aspx
Another interesting article on nuclear powered ships:
http://www.brighthub.com/engineering/marine/articles/26364.aspx
If the hydrogen fuel cell water taxi doesn't kick off at least there's the nuclear powered water taxi option ;-)
### Learning resource for Marine Engineers
(04/09/09)
Anyone studying marine engineering subjects might find this website useful:
http://www.marinediesels.info/
Although it's geared towards the big ship engines, it has lots of relevant info for smaller ones and associated machinery with neat diagrams/animations.
### First Hydrogen Fuel Cell Water Taxi
(03/09/09)
A few months ago you read about the first hydrogen fuel cell commercial charter boat and aircraft in Germany, here's the first water taxi launched in 2003 using this technology:
http://www.marinelog.com/DOCS/NEWSMMIII/MMIIIOct16d.html
Build some nuclear/solar/wind/ocean current power stations to make lots of electricity (these don't pump CO2 into the atmosphere) in order make hydrogen gas from sea water, hydrogen gas filling stations and you have a true zero emission transport system. Another option looked at is an engine that burns hydrogen gas(highly flammable) in a combustion chamber directly rather than using fuel cells to make electricity which drive electric motors:
http://www.atzonline.com/index.php;do=show/site=a4e/sid=5666422124a9fbc2f268fd257932636/alloc=1/id=9413
Photos attached: lifeboat drill today at the maritime museum. Note the plaque has a small typo, should read 21.2KW
### How many barges can you tow at once?
(01/09/09)
Checkout these interesting articles:
http://cargolaw.com/2009nightmare_margaret.html
Talk about heavy duty tow job, can you count how many barges they are towing?!?!! And photos about a collision between two ships M/V Marti Princess & M/V Renate Schulte June 2009:
http://cargolaw.com/2000nightmare_singles.only.html
### Onboard the Columbian Navy training ship ARC Gloria
(30/08/09)
If you haven't heard the Gloria is in Sydney for another 4 days and is docked in Circular Quay, she's
open to the public (free entry) and went onboard today, unfortunetly I couldn't sneek in the engine room
to take some more photos because of tight security but here are some to clog up your mailbox ;-) | {} |
# Curvature sign-changing Friedman models
Isotropy and homogeneity of space leads to the spacetime metric of the form $$ds^2=-dt^2+d\sigma_k^2,$$ where $$d\sigma_k^2$$ is the metric on one of the standard manifolds (the 3-sphere, Euclidean 3-space, and the hyperbolic 3-space) depending on the curvature $$k$$. Here $$k$$ may depend on $$t$$, and there seem to be nothing to prevent $$k$$ from changing its sign.
However, the Robertson-Walker model assumes $$ds^2=-dt^2+a(t)^2d\sigma_k^2,$$ where now $$k$$ is fixed, and the time evolution of the geometry is delegated to the scale factor $$a(t)$$. This means that the curvature sign-change is forbidden in the Robertson-Walker models.
My question is: Are there cosmological models where the space is allowed to change the sign of its curvature, or is there an argument that it simply cannot happen?
RW assumes that matter is uniformly distributed over the spatial slices, and elliptic, flat, and hyperbolic geometries have very different distributions, in terms of the amount of matter within a given distance of any given point. There's no way you could move the matter around to be homogeneous in a different geometry without violating homogeneity in the process. So homogeneity is enough to force $$k$$ to be constant, it isn't a separate assumption.
The real world is obviously somewhat inhomogeneous, and if the size of the universe (or the approximately RW part of it) is small compared to the radius of curvature, then the value of $$k$$ could be somewhat ill-defined. This isn't really a change of geometry, though, it's just that different RW models with different values of $$k$$ would all approximate the reality about equally well. | {} |
# Formula for partial sum of Riemann zeta function [duplicate]
Possible Duplicate:
Finite Sum of Power?
Suppose $f(s,k) = \sum_{n=1}^k n^{-s}$ is the Riemann zeta function truncated at the k-th term. I read on mathoverflow that there is a formula for $f(s,k)$ in terms of Bernoulli numbers, but I can't find it on the web. Would someone happen to know it or could point to a link? I am primarily interested in the case when $s$ is a negative real number.
Thanks!
-
## marked as duplicate by J. M., Argon, BenjaLim, Rudy the Reindeer, Asaf KaragilaJul 23 '12 at 12:22
Thank you all so much! These are wonderful answers and links! – Thad Jul 12 '12 at 21:45
Perhaps that you are thinking at the formula proposed by Woon 'A New Representation of the Riemann Zeta Function zeta(s)'.
-
Presumably mathoverflow was talking about Faulhaber's formula $$\sum_{k=1}^n k^p = \frac{B_{p+1}(n+1)-B_{p+1}(0)}{p+1}$$ in terms of Bernoulli polynomials. If $p$ is a positive integer, then the coefficients of the Bernoulli polynomials are essentially Bernoulli numbers.
-
Faulhaber's polynomial provides the answer when $s \in \mathbb{Z}^{-}$. If $s \in \mathbb{R}^-$, a good approximation can be obtained using Euler-Maclaurin which also contain the Bernoulli numbers.
-
Note that
$$\sum_{n=1}^k n^{-s}=H^{(s)}_k$$
where $H^{(s)}_k$ is the generalized harmonic number.
Some identities are mentioned here, e.g.
$$H^{(s)}_k=\frac{(-1)^{-s}B_{-s+1}+B_{-s+1}(k+1)}{-s+1}$$
- | {} |
## Playing Games on a Cloud GPU
From: andrew cooke <andrew@...>
Date: Sat, 10 Oct 2015 16:32:03 -0300
I assumed this was impossible. Apparently not. If I had the time and energy
I guess I could do the maths. But anyway -
Andrew | {} |
Calculus 3 Problem (explain solution)
1. Oct 18, 2009
ttran1117
1. The problem statement, all variables and given/known data
Put the equation: p = 2 sin (x) cos (y) into rectangular coordinates. Identify the surface
3. The attempt at a solution
I tried to look at all the identities but I can't seem to figure out which one to use. I have the solutions to this problem, which follows:
p^2 = 2 p sin x cos y
=> x^2 + y^2 + z^2 = 2x (Where did this come from?)
=> x^2 - 2x + y^2 + z^2 = 0
=> (x^2-2x+1) + y^2 + z^2 = 1, which is a sphere of axis (1,0,0)
Can anyone explain the solution? Thank you
2. Oct 18, 2009
LCKurtz
Apparently you are dealing with spherical coordinates and the variable you are calling p is actually the spherical coordinate usually denoted as $\rho$. And, what's worse, the x and y in your equation also don't represent the cartesian x and y. Here's what I think your given equation should be:
$$\rho = 2\sin(\phi)cos(\theta)$$
where $(\rho,\phi, \theta)$ are the spherical coordinates of (x,y,z). Try following your argument knowing that and using the usual spherical coordinate formulas.
3. Oct 18, 2009
ttran1117
You're right. That is supposed to be the right equation, but I just used x and y because I didn't understand how to use the symbols lol. I was/am browsing through my textbook and notes, but was unable to find to relate rho, phi, and theta to spherical coordinates. I understand that x^2 + y^2 and z^2 is the spherical formula, but I still don't understand the 2x portion.
4. Oct 18, 2009
LCKurtz
5. Oct 18, 2009
ttran1117
Oh! I finally get it now lol. thank you | {} |
- - 3.3.7 MathML - Making Sub-Expressions Invisible mphantom
The mphantom element renders invisibly, but with the same size and other dimensions, including baseline position, that its contents would have if they were rendered normally. Mphantom can be used to align parts of an expression by invisibly duplicating sub-expressions.
### $MPhantom Test x + y + z x + y + z$
#### MathML
```<math mathsize="70">
<mspace linebreak="newline" indentalign="center"></mspace>
<mtext style="border:1px;">MPhantom Test</mtext>
<mspace linebreak="newline" indentalign="center"></mspace>
<mfrac>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mi>y</mi>
<mo>+</mo>
<mi>z</mi>
</mrow>
<mrow>
<mi>x</mi>
<mphantom>
<mo>+</mo>
<mi>y</mi>
</mphantom>
<mo>+</mo>
<mi>z</mi>
</mrow>
</mfrac>
[/itex]
``` | {} |
# Man connected to harness standing on plank
1. Nov 18, 2015
### Jtwa
1. The problem statement, all variables and given/known data
A professor (m= 75 kg )is seated on a light harness connected to a rope and pulley system. The professor's feet touch a uniform plank (mplank = 15kg) which is supported by a hinge at the wall. A bucket (M) is suspended from the right end of the plank.
m = 75kg
mplank = 15kg
l = 2m
L = 4.9m
Find: Label all the forces on a FBD
Find: T if M=0
2. Relevant equations
ΣMhing = 0
3. The attempt at a solution
I took the moment about the hinge and looked at the man by himself. I think I'm drawing my FBD diagram incorrectly.
2. Nov 19, 2015
### BvU
Hello JT,
From your drawing it's clear that the rope is attached to the end of the plank. That should be in the problem statement !
If prof is sitting in the harness, I expect one more force in his FBD. Otherwise I think you have most of it covered. Fry is the only horizontal force I see, so it may well be 0....
3. Nov 19, 2015
### J Hann
Have you tried writing the equations for the torques about the hinge end of the plank?
Also, you know that T is constant throughout the length of the rope.
This greatly would simplify the solution since you don't need to consider the forces
acting through the hinge.
4. Nov 19, 2015
### haruspex
Well, not quite. Since the rope is attached to the end of the plank, the section of rope below the plank will be at a different tension.
5. Nov 19, 2015
### BvU
Yes, but the problem statement reads M = 0
6. Nov 19, 2015
### haruspex
Which post is that in response to? It does not appear to contradict my post #4.
Also, that M=0 condition is only for the final part of the question.
7. Nov 19, 2015
### Mister T
$T$ is the tension in the section of rope above the plank. The section below will have a tension equal to $Mg$ which will generally be different than $T$, particularly if $M=0$.
8. Nov 19, 2015
### BvU
You are absolutely right ! (Haru and T2)
9. Nov 21, 2015
### Jtwa
Since the rope is connected to the man, why isn't T=(mass of man)*g
10. Nov 21, 2015
### BvU
Part of his weight is taken by the harness !
11. Nov 22, 2015
### Jtwa
I'm still having trouble understanding this question. Can someone draw a FBD ? Is Normal Force suppose to be on the FBD?
12. Nov 22, 2015
### haruspex
No, that's why it could have been mg. The reason that T is not mg is that not all of the weight is taken by the harness.
13. Nov 22, 2015
### haruspex
An FBD relates to a single rigid body. There are two appropriate FBDs here, one for the man and one for the plank.
Your diagram depicted both, which is ok except that where those two bodies interact you need to show the equal and opposite forces between them.
14. Nov 22, 2015
### BvU
Part of his weight = not all of the weight
15. Nov 22, 2015
### haruspex
It's a question of emphasis in English. If you write that the reason that T is not mg is that part of his weight is taken by the harness it implies that the part taken by the harness accounts for the discrepancy. If you mean that the part not taken by the harness accounts for it then you need to write "only part of his weight...".
16. Nov 23, 2015
### BvU
Didn't want to give too much emphasis, just get the OP to think it over.
Non-native english typist... But then again, weren't you in Australia ?
17. Nov 23, 2015
### haruspex
I am now.
18. Nov 23, 2015
### BvU
Can't beat Oxford English | {} |
This is the part 2 of the ongoing series of blogs, where I write about the how-to of the molecular modelling. These are focused mainly on its software side (GAMESS) instead of the theory.
Optimization is a process is that is routine in molecular modelling. It is generally used to find stationary points where the gradient of the energy is zero. These stationary points are energy minima, maxima which you would call reactants, products, transition states etc. (Usually optimization means finding the minima, but transition state search works on the same principle)
## How does optimization work?
We can represent a molecule by the 3D cartesian coordinates of its atoms. If the QM program has a set of cartesian coordinates and atoms, it can approximate to the solution of the Schrödinger’s equation, which would give the total energy of that system. When any of the atoms are moved, that energy will change. Each atom can be moved in 3 directions (x,y,z) so we can express the energy of the system as a function of the cartesian coordinates of each of its atoms —
E=f(x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},...)
Now, the optimized i.e. lowest energy structure would be the set of coordinates where E is minimum. That means the gradient (i.e. first derivative) of energy with respect to all coordinates has to be zero. Additionally, the second derivative has to be positive.
Optimization algorithms in quantum chemistry are influenced by the optimization method of Newton. Newton’s original method takes a initial set of coordinates and takes iterative steps to reach the stationary points. Each step requires the first and second derivatives of the E. As calculating second derivatives is costly, especially for bigger systems, there are so-called quasi-Newton algorithms that do not require accurate second-derivatives.
Most quantum chemistry programs including GAMESS, use the quasi methods. These methods guess the approximate second derivatives (often called guess hessian) but use accurate first derivatives to get to the lowest energy structure.
## Choice of coordinate system
Writing the energy in terms of cartesian coordinates is not the only way. We can also write the energy in terms of chemically intuitive properties of the molecule like bond lengths(r), bond angles(α), torsional angles(β) etc.
E=f(l_{1},l_{2},...,\alpha_{1},\alpha_{2},...,\beta_{1},\beta_{2},...)
This coordinate system is called the internal coordinate system. Notice however, that the number of internal coordinates must be 3N-6 if N is the number of cartesian coordinates. In cartesian, there are 6 degrees of freedom(e.g. all atoms moving in x direction, all atoms rotating around an axis etc.) which represent the whole molecule moving in space, or rotating on an axis. These displacements do not change the energy in any way, and are eliminated in the internal coordinate system. (In case of linear molecules, there are 3N-5 internal coordinates, as only two rotational axes exist.)
There can be multiple choices of internal coordinates (any combination would work, as long as there are 3N-6 coordinates).
## Using delocalised internal coordinates in GAMESS
There are multiple ways to use internal coordinates.
When Avogadro generates input for GAMESS, by default the molecule is represented in cartesian coordinates. In this case, you can set in $CONTRL, NZVAR=number of internal coordinates i.e. 3N-6 (or 3N-5, if linear). This requests the program to use internal coordinates for optimization. $CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE DFTTYP=B3LYP NZVAR=33 $END$STATPT OPTTOL=0.0004 NSTEP=100 $END$ZMAT DLC=.t. AUTO=.t. $END Top part of input file for benzene You also have to add$ZMAT DLC=.t. AUTO=.t. $END. This instructs the program to automatically construct internal coordinates from cartesians. (The coordinates generated are a certain type called delocalised redundant internals) The program detects bonds by checking if the distance between two atoms is smaller than the sum of their van der Waals radii. This might fail if there are two atoms connected by a weak interaction, like a hydrogen bond. Two water molecules connected by an H-bond In that case, the program needs to be told about the weak interaction by adding the keyword NONVDW to$ZMAT.
$BASIS GBASIS=N31 NGAUSS=6 NDFUNC=1 NPFUNC=1 DIFFSP=.TRUE. #END$CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE DFTTYP=B3LYP NZVAR=12 $END$STATPT OPTTOL=0.0004 NSTEP=100 $END$ZMAT DLC=.t. AUTO=.t. NONVDW(1)=2,4 $END This keyword takes an array of numbers and reads two at a time: NONVDW(1)=i,j,k,l,m,n,…. this represents bonds between atom i and atom j, atom k and l, atom m and n and so on. (Hint: To see the labels in Avogadro, check the ‘label’ box on left panel, and then click the spanner, and change the ‘Text’ to ‘Atom number’.) ## Using z-matrix input Another way to use internal coordinates would be to supply them directly to GAMESS in the$DATA section. The internal coordinates are usually written in a specific format called the Z-matrix. Avogadro can generate the z-matrix, however, to get that you have to go through Extensions>Gaussian and then select ‘Z-matrix(compact)’ in the Format option.
Z-matrix for water-water system
The z-matrix starts after the charge and multiplicity (0 1 in this case). Copy that text, and paste in into the $DATA section of the GAMESS input file. $BASIS GBASIS=N31 NGAUSS=6 NDFUNC=1 NPFUNC=1 DIFFSP=.TRUE. $END$CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE DFTTYP=B3LYP COORD=ZMT
NZVAR=12 $END$STATPT OPTTOL=0.0004 NSTEP=100 $END$DATA
Title
C1
C 6.0 -5.80406 -1.22088 0.00000
O 8.0 -4.73406 -1.22088 0.00000
H 1.0 -6.16072 -0.32416 0.46215
H 1.0 -6.16073 -2.06948 0.54550
H 1.0 -6.16073 -1.26901 -1.00766
H 1.0 -4.41073 -1.17726 0.91348
$END Don’t forget to put COORD=ZMT in$CONTRL so that GAMESS expects Gaussian style z-matrix input. Inputting NZVAR is also required to instruct the program to use internal coordinates. The benefit of this method is that you can edit and modify the internal coordinates yourself, if required.
There are also other methods for inputting various types of internal coordinates, but I am not mentioning them here.
## Effect of coordinate choice on optimization
Using internal coordinates usually speeds up the optimization by a large extent. Consider the following benchmark for the water-water system (with B3LYP/6–31+G(d)):
Cartesian coordinates Delocalised internal coordinates Z-matrix internal coordinates Number of optimization steps 21 15 17 Time taken (minutes) 2.3 1.7 1.8
Optimization of water-water system
As you can see, auto generated internal coordinates are the best choice, and it can cut down the optimization time by a lot.
In case of molecules with rings, the z-matrix method does not work very well. In that case use the auto generation method, or if that fails, use cartesian. Also, there are some systems where the bond angles, or dihedral angles are 180 degrees. Internal coordinates can run into problems in those cases too.[ref-1]
The bottom line is that use cartesian coordinates as the last resort.
Reference-1: https://doi.org/10.1002/qua.560440821
GAMESS: https://www.msg.chem.iastate.edu/gamess/ | {} |
Convergence of some object depending on functions with compact support
Let $G$ be a locally compact group with unimodular Haar measure $\mu$. We consider the Hilbert space $\mathscr{H}:= L_{\mu}^2(G)$ together with the unitary representation $\pi : G \to U(\mathscr{H})$ given by $\pi(g): \mathscr{H} \to \mathscr{H}, f \mapsto f \circ r_g$, where $r_g$ is right multiplication by $g$. Hence $(\pi(g)f)(x) = f(xg)$.
We studies the following: For a continuous function $\varphi \in C_c(G)$ with compact support we define $$\pi(\varphi):= \int_G \varphi(g)\pi(g) \, d\mu(g).$$ More explicitly, for a measurable function $f: G \to \mathbb{C}$ we define $$(\pi(\varphi)f)(x) :=\int_G \varphi(g)f(xg) \, d\mu(g).$$
My question in now: Does this define a well defined representation of $C_c(G)$ on $\mathscr{H}$, where the problem is, that if $f \in L_{\mu}^2(G)$, then we need to show that $\pi(\varphi)f$ is in $L_{\mu}^2(G)$.
I doubt that this is true for a general $G$. However, I can prove the statement if $G$ is compact as follows: Note that if $G$ is compact, then $L_{\mu}^2(G) \subset L_{\mu}^1(G)$. Hence for $f \in L_{\mu}^2(G)$, \begin{align*} ||\pi(\varphi)f||_2^2 &= \int_G|(\pi(\varphi)f)(x)|^2 \, d\mu(x) \\ &= \int_G \bigg| \int_G \varphi(g)f(xg) \, d\mu (g) \bigg|^2 d\mu(x) \\ & \leq ||\varphi||_{\infty}^2 \int_G \bigg| \int_G f(xg) \, d\mu (g) \bigg|^2 d\mu(x) \\ &\leq ||\varphi||_{\infty}^2 \int_G ||f||_1^2 \,d \mu(x) \\ &= ||\varphi||_{\infty}^2 \cdot ||f||_1^2 \cdot \mu(G) < \infty. \end{align*} Where we used the invariance of the Haar measure in line 4. And the last term is less than infinity, since $\varphi$ is continuous of compact support and hence bounded, $L_{\mu}^2(G) \subset L_{\mu}^1(G)$ and hence for $f \in L_{\mu}^2(G)$ we have $||f||_1 < \infty$ and finally since $G$ is compact, the Haar measure is finite.
So the problem is can, one do a similar calculation if $G$ is not compact, or if one can find a counterexample.
It's true: $\pi(\varphi)f\in L^2(G,\mu)$.
Let $M$ be the support of $\varphi$, so $$(\pi(\varphi)f)(x) :=\int_M \varphi(g)f(xg) \, d\mu(g).$$ By the Cauchy-Schwarz inequality, we have $$|(\pi(\varphi)f)(x)|^2\le \|\varphi\|^2_2\int_M|f(xg)|^2d\mu(g)=\|\varphi\|^2_2\int_{xM}|f(g)|^2d\mu(g),$$ so $$\int_G|(\pi(\varphi)f)(x)|^2d\mu(x)\le \|\varphi\|^2_2\int_G\int_{G}\mathbb{1}_{xM}(g)|f(g)|^2d\mu(g)d\mu(x).$$ Since $g\in xM$ $\Leftrightarrow$ $x\in gM^{-1}$, this yields (I should assume $G$ $\sigma$-compact to apply Fubini, but otherwise since $f$ has $\sigma$-compact support I apply it inside a suitable $\sigma$-compact open subgroup) $$\int_G|(\pi(\varphi)f)(x)|^2d\mu(x)\le \|\varphi\|^2_2\int_G\int_{gM^{-1}}d\mu(x)|f(g)|^2d\mu(g).$$ So $$\int_G|(\pi(\varphi)f)(x)|^2d\mu(x)\le \|\varphi\|^2_2\mu(M^{-1})\int_G|f(g)|^2d\mu(g)=\|\varphi\|^2_2\mu(M^{-1})\|f\|_2^2<\infty.$$
Note that I only used (twice) left-invariance of $\mu$ (in the non-unimodular case, the right-regular representation $\pi$ is not unitary, however).
• Thank you very much. To simplify a little: \begin{align*} ||\pi(\varphi)f||_2^2 &= \int_G |(\pi(\varphi)f)(x)|^2 \, d\mu(x) \\ &= \int_G \bigg| \int_{\mathrm{supp}(\varphi)} \varphi(g)f(xg) \, d\mu(g) \bigg|^2 \, d\mu(x) \\ & \leq ||\varphi||_2^2 \int_G\int_{\mathrm{supp}(\varphi)} |f(xg)|^2 \, d\mu(g)d\mu(x) \\ &= ||\varphi||_2^2 \int_{\mathrm{supp}(\varphi)} \int_G |f(xg)|^2 \, d\mu(x)d\mu(g) \\ &= ||\varphi||_2^2 \int_{\mathrm{supp}(\varphi)} \int_G |f(x)|^2 \, d\mu(x)d\mu(g) \\ &= \mu(\mathrm{supp}(\varphi)) \cdot ||\varphi||_2^2 \cdot ||f||_2^2 < \infty. \end{align*} – Constantin K Mar 31 '18 at 10:09
• Yes. Actually you're using right-invariance of $\mu$ and not left as I did. In this case the right-regular representation is unitary. Said otherwise: for $G$ possibly non-unimodular and $\mu$ left-invariant, my argument works for the right-regular representation, and your argument works for the left-regular representation (these two representations are of distinct interest when $G$ is non-unimodular; only the left one is unitary). – YCor Mar 31 '18 at 10:40 | {} |
# Consider a badminton racket with length scales as shown in the figure.
Question:
Consider a badminton racket with length scales as shown in the figure.
If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, $\frac{r}{2}$ distance from the end $\mathrm{A}$ of the handle will be ........ $\mathrm{Mr}^{2}$.
Solution:
$I=\left[I_{1}+M\left(\frac{5}{2} r\right)^{2}\right]+\left[I_{2}+M\left(\frac{13 r}{2}\right)^{2}\right]$
$=\left[\frac{\mathrm{M}\left(36 \mathrm{r}^{2}\right)}{12}+\frac{\mathrm{M}\left(25 \mathrm{r}^{2}\right)}{4}\right]+\left[\frac{\mathrm{Mr}^{2}}{2}+\frac{169 \mathrm{Mr}^{2}}{4}\right]$
=52 \mathrm{Mr}^{2}
Ans. $52.00$ | {} |
## Algebra 1
$2 \sqrt 2 ( -2 \sqrt 32 + \sqrt 8 )$ We multiply the brackets using the distributive property. $-4 \sqrt 64 + 2 \sqrt 16$ *** Take the square root of 64 which is 8. Because 8 x 8 = 64 *** Take the square root of 16 which is 4. Because 4 x 4 = 16 $-4 (8) + 2 (4)$ $-32 + 8$ We add the numbers together -24 | {} |
# Properties
Label 92400hd Number of curves $6$ Conductor $92400$ CM no Rank $1$ Graph
# Related objects
Show commands for: SageMath
sage: E = EllipticCurve("hd1")
sage: E.isogeny_class()
## Elliptic curves in class 92400hd
sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.ia6 92400hd1 [0, 1, 0, 13992, 185051988] [2] 1474560 $$\Gamma_0(N)$$-optimal
92400.ia5 92400hd2 [0, 1, 0, -4788008, 3959423988] [2, 2] 2949120
92400.ia4 92400hd3 [0, 1, 0, -10178008, -6594196012] [2] 5898240
92400.ia2 92400hd4 [0, 1, 0, -76230008, 256149683988] [2, 2] 5898240
92400.ia3 92400hd5 [0, 1, 0, -75852008, 258816095988] [2] 11796480
92400.ia1 92400hd6 [0, 1, 0, -1219680008, 16394802983988] [2] 11796480
## Rank
sage: E.rank()
The elliptic curves in class 92400hd have rank $$1$$.
## Complex multiplication
The elliptic curves in class 92400hd do not have complex multiplication.
## Modular form 92400.2.a.hd
sage: E.q_eigenform(10)
$$q + q^{3} + q^{7} + q^{9} + q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$
## Isogeny matrix
sage: E.isogeny_class().matrix()
The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.
$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$
## Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels. | {} |
# Mathematical Foundations of Probability Theory
@article{Lo2018MathematicalFO,
title={Mathematical Foundations of Probability Theory},
author={Gane Samb Lo},
journal={arXiv: Probability},
year={2018}
}
• G. Lo
• Published 6 August 2018
• Economics
• arXiv: Probability
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited theory. The book might have assigned the title : From Measure Theory and Integration to Probability Theory. The fundamental aspects of Probability Theory, as described by the keywords and phrases below, are presented, not from experiences as in the book \textit{A…
7 Citations
### Weak Convergence (IIA) - Functional and Random Aspects of the Univariate Extreme Value Theory
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• 2018
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In
### Finiteness of Record values and Alternative Asymptotic Theory of Records with Atom Endpoints
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Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such theories could not
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• 2020
The representation Skorohod theorem of weak convergence of random variables on a metric space goes back to Skorohod (1956) in the case where the metric space is the class of real-valued functions
### Study on A Direct Construction of the Standard Brownian Motion
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In this note, we combine the two approaches of Billingsley (1998) and Csőrgő and Revesz (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a
### Suppressing information storage in a structured thermal bath
• Physics
• 2021
Quantum systems interacting with environments tend to have their information lost from transmission through the correlations generated with the degrees of freedom of the environment. For situations
### On the Glivenko-Cantelli theorem for the functional empirical process using associated sequences
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Using a general strong law of large number proved by Sangare and Lo in \cite% {sanglo} and the entropy numbers, we provide a functional Glivenko-Cantelli theorem for arbitrary random variables (rv's).
### On the Law of Large Numbers for Nonlinear Mean Random Variables
We consider variants of the law of large numbers with respect to the average power, average geometric and mean harmonic systems of random variables and establish various forms of convergence of the
## References
SHOWING 1-10 OF 40 REFERENCES
### Convergence of probability measures
The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the
### A Course in Probability Theory
This edition of A Course in Probability Theory includes an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.
### Measure Theory and Integration By and For the Learner
• Education
• 2017
Any student who goes through the materials, alone or in a small group or under the supervision of an assistant will gain a very solid knowledge in the subject and ensure a sound foundation for studying disciplines such as Probability Theory, Statistics, Functional Analysis, etc.
### Probability Theory
• Mathematics
Encyclopedia of GIS
• 2017
In this chapter, the authors make use of the formalizations of measure theory and Lebesgue integration in HOL4 to provide a higher-order-logic formalization of probability theory (Mhamdi, 2013). For
### A flexible application of the Stone-Weierstrass Theorem in General and Application in Probability Theory
• Mathematics
Journal of Mathematical Facts and short papers
• 2019
When applying the classical Stone-Weierstrass common version in Probability Theory for example but in other fields also, some problems may arise if all points of the compact set are not separated. A
### Counterexamples in Probability
RANDOM EVENTS AND THEIR PROBABILITIES: Classes of Random Events Probabilities Independence of Random Events Diverse Properties of Random Events and their Probabilities RANDOM VARIABLES, DISTRIBUTIONS
### Introduction To Measure And Probability
The introduction to measure and probability is universally compatible with any devices to read and will help you to enjoy a good book with a cup of coffee in the afternoon instead of coping with some malicious virus inside their computer.
### A simple proof of the theorem of Sklar and its extension to distribution functions
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated. | {} |
## Algebra 1: Common Core (15th Edition)
There is only one solution, $0$
$s^2-35=-35$ $s^2=0$ $s=0$ There is one solution, $0$ | {} |
write.matrix {MASS} R Documentation
Write a Matrix or Data Frame
Description
Writes a matrix or data frame to a file or the console, using column labels and a layout respecting columns.
Usage
write.matrix(x, file = "", sep = " ", blocksize)
Arguments
x matrix or data frame. file name of output file. The default ("") is the console. sep The separator between columns. blocksize If supplied and positive, the output is written in blocks of blocksize rows. Choose as large as possible consistent with the amount of memory available.
Details
If x is a matrix, supplying blocksize is more memory-efficient and enables larger matrices to be written, but each block of rows might be formatted slightly differently.
If x is a data frame, the conversion to a matrix may negate the memory saving.
Side Effects
A formatted file is produced, with column headings (if x has them) and columns of data.
