prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the infall rate and gas density in the magnetized model compare to non-magnetized accretion?

Read the following text and answer briefly.

Context 1: \section{Introduction}
The averaged quantities can be obtained in two different ways in
magnetohydrodynamics  The first way is to solve 3D MHD equations
and then average the results  The second way is to solve some
system of equations on averages  Combination of numerical
simulations and averaged theory brings phenomenology that can
describe observations or experimental data 

The problem of spherically symmetric accretion takes its origin
from Bondi's work \citep{bondi}  He presented idealized
hydrodynamic solution with accretion rate $\dot{M}_B $ However,
magnetic field $\vec{B}$ always exists in the real systems  Even
small seed $\vec{B}$ amplifies in spherical infall and becomes
dynamically important \citep{schwa} 

Magnetic field inhibits accretion \citep{schwa}  None of many
theories has reasonably calculated the magnetic field evolution
and how it influences dynamics  These theories have some common
pitfalls  First of all, the direction of magnetic field is usually
defined  Secondly, the magnetic field strength is prescribed by
thermal equipartition assumption  In third, dynamical effect of
magnetic field is calculated with conventional magnetic energy and
pressure  All these inaccuracies can be eliminated 

In Section 2\ref{section_method} I develop a model that abandons
equipartition prescription, calculates the magnetic field
direction and strength and employs the correct equations of
magnetized fluid dynamics  In Section 3\ref{results} I show this
accretion pattern to be in qualitative agreement with Sgr A*
spectrum models  I discuss my assumptions in Section 4
\ref{discussion} 

\section{Analytical method}\label{section_method}
 Reasonable turbulence evolution model is the key difference of my
 method  I build an averaged turbulence theory that corresponds to
numerical simulations  I start with the model of isotropic
turbulence that is consistent with simulations of collisional MHD
in three regimes  Those regimes are decaying hydrodynamic
turbulence, decaying MHD turbulence and dynamo action  I introduce
effective isotropization of magnetic field in 3D model 
Isotropization is taken to have a timescale of the order of
dissipation timescale that is a fraction $\gamma\sim1$ of the
Alfven wave crossing time $\tau_{\rm diss}=\gamma r/v_A $

Common misconception exists about the dynamical influence of
magnetic field  Neither magnetic energy nor magnetic pressure can
represent $\vec{B}$ in dynamics  Correct averaged Euler and energy
equations were derived in \citep{scharlemann} for radial magnetic
field  Magnetic force $\vec{F}_M=[\vec{j}\times\vec{B}]$ can be
averaged over the solid angle with proper combination of
$\vec{\nabla}\cdot\vec{B}=0 $ I extend the derivation to random
magnetic field without preferred direction  Dynamical effect of
magnetic helicity \citep{biskamp03} is also investigated  I
neglect radiative and mechanical transport processes 

The derived set of equations requires some modifications and
boundary conditions to be applicable to the real astrophysical
systems  I add external energy input to turbulence to balance
dissipative processes in the outer flow  The outer turbulence is
taken to be isotropic and has magnetization $\sigma\sim1 $
Transonic smooth solution is chosen as possessing the highest
accretion rate as in \citep{bondi} 

\begin{figure}\label{fig1}
  \includegraphics[height= 5\textheight]{velocities}
  \caption{Normalized to Keplerian speed characteristic velocities of magnetized flow  Horizontal lines correspond to self-similar solution $v\sim r^{-1/2} $}
\end{figure}

\section{Results \& Application to Sgr A*}\label{results}

\begin{figure}\label{fig2}
  \includegraphics[height= 5\textheight]{magnetization}
  \caption{Plot of magnetization $\sigma=(E_M+E_K)/E_{Th}$ with radius }
\end{figure}
The results of my calculations confirm some known facts about
spherical magnetized accretion, agree with the results of
numerical simulations and have some previously unidentified
features 

Initially isotropic magnetic field exhibits strong anisotropy with
larger radial field $B_r $ Perpendicular magnetic field
$B_\perp\ll B_r$ is dynamically unimportant in the inner accretion
region Fig\ref{fig1}  Because magnetic field dissipates, infall
onto the black hole can proceed \citep{schwa} 

Turbulence is supported by external driving in the outer flow
regions, but internal driving due to freezing-in amplification
takes over in the inner flow Fig\ref{fig2}  Magnetization of the
flow increases in the inner region with decreasing radius
consistently with simulations \cite{igumen06}  Density profile
appears to be $\rho\sim r^{-1 25}$ that is different from
traditional ADAF scaling $\rho\sim r^{-1 5}$ \citep{narayan}  Thus
the idea of self-similar behavior is not supported 

Compared to non-magnetized accretion, infall rate is 2-5 times
smaller depending on outer magnetization  In turn, gas density is
2-5 times smaller in the region close to the black hole, where
synchrotron radiation emerges \citep{narayan}  Sgr A* produces
relatively weak synchrotron \citep{narayan}  So, either gas
density $n$ or electron temperature $T_e$ or magnetic field $B$
are small in the inner flow or combination of factors works  