References
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
write.table | {} |
Equivalent metrics using open balls
Let $d$ and $p$ be two metrics on a set $X$ and let $m$ and $n$ be positive constants such that $md(x,y) \leq p(x,y) \leq nd(x,y)$ for every $x,y \in X$. Show that every open ball for one metric contains an open ball with the same center for the other metric.
Well to show that every open ball for $p$ contains and open ball for $d$, I have the following -
We have a $p$ open ball $B_{\epsilon}^p(x)$ and we want to find a $\delta > 0$ such that $$B_{\delta}^d(x) \subseteq B_{\epsilon}^p(x)$$
We know that $$d(x,y) \geq \frac{p(x,y)}{n}$$
So if we take $\delta = \frac{\epsilon}{n}$ we have
$$B_{\epsilon}^p(x) = \{ y \in X | p(x,y) < \epsilon\}$$ $$B_{\delta}^d(x) = \{ y \in X | d(x,y) < \frac{\epsilon}{n}\}$$
and the $d$ open ball will be the same size or smaller than the $p$ open ball.
It's hard to explain it properly with just notation, it seems alot clearer when I draw out diagrams on paper and sub in actual numbers for $n$ and $\epsilon$. Have I got the general idea correct?
-
Your choice of $\delta$ does indeed work. Here’s a way of explaining it that may be a bit clearer.
You want to choose your $\delta$ so that if $d(x,y)<\delta$, then $p(x,y)<\epsilon$; that will ensure that if $y\in B_\delta^d(x)$, then $y\in B_\epsilon^p(x)$ and hence that $B_\delta^d(x)\subseteq B_\epsilon^p(x)$. You know that $p(x,y)\le nd(x,y)$, so if $d(x,y)<\delta$, then $p(x,y)<nd(x,y)<n\delta$. As long as you choose $\delta\le\frac{\epsilon}n$, you’ll then have
$$p(x,y)<nd(x,y)<n\delta\le\epsilon\;,$$ | {} |
### Primary 6 Problem Sums/Word Problems - Try FREE
Score :
(Single Attempt)
#### Question
The figure shown here is made up of a semi circle and 3 squares.
The diameter of the semi circle is 40 cm and its centre is X.
There is a large square, medium square and small square.
The ratio of the length of the small square to the medium square is 2 : 3.
(a) What is the area of the entire figure?
(b) What is the perimeter of the entire figure?
[ Take π to be 3.14 ]
Notes to students:
1. If the question above has parts, (e.g. (a) and (b)), given that the answer for part (a) is 10 and the answer for part (b) is 12, give your answer as:10,12
(a)____cm^2, (b)_____cm | {} |
# Finite Math Examples
Determine if Injective (One to One)
Function is said to be injective or one-to-one if every element in the range is an image of at most one element from the domain.
An injective function is called a one-to-one function
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move to the left side of the equation by subtracting it from both sides.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Factor out of .
Simplify the denominator.
Rewrite.
Multiply by to get .
Simplify .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Factor out of .
Simplify the denominator.
Rewrite.
Multiply by to get .
Simplify .
-----Begin simplification-----
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Factor out of .
Simplify the denominator.
Rewrite.
Multiply by to get .
Simplify .
-----Begin simplification-----
The final answer is the combination of both solutions.
There is more than value for some values, which means that is not an equation of a function.
Not Injective (Not One-to-One)
We're sorry, we were unable to process your request at this time
Step-by-step work + explanations
• Step-by-step work
• Detailed explanations
• Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month$--.--/year (--%) | {} |
# Two conducting spheres of radii 3 cm and 1 cm are separated by a distance of 10 cm in free space. If the spheres are charged to same potential of 10 V each, the force of repulsion between them is
$(A)\;\large\frac{1}{3} \times 10^{-9}\;N$ | {} |
Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1075.34028
Bohner, M.; Saker, S.H.
Oscillation of second order nonlinear dynamic equations on time scales.
(English)
[J] Rocky Mt. J. Math. 34, No. 4, 1239-1254 (2004). ISSN 0035-7596
The authors consider the nonlinear second order dynamic equation $$(p(t)x^\Delta)^\Delta+q(t)(f\circ x^\sigma)=0,\tag{1}$$ where $p$ and $q$ are positive, real-valued continuous functions, and the nonlinearity $f:\Bbb{R}\to\Bbb{R}$ satisfies the sign condition $xf(x)>0$ and the superlinearity condition $f(x)>K x$ for some $K>0$ and every $x\neq 0$. Two cases, depending on the convergence of the integral $$\int _1^\infty\frac 1{p(t)}\Delta t\tag{2}$$ are discussed separately. New sufficient conditions involving the integral over the coefficients of equation (1) which guarantee that all solutions are oscillatory (in the case when (2) is divergent) or either oscillatory or convergent to zero (in the case of convergence of the integral (2)) are derived. The sharpness of these criteria is shown on the example of the Euler dynamic equation. The authors' main tool is the Riccati transformation.
[Robert Mař\'ik (Brno)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
39A12 Discrete version of topics in analysis
39A10 Difference equations
Keywords: dynamic equation; Riccati transformation; Riccati equation; oscillation; Kamenev-type criteria; Euler dynamic equation; measure chain; time scales
Highlights
Master Server | {} |
# Drop in results upon addition of new features in random forest model
I am training a classification random forest for object detection in images. I have several features (like HoG, edge features etc) which work good enough separately. But when I train using all features together, the results don't improve. E.g. area under curve are as follows:
HoG Features: 0.90
edge Features: 0.81
Combined together: 0.86
I am using scikit-learn random forest library, # of trees = 200, information gain = 'entropy', 2 classes and I have 4000 training examples.
• Area under what curve? 200 trees seems small. How many features? – Sycorax Apr 5 '16 at 2:23
• sensitivity vs specificity. Hog features = 2500, Edge Features = 2700. Trees size kept small due to time constraints – Azhar Apr 5 '16 at 2:42
• It's plausible that your forest isn't diverse enough; try adding more trees. Moreover, by setting minimum node size to be larger, you can get calibrated probabilities while reducing training time per tree. – Sycorax Apr 5 '16 at 2:44
• Increased the tree size to 100, no improvement – Azhar Apr 5 '16 at 20:18
• If you had 200 trees before, 100 trees is a decrease. – Sycorax Apr 5 '16 at 20:19
You could try increasing max_features to combat this. | {} |
# Nonabelian Cohen–Lenstra moments
@article{Wood2019NonabelianCM,
title={Nonabelian Cohen–Lenstra moments},
author={Melanie Matchett Wood and Philip Matchett Wood},
journal={Duke Mathematical Journal},
year={2019}
}
• Published 15 February 2017
• Mathematics
• Duke Mathematical Journal
In this paper we give a conjecture for the average number of unramified $G$-extensions of a quadratic field for any finite group $G$. The Cohen-Lenstra heuristics are the specialization of our conjecture to the case that $G$ is abelian of odd order. We prove a theorem towards the function field analog of our conjecture, and give additional motivations for the conjecture including the construction of a lifting invariant for the unramified $G$-extensions that takes the same number of values as…
## Figures from this paper
### The Distribution of H8-Extensions of Quadratic Fields
• Mathematics
International Mathematics Research Notices
• 2020
We compute all the moments of a normalization of the function that counts unramified $H_{8}$-extensions of quadratic fields, where $H_{8}$ is the quaternion group of order $8$, and show that the
### Moments of unramified 2-group extensions of quadratic fields
We formulate a conjecture about moments of unramified extensions $L/K$ with $\left[K:\mathbb{Q}\right]=2$, $G\left(L/K\right)=H$ and $G\left(L/\mathbb{Q}\right)=G$ for any 2-group $G$. We prove a
### Higher genus theory
• Mathematics
• 2019
In $1801$, Gauss found an explicit description, in the language of binary quadratic forms, for the $2$-torsion of the narrow class group and dual narrow class group of a quadratic number field. This
### Presentations of Galois groups of maximal extensions with restricted ramification
Motivated by the work of Lubotzky, we use Galois cohomology to study the difference between the number of generators and the minimal number of relations in a presentation of the Galois group $G_S(k)$
### Cohen-Lenstra heuristics and local conditions
• M. Wood
• Mathematics
Research in Number Theory
• 2018
We prove function field theorems supporting the Cohen–Lenstra heuristics for real quadratic fields, and natural strengthenings of these analogs from the affine class group to the Picard group of the
### Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg)
• Mathematics
Commentarii Mathematici Helvetici
• 2022
We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of
### Non-abelian Cohen--Lenstra Heuristics in the presence of roots of unity
For a Galois extension K/Fq(t) of Galois group Γ with gcd(q, |Γ|) = 1, we define an invariant ωK , and show that it determines the Weil pairing of the curve corresponding to K and it descends to the
### Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations
We study solutions to the Brauer embedding problem with restricted ramification. Suppose $G$ and $A$ are a abelian groups, $E$ is a central extension of $G$ by $A$, and
### Effective convergence of coranks of random Rédei matrices
• Mathematics
• 2020
We give effective estimates for the $l^1$-distance between the corank distribution of $r \times r$ Redei matrices and the measure predicted by the Cohen--Lenstra heuristics. To this end we pinpoint a
## References
SHOWING 1-10 OF 72 REFERENCES
### Cohen–Lenstra Moments for Some Nonabelian Groups
Cohen and Lenstra detailed a heuristic for the distribution of odd p-class groups for imaginary quadratic fields. One such formulation of this distribution is that the expected number of surjections
### Non-abelian Cohen–Lenstra heuristics over function fields
• Mathematics
Compositio Mathematica
• 2017
Boston, Bush and Hajir have developed heuristics, extending the Cohen–Lenstra heuristics, that conjecture the distribution of the Galois groups of the maximal unramified pro- $p$ extensions of
### The Distribution of H8-Extensions of Quadratic Fields
• Mathematics
International Mathematics Research Notices
• 2020
We compute all the moments of a normalization of the function that counts unramified $H_{8}$-extensions of quadratic fields, where $H_{8}$ is the quaternion group of order $8$, and show that the
### Moments of unramified 2-group extensions of quadratic fields
We formulate a conjecture about moments of unramified extensions $L/K$ with $\left[K:\mathbb{Q}\right]=2$, $G\left(L/K\right)=H$ and $G\left(L/\mathbb{Q}\right)=G$ for any 2-group $G$. We prove a
### On a Cohen–Lenstra heuristic for Jacobians of random graphs
• Mathematics
• 2014
In this paper, we make specific conjectures about the distribution of Jacobians of random graphs with their canonical duality pairings. Our conjectures are based on a Cohen–Lenstra-type heuristic
### Cohen-Lenstra heuristics and local conditions
• M. Wood
• Mathematics
Research in Number Theory
• 2018
We prove function field theorems supporting the Cohen–Lenstra heuristics for real quadratic fields, and natural strengthenings of these analogs from the affine class group to the Picard group of the
### Random matrices, the Cohen–Lenstra heuristics, and roots of unity
The Cohen-Lenstra-Martinet heuristics predict the frequency with which a fixed finite abelian group appears as an ideal class group of an extension of number fields, for certain sets of extensions of
### The Hasse norm principle for abelian extensions
• Mathematics
• 2015
Abstract:We study the distribution of abelian extensions of bounded discriminant of a number field $k$ which fail the Hasse norm principle. For example, we classify those finite abelian groups $G$
### Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II
• Mathematics
• 2012
We prove a version of the Cohen--Lenstra conjecture over function fields (completing the results of our prior paper). This is deduced from two more general theorems, one topological, one arithmetic: | {} |
## The Apollonian parabola
Some say that Archimedes and Apollonius of Perga (modern Murtina in Turkey; the center of the great yavana temple of the goddess Artemis in the days of Apollonius) were the two great yavana-s who might have rivaled Karl Gauss or Leonhard Euler in their in intellectual achievements. Beyond doubt a whole lot of modern knowledge rests on the foundation of Apollonius and in the west one could perhaps say that a Kepler or a Newton may have never shone forth had that Apollonian foundation not existed. Indeed, even today the study of Apollonius is a profound experience for the man who can do so. As with yavana religion much of their knowledge including the books of Apollonius were lost due to the ravages of pretonmāda in the west. Not surprisingly even at a later age the Lord Protector of England the duke of Somerset was burning books with yavana geometrical diagrams at the Oxford university.
Ironically in the world of its younger sister, the marūnmāda, Apollonius held a great fascination among those influenced by (Neo)-Platonism. Among the marūnmatta-s, their intellectual ibn Sina from Persia was perhaps the most fascinated by Apollonius. This allowed the preservation of much more of his works than in the west. Not surprisingly later marūnmatta-s referring to his work said that while his Qoranic studies were fine, he should be accused of kaffr-hood, and “innovation” derived from yavana and Hindu knowledge. Indeed, some mullahs suggested that he should have been cut pieces and feed to raptors. Nevertheless, his studies on yavana geometry and Hindu trigonometry has resulted in some interesting preservations which would have otherwise been lost. One such we shall discuss here is an Apollonian construction of a parabola using the geometric mean theorem. It goes thus in modern terminology:
1) Let point O be the origin. Take a point A on the x-axis at a given negative coordinate $(-a,0)$.
2) Let B be a point moving on the x-axis from the origin in the positive direction.
3) Draw a circle with diameter as $\overline{AB}$.
4) Draw the tangent to this circle at point B. It will be perpendicular to the x-axis.
5) The above circle cuts the y-axis at points C and D. Draw lines through these points which are parallel to the x-axis.
6) The above pair of lines will intersect the tangent to the circle at point B at points E and F.
7) The locus of points E and F as B moves along the x-axis is the desired parabola.
From the construction we see:
$\overline{OA}=a$; The x-coordinate of the parabola is $\overline{OB}=x$; The y-coordinate of the parabola is $\overline{OC}=\overline{OD}=y$. Given the circle used for the construction we notice that $\overline{OC}=\overline{OD}$ is the geometric mean of $\overline{OA}$ and $\overline{OB}$ because $\overline{AB}$ is the diameter of the circle (geometric mean theorem). Thus we get:
$y=\sqrt{ax}$
$\therefore y^2=ax$
which is the equation of our desired parabola. | {} |
# Run/File Tags
## Run/File Tags
In order to characterize physics data it is useful to assign meta data to different levels of data abstraction. For data produced and used in the ALICE experiment a three layered structure is implemented:run level meta data, file level meta data and event level meta data.
This page is dedicated to the first two categories the run and file level metadata. The run and file meta data will be stored in the ALICE File Catalog. A directory structure within this database will ensure minimization of meta data duplication. For detailed information about the metadata fields at the run and file level, an internal note is ready by Markus Oldenburg.
### Structure of the file catalog
The file catalog, where ALICE files will be registered, has the following structure:
• Simulated data: /sim////
where:
• Year: Can take a value like 2007, 2008 etc.
• AcceleratorPeriod: Can take a value relevant to the LHC period (LHC07a, LHC08b, ...).
• RunNumber: Is the run identifier (0001,...).
• ProductionType: Gives information about the specific simulation which was run, which includes the conditions applied: Ideal, Full, Residual (PDC06_Residual).
It is also foreseen to have several subdirectories where the files will be grouped according to their type. The decided subdirectories are the following:
• raw/: Storage of raw data.
• reco//cond/: This will link to the directory where all the calibration and condition files used for this Pass will be stored.
• reco//ESD/: The directory where the ESDs and the tag files will be stored for each Pass.
• reco//AOD/: The directory where the AODs of this Pass will be stored.
The file names of the stored ALICE data will be kept simple, and only unique in the current subdirectory, for example: .AliESDs.root for ESD files, where ‹ is the identifier of the corresponding raw data file (.raw.root, also called raw data chunk). Therefore different subdirectories (for example the reco//ESD directories for different parent directories) may contain files with the same name but with different content. Nevertheless, the GUID scheme (and the directory structure) makes sure that these files can be distinguished.
### Run/File meta data tags
Tag Name Data Format ) Data Source ) run comment Text DAQ logbook run type Text (physics,pedestal,...) DAQ logbook run start time yyyymmddhhmmss DAQ logbook run stop time yyyymmddhhmmss DAQ logbook run stop reason Text (normal,beam loss...) DAQ logbook magnetic field setting Text (FullField,HalfField, ZeroField...) DCS collision system Text (PbPb,pp,...) DCS collision energy Text (5.5TeV) DCS trigger class DAQ logbook detectors present in run bitmap: 0=not included, 1=included DAQ logbook number of events in this run Integer DAQ logbook run sanity flag bit or bit mask, default 1=OK Manually
For the reconstructed data:
Tag Name Data Format ) Data Source ) production tag Text reconstruction production software library version Text (AliRoot::v4-04-Rev-05) reconstruction calibration/alignment setting Text reconstruction
For simulated data:
Tag Name Data Format ) Data Source ) generator Text (HIJING,PYTHIA,...) offline generator version Text offline generator comments Text offline generator parameters Text offline detector geometry offline detector configuration bitmap: 0=not included, 1=included offline simulation comments Text offline
### How to query the file catalog
We assume that a user wants to query the file catalog and extract a collection of ESD files. The files that he/she wants to have should fulfill the following criteria:
• They correspond to the 2008 run.
• They were created during the first period of the machine at that year.
• They were created from the third pass of the reconstruction.
The first thing one should do is have an active alien session.
$find -x collection /alice/data/2008/LHC08a/*/reco/Pass3/* AliESDs.root If he/she wants to store this collection then all is needed to be done is to redirect the output to a xml file:$find -x collection /alice/data/2008/LHC08a/*/reco/Pass3/* AliESDs.root > collection.xml
If there is a need to restrict further the output by imposing some selection criteria at the run/file level then if for example we need that the ESDS from the previous example:
• Correspond to pp collisions.
• Were created between the 19th and the 20th of March 2008 (10:20:30).
then the above command is modified accordingly:
\$find -x collection /alice/data/2008/LHC08a/*/reco/Pass3/* AliESDs.root Run:collision_system=”pp” and Run:stop"2008-03-19" > collection.xml | {} |
# How do you solve 35k^2 - 22k + 7 = 4 by factoring?
Aug 7, 2015
Factor: $y = 35 {k}^{2} - 22 k + 7 = 4$
Ans: (5x - 1)(7x - 3)
#### Explanation:
$y = 35 {k}^{2} - 22 k + 3 =$35(x - p)(x - q).
I use the new AC Method to factor trinomials.
Converted trinomial $y ' = {k}^{2} - 22 k + 105$. p' and q' have same sign.
Factor pairs of (105) --> ...(3, 35)(5, 21)(7, 15). This sum is 22 -= -b.
Then p' = -7 and q' = - 15.
Therefor, $p = \frac{p '}{a} = - \frac{7}{35} = - \frac{1}{5}$ and $q = - \frac{15}{35} = - \frac{3}{7}$
Factored form: $y = 35 \left(x - \frac{1}{5}\right) \left(x - \frac{3}{7}\right) = \left(5 x - 1\right) \left(7 x - 3\right)$ | {} |
Bulletin of the Korean Mathematical Society
( Vol.42 NO.1 / 2005 )
Title
Contractions of Class $\mathcal Q$ and Invariant Subspaces(eng)
Author
B. P. Duggal ,C. S. Kubrusly ,N. Levan
MSC
47A15, 47B20
Publication
Page
169-177 Page
Abstract
1. Introduction
2. Operators of class $\mathcal Q$
3. Invariant subspace theorem for contractions of class $\mathcal Q$
Own Status
Keyword
paranormal operators, invariant subspaces, proper contractions
Note
Summary
A Hilbert Space operator $T$ is of class $Q$ if
$T^{2*}T^2-2kern1ptT^*T+I$ is nonnegative. Every paranormal
operator is of class $Q$, but class-$Q$ operators are not
necessarily normaloid. It is shown that if a class-$Q$
contraction $T$ has no nontrivial invariant subspace, then it is a
proper contraction. Moreover, the nonnegative operator
$Q=T^{2*}T^2-2kern1ptT^*T+I$ also is a proper contraction.
Attach
DVI PDF | {} |
+0
# Has anyone worked out where the private messages have gone?
+5
784
17
+112006
Has anyone worked out where the private messages have gone?
Also, some of the posts are not displaying
for example
I posted "Become a member:Why would you want to" last night. It is there when I search, but it does not come up in the recent posts. Maybe it is just a problem for a few posts over the change over time?
Maybe this should be our thread for problems and difficulties with the new system.
Apr 13, 2014
#1
+60
0
It may be just me (Cphill), but I tried to log in at my local library.....unfortunately, I had forgotten my password (my home computer stores it automatically) and after a few attempts at guessing it unsuccessfully, I got "locked" out. (I'm an idiot - what can I say ??)
Well, when I got back home, I still couldn't log in, so I just created a new user name - namely, mine...so now, "Cphill" is just "Chris"......
Mmmmm.......looks like a few "bugs" have shown up at the picnic...
Apr 13, 2014
#2
+112006
0
Mmmm Yes a few ants!
Thanks for letting us know Chris. Hopefully Andre will help us get you back up with your original username.
I just used the built in Latex.
I couldn't get align to work and it is not particularly friendly for long displays. (Which mine was)
It may be quite nice for little displays. We will see.
---------------------------------
I have already written to Andre regarding the lack of member section and the missing messages.
I will write another regarding your lock out problem and other issues but i might let them build up a little first.
Hopefully it will all be sorted out quite quickly.
I was looking at the emicons but I don't think I like the new set very much. (that one is ok)
Apr 13, 2014
#3
+14
0
Im so sorry that im bothering you guys on a thread that doesnt apply to my question but i dont know how to contact you guys privately, anyways melany i was wondering if you could have a look at the problem you had helped me with a bit back,
$$\mathrm{\ }$$
### (T*(cos(45)/cos(30)))*sin(30) + (T*sin(45) - 50 = 0
The response you gave was well worked but the solution wasnt right (at least i dont think it was) anyways the correct anwser should be 45. Think you could help me
Apr 13, 2014
#4
+60
0
One more problem I've noticed.....I can't tell if someone is online or not......am I missing something???
Apr 13, 2014
#5
+2
0
Funny; I have the same log-in problem as Chris:(
Seems like Mr. Massow is experimenting again, which is alright. Guess we'll just have to wait and see how it all turns out.
<= This emoticon is somewhat cute though.
Cheers, ~Kitty<3
Apr 13, 2014
#6
+112006
0
Hi Chris,
I think I mentioned that problem in the email that I have already sent to Andre. The whole 'member' section is missing.
Actually I am hoping that Andre is reading this thread. There has been at least one 'admin' response to a question this morning.
Hi Kitty,
It is nice to know that you are around. And yes, we all hope that aAdre can 'spray' the bugs soon. A good does of Pyrethrum might do it. I hope that are not SUPER bugs that have become genetically immune. (There is no laughing icon!)
Another problem? Also you can't copy and paste in here.
Apr 13, 2014
#7
+60
0
One more problem.....no "preview" function/button ??
I liked that one A LOT !!!
Apr 13, 2014
#8
+2353
0
Wow! the whole thing changed! Wicked!
$$\begin{pmatrix} a&w&e&s&o&m&e \\ :)&:)&:)&:)&:)&:)&:) \end{pmatrix}$$
Apr 13, 2014
#9
+31509
0
Looks like the old maths stuff doesn't display. I note there are two new maths buttons. Let's see if they work:
$${\left({\frac{{\mathtt{12}}{!}}{{\mathtt{8}}{!}{\mathtt{\,\times\,}}({\mathtt{12}}{\mathtt{\,-\,}}{\mathtt{8}}){!}}}\right)} = {\mathtt{495}}$$ This is Math(Input=Result)
Can't see how Math(Input) works!
Apr 13, 2014
#10
+31509
0
Hmm! Math(Input=Result) doesn't display properly after posting!
Ok, it does now! Weird, it didn't at first, it showed an icon!
Now back to an icon!!!!!
Apr 13, 2014
#11
+112006
0
Well, the only key top answerer who is unaccounted for is Rom.
It is nice to 'see' all you others here! Hopefully private messaging will be restored soon.
When I tried to sign in on my smart phone I got the most severe warning that I have ever seen. It did not trust the sign in security on this new site. I decided to take it seriously and I did not sign in. My lap top, which also has google chrome is not complaining at all. Computers are a mystery to me!
Enjoy the rest of your day.
Apr 13, 2014
#12
+31509
0
Although the questions are ordered latest first the answers aren't. This is annoying when the thread is very long (e.g. End of day wrap). Previously we could choose to go in at either the first or the last post in a thread.
Apr 13, 2014
#13
+112006
0
When questions are answered they are not moving to the top of the forum.
This means that they are hard to keep track of and rubbish new posts supercede high value older posts that people are still answering.
Please Andre, this will not work for us.
Also, I have not been able to upload any pictures.
Apr 13, 2014
#14
+60
0
Here's the main problem with the "new" system: The "old" one worked a lot better....I'm all for "improvements," but this "improvement" is clunky, at best......
(At least bring back the old "math input".......this new thing isn't intuitive at all !!)
Apr 13, 2014
#15
+31509
0
Apr 13, 2014
#16
+60
0
Bring back the Private Messaging...it is sometimes very helpful to be able to communicate with the other users !!! Plus...airing all our gripes about the new system on the Forum pages coudn't inspire much confidence in the people who have questions......
Apr 14, 2014
#17
+2592
0
I still have the "Internal sever error" problem with my profile... i can access other ppls profiles just not my own.. i can even access the message center...
Apr 23, 2014 | {} |
# Axial and central symmetry
An axial symmetry is a transformation, therefore each point $P$ on the plane maps another point $P'$ also of the plane, so that the axis $e$ would be the perpendicular bisector of the segment $PP'$. The axial symmetries are inverse isometries, because they preserve the distances between its points and its homologous, but its orientation is inverse. The axial symmetry not only appears between an object and its reflection, since many figures that can break in two sections by means of a line are symmetrical with regard to the line. These objects have one (or more) symmetry axes.
The axial symmetry happens when the points of a figure coincide with the points of another one, taking as a reference a line that is known by the name of axis of symmetry. In the axial symmetry we find the same phenomenon as in an image reflected in the mirror.
We call the points that belong to the symmetrical figure homologous points, that is to say, $A’$ is homologous of $A$, $B’$ is homologous of $B$, and $C’$ is homologous of $C$. Besides, the existing distances between the points of the original figure are equal to the distances between the points of the symmetrical figure. In this case: The axial symmetry can also happen in an object with regard to one or more symmetry axes.
If we bend the figure on the traced symmetry axis, we might observe clearly that the points of the opposite parts coincide, that is to say, both parts correspond.
Next, we are going to study the expression in coordinates of the axial symmetries.
Let $P = (x, y)$ and $P '= (x', y ')$ be two points of the plane let's give its expression in coordinates according to the position of its axis:
• The symmetry axis is the y-coordinate axis:
In this case the algebraic representation of the transformation can be done by means of the following system:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} \cdot \begin{pmatrix} x \\ y \end{pmatrix}$$
Next, we are going to calculate the symmetrical of the point $P$ by means of a symmetry which axis is they-coordinate axis. Let $P = (2,2)$ be a point of the plane, then its symmetrical is calculated by means of the following equations system:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} \cdot \begin{pmatrix} 2 \\ 2 \end{pmatrix} \Rightarrow \left\{ \begin{array}{l} x'=-2 \\ y'=2 \end{array} \right.$$
Therefore, the symmetrical point regarding the y-coordinate axis is the point $P'=(-2,2)$.
• The symmetry axis is the x-coordinate axis:
In this case the algebraic representation of the transformation can be done by means of the following system: $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} x \\ y \end{pmatrix}$$
We continue with the previous example, let's remember that we had a point P of coordinates $(2,2)$ and in the previous example we had calculated its symmetrical regarding the $y$-coordinate axis. Now we are going to calculate its symmetrical with regard to the $x$-coordinate axis, and we will call this new point $P"$.We calcute its coordinates by means of the following equations system:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} 2 \\ 2 \end{pmatrix} \Rightarrow \left\{ \begin{array}{l} x'=2 \\ y'=-2 \end{array} \right.$$
Therefore, the symmetrical point with regard to the x-coordinate axis is the $P''=(2,-2)$.
To finish, of axial symmetries, we are going to study what happens with the composition of axial symmetries:
• The composition of two symmetries with the parallel axes $e$ and $e'$ is translation, which vector has the length twice the distance between the axes, the direction is perpendicular to the axes and its sense is the one that goes from $e$ to $e'$.
• The composition of two symmetries with the perpendicular axes $e$ and $e'$ is a central symmetry with regard to the point where two axes of symmetry meet.
We take again the point $P = (2,2)$ and we are going to apply a symmetry to it regarding the y-coordinate axis and then a symmetry regarding the $x$-coordinate axis. By the last example, the symmetrical point for the $y$-coordinate axis was the point $P' = (-2,2)$. Then, to calculate the symmetrical regarding the $x$-coordinate axis, we solve the following equations system:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} -2 \\ 2 \end{pmatrix} \Rightarrow \left\{ \begin{array}{l} x'=-2 \\ y'=-2 \end{array} \right.$$
If first we do the symmetry regarding the x-coordinate axis and then the symmetry concerning the y-coordinates axis, we will get to the same point $Q=(-2, -2)$. As we will see in a while, this transformation is called an axial symmetry.
A central symmetry, centered at point $O$, is a movement of the plane where every point $P$ of the plane has to map to another point $P'$, being $O$ the average point of the segment of endpoints $P$ and $P'$. Note that a central symmetry is equivalent to a rotation of $180^\circ$.
A point is a centre of symmetry of a figure if it defines a central symmetry.
Next we are going to see the expression in coordinates of a central symmetry changing the center of symmetry.
• Coordinates by means of a center symmetry $O=(0,0)$:
In the following image we see how a central symmetry behaves being the centre the origin of coordinates of a point:
Next, a triangle and its homologous are seen by means of a symmetry:
In both cases, the transformation has the following system associate: $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} x \\ y \end{pmatrix}$$
Given the segment $AB$ formed by the points $A = (1,0)$ and $B = (2,3)$, we are going to calculate its symmetry regarding the centre of coordinates. To do it, we will calculate the symmetry of the points $A$ and $B$. Precisely, the symmetrical of $A$ is $A'$:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} 1 \\ 0 \end{pmatrix} \Rightarrow \left\{ \begin{array}{l} x'=-1 \\ y'=0 \end{array} \right.$$
Therefore $A '= (-1,0)$ . The symmetrical of the point $B$ is $B'$:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} 2 \\ 3 \end{pmatrix} \Rightarrow \left\{ \begin{array}{l} x'=-2 \\ y'=-3 \end{array} \right.$$
Therefore, the symmetry of the segment $AB$ is the segment $A'B'$ that passes through the points $A' = (-1,0)$ and $B '= (-2, -3)$.
• Coordinates by means of a center symmetry $O=(a, b)$:
A point $P'$ homologous to a point $P=(x, y)$ by means of a central symmetry of center $O=(a, b)$:
And the figure homologous to a triangle has this form:
Therefore, its associated system, is: $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} 2a \\ 2b \end{pmatrix}$$
where we remember that the values $(a, b)$ are the coordinates of the centre of the symmetry.
We are going to consider the center of the central symmetry $O = (1,2)$ and we want to calculate the symmetrical regarding $O$ of the point $A = (3,7)$. Then, for the system of equations associated with the central symmetry with origin $O=(a, b)$, the coordinates of the symmetrical point are:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \cdot \begin{pmatrix} 3 \\ 7 \end{pmatrix} + \begin{pmatrix} 2\cdot 1 \\ 2\cdot 2 \end{pmatrix} \Rightarrow \left\{ \begin{array}{l} x'=-3+2=-1 \\ y'=-7+4=-3 \end{array} \right.$$
Therefore, the symmetrical of the point $A$ regarding the centre $O = (1,2)$ it is the point $A'= (-1, -3)$.
To finish this section about axial symmetries, we are going to see what happens when we compose more than one central symmetry simultaneously:
• Symmetries composition with the same centre: As a center symmetry $O$ is equivalent to a rotation with center $O$ and range $180^\circ$, when applying another transformation, the angle will be $360^\circ$, so the same figure is obtained, that is called a regression. It is an involutive transformation.
• Symmetries composition with different center: The composition of two central symmetries with different center is a translation. | {} |
# Saving Option
## Recommended Posts
Hello, I am making a DOS game and I was wondering.. how would I make it if a user presses the S key then it will save their progress? IDE: Dev-C++ Language: C++
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You would use File I/O. When the user presses s, you would save the important variable information to a file.
If you need an example, then just ask.
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If this is a console program, than I would wager to say that the only time the program pauses is when it waits for user input. In this case, the easiest (but perhaps not the most elegant) solution then would be to provide an if statement to check if the user wants to save instead of continuing.
Basically, every time you read input, you have to remember to perform this check. Which is why it's somewhat inelegant; but the only other solution I can think of is to use multithreading, and have one thread be devoted entirely to catching the 's' key. But that opens up a whole other can of worms: how would you know that the 's' keypress represents a request to save, and not simply input to a prompt? How would you stop the main thread from continuing if there is a request to save? etc. etc.
So, yeah, just stick to the first option [smile]
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Quote:
Original post by Chad SmithYou would use File I/O. When the user presses s, you would save the important variable information to a file.If you need an example, then just ask.Chad
Can I get an example please? :P
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To use file i/o in C++, you will need to use ifstream (for reading) and ofstream(for writing), a very simple example:
#include <fstream> // for ifstream and ofstream#include <iostream>// creates an ofstream object associated with somefile.txt and open the file:std::ofstream output("somefile.txt");if (!output){ std::cout << "Oh no, an error occured!"; //do something about it}output << "this text will now be in somefile.txt";output.close(); // file will be closed when output gets destroyed on scope exit, this will close it right now.
ifstream is similar.
Another option is to use xml, which I find personally easy to use for these purposes. This way you don't have to deal with a lot of issues when reading a file. There is a fine and small library for this, TinyXml, and the xml part of this gamedev article might help you.
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## LATEX-L@LISTSERV.UNI-HEIDELBERG.DE
Options: Use Classic View Use Monospaced Font Show HTML Part by Default Condense Mail Headers Topic: [<< First] [< Prev] [Next >] [Last >>]
Sender: Mailing list for the LaTeX3 project <[log in to unmask]> Date: Mon, 15 Mar 2010 10:51:32 +0000 Reply-To: Mailing list for the LaTeX3 project <[log in to unmask]> Message-ID: <[log in to unmask]> MIME-Version: 1.0 Content-Transfer-Encoding: 7bit In-Reply-To: <[log in to unmask]> Content-Type: text/plain; charset=ISO-8859-1; format=flowed From: Joseph Wright <[log in to unmask]> Parts/Attachments: text/plain (78 lines) On 14/03/2010 23:22, Will Robertson wrote: > On 14/03/2010, at 11:36 PM, Will Robertson wrote: > >> The code is somewhat tentative but I think it shows this approach is valid. Any comments or suggestions? > > Well, I do notice that etex.sty does a lot of this stuff as well, so I really should be working off that package rather than re-inventing the relevant parts of it... in fact, it almost replaces entirely the need for the expl3 stuff; just need to say (I think) > > \let \int_new:N \globcount > \let \int_new_local:N \loccount > > etc. etc. > > Should have looked in there first :) I didn't realise it provided support for local registers already. So the question "is this okay on LaTeX2e" is not a problem (as expl3 loads etex anyway). One thing I'd be tempted to do would be: \int_new:N \l_scratch_int % Local \int_gnew:N \l_some_int % Global where \int_new:N checks \currentgrouplevel, and allocates from the global pool (low to high numbers) if it's used outside of any group, and from the local pool (high to low numbers) otherwise. (This is pretty easy to do, and I'd hope is not too "costly".) My reasoning for this is that we have set/gset, and so are (in the main) favouring local unless specified. --- I had a look at what the original example was for local declarations. The lead off was the C++ model: for (...) { int j = ... } which is considered better than: int j; for (...) { j = ... } (I know very little C++, so I'm going to assume that this is correct!) The LaTeX2e analogy was then: \whiledo{...}{ \newcount\j } But the allocations here are all at the same group level, so I'm not sure that the example quite works. I guess better is \cs_set:Npn \some_function: #1... { \group_begin: \int_new:N \l_some_int % Assuming my new/gnew approach => local. % Do stuff \group_end: } Now that's okay provided there is no nesting of \some_function:, as local in a TeX sense is not the same as local in an OO sense. Assignments aren't expandable and so we are safe from some kind of recursive, expansion-based nesting. However, are we safe from all nesting? I can't currently think of a realistic example where we might run into trouble, but perhaps I'm lacking imagination. --- My conclusion from the above is I'm quite happy to go for local assignments and a C++-like model for where variables should be created, unless there is a good reason to think that some kind of nested _new situation is likely to occur. Even then, I guess you can just warn about it. -- Joseph Wright | {} |
Let $f:[a,b] \rightarrow \mathbb{R}$ be a bounded function and continuous on $(a,b)$. Prove $f$ is Riemann integrable on $[a,b]$
I'm trying to prove that if $f:[a,b] \rightarrow \mathbb{R}$ is a bounded function, and assuming that $f$ is continuous on $(a,b)$ then $f$ is Riemann integrable on $[a,b]$. Here's my attempt at the proof:
Since $f$ is continuous, by definition $\exists \delta$ such that $\forall \epsilon > 0$:
$|x - y| < \delta \rightarrow |f(x) - f(y)| < \epsilon$
Now I'm going to guess that I'm supposed to use either the theorem:
$f$ is Riemann integrable iff $\forall \epsilon > 0, \exists \text{ partition, } P \text{ s.t } U(f,p) - L(f,p) < \epsilon$
or the theorem:
$f$ is Riemann integrable with Riemann integral I iff $\forall \epsilon > 0, \exists \text{ a partition P s.t. } U(f,p)-\epsilon < I < L(f,p) + \epsilon$
to create some sort of epsilon argument. I'm going to try using the first one because if I'm being honest, I wouldn't know how to go about with the second.
Let $P$ be a partition of $[a,b]$ such that $P=\{a = x_0, x_1, \ldots, x_n = b\}$ where the distance between each $x_i$ and $x_{i+1}$ is less than $\delta$ (because of continuity?). And then our sup and inf will exist somewhere within our partition:
$M_i = \sup(f(x))$ where $x\in (x_i, x_{i+1})$
$m_i = \inf(f(x))$ where $x \in (x_i, x_{i+1})$
And here's where I'm stuck. Help or advice would be much appreciated!
• Hints: use a partition such that the first rectangle (the one containing $a$) is narrow enough so that $(M_0 - m_0) \times \text{width}$ is less than $\epsilon/3$, and similarly for the last rectangle (the one containing $b$). You will need the boundedness in order to do this. Then, use uniform continuity on $[x_1, x_{n-1}]$. – Bungo Dec 8 '16 at 2:08
• @Bungo Sorry, but I don't quite understand how to set up the partition. Do we let the partition be something like $P_N = \{a + \frac{0 \cdot (b-a)}{N}, a + \frac{1 (b-a)}{N}.... a+\frac{N(b-a)}{N} = b$? – Nikitau Dec 8 '16 at 2:29
• You can define it that way (uniformly spaced) but only if you make $N$ sufficiently large. How large does it need to be? Well, if we let $\Delta = (b-a)/N$ for brevity, we would like to simultaneously satisfy $(M_0 - m_0) \Delta < \epsilon / 3$, and $(M_N - m_N) \Delta < \epsilon / 3$, and $\sum_{j=1}^{N-1}(M_j - m_j)\Delta < \epsilon/3$. For the first two conditions, use the boundedness of $f$, and for the last one, use the uniform continuity of $f$ on any closed bounded interval contained in $(a,b)$. Work out how large $N$ has to be to satisfy each condition, then choose the max. – Bungo Dec 8 '16 at 2:34
• Do you already know that a bounded continuous function is integrable? The two additonal points cannot do anything to the integral. – Jacob Wakem Dec 8 '16 at 2:46
• @Alephnull I do know the proof where if f is continuous on closed [a,b], then f is RI on [a,b]. Would the proof then be completely analogous to that? – Nikitau Dec 8 '16 at 2:52 | {} |
# Reducing font size in equation
I wanted to type an equation in LaTeX. But it is too long to fit into one line. It involves big arrays with many columns so I cannot split it. I wanted to reduce the font size so that it can fit in one line. However, \small doesn't work in the equation environment.
-
Can we see the actual equation? Perhaps we could then suggest some alternatives. – Gonzalo Medina Jun 19 '12 at 20:31
Will \scriptstyle and \scriptscriptstyle work? – azetina Jun 19 '12 at 20:31
as a last resort, just pack the whole thing into a \scalebox and shrink as much as necessary. rewriting as much as possible would be advisable first. – barbara beeton Jun 19 '12 at 20:38
I agree with Gonzalo, don't scale unless nothing else can be done. If the equation is so large that scaling is needed, chances are that scaling the equation will not make it be more understandable for the reader. In most cases a rewrite is a better option. – daleif Jun 20 '12 at 14:49
Just put \small before the equation and \normalsize after it if you want to shrink the font, but it's usually better to use an ams multi-line equation environment than to change font size.
It's actually easier to only do the part of a size change command that affects math without changing the baseline to avoid the problems @barabara-beeton mentions. This is a \tiny (5pt) equation in a \large paragraph text, to highlight the differences, and to show that the above and below display skips are not altered.
\documentclass{article}
\showoutput
\showboxdepth3
\begin{document}
\large
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
$$abc+xyz=44$$
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
\begingroup\makeatletter\def\f@size{5}\check@mathfonts
$$abc+xyz=44$$\endgroup
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
\end{document}
with AMS align this would produce:
\documentclass{article}
\usepackage{amsmath}
\showoutput
\showboxdepth3
\begin{document}
\large
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
\begin{align}
abc&+xyz&&=44\\
x&-y&&=2\\
a&+b&&=77
\end{align}
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
hghghga hghghga hghghga hghghga hghghga hghghga hghghga
\begingroup\makeatletter\def\f@size{5}\check@mathfonts
\def\maketag@@@#1{\hbox{\m@th\large\normalfont#1}}%
\begin{align}
abc&+xyz&&=44\\
x&-y&&=2\\
a&+b&&=77
\end{align}\endgroup
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb
\end{document}
-
however, unless there's a paragraph break before the display, the baselines of the preceding paragraph will be fouled up, and if there is a blank line/pargraph break before the display, the vertical space preceding the display will be fouled up, and a page break would also be allowed because of the paragraph break. there's no good (automatic) mechanism defined for this yes, as far as i know. – barbara beeton Jun 19 '12 at 21:42
@barbarabeeton yes I was going to mention that. If there were a MWE I'd have probably shown it with a correction for baselinskip. I suppose I should make one. It can't be that hard can it to insert a par while preserving the predispolay skip. – David Carlisle Jun 19 '12 at 22:15
@barbarabeeton something like the code in the updated answer? – David Carlisle Jun 19 '12 at 23:08
make it a 3-line display and i'll be happier. – barbara beeton Jun 20 '12 at 13:04
@barbarabeeton 3 line display added, so you should be happy, but I guess you wanted tighter line spacing in the display? – David Carlisle Jun 20 '12 at 13:58
Similar to How to make math font huge, you can use \scalebox to scale down the equation, or \resizebox the box to a specific width to reduce the size. The first is the normal display mode equation, followed by the scaled version with \scalebox and \resizebox:
## Code:
\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}%
\newcommand*{\Resize}[2]{\resizebox{#1}{!}{$#2$}}%
\begin{document}
$y = \sin^2 x$
%
$\Scale[0.5]{y = \sin^2 x}$
%
$\Resize{1cm}{y = \sin^2 x}$
\end{document}
-
Perhaps you could also mention \resizebox{\textwidth}{!}{...} to not have to guess scaling factors. – Gonzalo Medina Jun 19 '12 at 21:00
And use \sin, please! :) – egreg Jun 19 '12 at 21:02
@GonzaloMedina: Done. – Peter Grill Jun 19 '12 at 21:37
@egreg: How embarrassing! Have corrected it. – Peter Grill Jun 19 '12 at 21:37
@PeterGrill ;-) – egreg Jun 19 '12 at 21:38
The following illustrates font size alterations in mathmode:
\documentclass[letterpaper]{article}
\usepackage{graphicx} % Necessary to use \scalebox
\usepackage{amsmath,amssymb}
\begin{document}
\noindent
normal: $x^2 + 2xy + y^2$\\
displaystyle: ${\displaystyle x^2 + 2xy + y^2}$\\
scriptstyle: ${\scriptstyle x^2 + 2xy + y^2}$\\
scriptscriptstyle: ${\scriptscriptstyle x^2 + 2xy + y^2}$\\
textstyle: ${\textstyle x^2 + 2xy + y^2}$
\noindent
\scalebox{0.5}{%
normal: $x^2 + 2xy + y^2$}
\end{document}
This yields:
Note that:
• \displaystyle gives the command to switch the math font size to normal size for displayed formulas.
• \textstyle is used to go back to normal size font for inline formulas.
• \scriptstyle is used to set the math font to a size used for subscripted and superscripted symbols.
• scriptscriptstyle provides the normal size for doubly subscripted and superscripted symbols.
When using the \scalebox command from the graphicx package one can specify the width (or height) and the other dimension will be scaled proportionally. In a similar manner you can specify both dimensions, but in this case it is all about aesthetics. Therefore we have the following under the \scalebox command:
• \scalebox{h-dimension}{v-dimension}{content to be scaled}: both dimension stated.
• \scalebox{h-dimension}{content}: both arguments (h-dim and v-dim) scaled with respect to the stated dimension.
- | {} |
$$\renewcommand\AA{\unicode{x212B}}$$
# SavePlot1D v1¶
## Summary¶
Save 1D plots to a file
## Properties¶
Name
Direction
Type
Default
Description
InputWorkspace
Input
Workspace
Mandatory
Workspace to plot
OutputFilename
Input
string
Name of the image file to savefile. Allowed extensions: [‘.png’]
OutputType
Input
string
image
Method for rendering plot. Allowed values: [‘image’]
XLabel
Input
string
Label on the X axis. If empty, it will be taken from workspace
YLabel
Input
string
Label on the Y axis. If empty, it will be taken from workspace
SpectraList
Input
long list
Which spectra to plot
SpectraNames
Input
str list
Override with custom names for spectra
Result
Output
string
PopCanvas
Input
boolean
False
If true, a Matplotlib canvas will be popped out , which contains the saved plot.
## Description¶
Save 1D plots to a png file, as part of autoreduction. Multiple spectra in the same workspace will be represented by curves on the same plot. Groupped workspaces will be shown as subplots. If the workspace has more than one spectra, but less or equal to ten, labels will be shown.
Note
The figures contain lines between points, no error bars.
Note
Requires matplotlib version>= 1.2.0
## Usage¶
#create some workspaces
CreateWorkspace(OutputWorkspace='w1',DataX='1,2,3,4,5,1,2,3,4,5',DataY='1,4,5,3,2,2,3,1',DataE='1,2,2,1,1,1,1,1',NSpec='2',UnitX='DeltaE')
CreateWorkspace(OutputWorkspace='w2',DataX='1,2,3,4,5,1,2,3,4,5',DataY='4,2,5,3,3,1,3,1', DataE='1,2,2,1,1,1,1,1',NSpec='2',UnitX='Momentum',VerticalAxisUnit='Wavelength',VerticalAxisValues='2,3',YUnitLabel='Something')
wGroup=GroupWorkspaces("w1,w2")
#write to a file
try:
import mantid
filename=mantid.config.getString("defaultsave.directory")+"SavePlot1D.png"
SavePlot1D(InputWorkspace=wGroup,OutputFilename=filename)
except:
pass
Output:
The file should look like
## Usage in autoreduction¶
# create some workspaces
CreateWorkspace(OutputWorkspace='w1',DataX='1,2,3,4,5,1,2,3,4,5',DataY='1,4,5,3,2,2,3,1',DataE='1,2,2,1,1,1,1,1',NSpec='2',UnitX='DeltaE')
# get the div html/javascript for the plot
div = SavePlot1D(InputWorkspace='w1', OutputType='plotly')
from postprocessing.publish_plot import publish_plot
request = publish_plot('TESTINSTRUMENT', 12345, files={'file':div})
print("post returned {}".format(request.status_code))
To see what the result looks like on your local system, add the Filename argument (.html extension) and change to OutputType='plotly-full'.
Categories: AlgorithmIndex | DataHandling\Plots
## Source¶
Python: SavePlot1D.py | {} |
Thread: Continuous function from (0,1) to [0,1]
1. Continuous function from (0,1) to [0,1]
I came across a very confusing question.
Which of the following statements are true about the open interval $(0,1)$ and the closed interval $[0,1]$?
1. There is a continuous function from $(0,1)$ onto $[0,1]$.
2. There is a continuous function from $[0,1]$ onto $(0,1)$.
3. There is a continuous one-to-one function from $(0,1)$ onto $[0,1]$.
It's immediately clear to me that 3 is wrong because the inverse image of a closed set has to be closed and it isn't, but what about the other two?
Statement 2 requires that the function be onto but not one-to-one. If it is onto, then the entire closed unit interval gets mapped to the open unit interval, so the inverse image of $(0,1)$ should be $[0,1]$ and open sets should have on open inverse image.
Why doesn't the same argument work for statement 1? The answer key of the book says that statement one is the only correct one. If one is indeed true, is there a simple example of such a continuous function?
2. Originally Posted by eeyore
I came across a very confusing question.
Which of the following statements are true about the open interval $(0,1)$ and the closed interval $[0,1]$?
1. There is a continuous function from $(0,1)$ onto $[0,1]$.
2. There is a continuous function from $[0,1]$ onto $(0,1)$.
3. There is a continuous one-to-one function from $(0,1)$ onto $[0,1]$.
It's immediately clear to me that 3 is wrong because the inverse image of a closed set has to be closed and it isn't, but what about the other two?
Statement 2 requires that the function be onto but not one-to-one. If it is onto, then the entire closed unit interval gets mapped to the open unit interval, so the inverse image of $(0,1)$ should be $[0,1]$ and open sets should have on open inverse image.
Why doesn't the same argument work for statement 1? The answer key of the book says that statement one is the only correct one. If one is indeed true, is there a simple example of such a continuous function?
I don't think (1) is correct either: if f: (0,1) --> [0,1] is cont. and onto, then if w in (0,1) is s.t. f(w) = 1 we get f|: (0,1) - {w} --> [0,1) is onto
and continuous (with f| = the restriction of f).
But this can't be correct since (0,1) - w is not connected (it isn't an interval) whereas [0,1) is...
(3) is then same as (1) above (the argument about closed set doesn't work because both (0,1) and [0,1] are closed wrt the inherited topology of R)
About (2) a simmilar argument as above (taking out 1 and f(1)) shows it can't be either, or you can say that continuous images of compact sets are compact, and [0,1] is compact but (0,1) is not.
Tonio
3. I think 1 is true. You can construct an homeomorphism from [1/2,3/4] to [0,1] and then define f constant as 0 on (0,1/2] and 1 on [3/4,1). The problem with the given argument by Tonio is that w such that f(w)=1 can't be unique. In fact, this argument of Tonio shows that there is no a continuous bijection between (0,1) and [0,1], that is that 3 is not correct, but one needs to use inverse because connection is preserved by images and not preimages. | {} |
Rotate sprite along the angle between two objects
Im trying to make flames follow my object, I set the direction for my moving object using the points between it and another object (using static destination for testing).
No matter what I do I cannot use the radians (which I use to set the direction), translate them to degrees, then rotate my flames so it looks like they are following it (like a comet).
What I try:
sprite.setPosition(pos.x, pos.y);
degrees = radians * 180 / MathUtils.PI; //calculate degrees
fireSprite.setPosition(sprite.getX(), sprite.getY());
fireSprite.setRotation((float)degrees); //rotate according to degrees
I move the object like this:
pos.x += 200 * Math.cos(radians) * delta;
pos.y += 200 * Math.sin(radians) * delta;
Am I missing something in the math? I feel like it should work.
An example of result from calculations:
radians: -1.8745297149164084, degrees: -107.4026382478209
The flames face the wrong direction, and not in a any sort of pattern I can use to debug my problem.
• Why 540 - pos? Where does this come from? Try 0-pos.x... – Majte Oct 25 '15 at 16:36
• As I said, Im using these values for testing. those values represent the bottom-mid of my screen – Green_qaue Oct 25 '15 at 16:44
• does rotation need to be in non-radians? – Majte Oct 25 '15 at 17:05
• @Majte unfortunately yes, as far as I know. – Green_qaue Oct 25 '15 at 17:55
• you are calculating the angle between the bottom mid and the position of the object. How is this supposed to follow your object like a comet trait? You need to set the rotation to be the atan2 of the velocity vector of your moving object. – Majte Oct 25 '15 at 18:20
You can try taking the vector from the ship (or whatever you have) to the target position, then get the angle of that. libGDX's Vector2 class has most of the methods you need.
Something like this might work for you;
// Get these from where ever you have them
Vector2 shipPosition = new Vector2(100, 100);
Vector2 targetPosition = new Vector2(0, 540);
// Calculate the vector from the ship to the target
Vector2 fromShipToTarget = new Vector2(targetPosition).sub(shipPosition);
// Get the angle of the ship-to-target
float angle = fromShipToTarget.angle();
// Set the origin so that the sprite is rotated around its center, not its corner
fireSprite.setOrigin(fireSprite.getWidth() / 2.0f, fireSprite.getHeight() / 2.0f);
fireSprite.setPosition(shipPosition.x, shipPosition.y);
fireSprite.setRotation(angle);
The angle method on Vector2 will give you the angle of the vector towards the positive y-axis so if you have two points (0, 0) and (1, 1) the above example will yield a vector of 45 degrees.
Here is the code I use to get the angle of a 2d vector, hopefully it is what your are looking for. (using our own library functions, most of which should be obvious)
float zVec2f::getAngle () const
{
//straight up, 0.0f degrees
zVec2f up(0.0f, -1.0f);
//angle between up vector and our vector
zVec2f normal = *this;
if ( normal.normaliseSafe() ) // returns true if it was possible to normalize vector
{
float angle = acosf(zDot(normal,up));
//compensate for the fact that acos only
//gives us 0->Pi (mirror along 180 degree line)
if ( x < 0.0f)
{
angle += (2.0f * (zPIf - angle));
}
zASSERT(angle>=0.0f);
zASSERT(angle<=zPI2f);
return angle;
}
return 0.0f;
}
• This function reinvents the wheel and is really too long. I can’t recommend anyone uses it. It can be rewritten in one single line: float zVec2f::getAngle () const { return atan2f(this->x, - this->y); } – sam hocevar Apr 24 '16 at 17:07 | {} |
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Square Root
Tool to compute and simplify a square root. The square root for a number N, is the number noted sqrt(N) that, multiplied by itself, equals N.
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# Square Root
## Batch Square Root Computation
### How to calculate a square root?
The dCode square root calculator allows both positive or negative numbers (thus having complex roots) and returns answers with an exact value or an approximate value (the precision can be adjusted by defining a minimum number of significant digits)
Example: $\sqrt{4} = 2$ and $\sqrt{-1} = i$
### How to simplify a square root?
Root calculations have properties similar to exponentiation:
$$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \\ \sqrt{ \frac{a}{b} } = \frac{\sqrt{a}}{\sqrt{b}}$$
For any positive real number $a \in \mathbb{R}_+^*$
$$\sqrt{a^2} = a \\ \left( \sqrt{a} \right)^2 = a$$
Therefore
$$\sqrt{a^2 \times b} = a \sqrt{b}$$
### How to simplify a fraction with square root?
If the denominator is a radical, then multiply the numerator and the denominator by it to make it disappear.
$$\frac{a}{\sqrt{b}} = \frac{a\sqrt{b}}{\sqrt{b}^2} = \frac{a\sqrt{b}}{b}$$
If the denominator is an addition or subtraction of roots, then apply the remarkable identity: $(a+b)(a-b) = a^2-b^2$
$$\frac{a}{\sqrt{b}+\sqrt{c}} = \frac{a(\sqrt{b}-\sqrt{c})}{(\sqrt{b}+\sqrt{c})(\sqrt{b}-\sqrt{c})} = \frac{a\sqrt{b}-a\sqrt{c}}{b-c}$$
$$\frac{a}{\sqrt{b}-\sqrt{c}} = \frac{a(\sqrt{b}+\sqrt{c})}{(\sqrt{b}-\sqrt{c})(\sqrt{b}+\sqrt{c})} = \frac{a\sqrt{b}+a\sqrt{c}}{b-c}$$
### How to write a square root?
In Unicode format there is the character (U+221A).
In computer formulas, sqrt() function is most often used.
### What doest sqrt means?
The word sqrt is generally used in the formula to indicate a square root, the word comes from the contraction of square root.
Example: sqrt(2) = $\sqrt{2}$
### What is a square number?
A square number is the square of an integer.
Example: $3$ is an integer, $3^2 = 3 \times 3 = 9$ then $9$ is a square number.
If the square root of a number $x$ is an integer, then $x$ is a square number.
## Source code
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# Math Help - Hyperbolic functions
1. ## Hyperbolic functions
I have to find the integral of 1/((25x^2-49)^1/2) using hyperbolic functions. I'm not sure how to start to know which functions to use, thanks
2. It sounds like you are expected to know (or be able to determine from a table) the derivatives of the inverse hyperbolic functions. In particular, the one that is useful in this problem would be:
$\frac{d}{dx} \cosh^{-1}(x) = \frac{1}{\sqrt{x^2-1}}$
(for $x>1$)
Can you solve this with this information?
3. I wrote x as 7cosh(u) and ended up with arccosh(x/2) between 7 and 14, i'm not sure that this is right?
4. You didn't say what the original endpoints were.
I'm not sure which simplification method you use, but this is how I get it:
$\int \frac{1}{\sqrt{25x^2-49}} dx$
$=\frac{1}{7} \int \frac{1}{\sqrt{\tfrac{25}{49}x^2-1}} dx$
$=\frac{1}{7} \int \frac{1}{\sqrt{\left(\tfrac{5}{7}x\right)^2-1}} dx$
Let $u=\tfrac{5}{7}x$ and $du=\tfrac{5}{7}dx$.
$=\frac{1}{5} \int \frac{1}{\sqrt{u^2-1}} du$
$=\tfrac{1}{5} \cosh^{-1} u + C$
$=\tfrac{1}{5} \cosh^{-1}\left(\tfrac{5}{7}x\right) + C$
And this is valid for $u>1 \implies x>\tfrac{7}{5}$. | {} |
Back to Adaptive Vision Library Lite website
You are here: Start » Region Basics » CreateBoxRegion
# CreateBoxRegion
Creates a rectangular region corresponding to a given box.
### Syntax
void avl::CreateBoxRegion
(
const avl::Box& inBox,
int inFrameWidth,
int inFrameHeight,
avl::Region& outRegion
)
### Parameters
Name Type Range Default Description
inBox const Box& A box defining pixels that will be converted to white elements
inFrameWidth int 0 - Width of the created region's frame (not to be confused with the width of the box!)
inFrameHeight int 0 - Height of the created region's frame (not to be confused with the height of the box!)
outRegion Region& Output region
### Description
The operation creates a region containing pixels lying inside the inBox.
The inFrameWidth and inFrameHeight parameters most often should be set equal to the dimensions of the image this region will be used with. If the input box exceeds these dimensions, the output region will be cropped.
### Hints
• Remember to set inFrameWidth and inFrameHeight inputs to specify the region frame.
### Examples
CreateBoxRegion run with inBox = Box(50,100,200,100).
### Errors
Error type Description
DomainError Output region too big in CreateBoxRegion. | {} |
Stream: new members
Topic: gcd
Kevin Lacker (Sep 30 2020 at 18:25):
new navigating-the-docs question. I'm looking for where gcd is defined. search leads me to https://github.com/leanprover-community/mathlib/blob/5fd2037/src/data/nat/gcd.lean#L162 which has a comment saying, here is where gcd is defined. however, there doesn't actually seem to be a definition here? it only imports one file, https://github.com/leanprover-community/mathlib/blob/5fd2037/src/data/nat/basic.lean , but that file doesn't mention "gcd" at all. 1/ where is gcd defined, and 2/ what is the right way for me to discover this for myself
Bryan Gin-ge Chen (Sep 30 2020 at 18:26):
It's defined in core: docs#nat.gcd
If you type nat.gcd into the search window and wait (don't hit "search"!) then choose the first option, it should take you to this declaration.
Bryan Gin-ge Chen (Sep 30 2020 at 18:27):
In emacs it should be possible to peek / navigate to the definition of nat.gcd, which is another way of finding out where any given definition is.
Kevin Lacker (Sep 30 2020 at 18:28):
so everything under that "init" directory is automatically imported?
Bryan Gin-ge Chen (Sep 30 2020 at 18:29):
Yep, unless you put prelude at the top of your file.
Last updated: May 11 2021 at 22:14 UTC | {} |
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# An analysis framework for the integration of broadband NIRS and EEG to assess neurovascular and neurometabolic coupling
## Abstract
With the rapid growth of optical-based neuroimaging to explore human brain functioning, our research group has been developing broadband Near Infrared Spectroscopy (bNIRS) instruments, a technological extension to functional Near Infrared Spectroscopy (fNIRS). bNIRS has the unique capacity of monitoring brain haemodynamics/oxygenation (measuring oxygenated and deoxygenated haemoglobin), and metabolism (measuring the changes in the redox state of cytochrome-c-oxidase). When combined with electroencephalography (EEG), bNIRS provides a unique neuromonitoring platform to explore neurovascular coupling mechanisms. In this paper, we present a novel pipeline for the integrated analysis of bNIRS and EEG signals, and demonstrate its use on multi-channel bNIRS data recorded with concurrent EEG on healthy adults during a visual stimulation task. We introduce the use of the Finite Impulse Response functions within the General Linear Model for bNIRS and show its feasibility to statistically localize the haemodynamic and metabolic activity in the occipital cortex. Moreover, our results suggest that the fusion of haemodynamic and metabolic measures unveils additional information on brain functioning over haemodynamic imaging alone. The cross-correlation-based analysis of interrelationships between electrical (EEG) and haemodynamic/metabolic (bNIRS) activity revealed that the bNIRS metabolic signal offers a unique marker of brain activity, being more closely coupled to the neuronal EEG response.
## Introduction
Over the past few decades, neuroimaging technologies have allowed us to advance our knowledge of the mechanisms underlying human brain function, both in health and disease. Functional neuroimaging methodologies are widely used in the fields of cognitive neuroscience and neuropsychology in order to investigate the relationship between a specific task or mental function and the corresponding patterns and/or locations of brain activity. Different functional neuroimaging techniques are based on different principles, and can be broadly categorized as: electrophysiological (e.g., electroencephalography (EEG) and magnetoencephalography (MEG)), haemodynamic (e.g., functional magnetic resonance spectroscopy (fMRI) and functional near-infrared spectroscopy (fNIRS)), and metabolic (e.g. fluorodeoxyglucose positron emission tomography (FDG-PET) and broadband near infrared spectroscopy (bNIRS)). Each of these capture different and complimentary aspects of brain function, distinguished by the complex sequence of neurophysiology that underlies the generation of their signals. Furthermore, each modality has strengths and limitations that largely depend on the spatiotemporal characteristics of the signal. Electrophysiological recordings provide direct measures of neuronal activity with high temporal resolution but poor spatial resolution, while haemodynamic and metabolic imaging methods are able to indirectly assess brain activity by capturing the physiological changes linked to neurovascular and neurometabolic coupling, with better spatial specificity but lower temporal resolution. It has therefore become increasing popular to fuse data from multiple imaging modalities to yield a more detailed understanding of brain dynamics.
Among these, the use of optical methods, and particularly fNIRS is growing exponentially1. This growth can be attributed to its suitability for use with a wide range of populations and experiments in more ecological settings not afforded by other imaging modalities (i.e., portability, low sensitivity to movements, safety; see Pinti et al.2 for a review2) and for multimodal imaging (i.e., ease of integration and lack of interference with other neuroimaging methods). fNIRS measures the changes in brain tissue concentration of oxygenated (HbO2) and deoxygenated (HHb) haemoglobin. These in turn reflect the changes in cerebral blood flow (CBF) that follows neuronal activation, a physiological phenomenon referred to as neurovascular coupling3. When a brain area becomes active and neurons increase their rate of firing in response to a certain task, an increase in the metabolic demand for oxygen and glucose is observed in that area. This metabolic demand causes an oversupply of CBF in compensation. Therefore, we observe an increase in HbO2 and tissue metabolism and a decrease in HHb following neuronal firing. fNIRS measurements are obtained by shining near infrared (NIR) light (650–950 nm) into the head and collecting the backscattered light to quantify the changes in light absorbance; the changes in HbO2 and HHb concentrations are then derived using the modified Beer-lambert law (MBLL) algorithm. The current commercially available instruments are equipped with several light sources and detectors, i.e. multi-channel, allowing simultaneous measurements at different locations on the head.
Light sources used in traditional NIRS systems typically emit light at 2 or 3 wavelengths in the NIR range, which allow users to resolve changes in HbO2 and HHb concentrations only. However, for several years our team has been developing a technological and methodological extension to fNIRS called broadband NIRS (bNIRS). bNIRS is an optical-based neuroimaging technology that utilizes hundreds of NIR wavelengths with the capacity to measure an additional brain tissue chromophore, cytochrome-c-oxidase or CCO. CCO is the terminal enzyme of the electron transport chain in the mitochondria and is responsible for catalysing 95% of oxygen to produce energy in the form of ATP; CCO thus provides an indicator of cerebral cellular oxygen metabolism. bNIRS can quantify the redox state of cytochrome-c-oxidase (oxCCO), that contributes to the NIR spectrum of the brain tissue together with haemoglobin. Absorption in the NIR range, with a peak at ~ 830 nm, is dominated by one of the CCO copper sites in its oxidized form (oxCCO). This signal can be measured using bNIRS. For a complete overview on bNIRS-based measurements of oxCCO, see Bale and colleagues (2016) for review. Measuring oxCCO presents several challenges. For instance, oxygenation measurements are easier to perform as HbO2 and HHb are present in higher concentration than CCO. HbO2 and HHb signals can hence mask oxCCO signals and proper algorithms, wavelengths and extinction spectra are necessary to avoid cross talk and ensure that changes in all three chromophores are properly resolved4. However, it has been demonstrated that oxCCO can provide more specific brain signals than haemoglobin5. This may be due to the fact that CCO is more concentrated in the intracerebral compartment6 and is less contaminated by the extracerebral layers, while haemoglobin signals can be strongly confounded by systemic contamination from the extracerebral layers7. A previous study by de Roever and colleagues has demonstrated this further by investigating both haemodynamic and metabolic activity during a functional task at different depths and confirming that higher oxCCO responses can be found in deeper channels rather than in the superficial ones, while haemodynamic responses were observed in all the channels8.
The development of bNIRS instruments using the full spectrum of NIR light and novel algorithms (i.e., ‘UCLn’9) have aided in overcoming some of the aforementioned technical issues and can robustly estimate both haemoglobin and oxCCO changes. Therefore, bNIRS presents a truly unique method to monitor both the changes in brain oxygenation and haemodynamics (∆HbO2 and ∆HHb) and in metabolism (∆oxCCO) induced by neuronal activation simultaneously and non-invasively (Note: For simplicity, we will use ‘brain haemodynamics’ to refer to ‘brain oxygenation and haemodynamics measurements’ throughout the manuscript).
The possibility of assessing how the energy is supplied and used by the brain under different conditions paves the way for novel fundamental investigations of the mechanisms underlying neurovascular coupling and has the potential to advance our understanding of brain physiology and cognitive functioning both in health and in disease. Previous studies have suggested that, in order to properly understand the functioning of the brain and its alteration, it is important to consider not only the differences in metabolism across regions but to also account for the underlying brain activity. It has also been demonstrated that high neuronal activity is typically associated to high metabolic supply in a healthy brain, and that brain regions may show different relationships between activity demand and metabolic supply (e.g., metabolism may fall behind neuronal activity in a certain region depending on which metabolic substrate is used), which in turn may be altered in case of neuropsychiatric disorders or disease10. For instance, Shokri-Kojori and colleagues (2019) have recently demonstrated how alcohol intoxication can alter the relationship between neuronal activity and glucose metabolism as measured by fluorodeoxyglucose-positron emission tomography (FDG-PET) and fMRI. However, gold standard neuroimaging technologies such as PET and fMRI do not allow the monitoring of both metabolic and neuronal activity of the brain simultaneously and separate testing sessions are required, which in turn can be problematic for clinical populations. Here, we propose that bNIRS can be an ideal candidate to gather data on both the brain metabolic supply and oxygenation/haemodynamic changes and to evaluate their relationship simultaneously and non-invasively.
To date, there are no commercially available bNIRS instruments and existing systems are developed entirely in laboratories11,12. Therefore, the use of bNIRS is not as popular as fNIRS yet. Few functional activation studies with bNIRS have been performed on adults (see Bale et al.4 for review)6,8,13,14,15,16 and only two in infants17,18. In particular, conventional stimulation protocols have mainly been employed thus far, such as visual14 and auditory15 stimulation or anagram solving tasks6,13. Results from these studies were derived using basic analytical approaches, such as block-averaging combined with t-tests to infer functional activity at a group level6,8,13,14,15,16,17. However, none of these basic statistical approaches utilizes and take into consideration the haemodynamic and metabolic response and, importantly, their interrelationship. Moreover, the coupling of neural and vascular responses (also known as neurovascular coupling) is not very well understood, particularly in pathology, primarily due to the lack of availability of feasible techniques. While the measurement of haemodynamic and metabolic activity through the use of bNIRS systems provide an understanding on one end of neurovascular coupling, investigation still needs to be done to understand how neural electrical activity relates to metabolic and haemodynamic activity in order to obtain a more holistic understanding of basic biological mechanisms in the brain. EEG offers a measurement of neuronal functioning by measuring the brain electrical activity directly. Therefore, the combination of bNIRS and EEG has the potential to provide enhanced and holistic information on neurovascular coupling and a window into brain oxygenation, haemodynamics, metabolism and neuronal function. Previous studies have combined fMRI and EEG for the purposes of this exploration19,20,21,22. Studies have also combined fNIRS with EEG to investigate neurovascular coupling in both clinical and non-clinical applications (see Chiarelli et al.23 for review) and have demonstrated the strength of fNIRS-EEG as multimodal tool to assess both the brain electrical and haemodynamic activity. However, the haemodynamic and electrical signals measured by fNIRS and EEG do not have exact spatiotemporal correspondence23 and have very different time resolution (order of seconds for fNIRS, order of milliseconds for EEG). Therefore, the integration of haemodynamic data with EEG presents several challenges and new methods need to be explored. In addition, previous works did not include bNIRS derived metabolic measures and thus did not evaluate the relationship between brain neuronal and metabolic activity.
Generally, statistical modelling procedures are commonly employed in functional neuroimaging studies24 to characterize and localize the neural responses to cognitive tasks and to infer functional activity. They usually make use of General Linear Models (GLMs)25 to deal with the complex characteristics of functional neuroimaging data. The canonical GLM is a well-established regression approach extensively used for haemodynamic-based neuroimaging data analysis, such as for fMRI25 and fNIRS26. It is able to capture cerebral activity by fitting the experimental data with a model of functional activity built through the convolution of a boxcar function, describing the experimental protocol, with a Haemodynamic Response Function (HRF)25. The canonical HRF reflects the changes in CBF in response to neuronal activation and is usually modelled as a linear combination of two Gamma functions. The advancements in neuroimaging statistical methodologies have made possible to have freeware software platforms implementing processing and canonical GLM-based statistical analyses of fNIRS haemodynamic data (e.g., Ye et al.2727 or Sutoko et al.2828) but these do not take into consideration metabolic signals and deal only with HbO2 and HHb. In addition, there is no analogous of the HRF for oxCCO at the moment. Therefore, the existing statistical framework needs to be expanded for bNIRS to make inferences on both haemodynamic and metabolic neuroimaging data. For instance, de Roever and colleagues (2017) experimented with the use of deconvolution GLM using Gaussian basis function with no a-priori assumption on the shape of the haemodynamic and metabolic responses for short-separation channel regression (i.e., remove the extra-cerebral interference from long separation channels). Results showed that this method was suitable to recover both the haemodynamic and metabolic responses while at the same time removing scalp contamination as measured by short-separation channels29.
With the advent of the bNIRS technology, which provides the capacity for imaging both brain haemodynamics and metabolism (HbO2, HHb, oxCCO), there is an urgent need for new methods and tools that will enable extension of the more advanced statistical approaches typically used for haemodynamic neuroimaging data to the analysis of bNIRS-derived metabolic signals. In this paper, we demonstrate the use of bNIRS to monitor the haemodynamic and metabolic activity of the visual cortex of healthy adults and we establish a new analysis framework for the localization of brain activity and the fusion of haemodynamics with metabolic and neuronal information. In particular, we present a novel analysis pipeline that allows us to (i) pre-process and denoise the bNIRS signals, (ii) construct a statistical framework that can be used to test hypothesis about functional haemodynamic and metabolic imaging data (iii) combine the information derived from the analysis of haemodynamic and metabolic data to assess the relationship between the brain haemodynamics and metabolism during functional activity, and (iv) construct a data analysis pipeline that allows the integration of bNIRS signals with EEG in order to obtain a more holistic understanding of neurovascular coupling mechanisms. Our analysis pipeline: (1) includes steps to minimize physiological noise and motion artifacts; (2) is based on the GLM framework employing FIR basis functions to overcome the issue of making assumptions on the models of haemodynamic and metabolic responses; (3) expands on the use of two indices reflecting the correspondence between cerebral metabolism and brain haemodynamics (relative power and relative cost) recently developed by Shokri-Kojori and colleagues (2019) using FDG-PET and fMRI10 to measures extracted from bNIRS data; (4) assesses the similarity and time dynamic relationship between the bNIRS and EEG gamma band activity. We demonstrate the use of the proposed pipeline on bNIRS data recorded on healthy adults during a visual stimulation task.
## Results
### bNIRS pre-processing
Following the conversion of the raw intensity spectra into raw concentration changes (Phase 1, Fig. 10), we visually inspected the raw ΔHbO2, ΔHHb, and ΔoxCCO signals to identify the channels with a low signal to noise ratio. An example of a noisy channel from one participant is shown in Fig. 1A: where the time-series data exhibit higher than normal amplitude changes (≥ 5 mol/L) particularly for HHb and oscillations appear random and not task-related; their frequency spectra indeed resemble the spectrum of white noise, suggesting that the optical coupling between the optode and the head was not optimal in this case30.
In Fig. 1B, the raw ΔHbO2, ΔHHb, and ΔoxCCO from a good quality channel from the same participant is shown, where the signals’ changes are within a more physiological range (~ 1–1.5 mol/L), and the corresponding FFTs have the typical 1/f decreasing trend and the task-related frequency can be clearly identified around 0.014 Hz (Fstim = 1/72 s; i.e. every 72 s a new hemifield stimulus was presented) for all three chromophores.
Following this procedure, we excluded channel 13, 15 and 16 for one participant as no heart rate component could be detected and the signals’ characteristics resembled white noise features. All channels were included for the rest of our cohort, suggesting that the 3D printed optode holder was effective in maximizing signals quality and the optimal coupling while minimizing the holder displacements.
The preprocessing steps successfully allowed minimization of the unwanted noisy components in our data. In terms of motion artifacts, an example of the application of the wavelet-based method to our haemodynamic and metabolic data of one participant is shown in Fig. 2A.
It can be observed that the wavelet filtering was able to properly correct the fast spikes due to rapid head movements and temporary displacement of the optodes while preserving the haemodynamic/metabolic modulations of our signals. In addition, the band-pass filter was effective in removing both the slow trends in the data and smoothing the higher frequencies (Fig. 2B), with the final chromophore signals centered around the zero-level and with an amplitude comprised between -1 and 1 µmol/L that are typical concentration changes during functional brain activity31.
### bNIRS statistical analysis
In Fig. 3, we present the results of the application of the FIR-based GLM to ΔHbO2, ΔHHb, and ΔoxCCO. In particular, the group-averaged estimated responses ΔHbO2, ΔHHb, and ΔoxCCO are shown for all the channels for the Right and Left experimental conditions.
These results demonstrate that the FIR basis functions are able to capture the haemodynamic and metabolic responses to our functional task, recovering an average response with the typical trend of fNIRS data recorded with block-designed experiments (i.e., increase in ΔHbO2 and decrease in ΔHHb)2 and with larger changes in the contralateral channels to the visual stimulus. To localize functional brain activity at the group level, we carried out a channel-wise one sample t-tests against 0 on the median β2-values values extracted from the ΔHbO2, ΔHHb, and ΔoxCCO estimated responses. Group-level results are included in Fig. 3, where red circles represent statistically significant ΔHbO2 changes, blue circles statistically significant ΔHHb changes, and green circles statistically significant ΔoxCCO changes (p < 0.005, FDR corrected for multiple comparisons). Group-level t-values for each chromophore and channel are reported in Supplementary Table 2.
### Integration of bNIRS haemodynamic and metabolic data
To evaluate the relationship between brain haemodynamics and metabolism, we computed the rPWR and rCST combining the median β-values of ∆HbO2 or ∆HHb with the median β-values of ∆oxCCO, which we extracted from the GLM. In Fig. 4, we show the haemodynamics vs metabolism plot for the Right stimulation condition as an example. On the left, we show the results using the median β-values of ∆HbO2 and ∆oxCCO averaged across participants, while on the right we show the median β-values of ∆HHb and ∆oxCCO averaged across participants, in the mean–variance-normalized map. Magenta circles represent bNIRS channels located in the left hemisphere (# 1–8) and black crosses channels located in the right hemisphere (# 9–16). The rPWRHbO2 / rPWRHHb axes are shown in light blue and the rCSTHbO2/ rCSTHHb axes are shown in orange. Through this visualization, the map is divided into four quadrants based on the magnitude and direction of the changes in HbO2/HHb and oxCCO. For instance, channels in the top right quadrant exhibit a greater increase in HbO2 and oxCCO, and a greater decrease in HHb, leading to a high rPWR; e.g. channel 7 has z(HbO2) = 1, z(HHb) = 0.57, z(oxCCO) = 0.84, corresponding to rPWRHbO2 = 1.3 and rCSTHbO2 = -− 0.1, and rPWRHHb = 1 and rCSTHHb = 0.19, suggesting that during the right hemifield stimulation, the primary visual cortex (V1) is characterized by concurrent changes in haemodynamics and metabolism (high rPWR), with nearly null mismatch (low rCST). In our case, almost all the channels are located in the top right and bottom left quadrants, suggesting that functional brain activity of the visual cortex to our task is associated to consistent changes in haemodynamics and metabolism as expected in a healthy population (i.e., greater increase in HbO2 and oxCCO, and greater decrease in HHb in the areas responding to the experimental task; greater decrease in HbO2 and oxCCO and greater increase in HHb in the unstimulated areas).
In order to localize the patterns of significant rPWR and rCST within the occipital cortex, we carried out channel-wise one sample t-tests against 0 on rPWRHbO2, rPWRHHb, rCSTHbO2, rCSTHHb. Group-level results for rPWR are shown in Fig. 5. t-values maps for rPWRHbO2 and rPWRHHb of each experimental condition (Right/Left) are presented, where magenta circles indicate the statistically significant channels (p < 0.05) that survived the FDR correction.
We did not find any significant result for rCST, except for channel 10 covering the right V1-V2 regions (Supplementary Table 1) where we found a significant reduction in the coupling between HHb and oxCCO for the right hemifield stimulation, with changes in HHb exceeding the changes in oxCCO in respect to the rest of the channels. Group-level t-values for both rPWR and rCST are included in Supplementary Tables 3 and 4 respectively.
### Integration of bNIRS and EEG data
The cross-correlations between bNIRS and EEG were computed as described in the Methods section. For each EEG electrode and bNIRS channel combination, time window, chromophore and condition, the FDR-corrected significant correlations and their corresponding time lags were identified. In Figure g A we show the results from the earliest time window (1–16 s) during which the stimuli were being presented; Fig. 6B shows the time windows corresponding to the maximum significant correlation for each EEG-bNIRS measurement pair. The correlations are shown for each of the chromophores and conditions. The channels without any correlations are those where either the EEG gamma band activity was non-significant or the cross-correlation was non-significant after statistical analysis.
For the earliest time window (1–16 s), i.e. the time of stimulus presentation (Fig. 6A), our analysis demonstrates a predominantly negative correlation between EEG and oxCCO during the Right stimulation and a weaker negative correlation during the Left stimulation, with a median correlation of rRightStim = -− 0.7 for the left hemisphere and of rLeftStim = -0.65 for the right hemisphere respectively. Within this early window, correlations between EEG and haemodynamics were almost absent during the Right stimulation and weak for the Left stimulation. The EEG and the bNIRS haemodynamic signals reached the highest correlation at different time windows than the EEG and the bNIRS metabolic signals (Fig. 6B). In particular, this occurred in the final time window of 10–25 s, with the EEG and HbO2 showing a positive correlation but somewhat weaker for the Right stimulation, with a median correlation in the left hemisphere of rLeftStim = 0.69. The EEG and HHb within that same window demonstrated a strong negative correlation independent to the stimuli, with a median correlation in the right hemisphere of rRightStim = -− 0.73, rLeftStim = − 0.83, and of rRightStim = − 0.84, rLeftStim = − 0.81 in the left hemisphere. Our results suggest that there is an earlier association between the electrical neural activity and the brain metabolic response (oxCCO) respect to the hemodynamic response (HbO2 and HHb) and that this happens at specific brain locations. In fact, the maximum correlation between the EEG and the oxCCO is observed at earlier time windows, that are 4–19 s for the Right stimulation (with EEG preceding the oxCCO response by 4 s) and 1–16 s for the Left stimulation (with oxCCO preceding the EEG by 2.25 s). Such negative significant correlations appear strongly and localized, only between EEG electrode Cz and oxCCO Channel 14 independently to the stimuli.
To further demonstrate how the relationship of the EEG and bNIRS correlations evolves over time, the correlations were collapsed across EEG electrodes and bNIRS channels over the left and right hemispheres to obtain a median correlation and a range (maximum to minimum) at each time window (Fig. 7).
Taken together with the results shown in Fig. 6, this further sheds a light on the relationship between bNIRS signals and neural activity. More specifically, it can be observed that: (i) HbO2 is seen to have a significant positive correlation in the left hemisphere during the left stimulation at later time windows (TW > 6–21 s); (ii) the EEG and HHb correlation is significant and negative and is independent to the hemisphere and stimulation. During the Left stimulation, significant correlations between the EEG and HHb can be observed as early as the first time window (1–16 s) although the maximum correlation occurs in the last time window (10–25 s); (iii) the correlations between EEG and oxCCO are significant and negative except in the right hemisphere during the Left stimulation (i.e. the contralateral hemisphere to stimulus presentation). Most interestingly however, the negative correlations are observed only in early time windows and it can be observed that a transition in the correlation between oxCCO and EEG occurs from negative to positive in the 6- 21 s time window. Supplementary Figs. 35 show the maximum correlations between the bNIRS signals and the EEG signal across all the windows from 1–16 s to 10–25 s.
Overall, differing time dynamics between the haemodynamic bNIRS signals and EEG and the metabolic signal and EEG can be observed with oxCCO correlating with EEG in earlier time windows and in a stimulus-dependent fashion; indicating further the different physiological information provided by oxCCO.
## Materials and methods
### Participants and experimental protocol
Thirteen healthy adults (31 ± 8 years of age, 9 males/4 females) were recruited and underwent a visual stimulation task. All participants had normal or corrected-to-normal vision and provided written informed consent in accordance with the guidelines approved by the University College London local research ethics committee. In addition, informed consent was obtained for publication of identifying images (i.e., Fig. 9C) in an online open-access publication.
The visual stimulation task was designed in Psychtoolbox (MATLAB, Mathworks, USA) and consisted of right and left hemifield stimuli made of reversing black and white checkerboards (2° check size; reversal rate of 15 Hz) and isoluminant red and green checkerboards (0.25° check size; reversal rate of 2 Hz). These are known to activate the visual system pathways19. All participants were instructed to focus on a red fixation cross present in the centre of the screen. The visual stimulation task was structured as a block-design, with 16 blocks per condition (Right and Left) lasting 18 s spaced out by 18 s rest periods (Fig. 8). These timings correspond to a hemifield stimulation frequency of ~ 0.014 Hz. Both task and rest blocks were presented on a grey background. Right and left stimuli were alternated throughout the blocks in a fixed order (right, left, right, left, etc.) and the same sequence was used for all the participants.
### Equipment
Participants’ brain haemodynamics (HbO2 and HHb) and metabolism (oxCCO) were monitored over the visual cortex using an in-house developed multichannel bNIRS instrument (see Phan et al.16 for a description of the hardware). Briefly, the bNIRS system is equipped with two halogen bulbs emitting light in the NIR range (504–1068 nm) and two spectrometers (customized lens spectrographs and front illuminated CCD cameras (PIXIS512f. from Princeton Instruments)). Light is guided onto the scalp through four fiber optics bundles (sources) and the back-scattered light is collected by the spectrographs through ten fiber optics (detectors). This creates 16 measurement channels (i.e. the mid-point between a source and a detector), with a source-detector separation of 3 cm. The optodes configuration (i.e., spatial arrangement of light sources and detectors and corresponding channels) is shown in Fig. 9A. Raw intensity spectra were sampled at 0.35 Hz.
In addition to bNIRS, EEG was used to measure neural activity using a commercial wireless gel-based EEG system. The Enobio system (Neuroelectrics, Spain) was used to acquire the data and consisted of 26 measurement locations on the head which are shown in Fig. 9B. The data was sampled at a frequency of 500 Hz. The visual stimulation task in Psychtoolbox sent event markers using serial port communication to both the bNIRS and EEG systems. The bNIRS and EEG were then synchronized using these event markers.
The bNIRS fiber bundles were attached to a 3D printed optode holder (Fig. 9C) that was custom-made with a curved neoprene band to follow the curvature of the head and maximize the optical coupling. This was placed on the back of participants’ heads on top of the EEG cap to monitor the haemodynamic and metabolic changes in the occipital cortex bilaterally. Combined bNIRS and EEG headgear was custom built for simultaneous acquisition of NIRS and EEG data and consisted of a NIRS headband and an EEG cap.
In order to position the headgear in a reliable way across all participants, the measurement from the Nasion to the Inion was performed and used to identify other 10–20 anatomical landmarks along the midline such as Fz, Cz, Pz and Oz for each participant. The bNIRS-EEG headgear was then positioned such that the bottom medial detector of the NIRS headband was positioned in correspondence with the Oz landmark. Then, the EEG cap was adjusted such that the Fz, Cz and Pz electrodes were positioned over their identified anatomical locations on each subject. Following this, the locations of all bNIRS optodes and EEG electrodes were recorded through a 3D magnetic digitizer (Patriot, Polhemus, Vermont). This information was used to co-register the bNIRS channels locations onto a standard brain template. The NIRS-SPM software package27 was then used to obtain the MNI coordinates of the bNIRS channels and the corresponding anatomical locations. The group median MNI coordinates and the atlas-based probabilistic brain anatomical locations are reported in Supplementary Table 1. In the labelling of EEG channels, channels labelled “T1” and “T2” (Fig. 9B) do not refer to channels over the temporal cortex, rather the occipito-parietal region.
### Data analysis pipeline
In this section, we describe our suggested approach for the extraction of meaningful information from the bNIRS haemodynamic, metabolic data and EEG data. In particular, the procedure allows us to: (i) remove the most common noise components in the bNIRS signals such as physiological noise and motion artifacts to improve reliability of the extracted information; (ii) extract measures of brain haemodynamic and metabolic responses in a statistical framework overcoming the issues of modelling the brain response; (iii) combine the haemodynamic and metabolic features to evaluate the relationship between energy supply and utilization during functional brain activity and (iv) integrate the haemodynamic and metabolic signals with EEG to investigate their interrelationship and time dynamics.
The data analysis pipelines for both bNIRS and EEG, as well as the procedure for the combined NIRS-EEG analysis are outlined in Fig. 10.
### bNIRS pre-processing
The bNIRS data analysis consists of the following steps.
#### Phase 1—Data conversion
Raw intensity spectra were first converted into changes in light absorbance (or optical density, ΔOD) using 120 wavelengths (from 780 to 900 nm) to minimize the cross-talk and improve the estimation of haemodynamic and metabolic signals16. Raw intensity spectra were first converted into changes in light absorbance (or optical density, ΔOD). The UCLn algorithm was then used to compute the changes in HbO2, HHb, oxCCO (ΔHbO2, ΔHHb, ΔoxCCO) by means of the modified Beer-Lambert Law (MBLL)9. Wavelength-varying differential pathlength factors (DPFs) were used, assuming DPF = 6.26 at 807 nm as described by Phan et al.1616.
#### Phase 2—Data preprocessing
Raw concentration changes in ΔHbO2, ΔHHb, and ΔoxCCO were first visually inspected to identify noisy channels (e.g., channels with a low signal-to-noise ration due to detector saturation or poor optical coupling) to be excluded from further analyses. This step was carried out looking at the signals both in the time-domain and in the frequency domain. In particular, the assessment of the frequency content of the bNIRS time-series through e.g. the Fast Fourier Transform (FFT) is useful not only to identify the channels, which do not include physiologically-meaningful information, but also to identify the task frequency component to preserve following the preprocessing31.
Artifacts due to head movements were corrected using the wavelet-based method as implemented in the Homer2 software package32,33, considering an interquartile range threshold (iqr) of 1.5. This method was chosen because it was previously demonstrated to be one of the most effective for the recovery of the haemodynamic response34.
In order to minimize very low and high frequency physiological noise, a band-pass filter was applied to the ΔHbO2, ΔHHb, and ΔoxCCO signals using a 150th order FIR band-pass filter in the range [0.008 0.1] Hz. This ensured that at least 3 harmonics of the Fstim for the Right and Left stimulation (Fstim = 1/72 s = ~ 0.014 Hz) as well as of the task presentation frequency regardless the condition (i.e., a task block every 36 s (18 s rest + 18 s task) corresponding to ~ 0.09 Hz) were included in the filter’s passband and that the filter was stable31. However, a low-pass cut-off frequency of 0.1 Hz does not remove the impact of Mayer waves. This is a well know issue in the fNIRS community and many different methods have been explored to reduce it. In fact, band-pass filters are not able to minimize the impact of Mayer waves as these share a common spectral range with the haemodynamic changes, and, in order to preserve the haemodynamic response, more advanced methods are needed, such as short-separation channels or monitoring blood pressure changes35.
### bNIRS statistical analysis
Phase 3—Data analysis: brain activity localization. To extract indices reflecting functional brain haemodynamic and metabolic activity and localize the brain regions responding to the experimental task, we expand the use of the GLM by using the FIR basis functions. This avoid the need of assuming any prior shape and model for the haemodynamic and metabolic responses as in the canonical GLM.
The FIR basis set is one of the most flexible basis functions which fits the measured signals with a series of contiguous boxcar functions (i.e., unitary impulses) translated over time and lasting ∆t = T/KFIR each (i.e., the bin width), where T is the duration of the brain response/stimulation period and KFIR is the model order36. This applied to each experimental condition will constitute the design matrix. A visual representation on how the design matrix regressors are generated is shown in Supplementary Fig. 1.
Here, we used a bin width ∆t = 2.88 s to match our acquisition interval (i.e. 1/0.35 Hz) with the FIR functions approximating delta-functions36. A β-value is then estimated using the ordinary least square estimation for each time bin and represents the weight of each basis function/delta function that best fits the input data in each time bin for each stimulation block. This results in an ‘averaged’ response T-seconds long36 that corresponds to the estimated haemodynamic/metabolic response to each experimental condition.
In our case, we have two experimental conditions (Right and Left) that we modelled in the design matrix. For each condition, we modelled a block lasting 36 s (i.e., our stimulation cycle) ranging from 2 s prior the stimulus onset to 34 s after the stimulus onset. Therefore, a FIR set of thirteen 2.88 s-long bins from -2 to 34 s respect to the onset was used for each task block. An example of design matrix for one participant is shown in Supplementary Fig. 1.
Hence, the resulting estimated haemodynamic/metabolic response was made of 13 β-values. The GLM-FIR procedure was applied to each channel of each participant and for ∆HbO2, ∆HHb, ∆oxCCO separately. We thus obtained an ‘averaged’ response for ∆HbO2, ∆HHb, ∆oxCCO of each channel and participant. To assess whether and where significant activations occur at the group level, we first baseline-corrected the estimated responses by subtracting the median value of the 2 s prior the stimulus onset; then, we collected the median β-value of the response in the time window 8–29 s after the stimulus onsets, which included the largest change in the responses. The median β-values computed across the 8–29 s time window for each chromophore and participant were used to run the group-level statistics and infer where statistically significant (p < 0.05) brain activity occurs. We tested for normality of our samples of median β-values using the Kolmogorov–Smirnov test at 5% significance level. All our data resulted normally distributed. We then used a one sample channel-wise t-test against 0 to test if significant changes in ∆HbO2, ∆HHb, ∆oxCCO occurred in response to the visual task, and we corrected for multiple comparisons by means of the FDR correction37 for number of channels.
### Integration of bNIRS haemodynamic and metabolic data
#### Phase 4 – Data analysis: metabolism-haemodynamics coupling
The analysis of the relationship between the haemodynamic and metabolic activity of the brain has the potential to unveil information regarding the energetic processes in the healthy brain in response to a particular stimulus and allow us to quantify and detect any deviations that are due to disorders and/or injury. Here, we adapt the use of the method developed by Shokri-Kojori and colleagues (2009) to compute two indices that reflect the coupling between the magnitude of brain metabolism and of activity10. In particular, these are: (1) the relative power (or rPWR), which reflects the extent of concurrent energy supply and utilization; (2) the relative cost (or rCST), which reflects the extent to which metabolism exceeds or falls behind the intensity of brain activity. When there is a proportional change in brain metabolism and activity, most of the common variance will be accounted for by rPWR, while the higher is the disproportion between energy supply and utilization, the more the variance will be accounted for by rCST. High values of rPWR are usually observed in metabolically demanding and high functioning brain regions (i.e., visual and default mode networks), indicating high metabolism and activity respect to the rest of the brain. High values of rCST were suggested to be related to the use of alternative metabolic pathways (e.g., aerobic glycolysis vs oxidative phosphorylation) or of alternative metabolic substrates (e.g., glucose vs ketone bodies); brain regions associated to high-level cognitive functions also showed a higher metabolic cost possibly due to use of faster but inefficient metabolic pathways10.
rPWR and rCST are calculated in a mean–variance-normalized (i.e. z-scored) haemodynamics-metabolism map by performing a 45° rotation of the axes (see Fig. 1d–f in Shokri-Kojori et al. (2009)). This procedure generates a rPWR axis, where the positive and negative ends correspond to high metabolism + high activity and low metabolism + low activity respectively, and a rCST axis perpendicular to rPWR, where the positive and negative ends correspond to high metabolism + low activity and low metabolism + high activity respectively. In a Cartesian coordinate system, rPWR and rCST are computed as in Eq. 110:
$$\left[ {\begin{array}{*{20}c} {rPWR} \\ {rCST} \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {{\text{cos}}\left( {45^\circ } \right)} & {{\text{sin}}\left( {45^\circ } \right)} \\ { - {\text{sin}}\left( {45^\circ } \right)} & {{\text{cos}}\left( {45^\circ } \right)} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {z\left( {activity} \right)} \\ {z\left( {metabolism} \right)} \\ \end{array} } \right]$$
(1)
The method was previously used by Shokri-Kojori et al. (2009) combining the cerebral metabolic rate of glucose (measured with FDG-PET) as the index of metabolic supply, and local spontaneous functional connectivity density as the index of brain activity (measured with fMRI). Here, we combine the median β-values of ∆HbO2 or ∆HHb extracted in Phase 3 as indicators of brain activity, with the median β-values of ∆oxCCO as indicators of brain metabolism. Therefore, we calculated rPWR and rCST for each channel and each participant using the z-scored median β-values across channels of ∆HbO2 and ∆oxCCO (rPWRHbO2 and rCST HbO2) and the z-scored median β-values of ∆HHb and ∆oxCCO across channels (rPWRHHb and rCST HHb). For the computation of rPWRHHb and rCST HHb, we inverted the sign of the HHb β-values so that the sign of rPWRHHb and rCST HHb matches with rPWRHbO2 and rCST HbO2. By plotting the median β-values of ∆HbO2 or ∆HHb against the median β-values of ∆oxCCO for each channel in a mean–variance-normalized map, it is possible to visualize which channel exhibits a greater association or mismatch between brain haemodynamic and metabolic activity respect to the others (e.g., Fig. 3).
In order to explore the patterns of rPWR and rCST within the visual cortex in response to the right and left hemifield stimuli, we used one sample t-test against 0 to localize the brain regions showing a significant positive association or mismatch between the intensity of brain activity and metabolism. Channel-wise t-tests vs 0 were run on the group rPWRHbO2 and rCST HbO2, and rPWRHHb and rCST HHb, and we corrected for multiple comparisons by means of the FDR correction for number of channels.
### EEG data analysis
All EEG data were analysed in MATLAB (Mathworks, USA) using the EEGLab toolbox (Schwartz Centre for Computational Neuroscience, UC San Diego, USA) and custom-built scripts. The EEG data analysis consists of the following steps.
#### Phase 1 – Data preprocessing
The raw EEG signal was band-pass filtered between 0.1 – 100 Hz and a notch filter (48 – 52 Hz) was applied to remove artifacts due to line noise. Following this, data were segmented into 1 s epochs such that each 18 s presentation of the stimulus yielded 18 × 1 s epochs. Each 1 s segment consisted of 200 ms of the previous epoch (to serve as a baseline) and therefore baseline correction was performed after segmentation. EEG epochs were automatically rejected for movement artifacts if the signal amplitude exceeded ± 100 mV at any individual channel. Additional rejection of bad segments was performed by visual inspection of each individual epoch to remove artifacts due to eye blinks, saccadic eye movements and facial muscle movements. Channels identified as noisy during the visual inspection were interpolated i.e. replaced with an average voltage of nearby channels. All EEG data was re-referenced to the average reference.
#### Phase 2 – Data analysis
The artifact free epochs were subjected to power analysis to calculate the power spectral density (PSD) in the gamma band (25 – 45 Hz). The gamma band was chosen specifically for this analysis as previous studies have demonstrated a strong correlation between haemodynamic activity and gamma band neural activity38,39,40. The epochs were averaged across trials to obtain an averaged gamma band response per participant.
#### Phase 3 – Statistical analysis
For each participant, the maximum gamma power was obtained. T-tests were performed to compare the maximum gamma power against the baseline gamma power and FDR correction was performed to correct for multiple comparisons. The channels that had a significant gamma band activation were included in the bNIRS-EEG analysis.
The PSD results are shown in Sect. 5 in the Supplementary Material.
### Integration of bNIRS haemodynamic and EEG data
In order to investigate the relationship between the haemodynamic and metabolic signals with underlying neural activity, a combined bNIRS-EEG analysis was performed. From here on EEG channels will be referred to as electrodes and bNIRS channels will be referred to as channels. This involved first deriving an appropriate EEG measure from the EEG data to match the sampling rate of the bNIRS signals. The EEG data were thus segmented as described previously and following this, for each of the 18 × 1 s epochs that formed one stimulus presentation/one trial, the mean PSD in the gamma band of each epoch was calculated. This measure was consequently averaged across trials to obtain a measure of mean gamma power at each electrode, for each participant. This procedure is outlined in Fig. 11. The mean PSD in the gamma band was used to perform one-sample t-tests to assess whether there was a statistically significant change in gamma power during the task with respect to the baseline. Only the electrodes that were statistically significant (p < 0.05; FDR corrected for multiple comparisons) were included in this analysis.
The bNIRS data were up-sampled to 1 s and cross-correlations between the task-averaged bNIRS signals (HbO2, HHb and oxCCO) and the EEG measure were performed using a sliding window approach. More specifically, the EEG measure was cross correlated with 15 s of the bNIRS signals in time windows from 1 – 16 s to 10 – 25 s in 1 s increments. This yielded 10 time windows of cross-correlations.
In the current analysis, the bNIRS channels were correlated with selected EEG electrodes that were located over the occipital, parietal and central-parietal regions and nearest to the bNIRS optodes. These channels have been indicated on Fig. 9B with orange circles.
Cross-correlations provide a measure of similarity between two time series where one time series x(t) may be related to another time series y(t) by a set time-lag or time-delay. At each time-lag, to obtain the cross-correlation between the two time-series, y(t) is shifted along and correlated with x(t) at each time point to obtain a correlation at each time-lag. Correlations are calculated both for positive and negative time-lags. In order to obtain positive time-lags, y(t) is shifted forward with respect to x(t) and to obtain negative time-lags, y(t) is shifted backwards with respect to x(t). The cross-correlation for time series x(t) and y(t) (where t = 0, 1, 2,…, N) is calculated using the following formula with the time-lag equal to d.
$$r\left( d \right) = \frac{{\sum \left[ {x\left( t \right)*y\left( {t - d} \right)} \right]}}{{\sqrt {\mathop \sum \nolimits_{t} \left( {x\left( t \right)} \right)^{2} } *\sqrt {\mathop \sum \nolimits_{i} \left( {y\left( {t - d} \right)} \right)^{2} } }}$$
where $$\stackrel{-}{x}$$ and $$\stackrel{-}{y}$$ are the means of x(t) and y(t) respectively and d = 0, 1, 2,…, N.
The cross-correlation between the two time-series yielded correlations between the pair of signals at a range of different time-lags. A positive time-lag indicated that the EEG time-series led the bNIRS signal and vice-versa for a negative time-lag. For each time window, for each subject, the maximum correlation and its corresponding time lag were identified. Bootstrapping was performed in order to reduce correlations that would occur due to the presence of autocorrelation in the bNIRS and EEG signals by randomly selecting and cross-correlating unmatched pairs for both signals (for example, the EEG signal of Subject 1 was correlated with the bNIRS signal of Subject 5). This procedure was repeated 121 times and a random sample of 11 subjects was selected to create a null distribution. Wilcoxon’s sign rank non-parametric test was used to compare the maximum correlation with the null distribution to assess the significance of the correlation. Following this, the FDR correction procedure was applied to correct for multiple comparisons37 for number of channels. The significant correlations after FDR correction were used to obtain the maximum cross-correlations for each time window, stimulation, chromophore (HHb, HbO2 and oxCCO) and channel combination. After FDR correction, for each chromophore and stimulation, the time window within which the chromophore had a maximum correlation with the EEG measure were identified.
## Discussion
In this study, we presented an analysis pipeline (Fig. 10) for the preprocessing and processing of both the bNIRS and EEG measurements. We demonstrated the use of the pipeline on data recorded at multiple locations in the visual cortex in a cohort of healthy adults, and showed how multichannel bNIRS can be used successfully to image both brain oxygenation/haemodynamics and metabolism simultaneously with EEG. The integration of oxygenation/haemodynamic and metabolic measures allows quantification and localization of brain activity and the subsequent integration with neural signals provides further insight into neurovascular coupling mechanisms. In particular, we showed that both the oxygenation/haemodynamic and metabolic signals carry information about task-related functional activity of the brain, encoding the stimulation frequency of our task as highlighted by the power spectral analysis (Fig. 1B). The preprocessing steps that we proposed resulted to be effective in minimizing the very low and high frequency noise in the bNIRS signals, while preserving the stimulation frequency (Fig. 2). In fact, when looking at the averaged time-series, the typical patterns of brain activity can be observed, with concurrent increase in HbO2 and oxCCO and decrease in HHb in response to the visual stimulation task (Fig. 3).
In order to leverage the advantage of bNIRS of providing simultaneous measures of brain activity and metabolism, we expanded and tested the use of two indices (rPWR and rCST) to integrate our haemodynamic and metabolic measures. These were previously developed by Shokri-Kojori and colleagues (2019) and used on FD-PET and fMRI data. More precisely, rPWR expresses the strength of the proportional change between brain activity and metabolism, while rCST quantifies the extent of the mismatch between brain activity and metabolism (i.e. how much metabolism exceeds activity and vice versa). In the study by Shokri-Kojori et al. (2009), rPWR and rCST were used to classify brain regions and resting-state networks based on the differences in the coupling metabolism-activity. For example, visual and default mode networks resulted in having the highest rPWR, being the most metabolically demanding regions, while the fronto-parietal networks showed the highest rCST, probably due to the higher metabolic cost of regions supporting high-level cognitive functions. Here, we demonstrated the feasibility to use rPWR and rCST during functional brain activity of the visual cortex by integrating measures of brain oxygenation/haemodynamics and metabolism extracted from HbO2, HHb and oxCCO. In case of this particular passive visual stimulation and healthy cohort, we expected to observe concurrent and greater increase in HbO2 and oxCCO and greater decrease in HHb in the regions involved in the task, with a balanced proportionality of the magnitude of the changes between these measurements. The rPWR and rCST have the potential to give insights into these proportional or disproportional changes between chromophore and thus into normal or different brain functioning.
Our results (Fig. 5) showed that the V1, V2, and V3 regions in the contralateral hemisphere to the stimulation exhibited the highest rPWR, meaning that those regions had the most coherent and highest changes in brain haemodynamic and metabolic activity respect to the rest of the channels. In particular, rPWRHbO2 and rPWRHHb were both significantly positive in the contralateral V1, V2, and V3 regions and negative in the ipsilateral V1, V2, and V3 regions. Looking also at the group-averaged curves in Fig. 3, these results suggest that positive values of rPWR correspond to those channels with the largest and concurrent changes in HbO2/HHb and oxCCO in respect to the rest of the channels, while negative rPWR to channels with smaller changes. Therefore, it seems that rPWR shows higher spatial sensitivity than the GLM-based group analysis, identifying fewer and highly localized significant channels only within the contralateral hemisphere to the stimulation. These results are consistent with previous evidence that in a healthy brain high functional activity is associated with high metabolic supply, and that stronger activations to visual hemifield stimulation are typically observed in the contralateral hemisphere. The results for rCST further confirmed our hypothesis as we only found a significant mismatch between HHb and oxCCO in right V1-V2 (channel 10), with changes in HHb exceeding the changes in oxCCO when compared to the rest of the channels during the Right visual stimulation. This might reflect the “blood stealing” phenomenon or a suppression of neuronal activity as evidenced by previous fMRI studies, according to which a reduction in the BOLD response (corresponding to deoxyhaemoglobin) can be observed in the unstimulated part of the visual cortex (i.e. the ipsilateral hemisphere to the hemifield stimulus)45. Although in Fig. 3 it appears that the HHb decreases and oxCCO increases as in normal neuronal activation, such changes in channel 10 are smaller than in the rest of the channels, with HHb changes exceeding oxCCO. This leads to a negative rCST, which may reflect a reduction of neuronal activity in that area respect to the rest of the visual cortex (smaller increase in oxCCO/reduced metabolic supply) and the “blood stealing” process with increase in blood flow in the stimulated hemisphere (i.e. the left one for the Right condition) and reduction in blood flow/BOLD response in the unstimulated areas (smaller decrease in HHb in right V1-V2). In fact, channel 10 does not exhibit significant rPWR either (Fig. 3) while the corresponding channels covering V1 and V2 in the left hemisphere shows patterns of neuronal activation (i.e., proportional changes in HbO2/HHb and oxCCO). No significant differences in rCST were found in the rest of the channels, supporting our hypothesis that in a healthy brain there typically is an agreement between energy supply and utilization. We expect rCST to be a more informative parameter in case of brain dysfunctions and damage, as it can help in identifying those regions showing an abnormal relationship between brain metabolism and activity and altered energy use in disease10.
Moreover, in order to investigate the relationship between oxygenation/haemodynamics and metabolic activity with neural activity, we carried out a combined bNIRS – EEG analysis which computed the cross-correlation of the time-series (Figs. 6, 7; Supplementary Fig. 35). This analysis revealed a positive relationship between HbO2, an inverse relationship with HHb and a time-dynamic relationship with oxCCO. Correlations observed in early time windows for oxCCO reveal a negative relationship with oxCCO and EEG which transition to a positive relationship in the later time windows. Moreover, a stimulus-dependent relationship was also observed for oxCCO and EEG, i.e. a positive relationship in the contralateral hemisphere and an inverse relationship in the ipsilateral hemisphere. Previous work by Logothetis et al.4646 has suggested a direct relationship between neural activity and blood oxygenation. In particularly, previous studies provide evidence of a strong correlation between gamma band activity and the BOLD response47,48,49,50. Many other studies provide evidence of an inverse relationship between the task-related fMRI BOLD response and EEG oscillatory activity51,52. While the bNIRS analysis showed differences in the spatial localization of brain activity in response to right and left stimulation, the combined bNIRS – EEG analysis showed a similar difference for both conditions for oxCCO only. Furthermore, an interesting observation was the difference in the significant maximal time window between HbO2, HHb and oxCCO, with oxCCO displaying maximum correlations in an earlier time window to both HbO2 and HHb. In majority of channels and stimulus combinations for oxCCO, HbO2 and HHb, a positive (adjusted) time-lag was observed implying that neural activity preceded the haemodynamic and metabolic activity. However, for the Left stimulation condition, in the contralateral hemisphere post-FDR correction, a significant negative time-lag was observed implying that the metabolic activity preceded the neural activity. Taken together with time-dynamic and stimulus-dependent relationship observed for oxCCO, these results imply that metabolic activity ties with neural activity more closely, occurring earlier than the observed changes in haemodynamic activity.
Taken together, our results suggest that the fusion of the bNIRS-derived haemodynamic and metabolic measures has the potential to unveil additional and complementary information regarding the functioning of the brain that are not so obvious when looking at haemodynamic responses alone. In fact, the stimulus-dependent contralateral-ipsilateral representation is clearer when considering the integration of oxCCO with EEG measures (Fig. 6) and oxCCO with HbO2 or HHb (Fig. 5) rather than when looking at each measurement separately (Fig. 3). Further, our analysis integrating bNIRS with EEG provides insights into neural mechanisms. Nonetheless, our study presents some limitations. The bNIRS instrument used here has a lower sampling frequency (~ 0.35 Hz) compared to commercially available fNIRS devices and a better reconstruction of the temporal profile of the haemodynamic and metabolic responses could be achieved with higher acquisition rates. A low acquisition rate can also introduce artifacts in the low frequency band of the bNIRS signals as high frequency physiological noise, such as heart rate (~ 1 Hz) and respiration rate (~ 0.2 Hz), are undersampled. In the present study, this undersampling issue should not represent a problem as: (i) the artifacts are introduced in the whole bNIRS time courses, i.e. both in the rest and task periods. Hence, when comparing the changes during the task versus the changes during the rest, they are subtracted and their impact is reduced; (ii) the GLM analysis proposed here is based on a fitting procedure and is not amplitude-based. Hence, the artifacts should not be picked up and the inference is carried out on the slower haemodynamic/metabolic components. In this regard, further work is being done to develop a novel multichannel bNIRS system that will allow a sampling rate > 1 Hz. Additionally, the FIR-based GLM used here requires that the trials of the same condition have the same duration; also, while on the one hand the FIR basis functions provides the highest degree of flexibility and are particularly useful when the focus is to characterize the shape of the response, on the other hand flexibility comes with a cost, with a high number of parameters to estimate (one per each time point of the stimulus) which increases the risk of overfitting and decreases the degrees of freedom53. We plan to investigate the use of other flexible basis functions to overcome these limitations, such as the impulse response model54. Another limitation of this study is that we did not employ methods to account for systemic changes, particularly from a hardware perspective. In order to recover the haemodynamic and metabolic responses robustly, it is recommended to measure physiological data (e.g. heart rate, respiration, blood pressure, etc.) alongside bNIRS recordings or to use short-separation channels that sample data from the extra-cerebral compartment of the head, to regress these out and minimize their impact on the NIRS-derived brain signals7. This is especially important for the haemodynamic signals (oxy- and deoxyhaemoglobin) that are more prone to systemic interferences than oxCCO, whereas oxCCO is more brain specific5,8. In this study, we used a passive visual stimulation task that does not recruit higher-level cognitive functions, and we monitored a relatively small group of healthy individuals (N = 13). Future studies will investigate how the patterns of rPWR and rCST change in other brain regions and in response to more active and demanding cognitive tasks in larger cohorts. More interestingly, we aim to test the feasibility of these indices on bNIRS data recorded i.e. on individuals with altered metabolism and neurovascular coupling mechanisms, and on clinical populations such as in case of neuropsychiatric disorders. The feasibility of this technology for clinical neuromonitoring was previously demonstrated55,56. For instance, bNIRS was used to monitor cerebral perfusion and oxidative metabolism in newborns with hypoxic-ischaemic encephalopathy and to prognosticate the neurodevelopmental outcome of such infants56. We believe that bNIRS is highly suitable for clinical cohorts as measurement can be obtained in naturalistic situations, where patients do not have to be restricted inside a noisy scanner like for fMRI or PET, and metabolism and brain activity can be monitored simultaneously with no need of multiple testing sessions.
### Ethical approval and informed consent
All research and methods were carried out in accordance with relevant guidelines and regulations. All experimental protocols were approved by the University College London local research ethics committee. All participants provided written informed consent in accordance with the guidelines approved by the University College London local research ethics committee.
## Data availability
The datasets generated during the current study are available from the corresponding author on reasonable request.
## References
1. 1.
Yücel, M. A., Selb, J. J., Huppert, T. J., Franceschini, M. A. & Boas, D. A. Functional near infrared spectroscopy: enabling routine functional brain imaging. Curr. Opin. Biomed. Eng. 4, 78–86 (2017).
2. 2.
Pinti, P. et al. The present and future use of functional near-infrared spectroscopy (fNIRS) for cognitive neuroscience. N. Y. Acad. Sci. 1464(1), 5 (2020).
3. 3.
Scholkmann, F. et al. A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology. NeuroImage 85, 6–27 (2014).
4. 4.
Bale, G., Elwell, C. E. & Tachtsidis, I. From Jöbsis to the present day: a review of clinical near-infrared spectroscopy measurements of cerebral cytochrome-c-oxidase. J. Biomed. Opt. 21(9), 091307 (2016).
5. 5.
Kolyva, C. et al. Cytochrome c oxidase response to changes in cerebral oxygen delivery in the adult brain shows higher brain-specificity than haemoglobin. NeuroImage 85, 234–244 (2014).
6. 6.
Kolyva, C. et al. Systematic investigation of changes in oxidized cerebral cytochrome c oxidase concentration during frontal lobe activation in healthy adults. Biomed. Opt. Express. 3(10), 2550–2566 (2012).
7. 7.
Tachtsidis, I. & Scholkmann, F. False positives and false negatives in functional near-infrared spectroscopy: issues, challenges, and the way forward. Neurophotonics 3(3), 031405 (2016).
8. 8.
de Roever, I., Bale, G., Cooper, R. J., & Tachtsidis, I. (2016). Cytochrome-C-oxidase exhibits higher brain-specificity than haemoglobin in functional activation. In Optics and the Brain (Optical Society of America, BTh4D-4).
9. 9.
Matcher, S. J., Elwell, C. E., Cooper, C. E., Cope, M. & Delpy, D. T. Performance comparison of several published tissue near-infrared spectroscopy algorithms. Anal. Biochem. 227(1), 54–68 (1995).
10. 10.
Shokri-Kojori, E. et al. Correspondence between cerebral glucose metabolism and BOLD reveals relative power and cost in human brain. Nat. Commun. 10(1), 1–12 (2019).
11. 11.
Nosrati, R., Vesely, K., Schweizer, T. A. & Toronov, V. Event-related changes of the prefrontal cortex oxygen delivery and metabolism during driving measured by hyperspectral fNIRS. Biomed. Opt. Express. 7(4), 1323–1335 (2016).
12. 12.
Rajaram, A. et al. Simultaneous monitoring of cerebral perfusion and cytochrome c oxidase by combining broadband near-infrared spectroscopy and diffuse correlation spectroscopy. Biomed. Opt. Express. 9(6), 2588–2603 (2018).
13. 13.
Ghosh, A., Tachtsidis, I., Kolyva, C., Cooper, C. E., Smith, M., & Elwell, C. E. (2012). Use of a hybrid optical spectrometer for the measurement of changes in oxidized cytochrome c oxidase concentration and tissue scattering during functional activation. In Oxygen Transport to Tissue XXXIII 119–124 (Springer, 2012).
14. 14.
Heekeren, H. R. et al. Noninvasive assessment of changes in cytochrome-c oxidase oxidation in human subjects during visual stimulation. J. Cereb. Blood Flow Metab. 19(6), 592–603 (1999).
15. 15.
Nosrati, R. et al. Cerebral hemodynamics and metabolism during cardiac arrest and cardiopulmonary resuscitation using hyperspectral near infrared spectroscopy. Circ. J. https://doi.org/10.1253/circj.CJ-16-1225 (2017).
16. 16.
Phan, P. et al. Multi-channel multi-distance broadband near-infrared spectroscopy system to measure the spatial response of cellular oxygen metabolism and tissue oxygenation. Biomed. Opt. Express. 7(11), 4424–4440 (2016).
17. 17.
Zaramella, P. et al. Brain auditory activation measured by near-infrared spectroscopy (NIRS) in neonates. Pediatr. Res. 49(2), 213–219 (2001).
18. 18.
Siddiqui, M. F. et al. Non-invasive measurement of a metabolic marker of infant brain function. Sci. Rep. 7(1), 1–6 (2017).
19. 19.
Liu, C. S. et al. Magnocellular and parvocellular visual pathways have different blood oxygen level–dependent signal time courses in human primary visual cortex. Am. J. Neuroradiol. 27(8), 1628–1634 (2006).
20. 20.
Scheeringa, R., Koopmans, P. J., van Mourik, T., Jensen, O. & Norris, D. G. The relationship between oscillatory EEG activity and the laminar-specific BOLD signal. Proc. Natl. Acad. Sci. 113(24), 6761–6766 (2016).
21. 21.
Sumiyoshi, A. et al. Coupling between gamma oscillation and fMRI signal in the rat somatosensory cortex: its dependence on systemic physiological parameters. Neuroimage 60(1), 738–746 (2012).
22. 22.
Yuan, H. et al. Negative covariation between task-related responses in alpha/beta-band activity and BOLD in human sensorimotor cortex: an EEG and fMRI study of motor imagery and movements. Neuroimage 49(3), 2596–2606 (2010).
23. 23.
Chiarelli, A. M., Zappasodi, F., Di Pompeo, F. & Merla, A. Simultaneous functional near-infrared spectroscopy and electroencephalography for monitoring of human brain activity and oxygenation: a review. Neurophotonics 4(4), 041411 (2017).
24. 24.
Bowman, F. D., Guo, Y. & Derado, G. Statistical approaches to functional neuroimaging data. Neuroimaging Clin. N. Am. 17(4), 441–458 (2007).
25. 25.
Friston, K. J. et al. Statistical parametric maps in functional imaging: a general linear approach. Hum. Brain Mapp. 2, 189–210 (1994).
26. 26.
Tak, S. & Ye, J. C. Statistical analysis of fNIRS data: a comprehensive review. NeuroImage 85, 72–91 (2014).
27. 27.
Ye, J. C., Tak, S., Jang, K. E., Jung, J. & Jang, J. NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy. NeuroImage 44(2), 428–447 (2009).
28. 28.
Sutoko, S. et al. Tutorial on platform for optical topography analysis tools. Neurophotonics 3(1), 010801 (2016).
29. 29.
de Roever, I., Bale, G., Cooper, R. J., & Tachtsidis, I. Functional NIRS measurement of cytochrome-c-oxidase demonstrates a more brain-specific marker of frontal lobe activation compared to the haemoglobins. In Oxygen Transport to Tissue XXXIX 141–147 (Springer, Berlin, 2017).
30. 30.
Pinti, P. et al. A review on the use of wearable functional near-infrared spectroscopy in naturalistic environments. Jpn. Psychol. Res. 60(4), 347–373 (2018).
31. 31.
Pinti, P., Scholkmann, F., Hamilton, A., Burgess, P. & Tachtsidis, I. Current status and issues regarding pre-processing of fNIRS neuroimaging data: an investigation of diverse signal filtering methods within a General Linear Model framework. Front. Hum. Neurosci. 12, 505 (2018).
32. 32.
Molavi, B. & Dumont, G. A. Wavelet-based motion artifact removal for functional near-infrared spectroscopy. Physiol. Meas. 33(2), 259 (2012).
33. 33.
Huppert, T. J., Diamond, S. G., Franceschini, M. A. & Boas, D. A. HomER: a review of time-series analysis methods for near-infrared spectroscopy of the brain. Appl. Opt. 48(10), D280–D298 (2009).
34. 34.
Brigadoi, S. et al. Image reconstruction of oxidized cerebral cytochrome C oxidase changes from broadband near-infrared spectroscopy data. Neurophotonics 4(2), 021105 (2017).
35. 35.
Yücel, M. A. et al. Mayer waves reduce the accuracy of estimated hemodynamic response functions in functional near-infrared spectroscopy. Biomed. Opt. Express 7(8), 3078–3088 (2016).
36. 36.
Henson, R., & Friston, K. Convolution Models for fMRI. Statistical Parametric Mapping: The Analysis of Functional Brain Images, 178–192 (Academic Press, New York, 2007).
37. 37.
Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. Ser. B Stat. Methodol. 57(1), 289–300 (1995).
38. 38.
Kayser, C., Kim, M., Ugurbil, K., Kim, D. S. & König, P. A comparison of hemodynamic and neural responses in cat visual cortex using complex stimuli. Cereb. Cortex 14(8), 881–891 (2004).
39. 39.
Niessing, J. et al. Hemodynamic signals correlate tightly with synchronized gamma oscillations. Science 309(5736), 948–951 (2005).
40. 40.
Scheeringa, R. et al. Neuronal dynamics underlying high-and low-frequency EEG oscillations contribute independently to the human BOLD signal. Neuron 69(3), 572–583 (2011).
41. 41.
Rajapakse, J. C., Kruggel, F., Maisog, J. M. & Yves von Cramon, D. Modeling hemodynamic response for analysis of functional MRI time-series. Hum. Brain. Mapp. 6(4), 283–300 (1998).
42. 42.
Monti, M. M. Statistical analysis of fMRI time-series: a critical review of the GLM approach. Front. Hum. Neurosci. 5, 28 (2011).
43. 43.
Colier, W. N. et al. Simultaneous near-infrared spectroscopy monitoring of left and right occipital areas reveals contra-lateral hemodynamic changes upon hemi-field paradigm. Vis. Res. 41(1), 97–102 (2001).
44. 44.
Tootell, R. B., Mendola, J. D., Hadjikhani, N. K., Liu, A. K. & Dale, A. M. The representation of the ipsilateral visual field in human cerebral cortex. Proc. Natl. Acad. Sci. 95(3), 818–824 (1998).
45. 45.
Smith, A. T., Williams, A. L. & Singh, K. D. Negative BOLD in the visual cortex: evidence against blood stealing. Hum. Brain. Mapp. 21(4), 213–220 (2004).
46. 46.
Logothetis, N. K., Pauls, J., Augath, M., Trinath, T. & Oeltermann, A. Neurophysiological investigation of the basis of the fMRI signal. Nature 412(6843), 150–157 (2001).
47. 47.
Foucher, J. R., Otzenberger, H. & Gounot, D. The BOLD response and the gamma oscillations respond differently than evoked potentials: an interleaved EEG-fMRI study. BMC Neurosci. 4(1), 22 (2003).
48. 48.
Magri, C., Schridde, U., Murayama, Y., Panzeri, S. & Logothetis, N. K. The amplitude and timing of the BOLD signal reflects the relationship between local field potential power at different frequencies. J. Neurosci. 32(4), 1395–1407 (2012).
49. 49.
Nir, Y. et al. Coupling between neuronal firing rate, gamma LFP, and BOLD fMRI is related to interneuronal correlations. Curr. Biol. 17(15), 1275–1285 (2007).
50. 50.
Uji, M., Wilson, R., Francis, S. T., Mullinger, K. J. & Mayhew, S. D. Exploring the advantages of multiband fMRI with simultaneous EEG to investigate coupling between gamma frequency neural activity and the BOLD response in humans. Hum. Brain Map. 39(4), 1673–1687 (2018).
51. 51.
Laufs, H. et al. EEG-correlated fMRI of human alpha activity. Neuroimage 19(4), 1463–1476 (2003).
52. 52.
Pedregosa, F., Eickenberg, M., Ciuciu, P., Thirion, B. & Gramfort, A. Data-driven HRF estimation for encoding and decoding models. NeuroImage 104, 209–220 (2015).
53. 53.
Huppert, T. J. Commentary on the statistical properties of noise and its implication on general linear models in functional near-infrared spectroscopy. Neurophotonics 3(1), 010401 (2016).
54. 54.
Bale, G. et al. Oxygen dependency of mitochondrial metabolism indicates outcome of newborn brain injury. J. Cereb. Blood Flow Metab. 39(10), 2035–2047 (2019).
55. 55.
Diop, M., Kishimoto, J., Toronov, V., Lee, D. S. & Lawrence, K. S. Development of a combined broadband near-infrared and diffusion correlation system for monitoring cerebral blood flow and oxidative metabolism in preterm infants. Biomed. Opt. Express. 6(10), 3907–3918 (2015).
56. 56.
Mitra, S. et al. Pressure passivity of cerebral mitochondrial metabolism is associated with poor outcome following perinatal hypoxic ischemic brain injury. J. Cereb. Blood Flow Metab. 39(1), 118–130 (2019).
## Acknowledgements
This work was supported by the Wellcome Trust (104580/Z/14/Z; 212979/Z/18/Z), the MRC (MR/S003134/1), the BBSRC [BB/J014567/1], the Birkbeck Wellcome Trust Institutional Strategic Support Fund (ISSF) and the ESRC (ES/V012436/1).
## Author information
Authors
### Contributions
M.F.S., A.D.L. and I.T. conceived and designed the study. M.S.F. and A.D.L. collected the data. M.F.S. and P.P. performed the data analysis with the collaboration of A.D.L., E.J.H.J. and I.T. P.P. and M.F.S. drafted the manuscript. All authors reviewed and approved the final manuscript.
### Corresponding author
Correspondence to Ilias Tachtsidis.
## Ethics declarations
### Competing interests
The authors declare no competing interests.
### Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## Rights and permissions
Reprints and Permissions
Pinti, P., Siddiqui, M.F., Levy, A.D. et al. An analysis framework for the integration of broadband NIRS and EEG to assess neurovascular and neurometabolic coupling. Sci Rep 11, 3977 (2021). https://doi.org/10.1038/s41598-021-83420-9
• Accepted:
• Published: | {} |
The response rate (responses divided by unique pageviews) varies across different pages. And in fact the pages with low response rate also tend to have a higher ratio of negative ratings. This suggests to me that many users who don't find a page helpful just leave without rating it. (I have looked at other factors that could have affected response rate but the correlations are very weak.)
I understand that it's problematic to generalize the result for pages that have a low response rate. But I'm reluctant to exclude these pages, since it seems that they may be the ones most in need of attention. In view of this, is it reasonable to ignore response rate per page and simply look at the positive to negative ratings ratio? Or is there a way I could account for response rate and still include these pages?
-
What is your mental model of decisions made by people visiting your site? Is there any difference between first-timers and people using your site regularly? Will regular visitors think of spending a second answering the question? Do you have any extra variables from analytics (Ggle's or others')? Non-response may be correlated with those variables... – Deer Hunter Dec 22 '12 at 18:27
Thanks for the tips, Deer Hunter. Some interesting avenues to explore there. Currently I just have the general analytics, not directly linked to responses and response rates. For example, I can look at things like average time on page for the pages that got lower response rates (not much correlation for that one), but I don't have the specific time on page numbers for only those visitors who didn't respond. – Joe Pairman Dec 23 '12 at 3:32 | {} |
A weight conversion calculator is a converting system which converts the weight of an object from one unit to other. Weight of a body is the force on that because of the gravitational attraction. There are many units exist in the case of weight of a body. Some of them are kg, g, lbs etc. The following section will explain how can we convert the weight from one unit to another.
## Steps for Weight Conversion
• Conversion from Kg to g:
If we need to convert a weight from Kg to g, we have to follow the given relation.
1Kg=1000g
1g=$\frac{1}{1000}$ Kg
• Conversion from Kg to lbs:
The relation between Kg and pounds (lbs) is given by
1Kg=2.2046lbs
• Conversion from mg to g:
The given relation is used for the conversion between the mg and g.
1000mg=1g
Here some basic idea about the conversion of weight is mentioned.
### Length Conversion Calculator
Weight Conversion Metric Unit for Weight Conversion Temperature Decimal Conversions Alternate Exterior Angles Converse Alternate Interior Angles Converse
Conversions Calculator conversion calculator length conversion calculator speed Decimal to Binary Conversion Calculator Decimal to Fraction Conversion Calculator Fraction to Decimal Conversion Calculator | {} |
# ContextLab/timecorr
Estimate dynamic high-order correlations in multivariate timeseries data
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## Overview
The timecorr toolbox provides tools for computing and exploring the correlational structure of timeseries data. There is one main function:
• timecorr is used to compute dynamic correlations from a timeseries of observations and to find higher order structure in the data, organized as a number-of-timepoints by number-of-features matrix. For examples, tutorials, and an API specification, please check out our readthedocs page.
## Basic usage
The timecorr function takes your data and returns moment-by-moment correlations during the same timepoints. timecorr also lets you explore higher order structure in the data in a computationally tractable way by specifiying a dimensionality reduction technique.
• timecorr computes dynamic correlations and return a result in the same format, but where each data matrix has number-of-timepoints rows and $\frac{n^2 - n}{2}$ features (i.e. a vectorized version of the upper triangle of each timepoint's correlation matrix).
• timecorr also lets you explore higher order structure in the data by projecting the correlations back onto the original number-of-timepoints by number-of-featuers space.
• You should format your data as a Numpy array or Pandas dataframe with one row per observation and one column per feature (i.e. things you're tracking over time-- e.g. a voxel, electrode, channel, etc.). You can then pass timecorr a single dataframe or a list of dataframes (each with the same numbers of timepoints and features).
Pick a weights_function
• How much the observed data at every timepoint contributes to the correlations at each timepoint.
Specify the weights_params
• Parameters for weights_function
Choose cfun for computing dynamic correlations
• The correlations may be computed within a single matrix, or across a list of such matrices. If a list of data matrices are passed, each data matrix is compared to the average of the other data matrices (isfc mode) or a similarity-weighted average of the other data matrices (wisfc mode). If only a single data matrix is passed, the correlations are computed with respect to the same data matrix.
• Computing correlations across a list is for finding shared correlation across sets of observations (e.g. from different experimental participants). If only a single data matrix is passed, across mode will behave the same as within mode. If a list of data matrices is passed, isfc mode computes each matrix's correlations with respect to the average of the others, and then averages across all of those correlations. wisfc mode behaves similarly, but computes weighted averages (e.g. based on inter-matrix similarities).
Choose rfun for reducing the data and exploring higher order structure
• By specifiying a reduction technique, rfun, timecorr takes a timeseries of observations and returns a timeseries of correlations with the same number of features. This is useful in that it prevents "dimension blowup" whereby running timecorr its own output squares the number of features-- thereby preventing the efficient exploration of higher-order correlations.
• This function may be called recursively to compute dynamic correlations ("level 1"), dynamic correlations between correlations ("level 2"), dynamic correlations between correlations between correlations ("level 3"), etc. If rfun is not specified, the returned data matrix will have number-of-timepoints rows and $\frac{n^2 - n}{2}$ features.
Toolbox documentation, including a full API specification, tutorials, and gallery of examples may be found here on our readthedocs page.
## Installation
### Recommended way of installing the toolbox
You may install the latest stable version of our toolbox using [pip](https://pypi.org):
pip install timecorr
or if you have a previous version already installed:
pip install --upgrade timecorr
### Dangerous (hacker) developer way of installing the toolbox (use caution!)
To install the latest (bleeding edge) version directly from this repository use:
pip install --upgrade git+https://github.com/ContextLab/timecorr.git
## Requirements
The toolbox is currently supported on Mac and Linux. It has not been tested on Windows (and we expect key functionality not to work properly on Windows systems). Dependencies:
• Python 3.4+
• Numpy >= 1.10.4
• Scipy >= 1.0.0
• Seaborn >= 0.8.1
• Matplotlib >=2.0.1
• Pandas >= 0.22.0
• Hypertools >= 0.4.2
## Citing this toolbox
If you use (or build on) this toolbox in your work, we'd appreciate a citation! Please cite the following paper:
Owen LLW, Chang TH, Manning JR (2019) High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns. bioRxiv: doi.org/10.1101/763821
## Contributing
Thanks for considering adding to our toolbox! Some text below has been borrowed from the Matplotlib contributing guide.
### Submitting a bug report
If you are reporting a bug, please do your best to include the following:
1. A short, top-level summary of the bug. In most cases, this should be 1-2 sentences.
2. A short, self-contained code snippet to reproduce the bug, ideally allowing a simple copy and paste to reproduce. Please do your best to reduce the code snippet to the minimum required.
3. The actual outcome of the code snippet
4. The expected outcome of the code snippet
### Contributing code
The preferred way to contribute to timecorr is to fork the main repository on GitHub, then submit a pull request.
• If your pull request addresses an issue, please use the title to describe the issue and mention the issue number in the pull request description to ensure a link is created to the original issue.
• All public methods should be documented in the README.
• Each high-level plotting function should have a simple example in the examples folder. This should be as simple as possible to demonstrate the method.
• Changes (both new features and bugfixes) should be tested using pytest. Add tests for your new feature to the tests/ repo folder.
• Please note that the code is currently in beta thus the API may change at any time. BE WARNED.
## Testing
To test timecorr, install pytest (pip install pytest) and run pytest in the timecorr folder
You can’t perform that action at this time. | {} |
Logic in Computer Science (LICS 2003)
Paper: About Translations of Classical Logic into Polarized Linear Logic (at LICS 2003)
Authors: Olivier Laurent Laurent Regnier
Abstract
We show that the decomposition of Intuitionistic Logic into Linear Logic along the equation A \rightarrow B = !A \multimap B may be adapted into a decomposition of classical logic into LLP, the polarized version of Linear Logic. Firstly we build a categorical model of classical logic (a Control Category) from a categorical model of Linear Logic by a construction similar to the co-Kleisli category. Secondly we analyse two standard Continuation-Passing Style (CPS) translations, the Plotkin and the Krivine’s translations, which are shown to correspond to two embeddings of LLP into LL.
BibTeX
@InProceedings{LaurentRegnier-AboutTranslationsof,
author = {Olivier Laurent and Laurent Regnier},
title = {About Translations of Classical Logic into Polarized Linear Logic},
booktitle = {Proceedings of the Eighteenth Annual IEEE Symp. on Logic in Computer Science, {LICS} 2003},
year = 2003,
editor = {Phokion G. Kolaitis},
month = {June},
pages = {11--20}, | {} |
Resonance occurs in cases where two or more Lewis structures with identical arrangements of atoms but different distributions of electrons can be written. She tries not to make anyone look silly by pointing out that it will depend on how you draw the Lewis structure. Fill in all missing lone pair electrons and formal charges in the structures below. Electronegativity predicts the opposite polarization. Like phosphate, phosphoryl chloride is tetrahedral in shape. Would you predict the same molecular structure from each resonance structure? The Lewis structure for the hydroxide ionIn the hydroxide ion (OH –), the entire structure is surrounded by a bracket, and the charge is placed outside the bracket. CLO4- 4. What is the hybridization of P in each structure? Formal charges are just that - a formality, a method of electron book-keeping that is tied into the Lewis system for drawing the structures of organic compounds and ions. In the Lewis structure of CIF, the formal charge on Cl is ____ and the formal charge on F is ____. A unbound oxygen atom has 6 valence electrons. AND, in the end, notes that the O=P(Cl)_3 is the more representative Lewis structure, and suggests that the OP consider the formal charge 0. Pictorial representations are often used to visualize electrons, as well as any bonding that may occur between atoms in a molecule. Question: A) CSe2 B) AlF2I C) N2O4 D)XeS64- E)POCl3 The Central Atom Is In Bold 1.Total Number Of Valance Electrons 2.Draw The Most Appropiate Lewis Diagram .Write The Formal Charges For The Central Atom 4.Does The Structure Exhibits Resonance (are There Equally Contributing Resonance Hybrid Structure. In particular, chemists use Lewis structures (also known as Lewis dot diagrams, electron dot diagrams, or electron structures) to represent covalent compounds. IMPORTANT: no Lewis diagram is complete without formal charges. AND, in the end, notes that the O=P(Cl)_3 is the more representative Lewis structure, and suggests that the OP consider the formal charge 0. (6 valence electrons in isolated atom) - (2 non-bonding electrons) - (½ x 6 bonding electrons) = 6 - 2 - 3 = 1. Step 3 & 4: The resonance Lewis electron dot structures of POCl3 are as follows: Fig. [PO4]3- 5. trichloridooxidophosphorus. Re: Lewis Structure of POCL3? For the best answers, search on this site https://shorturl.im/av0Wg. SO2Cl2 6. phosphorusoxychloride. Recognizing and distinguishing between neutral and charged bonding patterns will be helpful in learning reaction mechanisms. For organic chemistry, the common bonding patterns of carbon, oxygen, and nitrogen have useful applications when evaluating chemical structures and reactivity. POCL3 2. Why does salt solution conduct electricity? c. What orbitals can the P atom use to form the π bond in structure B? UNII-9XM78OL22K. ... Phosphorus oxychloride has the chemical formulas POCl3, with P as the central atom. How about the carbon atom in methanol? XeO4 7. Think about It The Lewis structure of POCl3 has a P=O bond because this arrangement reduces the formal charge on all the atoms to zero which is the preferred structure. In attempt to display superiority? Give the formal charge on each atom and the hybridization of the central atom.c. In chemistry, a formal charge (FC) is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity. 1.6: Lewis Structures & Formal Charges (Review), Organic molecules can also have positive or negative charges associated with them. A single line is used to represent one pair of shared electrons. The formal charge on an atom is calculated as the number of valence electrons owned by the isolated atom minus the number of valence electrons owned by the bound atom in the molecule: (number of valence electrons owned by the isolated atom), - (number of valence electrons owned by the bound atom), - (number of non-bonding electrons on the bound atom), - ( ½ the number of bonding electrons on the bound atom). You need a double bond between P and O to complete the octet rule for oxygen. In these diagrams, valence electrons are shown as dots that sit around the atom; any bonds that the atoms share are represented by single, dou… For the purpose of calculating formal charges, however, bond dipoles don’t matter - we always consider the two electrons in a bond to be shared equally, even if that is not an accurate reflection of chemical reality. A structure in which the formal charges are as close to zero as possible is preferred. CLO4- 4. phosphorus oxy-chloride. Answer to: Give the Lewis structure for POCl3. The molecular geometry of PCL3 is trigonal pyramidal with the partial charge distribution on the phosphorus. Calculate the formal charges in this structure. In the formal charge convention, we say that the oxygen 'owns' all 4 nonbonding electrons. Note: The review of general chemistry in sections 1.3 - 1.6 is integrated into the above Learning Objective for organic chemistry in sections 1.7 and 1.8. Electronic geometry, molecular shape, and cornell college. Negative formal charge should be on the most, Like charges should not be on adjacent atoms. Later, we will see how the concept of formal charge can help us to visualize how organic molecules react. She tries not to make anyone look silly by pointing out that it will depend on how you draw the Lewis structure. Fosforoxychlorid [Czech] Phosphorus chloride oxide (POCl3) Phosphoroxidchlorid. A formal charge of +1 is located on the oxygen atom. Calculate the formal charges in this structure. Have questions or comments? Double and triple bonds can also be communicated with lines as shown below. Oxychlorid fosforecny [Czech] phosphorousoxychloride. Count total # of electrons needed - “N” Element # e-Needed Legal. A spherical shell extending from r=1 cm to r=10 cm has a uniform charge density of \rho_{y},10mC/m^3 Write Lewis structures that involve minimum formal charges. Thus, oxygen in methanol has a formal charge of zero (in other words, it has no formal charge). Why is the structure $\ce{(Cl)2P - O - Cl}$ unfavourable compared to the two structures in the picture? Based on the Lewis structure given, the formal charge o 2. In the Lewis structure of CIF, the formal charge on Cl is ____ and the formal charge on F is ____. phosphorus trichloride oxide. So the formal charge on carbon is zero. While it can be helpful initially to write the individual shared electrons, this approach quickly becomes awkward. The oxygen owns 2 non-bonding electrons and 3 bonding elections, so the formal charge calculations becomes: formal charge on oxygen =. But we can be more specific than that - we can also state for each molecular ion that a, Now, let's look at the cationic form of methanol, CH, A very important rule to keep in mind is that. In order to minimize formal charge, how many bonds does phosphorus make to the other atoms in the molecule? Formal charge = [# of valence electrons] – [electrons in lone pairs + 1/2 the number of bonding electrons] Since the number of bonding electrons divided by 2 is equal to the number of bonds surrounding the … [NO4]3- I just need help with a few. During chemical reactions, it is common to have charge reactant, intermediates, and/or products. [NO4]3- I just need help with a few. Transcript: This is the H3PO4 Lewis structure: Phosphoric Acid. 0, 0. Complete the following resonance structures for POCl 3. a. For the Lewis structure you'll need to have a total charge for the molecule of 3-. A very important rule to keep in mind is that the sum of the formal charges on all atoms of a molecule must equal the net charge on the whole molecule. Complete the following resonance structures for POCl 3. a. Lewis structures, also known as Lewis-dot diagrams, show the bonding relationship between atoms of a molecule and the lone pairs of electrons in the molecule. Missed the LibreFest? On the basis of bond length and electronegativity, the Schomaker-Stevenson rule suggests that the double bond form is dominant, in contrast with the case of POF 3. Write (a) A Lewis structure for POCl3 following the octet rule. 5 years ago. … Determining Formal Charge Although we know how many valence electrons are present in a compound, it is harder to determine around which atoms the electrons actually reside. In the Lewis structure for H 3 PO 4 there are a total of 32 valence electrons. For each of the hydrogens in methanol, we also get a formal charge of zero: Now, let's look at the cationic form of methanol, CH3OH2+. When determining the best Lewis structure (or predominant resonance structure) for a molecule, the structure is chosen such that the formal charge on each of the atoms is as close to zero … Based on the Lewis structure given, the formal charge o 2. However, it only 'owns' one electron from each of the two covalent bonds, because covalent bonds involve the sharing of electrons between atoms. Anonymous. HSDB 784. Chemistry Chemistry: Principles and Reactions Phosphoryl chloride, POCl 3 , has the skeleton structure Write (a) a Lewis structure for POCl 3 following the octet rule. b. Watch the recordings here on Youtube! SOCl2 Lewis Structure - How to Draw the Lewis Structure for SOCl2 SOCl2 Lewis Structure - How to Draw the Lewis Structure for SOCl2 - YouTube Get the detailed answer: Phosphoryl chloride, POCl3, has the skeleton structure. During chemical reactions, it is common to have charge reactant, intermediates, and/or products. POCl3. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. How is Bohr’s atomic model similar and different from quantum mechanical model? Write (a) a Lewis structure for POCl 3 following the octet rule. Figuring out the formal charge on different atoms of a molecule is a straightforward process - it’s simply a matter of adding up valence electrons. HSDB 784. Fosforoxychlorid [Czech] Phosphorus chloride oxide (POCl3) Phosphoroxidchlorid. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. If you check the formal charges for POCl 3 you'll find that you need a double bond between the Phosphorous and Oxygen atom in order to have the formal charges equal zero. b. Log in, How to interpret and use chemical formula to go from moles of one substance to moles, atoms or grams of another. Line representations are only used for shared electrons. In the CO lewis structure, carbon has a formal charge of -1 and oxygen has a formal charge of +1. Where V = (7 +5 + 7 + 6 + 7 ) = 32 , V is the number of valence electrons of the POCl3.molecule. 3 Common ions with noble gas Which Lewis structure or structures are most appropriate according to the formal charges?The Lewis structure indicates that each Cl atom has three pairs of electrons that are not used in bonding (called lone pairs) and one shared pair of electrons (written between Other examples include P in POCl3, S in SO2, and Cl … of your answer in part a, write the Lewis structure of N2O (including resonance forms). OPCl3. What is the hybridization of P in each structure? Oxychlorid fosforecny [Czech] phosphorousoxychloride. In the Lewis structure of PO43- there are a total of 32 valence electrons. Formal charges are just that - a formality, a method of electron book-keeping that is tied into the Lewis system for drawing the structures of organic compounds and ions. Do I have to write out all the resonance structures? The two opposing effects seem to partially cancel to give a much less polar molecule than expected. See the Big List of Lewis Structures. POCL3 2. [PO4]3- 5. In a Lewis structure, formal charges can be assigned to each atom by treating each bond as if one-half of the electrons are assigned to each atom. Since the lone pair electrons are often NOT shown in chemical structures, it is important to see mentally add the lone pairs. [SO4]2- 3. Therefore, P = 6n + 2 – V = 6 * 5 + 2 – 32 = 0 So, there is no double bond. What does the question mean by "that involve minimum formal charges". Remember, PO4 3- has a negative three charge on the molecule. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Later, we will see how the concept of formal charge can help us to visualize how organic molecules react. 0 0. When drawing the structures of organic molecules, it is very important to show all non-zero formal charges, being clear about where the charges are located. In order to minimize formal charge, how many bonds does phosphorus make to the other atoms in the molecule? It is the well-known fact that if there is a vast difference of the electronegativity, there are more chances of polarity. Hardly. By signing up, you'll get thousands of step-by-step solutions to your homework questions. An isolated carbon owns 4 valence electrons. Lone pair (unshared) electrons are still shown as individual electrons. Phosphorus(V) oxide chloride. phosphorus trichloride oxide. The two opposing effects seem to partially cancel to give a much less polar molecule than expected. A structure that is missing non-zero formal charges is not correctly drawn, and will probably be marked as such on an exam! 2 shared electrons form a single bond shown as ‘:’ or ‘–‘, 4 shared electrons form a double bond shown as ‘::’ or ‘=’, 6 shared electrons form at triple bond shown as ‘:::’ or, Unshared electrons are also called ‘Lone Pairs’ and are shown as ‘:’. Draw, interpret, and convert between Lewis (Kekule), Condensed, and Bond-line Structures. d. Which resonance structure would be favored on the basis of formal charges? Would you predict the same molecular structure from each resonance structure? trichloridooxidophosphorus. These hypothetical formal charges are a guide to determining the most appropriate Lewis structure. UNII-9XM78OL22K. c. What orbitals can the P atom use to form the π bond in structure B? When it is bound as part of a methanol molecule, however, an oxygen atom is surrounded by 8 valence electrons: 4 nonbonding electrons (two 'lone pairs') and 2 electrons in each of its two covalent bonds (one to carbon, one to hydrogen). A formal charge of -1 is located on the oxygen atom. Phosphoryl chloride, POCl 3, has the skeleton structure. 1. We think so because all the atoms in (f) have a formal charge of zero. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. POCl3. What does the question mean by "that involve minimum formal charges". It features three P−Cl bonds and one strong P=O double bond, with an estimated bond dissociation energy of 533.5 kJ/mol. In terms of Lewis structures, formal charge is used in the description, comparison, and assessment of likely topological and resonance structures by determining the apparent electronic charge of each atom within, based upon its electron dot structure, assuming exclusive covalency or non-polar bonding. Phosphorus(V) oxide chloride. Source(s): lewis structure pocl3 formal charge: https://tr.im/zDESH. (The octet rule need not be followed.) (b) a Lewis structure in which all the formal charges … When drawing the structures of organic molecules, it is very important to show all non-zero formal charges, being clear about where the charges are located. 0, 0. XeO4 7. Methanol itself is a neutral molecule, but can lose a proton to become a molecular anion (CH3O-), or gain a proton to become a molecular cation (CH3OH2+). Electronegativity predicts the opposite polarization. The actual distribution of … Structure. Now, if we look at Lewis structures (e) and (f) with formal charges, we can predict with reason that structure (e) should be stable. Write Lewis structures that involve minimum formal charges. ClO3- 8. phosphorus oxy-chloride. The bonding picture has not changed for carbon or for any of the hydrogen atoms, so we will focus on the oxygen atom. SO2Cl2 6. O typically forms two bonds and maintains 2 lone pairs. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Organic molecules can also have positive or negative charges associated with them. Finally, don't be lured into thinking that just because the net charge on a structure is zero there are no atoms with formal charges: one atom could have a positive formal charge and another a negative formal charge, and the net charge would still be zero. For methoxide, the anionic form of methanol, the calculation for the oxygen atom is: = 6 - 6 - 1 = -1. 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Bond dissociation energy of 533.5 kJ/mol page at https: //shorturl.im/av0Wg this point, thinking back to you... It will depend on how you draw the Lewis structure for the Lewis structure of N2O ( resonance... | {} |
# Using idle time in turn-based (RPG) games for updating
If you take any turn based RPG game there will be large periods of time when nothing is happening because the game is looping over 'wait_for_player_input'. Naturally it seems sensible to use this time to update things.
However, this immediately seems to suggest that it would need to be threaded. Is this sort of design possible in a single thread?
loop:
if not check_something_pressed:
update_a_very_small_amount
else
keep going
But if we says 'a_very_small_amount' is only updating a single object each loop, it's going to be very slow at updating.
EDIT: I've tagged this language-agnostic as that seems the sensible thing, though anything more specific to Python would be great. ;-)
Second edit: This game is not planning on having any animated components; that is, I'm currently running it as a wait-for-player-input then update everything and draw. So rather than X FPS it depends on the user's speed.
Yes, its possible to do in a single thread. Generally speaking though, you'll want to be updating the objects every frame and not just when there are spare cycles. Your animations and movement will be disconnected from the frame rate and look rather choppy if you don't. If you're talking more about AI updates or something else that does not need to be real-time, I would put a timer on it. You should know what your target frame rate is and the idle time will be whatever is remaining after everything else has been completed.
Let's say you're targeting 60 FPS for your game. That leaves you with 16.667 ms to perform all of the work you need to do each frame. At the beginning of the game, get the current time using the highest resolution timer available, add 16.667 ms to it and store it somewhere. I think the function in python is time() though it has been a while since I worked in the language. After your processing is complete, enter a loop that checks the current time against the time you've recorded. If the current time is less than the frame end time, update_a_very_small_amount. I wouldn't worry much about the processing going past the end of the frame since your small update should be quick to process. It would only be a slight delay to the start of the next frame and you appear to have enough idle time to handle it.
After the frame has finished processing, add 16.667 ms to the time that was stored for the end of the last frame to find out where the end of the next frame should be. If you use the current time + 16.667 ms and the processing goes over, the end of the next frame will be pushed out by however much time the last frame ran over.
Re: Second Edit
To clarify, I use the term frame-rate here to indicate one iteration through the main loop. If it's based off of the user's input speed, I imagine that your goal is to simply make the game feel responsive. Otherwise you could just check for input and update everything each time through the loop even if it takes 10 seconds to do so. To make it feel responsive though, you'll probably want to check for input around 20 times per second which gives an effective frame rate of 20 FPS, even if you're not actually drawing these frames. This would give you 50 ms to update things before you need to check for input again.
For Python specifically you can try and use Coroutines to do calculations over multiple update calls.
... coroutines are program components that generalize subroutines to allow multiple entry points for suspending and resuming execution at certain locations...
PEP-0342 details coroutine implementation in Python.
You can create your own scheduler and tasks which can simulate multithreading on a single thread. This is the same way that Javascript frameworks allow for multithreaded like processing even though Javascript is run on a single process.
Yes this is possible. Your game will have some kind of main game loop. Something like this:
while(gameRunning)
{
checkUserInput()
updateGame()
renderGame()
}
In updateGame you can iterate over your game objects and update them "a little". If you are doing any heavy calculation in this method the game will simply hang. So you need a way to split up these calculations to run over several iterations of the game loop.
How to split them up, depends on the kind of game you are building. Suppose you are have a path finder routine which uses A* to calculate a path through a labyrinth. You would need to stop the algorithm after a certain amount of time or after a fixed amount of iterations, keep the calculated path so far and return control back to the game loop. The path finding will continue next time updateGame is called. You can even move the character along the partial path while it is still being calculated.
Most times you don't need to worry about the updateGame call taking too long.
"Premature optimization is the root of all evil!"
If you do hit a performance bottleneck in your update routine, that's the time to investigate and optimize. Since you cannot know in advance what parts of your game will take the most time to compute and might waste time optimizing the wrong stuff. | {} |
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### Re: [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe
Posted: April 08 2006
Niayesh Afshordi wrote:Again, this is not about the nature dark energy, but rather a very practical question about how you calculate say CMB power spectrum.
For example, if you only modify the bcakground evolution through some \rho_{DE}(z), and don't change perturbation equations (except for the implicit change in the timedependce of background variables), CMBfast (which is synchronous) and CMBeasy (in gauge invariant mode), will not give you the same answer.
Ah, I think I see. If you play with a(t) you're effectively changing Einstein's equations and you need to also go and change the equations for the metric perturbations. But if I'm understanding this correctly, the Boltzmann equations should be still be fine. $$\dot\delta_{cdm} = -\frac12 \dot h$$ in the synchronous gauge regardless, right? But the equation for $$\dot h$$ is different if $$(\dot a/a)^2 \ne 8\pi G \rho /3$$, and your point is that if you leave the $$\dot h$$ equation unchanged you'll get inconsistent and non-gauge-invariant results?
### Re: [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe
Posted: April 08 2006
Ben Gold wrote:
Ah, I think I see. If you play with a(t) you're effectively changing Einstein's equations and you need to also go and change the equations for the metric perturbations. But if I'm understanding this correctly, the Boltzmann equations should be still be fine. $$\dot\delta_{cdm} = -\frac12 \dot h$$ in the synchronous gauge regardless, right? But the equation for $$\dot h$$ is different if $$(\dot a/a)^2 \ne 8\pi G \rho /3$$, and your point is that if you leave the $$\dot h$$ equation unchanged you'll get inconsistent and non-gauge-invariant results?
Exactly!
One way to see this explicitly is by looking at the superhorizon perturbations. For these perturbations, due to causality, the evolution within a Hubble patch can be obtained by pertubing the Friedmann equations. Therefore, if you change the Friedmann equations (through introducing dark energy or modified gravity), you will also change the equations for super-horizon perturbations. For adiabatic perturbations, this is equivalent to saying that the Bardeen parameter:
$$\zeta \equiv \phi + {2(H^{-1}(z)\dot{\phi}+\phi)\over 3(1+w(z))}$$
is constant on super-horizon scales, where \phi is the metric perturbation in the longitudinal gauge. Notice that the perturbation equation that you arrive at by taking the derivative of $$\zeta$$, contains w(z) and its derivative, and thus, does not only depende on H(z).
While this gives a unique way of modifying perturbation equations when you modify the background evolution, it cannot be uniquely extended to sub-horizon scales. One may do this phenomenologically by introducing a speed of sound $$c^2_{s}$$ as the coefficient of the k^2 correction to the perturbation equation. However, things can be much more complicated, as perturbations won't remain adiabatic, and thus there will be additional degrees of freedom, and/or a more general dependence on k.
As Josh was suggesting, may be the easiest self-consistent thing to do is to set $$c^2_s=0$$, which is equivalent to extending the super-horizon equation (which is derived uniquely) to sub-horizon scales without any change. However, this is physically different from the limit of switching off DE perturbations. Instead, this may be the maximal amount of DE perturbations that you may hope to get, as DE clusters similar to dark matter. $$c^2_s=1$$, might be the closest physical limit to no perturbations.
There is also the $$c^2_s \rightarrow \infty$$ limit, but intuitively I think it should break causality.
### Re: [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe
Posted: April 09 2006
Jochen Weller wrote: I think they just wanted to show that even if they might have messed it up last time (which I am not sure if they did or did not), that it does not make a difference as soon as you combine data sets.
Jochen,
Year One was only done with perturbations switched on.
Cheers
Hiranya
### Re: [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe
Posted: April 09 2006
Susana Landau wrote:what about reionization and degeneration with primordial scalar index fluctuations (n_s) and scalar amplitude (A_s) ?
In section 3.2 they say that the polarization measurements now strongly constrain tau, and that other parameters (n_s, A_s) are insesitive to the reionization history.
However from fig 10 it follows that \tau is still degenerated with A_S , and n_s.
what do you think?
Susana,
Fig 10 shows exp(-2\tau), not \tau. Compared to the first year results, the extent of degeneracy of \tau with n_s and A_s has significantly decreased (e.g. Fig 1). Moreover, this degeneracy is broken not just in the LCDM model but also in a variety of others.
Cheers
Hiranya
### [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA
Posted: April 10 2006
Fergus
Perturbations in DGP are more complicated then just changing H(z).
Look at: astro-ph/0407489
### [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA
Posted: April 10 2006
Hiranya
where they also switched on for w<-1 ?
### [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA
Posted: April 10 2006
Jochen Weller mentioned involvement of other datasets. Well, I do not
know if this is the reason, but does anyone notice that Fig. 6a and 6b
are quite different? The redline is, as I understand it, the `WMAP only' model
power spectrum, but compare the P(k) value as given by this line, at e.g. k=0.03 (h/Mpc),
and you will see what I mean. Does anybody know how to resolve this?
I'd be grateful upon hearing.
And by the way, the y-axis has the wrong label. P(k) is in units of Mpc^3.
This is likely to be a trivial typo.
Another point of contention (non-trivial I think). Has anyone noticed that Fig.6a
and 6b are not only different, but either of them is also not the same as the WMAP
1st year spectrum, viz. Fig. 9 of Spergel et al (2003)? In that earlier plot, k
was just labelled in units of Mpc^-1 rather than h/Mpc, BUT no matter how I
played around with the various combinations of multiplying/dviding k by h=0.71,
and/or P(k) by h=0.71^3, I could not get Fig. 9 to agree with Fig. 6. Not even
close.
Obviously I am the unenlightened one who missed something. Should there ever be a
scenario under which the WMAP papers/authors might wish to explain things better?
What about the (highly improbable) scenario that there is in fact something strange
going on?
### Re: [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe
Posted: April 10 2006
Jochen Weller wrote:Fergus
Perturbations in DGP are more complicated then just changing H(z).
Look at: http://arxiv.org/abs/astro-ph/0407489
Um, that was really my point. :)
I was criticising the fact that so many theories assume that the growth factor and H(z) are controlled by the same physics. Why not consider the ad-hoc approach of modifying H(z) alone?
Niayesh Afshordi wrote: There is also the $$c^2_s \rightarrow \infty$$ limit, but intuitively I think it should break causality.
This is only an effective theory, trying to mimic a pure H modification, and not intending to represent the underlying physics. So the implications of setting $$c^2_s=\infty$$ don't worry me.
Not sure how WMAP chose to evaluate the perturbationless DE approach, and as Alessandro pointed out it was probably just to show that they are currently insignificant. But an infinite sound speed is how I would envisage it. Erases all dark energy perturbations, and thus the DM perturbations are solely dictated by H. The idea is to permit DE to influence the kinematics but not the dynamics. | {} |
$\require{\cancel}$ $\require{\stix[upint]}$
MATHEMATICS 9709
Cambridge International AS and A Level
Name of student Date Adm. number Year/grade Stream Subject Probability & Statistics 1 (S1) Variant(s) P63 Start time Duration Stop time
Qtn No. 1 2 3 4 5 6 7 Total
Marks 5 5 6 5 6 9 9 45
Score
Get Mathematics 9709 Topical Questions (2010-2021) $14.5 per Subject. Attempt all the 7 questions Question 1 Code: 9709/63/M/J/14/1, Topic: Representation of data Some adults and some children each tried to estimate, without using a watch, the number of seconds that had elapsed in a fixed time-interval. Their estimates are shown below. $$\begin{array}{llllllllllllllll} \text {Adults:} & 55 & 58 & 67 & 74 & 63 & 61 & 63 & 71 & 56 & 53 & 54 & 78 & 73 & 64 & 62 \\ \text {Children:} & 86 & 95 & 89 & 72 & 61 & 84 & 77 & 92 & 81 & 54 & 43 & 68 & 62 & 67 & 83 \end{array}$$$\text{(i)}$Draw a back-to-back stem-and-leaf diagram to represent the data.$[3]\text{(ii)}$Make two comparisons between the estimates of the adults and the children.$[2]$Question 2 Code: 9709/63/M/J/12/2, Topic: Representation of data The heights,$x \mathrm{~cm}$, of a group of young children are summarised by $$\Sigma(x-100)=72, \quad \Sigma(x-100)^{2}=499.2$$ The mean height is$104.8 \mathrm{~cm}$.$\text{(i)}$Find the number of children in the group.$\text{(ii)}$Find$\Sigma(x-104.8)^{2}$. Question 3 Code: 9709/63/M/J/14/2, Topic: The normal distribution There is a probability of$\frac{1}{7}$that Wenjie goes out with her friends on any particular day. 252 days are chosen at random.$\text{(i)}$Use a normal approximation to find the probability that the number of days on which Wenjie goes out with her friends is less than than 30 or more than 44.$[5]\text{(ii)}$Give a reason why the use of a normal approximation is justified.$[1]$Question 4 Code: 9709/63/M/J/15/2, Topic: Probability When Joanna cooks, the probability that the meal is served on time is$\frac{1}{5}$. The probability that the kitchen is left in a mess is$\frac{3}{5}$. The probability that the meal is not served on time and the kitchen is not left in a mess is$\frac{3}{10}$. Some of this information is shown in the following table. $$\begin{array}{|l|c|c|c|} \hline & \text{Kitchen left in a mess} & \text{Kitchen not left in a mess} & \text{Total} \\ \hline \text{Meal served on time} & & & \frac{1}{5} \\ \hline \text{Meal not served on time} & & \frac{3}{10} & \\ \hline \text{Total} & & & 1 \\ \hline \end{array}$$$\text{(i)}$Copy and complete the table.$[3]\text{(ii)}$Given that the kitchen is left in a mess, find the probability that the meal is not served on time.$[2]$Question 5 Code: 9709/63/M/J/18/2, Topic: The normal distribution The random variable$X$has the distribution$\mathrm{N}\left(-3, \sigma^{2}\right)$. The probability that a randomly chosen value of$X$is positive is$0.25$.$\text{(i)}$Find the value of$\sigma$.$[3]\text{(ii)}$Find the probability that, of 8 random values of$X$, fewer than 2 will be positive.$[3]$Question 6 Code: 9709/63/M/J/12/3, Topic: Permutations and combinations$\text{(i)}$In how many ways can all 9 letters of the word TELEPHONE be arranged in a line if the letters$\mathrm{P}$and$\mathrm{L}$must be at the ends?$[1]$How many different selections of 4 letters can be made from the 9 letters of the word TELEPHONE if$\text{(ii)}$there are no Es,$[1]\text{(iii)}$there is exactly$1 \mathrm{E}$,$[2]\text{(iv)}$there are no restrictions?$[4]$Question 7 Code: 9709/63/M/J/20/5, Topic: Discrete random variables A pair of fair coins is thrown repeatedly until a pair of tails is obtained. The random variable$X$denotes the number of throws required to obtain a pair of tails.$\text{(a)}$Find the expected value of$X$.$[1]\text{(b)}$Find the probability that exactly 3 throws are required to obtain a pair of tails.$[1]\text{(c)}$Find the probability that fewer than 6 throws are required to obtain a pair of tails.$[2]$On a different occasion, a pair of fair coins is thrown 80 times.$\text{(d)}$Use an approximation to find the probability that a pair of tails is obtained more than 25 times.$[5]\$
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Can be generalized to be quite powerful and therefore, hence it is a complete Web-based NA Meeting that! | {} |
# zbMATH — the first resource for mathematics
Sparse normalized subband adaptive filter algorithm with $$l_0$$-norm constraint. (English) Zbl 1349.93385
Summary: In order to improve the filters performance when identifying sparse system, this paper develops two sparse-aware algorithms by incorporating the $$l_0$$-norm constraint of the weight vector into the conventional Normalized Subband Adaptive Filter (NSAF) algorithm. The first algorithm is obtained from the principle of the minimum perturbation; and the second one is based on the gradient descent principle. The resulting algorithms have almost the same convergence and steady-state performance while the latter saves computational complexity. Whats more, the performance of both algorithms is analyzed by resorting to some assumptions commonly used in the analyses of adaptive algorithms. Simulation results in the context of sparse system identification not only demonstrate the effectiveness of the proposed algorithms, but also verify the theoretical analyses.
##### MSC:
9.3e+12 Filtering in stochastic control theory 9.3e+11 Estimation and detection in stochastic control theory 9.3e+26 Computational methods in stochastic control (MSC2010) 9.3e+13 Identification in stochastic control theory
Full Text: | {} |
# rfrfit
A Random Forest regressor. Random Forest is an estimator that fits number of regression decision trees on various sub-samples of the dataset and uses averaging to improve predictive accuracy and control over fitting.
## Syntax
parameters = rfrfit(X,y)
parameters = rfrfit(X,y,options)
## Inputs
X
Training data.
Type: double
Dimension: vector | matrix
y
Target values.
Type: double
Dimension: vector | matrix
options
Type: struct
n_estimators
The number of trees in the forest (default: 100).
Type: integer
Dimension: scalar
criterion
Function to measure quality of a split. 'mse' (default): mean squared error, 'mae': mean absolute error.
Type: char
Dimension: string
max_depth
The maximum depth of the tree. If not assigned, nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split.
Type: integer
Dimension: scalar
min_samples_split
The minimum number of samples required to split an internal node (default: 2). If integer, consider it as the minimum number. If float: (min_samples_split * n_samples) is taken as the minimum number of samples for each split.
Type: double | integer
Dimension: scalar
min_samples_leaf
The minimum number of samples required to be at a leaf node (default: 1). If number of samples are less than min_samples_leaf at any node, tree is not built further under that node. If integer: consider it as the minimum number. If float: (min_samples_leaf * number of samples) is taken as the minimum number of samples for each node.
Type: double | integer
Dimension: scalar
min_weight_fraction_leaf
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node (default: 0).
Type: double
Dimension: scalar
max_features
The number of features to consider when looking for the best split (default: number of features in training data). If integer: At each split, consider max_features. If float: At each split, consider floor(max_features * n_features).
Type: double | integer
Dimension: scalar
random_state
Controls the randomness of the model. At each split, features are randomly permuted. random_state is the seed used by the random number generator.
Type: integer
Dimension: scalar
max_leaf_nodes
Grow a tree with max_leaf_nodes in best-first fashion. Best nodes are defined by its reduction in impurity. If not assigned, then unlimited number of leaf nodes.
Type: integer
Dimension: scalar
min_impurity_decrease
A node will be split if this split reduces the impurity >= this value (default: 0).
Type: double
Dimension: scalar
bootstrap
Whether bootstrap samples are used when building trees (default: true). If false, the whole dataset is used to build each tree.
Type: Boolean
Dimension: logical
oob_score
Whether to use out-of-bag samples to estimate the R2 on unseen data (default: false).
Type: Boolean
Dimension: logical
## Outputs
parameters
Contains all the values passed to rfrfit method as options. Additionally it has below key-value pairs.
Type: struct
scorer
Function handle pointing to r2 function (R2 Coefficient of Determination).
Type: function handle
n_samples
Number of rows in the training data.
Type: integer
Dimension: scalar
n_features
Number of columns in the training data.
Type: integer
Dimension: scalar
oob_score
Score of the training dataset obtained using an out-of-bag estimate. It is set only when oob_score = true in options
Type: double
Dimension: scalar
oob_prediction
Prediction computed with out-of-bag estimate on training set. It is set only when oob_score = true in options.
Type: double
Dimension: vector
## Example
Usage of rfrfit with options
X = [1 2 3; 4 5 6; 7 8 9; 10 11 12; 13 14 15; 16 17 18; 19 20 21];
y = [1, 2, 3, 4, 5, 6, 7];
options = struct;
options.random_state = 3; options.criterion = 'mae';
parameters = rfrfit(X, y, options)
parameters = struct [
bootstrap: 1
criterion: mae
min_impurity_decrease: 0
min_samples_leaf: 1
min_samples_split: 2
min_weight_fraction_leaf: 0
model_name: model_1635312796851985
n_estimators: 100
n_features: 3
n_samples: 7
oob_score: oob_score not set to true while training
random_state: 3
scorer: @r2
] | {} |
# Modelling proximity effects in transition edge sensors to investigate the influence of lateral metal structures
16 Aug 2017
The bilayers of transition edge sensors (TESs) are often modified with additional normal-metal features such as bars or dots. Previous device measurements suggest that these features improve performance, reducing electrical noise and altering response times. However, there is currently no numerical model to predict and quantify these effects. Here we extend existing techniques based on Usadel's equations to describe TESs with normal-metal features. We show their influence on the principal TES characteristics, such as the small-signal electrothermal parameters $\alpha$ and β and the superconducting transition temperature $T_c$. Additionally, we examine the effects of an applied magnetic field on the device performance. Our model predicts a decrease in $T_c$, $\alpha$ and β as the number of lateral metal structures is increased. We also obtain a relationship between the length $L$ of a TES and its critical temperature, $T_c$ $\propto$ $L^{-0.7}$ for a bilayer with normal-metal bars. We predict a periodic magnetic flux dependence of $\alpha$, β and $I_c$. Our results demonstrate good agreement with published experimental data, which also show the reduction of $\alpha$, β and $T_c$ with increasing number of bars. The observed Fraunhofer dependence of critical current on magnetic flux is also anticipated by our model. The success of this model in predicting the effects of additional structures suggests that in the future numerical methods can be used to better inform the design of TESs, prior to device processing. | {} |
# Wine Glass Resonance Frequency
Tags:
1. Mar 29, 2016
### BobDylan22
1. The problem statement, all variables and given/known data
Question 1: When analysing AP French's Formula for Frequency of Wine glasses, what is the direct relationship between the Frequency heard (at different levels - fd) and the level of water from the top of the glass (d). I know that as the level of water from the glass decreases (meaning the water level is higher), the lower the frequency. However, is this relationship linear or quadratic, etc and why.
Question 2: If you graph (f0/fd)2 on the x axis and (1-(d/H*)4 on the y axis, is this relationship going to be linear or something else.
2. Relevant equations
The equation is in the picture below and above (Link is http://imgur.com/a0pQVdN)
3. The attempt at a solution
2. Mar 29, 2016
### BobDylan22
(f0/fd)^2
3. Mar 29, 2016
### Staff: Mentor
Hi BobDylan22, Welcome to Physics Forums.
It's better to upload and insert in-thread any images that are critical to the problem. I've inserted a copy into your original post. I also fixed the equations in your text to make them easier to parse. Note that you can use the x2 and x2 icons in the editing panel to insert subscripts and superscripts for equations (or use LaTeX notation).
You'll need to provide more explanation for your attempt at a solution. Describe your thinking behind your conclusions in more detail.
4. Mar 29, 2016
### rude man
If you let x = (1-(d/H*)4 and
y = (f0/fd)2
then if the other coefficients are constants, what do you get for your equation? Should be apparent if the relationship between y and x is linear or not.
Also, if you let y = (f0/fd) and
x = √{(1-(d/H*)4}, is that quadratic or not?
BTW it may interest you that a portion of the vibration has an inertial component, i.e. if you set up the vibration nodes at 0 and 180 degrees, then turn the glass say 90 degrees, the vibrations will follow the glass only about 2/3 of the way, i.e. ~60 deg. The so-called "Hemispherical Resonator Gyroscope (HRG)" is based on this phenomenon.
5. Mar 30, 2016
### BobDylan22
I know that if you graph x = (1-(d/H*)4 and y = (f0/fd)2, you get a linear line,
but what if you graph fd and d?
6. Mar 30, 2016
### rude man
OK, we've done question 2.
Question 1: let y = fd and x = d.
Then [f0/y]2 = 1 + a(1 - x/H)4
where a is the given constant.
In order for the relationship between y and x to be a quadratic, you have to be able to come up with constants α, β and γ such that
y = α + βx + γx2.
Considering just the binomial expansion of (1 - x/H)4, does that seem likely ?
7. Mar 30, 2016
### BobDylan22
Ok, but what I don't get is that as the distance from the top of glass to the top of water level decreases (becoming fuller), the frequency decreases. But this formula does not show that relationship. It shows the opposite.
8. Mar 30, 2016
### Staff: Mentor
Did you try plotting it just to get an idea of the shape of the curve? Assign some arbitrary values to the constants and plot fd versus d. Note that the way the given function is defined the fd is in the denominator on the left hand side. So if you rearrange to isolate it you'll get something of the form:
$$f(d) = \frac{f_o}{\sqrt{1 + a\left(1 - \frac{d}{h} \right)^4 }}$$
where fo, a, and h are chosen suitably.
9. Mar 30, 2016
### BobDylan22
10. Mar 30, 2016
### Staff: Mentor
I can't see how your spreadsheet does its calculations, but your results are certainly different from what I see plotting a function of the form I showed in my previous post. Here's a snip from a Mathcad worksheet:
The constants fo, a, and h were chosen arbitrarily just to get a feel for the form of the function.
11. Mar 30, 2016
### BobDylan22
I was graphing fd and d
12. Mar 31, 2016
### rude man
No way! As d goes down, f0/fd goes up but notice that fd is in the denominator on the left-hand side, so they both go down & up together.
13. Mar 31, 2016
### BobDylan22
Fo will always be the same. As d decreases, that means that the level of water in the glass increases, meaning lower frequency.
14. Mar 31, 2016
### rude man
15. Mar 31, 2016
### BobDylan22
No it doesn't. As the distance between the top of glass decreases (that means d decreases), which means the glass is more full, hence the frequency decreases.
16. Apr 2, 2016
### BobDylan22
No it doesn't. As the distance between the top of glass decreases (that means d decreases), which means the glass is more full, hence the frequency decreases.
17. Apr 2, 2016
### rude man
My last post on this thread: look again at your post 7. here is what you said: "Ok, but what I don't get is that as the distance from the top of glass to the top of water level decreases (becoming fuller), the frequency decreases. But this formula does not show that relationship. It shows the opposite."
The formula does NOT " ... show the opposite"!
18. Apr 2, 2016
### BobDylan22
So you are saying that the formula shows the correct relation? Can you please show me
19. Apr 2, 2016
### rude man
See my post 12. Read it carefully.
20. Apr 18, 2016
### BobDylan22
Thankyou, but is the relationship quadratic? | {} |
# What does this rule mean?
I read this rule in a book .it says, If $$a>0$$, $$a$$ is not equal to $$1$$ and $$a^x=a^y$$,then $$x=y$$. But I don't understand why the value of $$a$$ has to be greater than $$0$$. What if the value of $$a$$ was less than $$0$$? Wouldn't it be the same ?For example, if $$a=-2$$, for which other value of $$x$$,could I get $$4$$ other than $$2$$?
• You don't define a real exponential function $a^x$ for $a<0$. Just imagine the domain of that!!
– Pspl
Nov 6 '19 at 15:12
• Could you please explain what you mean to say? I am new to these rules.Thanks Nov 6 '19 at 15:19
• Ok! Using your own terms: what is the domain of $a^x$ where $a=-2$? Can you tell?
– Pspl
Nov 6 '19 at 15:20
• A silly example as well, $(-1)^1 = (-1)^3$ despite $1\neq 3$. Of course, you could change your statement to say $|a|$ is not equal to $1$ to cover this case. That said, even if you can't find another $y$ such that $(-2)^2 = (-2)^y$ that doesn't imply that for all $x,y$ if $(-2)^x=(-2)^y$ that it would imply $x=y$. Consider what happens when you start using fractions in the exponent instead. Nov 6 '19 at 15:28
• Could please give an example of what you mentioned in the last sentences? Nov 6 '19 at 16:52
When $$a<0$$ exponentiation is not well defined for $$x \in \mathbb R$$.
Note that for $$a>0$$, $$a\neq 1$$ the equality $$x=y$$ from $$a^x=a^y$$ holds since $$f(x)=a^x$$ is injective.
• Provided $a\neq1$. Nov 6 '19 at 15:20 | {} |
Tutorial: Generate an ML.NET image classification model from a pre-trained TensorFlow model
Learn how to transfer the knowledge from an existing TensorFlow model into a new ML.NET image classification model.
The TensorFlow model was trained to classify images into a thousand categories. The ML.NET model makes use of part of the TensorFlow model in its pipeline to train a model to classify images into 3 categories.
Training an Image Classification model from scratch requires setting millions of parameters, a ton of labeled training data and a vast amount of compute resources (hundreds of GPU hours). While not as effective as training a custom model from scratch, transfer learning allows you to shortcut this process by working with thousands of images vs. millions of labeled images and build a customized model fairly quickly (within an hour on a machine without a GPU). This tutorial scales that process down even further, using only a dozen training images.
In this tutorial, you learn how to:
• Understand the problem
• Incorporate the pre-trained TensorFlow model into the ML.NET pipeline
• Train and evaluate the ML.NET model
• Classify a test image
You can find the source code for this tutorial at the dotnet/samples repository. Note that by default, the .NET project configuration for this tutorial targets .NET core 2.2.
What is transfer learning?
Transfer learning is the process of using knowledge gained while solving one problem and applying it to a different but related problem.
For this tutorial, you use part of a TensorFlow model - trained to classify images into a thousand categories - in an ML.NET model that classifies images into 3 categories.
Select the right machine learning task
Deep learning
Deep learning is a subset of Machine Learning, which is revolutionizing areas like Computer Vision and Speech Recognition.
Deep learning models are trained by using large sets of labeled data and neural networks that contain multiple learning layers. Deep learning:
• Performs better on some tasks like Computer Vision.
• Requires huge amounts of training data.
Image Classification is a common Machine Learning task that allows us to automatically classify images into categories such as:
• Detecting a human face in an image or not.
• Detecting cats vs. dogs.
Or as in the following images, determining if an image is a(n) food, toy, or appliance:
Note
The preceding images belong to Wikimedia Commons and are attributed as follows:
The Inception model is trained to classify images into a thousand categories, but for this tutorial, you need to classify images in a smaller category set, and only those categories. Enter the transfer part of transfer learning. You can transfer the Inception model's ability to recognize and classify images to the new limited categories of your custom image classifier.
• Food
• Toy
• Appliance
This tutorial uses the TensorFlow Inception model deep learning model, a popular image recognition model trained on the ImageNet dataset. The TensorFlow model classifies entire images into a thousand classes, such as “Umbrella”, “Jersey”, and “Dishwasher”.
Because the Inception model has already been pre trained on thousands of different images, internally it contains the image features needed for image identification. We can make use of these internal image features in the model to train a new model with far fewer classes.
As shown in the following diagram, you add a reference to the ML.NET NuGet packages in your .NET Core or .NET Framework applications. Under the covers, ML.NET includes and references the native TensorFlow library that allows you to write code that loads an existing trained TensorFlow model file.
Multiclass classification
After using the TensorFlow inception model to extract features suitable as input for a classical machine learning algorithm, we add an ML.NET multi-class classifier.
The specific trainer used in this case is the multinomial logistic regression algorithm.
The algorithm implemented by this trainer performs well on problems with a large number of features, which is the case for a deep learning model operating on image data.
Data
There are two data sources: the .tsv file, and the image files. The tags.tsv file contains two columns: the first one is defined as ImagePath and the second one is the Label corresponding to the image. The following example file doesn't have a header row, and looks like this:
broccoli.jpg food
pizza.jpg food
pizza2.jpg food
teddy2.jpg toy
teddy3.jpg toy
teddy4.jpg toy
toaster.jpg appliance
toaster2.png appliance
The training and testing images are located in the assets folders that you'll download in a zip file. These images belong to Wikimedia Commons.
Wikimedia Commons, the free media repository. Retrieved 10:48, October 17, 2018 from: https://commons.wikimedia.org/wiki/Pizza https://commons.wikimedia.org/wiki/Toaster https://commons.wikimedia.org/wiki/Teddy_bear
Setup
Create a project
1. Create a .NET Core Console Application called "TransferLearningTF".
2. Install the Microsoft.ML NuGet Package:
• In Solution Explorer, right-click on your project and select Manage NuGet Packages.
• Choose "nuget.org" as the Package source, select the Browse tab, search for Microsoft.ML.
• Click on the Version drop-down, select the 1.4.0 package in the list, and select the Install button.
• Select the OK button on the Preview Changes dialog.
• Select the I Accept button on the License Acceptance dialog if you agree with the license terms for the packages listed.
• Repeat these steps for Microsoft.ML.ImageAnalytics v1.4.0, SciSharp.TensorFlow.Redist v1.15.0 and Microsoft.ML.TensorFlow v1.4.0.
2. Copy the assets directory into your TransferLearningTF project directory. This directory and its subdirectories contain the data and support files (except for the Inception model, which you'll download and add in the next step) needed for this tutorial.
4. Copy the contents of the inception5h directory just unzipped into your TransferLearningTF project assets/inception directory. This directory contains the model and additional support files needed for this tutorial, as shown in the following image:
5. In Solution Explorer, right-click each of the files in the asset directory and subdirectories and select Properties. Under Advanced, change the value of Copy to Output Directory to Copy if newer.
Create classes and define paths
1. Add the following additional using statements to the top of the Program.cs file:
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using Microsoft.ML;
using Microsoft.ML.Data;
2. Add the following code to the line right above the Main method to specify the asset paths:
static readonly string _assetsPath = Path.Combine(Environment.CurrentDirectory, "assets");
static readonly string _imagesFolder = Path.Combine(_assetsPath, "images");
static readonly string _trainTagsTsv = Path.Combine(_imagesFolder, "tags.tsv");
static readonly string _testTagsTsv = Path.Combine(_imagesFolder, "test-tags.tsv");
static readonly string _predictSingleImage = Path.Combine(_imagesFolder, "toaster3.jpg");
static readonly string _inceptionTensorFlowModel = Path.Combine(_assetsPath, "inception", "tensorflow_inception_graph.pb");
3. Create classes for your input data, and predictions.
public class ImageData
{
public string ImagePath;
public string Label;
}
ImageData is the input image data class and has the following String fields:
• ImagePath contains the image file name.
• Label contains a value for the image label.
4. Add a new class to your project for ImagePrediction:
public class ImagePrediction : ImageData
{
public float[] Score;
public string PredictedLabelValue;
}
ImagePrediction is the image prediction class and has the following fields:
• Score contains the confidence percentage for a given image classification.
• PredictedLabelValue contains a value for the predicted image classification label.
ImagePrediction is the class used for prediction after the model has been trained. It has a string (ImagePath) for the image path. The Label is used to reuse and train the model. The PredictedLabelValue is used during prediction and evaluation. For evaluation, an input with training data, the predicted values, and the model are used.
Initialize variables in Main
1. Initialize the mlContext variable with a new instance of MLContext. Replace the Console.WriteLine("Hello World!") line with the following code in the Main method:
MLContext mlContext = new MLContext();
The MLContext class is a starting point for all ML.NET operations, and initializing mlContext creates a new ML.NET environment that can be shared across the model creation workflow objects. It's similar, conceptually, to DBContext in Entity Framework.
Create a struct for Inception model parameters
1. The Inception model has several parameters you need to pass in. Create a struct to map the parameter values to friendly names with the following code, just after the Main() method:
private struct InceptionSettings
{
public const int ImageHeight = 224;
public const int ImageWidth = 224;
public const float Mean = 117;
public const float Scale = 1;
public const bool ChannelsLast = true;
}
Create a display utility method
Since you'll display the image data and the related predictions more than once, create a display utility method to handle displaying the image and prediction results.
1. Create the DisplayResults() method, just after the InceptionSettings struct, using the following code:
private static void DisplayResults(IEnumerable<ImagePrediction> imagePredictionData)
{
}
2. Fill in the body of the DisplayResults method:
foreach (ImagePrediction prediction in imagePredictionData)
{
Console.WriteLine($"Image: {Path.GetFileName(prediction.ImagePath)} predicted as: {prediction.PredictedLabelValue} with score: {prediction.Score.Max()} "); } Create a .tsv file utility method 1. Create the ReadFromTsv() method, just after the DisplayResults() method, using the following code: public static IEnumerable<ImageData> ReadFromTsv(string file, string folder) { } 2. Fill in the body of the ReadFromTsv method: return File.ReadAllLines(file) .Select(line => line.Split('\t')) .Select(line => new ImageData() { ImagePath = Path.Combine(folder, line[0]) }); The code parses through the tags.tsv file to add the file path to the image file name for the ImagePath property and load it and the Label into an ImageData object. Create a method to make a prediction 1. Create the ClassifySingleImage() method, just before the DisplayResults() method, using the following code: public static void ClassifySingleImage(MLContext mlContext, ITransformer model) { } 2. Create an ImageData object that contains the fully qualified path and image file name for the single ImagePath. Add the following code as the next lines in the ClassifySingleImage() method: var imageData = new ImageData() { ImagePath = _predictSingleImage }; 3. Make a single prediction, by adding the following code as the next line in the ClassifySingleImage method: // Make prediction function (input = ImageData, output = ImagePrediction) var predictor = mlContext.Model.CreatePredictionEngine<ImageData, ImagePrediction>(model); var prediction = predictor.Predict(imageData); To get the prediction, use the Predict() method. The PredictionEngine is a convenience API, which allows you to perform a prediction on a single instance of data. PredictionEngine is not thread-safe. It's acceptable to use in single-threaded or prototype environments. For improved performance and thread safety in production environments, use the PredictionEnginePool service, which creates an ObjectPool of PredictionEngine objects for use throughout your application. See this guide on how to use PredictionEnginePool in an ASP.NET Core Web API. Note PredictionEnginePool service extension is currently in preview. 4. Display the prediction result as the next line of code in the ClassifySingleImage() method: Console.WriteLine($"Image: {Path.GetFileName(imageData.ImagePath)} predicted as: {prediction.PredictedLabelValue} with score: {prediction.Score.Max()} ");
Construct the ML.NET model pipeline
An ML.NET model pipeline is a chain of estimators. Note that no execution happens during pipeline construction. The estimator objects are created but not executed.
1. Add a method to generate the model
This method is the heart of the tutorial. It creates a pipeline for the model, and trains the pipeline to produce the ML.NET model. It also evaluates the model against some previously unseen test data.
Create the GenerateModel() method, just after the InceptionSettings struct and just before the DisplayResults() method, using the following code:
public static ITransformer GenerateModel(MLContext mlContext)
{
}
2. Add the estimators to load, resize and extract the pixels from the image data:
IEstimator<ITransformer> pipeline = mlContext.Transforms.LoadImages(outputColumnName: "input", imageFolder: _imagesFolder, inputColumnName: nameof(ImageData.ImagePath))
// The image transforms transform the images into the model's expected format.
.Append(mlContext.Transforms.ResizeImages(outputColumnName: "input", imageWidth: InceptionSettings.ImageWidth, imageHeight: InceptionSettings.ImageHeight, inputColumnName: "input"))
.Append(mlContext.Transforms.ExtractPixels(outputColumnName: "input", interleavePixelColors: InceptionSettings.ChannelsLast, offsetImage: InceptionSettings.Mean))
The image data needs to be processed into the format that the TensorFlow model expects. In this case, the images are loaded into memory, resized to a consistent size, and the pixels are extracted into a numeric vector.
3. Add the estimator to load the TensorFlow model, and score it:
.Append(mlContext.Model.LoadTensorFlowModel(_inceptionTensorFlowModel).
ScoreTensorFlowModel(outputColumnNames: new[] { "softmax2_pre_activation" }, inputColumnNames: new[] { "input" }, addBatchDimensionInput: true))
This stage in the pipeline loads the TensorFlow model into memory, then processes the vector of pixel values through the TensorFlow model network. Applying inputs to a deep learning model, and generating an output using the model, is referred to as Scoring. When using the model in its entirety, scoring makes an inference, or prediction.
In this case, you use all of the TensorFlow model except the last layer, which is the layer that makes the inference. The output of the penultimate layer is labeled softmax_2_preactivation. The output of this layer is effectively a vector of features that characterize the original input images.
This feature vector generated by the TensorFlow model will be used as input to an ML.NET training algorithm.
4. Add the estimator to map the string labels in the training data to integer key values:
.Append(mlContext.Transforms.Conversion.MapValueToKey(outputColumnName: "LabelKey", inputColumnName: "Label"))
The ML.NET trainer that is appended next requires its labels to be in key format rather than arbitrary strings. A key is a number that has a one to one mapping to a string value.
5. Add the ML.NET training algorithm:
.Append(mlContext.MulticlassClassification.Trainers.LbfgsMaximumEntropy(labelColumnName: "LabelKey", featureColumnName: "softmax2_pre_activation"))
6. Add the estimator to map the predicted key value back into a string:
.Append(mlContext.Transforms.Conversion.MapKeyToValue("PredictedLabelValue", "PredictedLabel"))
.AppendCacheCheckpoint(mlContext);
Train the model
1. Load the training data using the LoadFromTextFile wrapper. Add the following code as the next line in the GenerateModel() method:
IDataView trainingData = mlContext.Data.LoadFromTextFile<ImageData>(path: _trainTagsTsv, hasHeader: false);
Data in ML.NET is represented as an IDataView class. IDataView is a flexible, efficient way of describing tabular data (numeric and text). Data can be loaded from a text file or in real time (for example, SQL database or log files) to an IDataView object.
2. Train the model with the data loaded above:
ITransformer model = pipeline.Fit(trainingData);
The Fit() method trains your model by applying the training dataset to the pipeline.
Evaluate the accuracy of the model
1. Load and transform the test data, by adding the following code to the next line of the GenerateModel method:
IDataView testData = mlContext.Data.LoadFromTextFile<ImageData>(path: _testTagsTsv, hasHeader: false);
IDataView predictions = model.Transform(testData);
// Create an IEnumerable for the predictions for displaying results
IEnumerable<ImagePrediction> imagePredictionData = mlContext.Data.CreateEnumerable<ImagePrediction>(predictions, true);
DisplayResults(imagePredictionData);
There are a few sample images that you can use to evaluate the model. Like the training data, these need to be loaded into an IDataView, so that they can be transformed by the model.
2. Add the following code to the GenerateModel() method to evaluate the model:
MulticlassClassificationMetrics metrics =
mlContext.MulticlassClassification.Evaluate(predictions,
labelColumnName: "LabelKey",
predictedLabelColumnName: "PredictedLabel");
Once you have the prediction set, the Evaluate() method:
• Assesses the model (compares the predicted values with the test dataset labels).
• Returns the model performance metrics.
3. Display the model accuracy metrics
Use the following code to display the metrics, share the results, and then act on them:
Console.WriteLine($"LogLoss is: {metrics.LogLoss}"); Console.WriteLine($"PerClassLogLoss is: {String.Join(" , ", metrics.PerClassLogLoss.Select(c => c.ToString()))}");
The following metrics are evaluated for image classification:
• Log-loss - see Log Loss. You want Log-loss to be as close to zero as possible.
• Per class Log-loss. You want per class Log-loss to be as close to zero as possible.
4. Add the following code to return the trained model as the next line:
return model;
Run the application!
1. Add the call to GenerateModel in the Main method after the creation of the MLContext class:
ITransformer model = GenerateModel(mlContext);
2. Add the call to the ClassifySingleImage() method as the next line of code in the Main method:
ClassifySingleImage(mlContext, model);
3. Run your console app (Ctrl + F5). Your results should be similar to the following output. You may see warnings or processing messages, but these messages have been removed from the following results for clarity.
=============== Training classification model ===============
Image: broccoli2.jpg predicted as: food with score: 0.8955513
Image: pizza3.jpg predicted as: food with score: 0.9667718
Image: teddy6.jpg predicted as: toy with score: 0.9797683
=============== Classification metrics ===============
LogLoss is: 0.0653774699265059
PerClassLogLoss is: 0.110315812569315 , 0.0204391272836966 , 0
=============== Making single image classification ===============
Image: toaster3.jpg predicted as: appliance with score: 0.9646884
Congratulations! You've now successfully built a machine learning model for image classification by applying transfer learning to a TensorFlow model in ML.NET.
You can find the source code for this tutorial at the dotnet/samples repository.
In this tutorial, you learned how to:
• Understand the problem
• Incorporate the pre-trained TensorFlow model into the ML.NET pipeline
• Train and evaluate the ML.NET model
• Classify a test image
Check out the Machine Learning samples GitHub repository to explore an expanded image classification sample. | {} |
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# Title: A mathematical finance approach to the stochastic and intermittent viscosity fluctuations in living cells
Abstract: Here we report on the viscosity of eukaryotic living cells as a function of the time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblastic cells are investigated using an active microrheological technique, where magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in mathematical finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1 - 10 s and 100 - 200 s, not previously disclosed. The shorter time is found being related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and statistical results from mathematical finance. The current approach could be exploited to reveal hidden features from biological complex systems, or determine new biomarkers of cellular metabolism.
Comments: 19 pages, 8 figures, 3 tables Subjects: Soft Condensed Matter (cond-mat.soft); Biological Physics (physics.bio-ph); Cell Behavior (q-bio.CB) Cite as: arXiv:2005.08002 [cond-mat.soft] (or arXiv:2005.08002v1 [cond-mat.soft] for this version)
## Submission history
From: Jean-Francois Berret [view email]
[v1] Sat, 16 May 2020 14:31:39 GMT (4066kb)
Æ´ÈýÕÅÓÎÏ·ÏÂÔØ | {} |
We are what we repeatedly do; excellence then is not an act but, a habit---Aristotle
Welcome to my google-page; here you can find all about my academic activities. You can email me if you want to collaborate or invite me for discussion/deliver lecture in Mathematics.
Assistant Professor
Department of Mathematics
Guru Nanak Dev University, Amritsar
Amritsar-143005, Punjab, India
Email(s): sonumaths@gmail.com
jitender.math@gndu.ac.in
Recent Research/Article(s)
(New)Jitender Singh. A Short Proof that Lebesgue Outer Measure of an Interval is Its Length. American Mathematical Monthly (2017Accepted for publication
Talks/Presentations
1. Chitkara University, HP, March 24, 2017: An introduction to Fourier Analysis.
2. Pt. Mohan Lal S. D. College for Women, Gurdaspur, March 31, 2015: Calculus
3. Academic Staff College, GNDU ASR, December 7, 2013: Fibonacci numbers in Nature
4. The Legacy of Ramanujan, University of Delhi, Dec. 18, 2012: Defining power sums of $n$ and $\varphi(n)$ integers
5. Academic Staff College, GNDU ASR, May 14, 2012: Geometry of Nature
6. ISI Kolkata Dec. 5, 2011: Modulated Rayleigh-Benard convection in ferrofluids
7. ICM 2010, Hyderabad Convention Center: Power Sums of $n$ and $\varphi(n)$ Integers
8. University of Warwick, July 2010: Suspended Sediments on onset of alternate river bars
9. Academic Staff College, GNDU Asr, 2009: Introduction to random number generation
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My Lecture notes/Assignments
Please correct me wherever you find any mistake(s).
1. Real Analysis I: 1 2 3 4 5 6 7 8 9 10
2. Topological Vector Spaces: TVS2
3. Topology(M.Sc. Maths): 0 1 2, 3,4
4. Calculus of Several Variables: 1 2 3 4 5 6 7 8 9 10
5. Algebra I: 1, 2, 3, 4,5, 6
6. B.Sc.(Hons.) Physics Sem I (MTL131): 1,2,3,4,5,6,7,8,9,10
7. B.Sc.(Hons.) Physics Sem II (MTL132): 1 2 3 4 5
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• Algebra I Major: 2010 Suppl.2010
• Sample Algebra I: M.Sc. I 2nd Minor: 20102011
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• Sample Topology: MSc. II 2009 | {} |
# How to calculate the implied volatility using the binomial options pricing model
I want to calculate IV for american options with dividends. So far I have found algorithms to calculate the option price given a volatility.
Please can you point me to paper or implementation (R, python or any other language) of an algorithm that can calculate the IV given option prices, risk free rate, dividends, etc.
-
There is a misunderstanding of such 'pricing' models that is even very prevalent here at QFbeta: BS, binomial models,... are not really pricing models, they are translation models between price <-> volatility. The price is volatility and that price is determined in the market through supply and demand. It is not that option prices are bought and sold but in reality volatility is bid and offered. So if you truly look for a model that models volatility then you need to dig a lot deeper than a simple binomial model (even the whole garch family does not add much value). – Matt Wolf Jun 15 '13 at 13:36
Thanks Matt for your perspective. But this question is more practical rather than philosophical. In your terms, what I'm looking for is the inverse function of price = f(volatility) for the Ross-Cox-Rubinstein aka binomial model. – Victor P Jun 15 '13 at 14:23
Here is a paper by the infamous Mark Rubinstein that should get you started.
http://www.haas.berkeley.edu/groups/finance/WP/rpf232.pdf
And here the trinomial tree version:
http://www.ederman.com/new/docs/gs-implied_trinomial_trees.pdf by no lesser than Derman and Kani.
This may also help with the actual computations:
http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2008-044.pdf
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You don't need an algorithm to solve that - just program a simple BS option calculator using standard BS with dividend in Excel and fix all the inputs except the volatility. Then use goal seek/solver to change the volatility to get the given price and as a result you will have the implied volatility of the price.
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Making BS assumptions to derive volatility from prices when the underlying translation tool was specified as binomial does not sound right to me unless I am missing something. – Matt Wolf Jun 16 '13 at 0:17
Indeed..however the approach should be the similar. Just set up the binomial tree and fix all the other inputs. The change of volatility should only affect 2 the up move and down move (at least in my CRR model). But I guess Veeken already solved it more beautifully. – Olorun Jun 16 '13 at 9:08
The approach is not similar. You can't push prices from a Binomial model through a BS pricer and say the resulting volatilities are the price equivalent from the Binomial model. – Matt Wolf Jun 16 '13 at 12:11
I tried to answer this in the comments but it got too long. simplest approach would be to guess a low and high volatility that is guaranteed to envelope the one to solve for. then compute the corresponding options prices at each of these guesses using your pricer. then while the difference between your guesses (the low/high volatility) is greater than some specified espilon, compute the price of an option at the average of your two guesses. Now adjust either your low volatility guess or high volatility guess depending on whether the price of the option at the average volatility is greater than or less than the price you are given from the market. This will then allow you to push up your low volatilty guess to where the average of the guesses was or push down your high guess to the average. Thus you bisect and iterate, and ultimately your two guesses are equal and given you the price of the option given from the market. This is the simple algo in so many words.
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Hmm, you seem to mix observed probabilities and prices together with risk-neutral probabilities and hence state-contingent prices. I do not see how you would end up with with a local volatility structure that is consistent with observed option prices. Where do you derive risk-neutral probability states that are necessary to fit the model to options prices in order to setup a volatility structure that is consistent with such prices? – Matt Wolf Jun 16 '13 at 12:42
Upon second read could it be that you misread the question? This is about deriving a volatility structure from observed options prices. What you are describing is similar to the Newton-Raphson root finder. For that you need a pricing/translation tool. The person asking this question wants to do it through the binomial/possibly trinomial model not Black Scholes. There are actually advantages to using a binomial model over black scholes despite it being more computationally intensive. I can elaborate if desired but just wanted to point out you most likely missed the point here. – Matt Wolf Jun 16 '13 at 12:55
yeah...i just stopped by before sleeping and clearly i didnt appreciate that indeed he may be looking for a local vol structure. but if he's not, and wants to assume $\sigma$ is constant, i fail to see how what i describe above won't work. – Veeken Jun 16 '13 at 13:37
maybe the asker can elaborate what he is really looking for... – Matt Wolf Jun 16 '13 at 13:52 | {} |
# Synthetic division
In Mathematics, there are two different methods to divide the polynomials. One is the long division method. Another one is the synthetic division method. Among these two methods, the shortcut method to divide polynomials is the synthetic division method. It is also called the polynomial division method of a special case when it is dividing by the linear factor. It replaces the long division method. In certain situations, you can find this method easier. In this article, we will discuss what the synthetic division method is, how to perform this method, steps with more solved examples.
## Synthetic Division of Polynomials
The Synthetic division is a shortcut way of polynomial division, especially if we need to divide it by a linear factor. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors. Thus, the formal definition of synthetic division is given as:
“Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1 and is generally used to find the zeroes of polynomials”
This division method is performed manually with less effort of calculation than the long division method. Usually, a binomial term is used as a divisor in this method, such as x – b.
If we divide a polynomial P(x) by a linear factor (x-a), which of the polynomial of the degree 1, Q(x) is quotient polynomial and R is the remainder, which is a constant term. We use the synthetic division method in the context of the evaluation of the polynomial using the remainder theorem, wherein we evaluate the polynomial P(x) at “a” while dividing the polynomial P(x) by the linear factor. (i.e) P(x)/(x-a).
Mathematically, it can be represented as follows:
P(x)/Q(x) = P(x)/(x-a) = Quotient + [Remainder/(x-a)]
(i.e)
P(x)/(x-a) = Q(x) +[R/(x-a)]
Hence, we can use the synthetic division method to find the remainder quickly, if “a” is the factor of the polynomial.
In the synthetic division method, we use only the numbers for calculation and this method avoids the usage of the variables.
Note:
• We can perform the synthetic division method, only if the divisor is a linear factor.
• In the synthetic division method, we will perform multiplication and addition, in the place of division and subtraction, which is used in the long division method.
## How to Perform a Synthetic Division?
If we want to divide polynomials using synthetic division, you should be dividing it by a linear expression and the first number or the leading coefficient should be a 1. This division by linear denominator is also called division through Ruffini’s rule(paper-and-pencil computation).
The requirements to perform the synthetic process method is given below:
• The divisor of the given polynomial should be of degree 1. It means that the exponent of the given variable should be 1. Such kind of divisor is considered as the linear factor.
• The coefficient of the divisor variable (say x) should be also equal to 1.
The process of the synthetic division will get messed up if the divisor of the leading coefficient is other than one. In case if the leading coefficient of the divisor is other than 1 while performing the synthetic division method, solve the problem carefully.
The basic Mantra to perform the synthetic division process is”
“Bring down, Multiply and add, multiply and add, Multiply and add, ….”
For example, we can use the synthetic division method to divide a polynomial of 2 degrees by x + a or x – a, but you cannot use this method to divide by x2 + 3 or 5x2 – x + 7.
If the leading coefficient is not 1, then we need to divide by the leading coefficient to turn the leading coefficient into 1. For example, 4x – 1 would become x – ¼ and 4x+9 would become x + 9/4. If the synthetic division is not working, then we need to use long division.
## Steps for Polynomial Synthetic Division Method
Following are the steps required for Synthetic Division of a Polynomial:
Step 1 To set up the problem, we need to set the denominator = zero, to find the number to put in the division box. Then, the numerator is written in descending order and if any terms are missing we need to use a zero to fill in the missing term. At last, list only the coefficient in the division problem. Step 2 Now, when the problem is set up perfectly, bring the first number or the leading coefficient straight down. Step 3 Then, put the result in the next column by multiplying the number in the division box with the number you brought down. Step 4 Write the result at the bottom of the row by adding the two numbers together Step 5 Until you reach the end of the problem, repeat steps 3 and 4. Step 6 Write the final answer. The numbers in the bottom row with the last number being the remainder and the remainder which is written as a fraction makes the final answer. The variables shall start with one power less than the real denominator and go down one with each term.
### Advantages and Disadvantages of Synthetic Division Method
The advantages of using the synthetic division method are:
• It requires only a few calculation steps
• The calculation can be performed without variables
• Unlike the polynomial long division method, this method is a less error-prone method
The only disadvantage of the synthetic division method is that this method is only applicable if the divisor of the polynomial expression is a linear factor.
### Synthetic Division Examples
Example 1:
Divide : $$\frac{2x^{3} – 5x^{2} + 3x + 7}{x-2}$$
Solution:
Following the steps as per explained above, to divide the polynomials given. Thus, we can get;
Synthetic Division Example 1
Example 2:
Divide : $$\frac{2x^{3} + 5x^{2} + 9}{x+3}$$
Solution:
As per the given question; we have two polynomials in numerator and denominator. The denominator consists of a linear equation, so we can easily apply the synthetic division method here.
Follow the step by step method as given below:
Example 3:
Divide : $$\frac{3x^{3} + 5x – 1}{x+1}$$
Solution:
Following the same steps as per previous examples.
Synthetic Division Example 3
Example 4:
Divide : $$\frac{4x^{3} – 8x^{2} -x +5}{2x – 1}$$
Solution:
As we know, the step to solve the given equation by synthetic division method, we can write;
Example 5:
Divide : $$\frac{x^{3} – 5x^{2} +3x + 7}{x – 3}$$
Solution:
Solving the given expression, by step by step method, we get;
### Synthetic Division of polynomials Practice Questions
Solve the following problems:
1. Find the quotient and remainder of the polynomial 2x3 -7x2 +0x+11, when it is divided by a linear factor x-3.
2. Solve the following polynomial equation and find its quotient and remainder. (9a2-39a-30)/(a-5)
3. Find Q(x) and R for the polynomial, P(x)=m3-3m+4 divided by the linear factor m-1.
## Frequently Asked Questions on Synthetic Division
### What is meant by synthetic division?
The synthetic division method is a special method of dividing polynomials. This method is a special case of dividing a polynomial expression by a linear factor, in which the leading coefficient should be equal to 1.
### What are the requirements of the synthetic division method?
The requirements of the synthetic division method are:
The divisor of the polynomial expression must have a degree of one (linear factor)
The leading coefficient of the variable in the divisor should be equal to 1.
### What is the Main Use of Synthetic Division?
Synthetic division is mainly used to find the zeroes of roots of polynomials.
### When Can You Use Synthetic Division?
Synthetic division is used when a polynomial is to be divided by a linear expression and the leading coefficient (first number) must be a 1. For example, any polynomial equation of any degree can be divided by x + 1 but not by x2+1
### Why is Synthetic Division Important?
Synthetic division is useful to divide polynomials in an easy and simple way as it breaks down complex equations into smaller and easier equations.
Learn more such maths concepts easily in a more personalised and effective way by downloading BYJU’S- The Learning App.
Test your knowledge on Synthetic division | {} |
# Monthly Archives: March 2013
## Dynamic Auctions and Wireless Links in Data Centers (Xia)
She wants to tackle the issues of traffic dynamics in large scale networks by injecting flexibility into design.
• design flexible spectrum auction systems to match dynamic traffic, since US auctions off large chunks of the spectrum covering the entire country.
• add flexible wireless links to address traffic hotspots in data centers. (Directional 60GHz links between the different racks that is configurable--but any racks in the way must repeat the signal, since 60GHz is line of sight).
• they use reflections off the ceiling to avoid these problems (3D Beamforming)
Dynamic spectrum auction
• most allocated spectrum sits idle.
• using an auction
• truthful auction as e dominant method to remove gain from cheating. Ex: Vicky auction (second price auction)
• she integrates allocation with pricing: greedy allocation based on bids, winner X pays the bid of its critical neighbor.
How is this different than how radio stations split their frequencies based on location?
Note the use of a Kautz $(d,k)$ graph overlay of nodes in the data centers, which allows them to handle arbitrary network size and incremental growth. They show that 92% of paths can run concurrently.
Filed under Big Data, Data Centers
## Minimum sum-of-squares clustering
See the PDF, page 4, for the problem description. Find $C$ cluster centers $z_j$ to minimize the sum of distances from each point to its cluster center.
MSSC is similar to the problem we are trying to solve in the $kn$ to $k$ groups of $n$ matching problem. Given $kn$ points, we would like to find the $n$ cluster centers that minimize the distance of any point $p_i$ to its nearest center $z_j$ (the centroid of that cluster). For fixed $n$ and dimensionality $d$ , it has been shown MSSC is solvable in $O((N)^{nd+1})$ , for $N$ input points. For general $d$ and input parameter $n$ (as in our case), the problem is shown to be NP-hard.
MSSC, however, differs from our problem statement, since we require the size of any cluster to be size $k$ such that the cluster center $z_i$ provides a good representation for $k$ points. The points in each cluster may be divided up to form $n$ groups, where each member comes from a unique cluster, thereby removing bias between the groups. Also, our initial problem statement proposes a greedy method, such that the smallest clusters are found first, whereas MSSC minimizes the sizes of all clusters.
Filed under Algorithms
## Big Data talk
Talk by Faculty candidate on Friday.
Big data computation model
• $n$ = number of vectors in $R^d$ seen so far
• $d$ = number of sensors (dimensionality)
• only have $\log n$ memory available on the system
• $M$ = number of cores
$k$ -median queries
• input: $P \in R^d$
• key idea: replace many points by a weighted average point $c \in C$
• $\sum_{p \in P} dist(p,Q) \approx \sum_{c \in C} w(c) * dist(c,Q)$ , where $C$ is the approximated core set.
Online algorithm to build core set: read in $1/\varepsilon$ points, compute $k$ -means and best-fit lines, then choose some of the furthest outliers, then compress that data. Read next $1/\varepsilon$ points, repeat, then compute the core set of those two sets to get a new core set. Then move on to next points until you read all $n$ and have a final core set. Then run off-line heuristic on this core set of size $k$ .
Does a $1+\varepsilon$ approximation.
References to consider:
1. Feldman, Landberg, STOC'11
• Coreset size: $kd/\varepsilon^2$
3. Har-Peled, Mazumdar, 04
4. Feldman, Wu, Julian, Sung and Rus. GPS Compression
Filed under Big Data, Core Sets, Talks
## Dynamic Voronoi Diagrams
Computational Geometry - An Introduction Through Randomized Algorithms; Mulmuley; 1994; pp 135-
Proposition 4.2.2: The total cost of maintaining a Voronoi diagram in a given update sequence is proportional to the total structural change during that sequence. This ignores a logarithmic factor in the cost of a deletion. It also ignores the cost of locating a conflicting vertex during addition. The expected (total) structural change during a random $(N,\delta)$ -sequence is $O(n)$ . | {} |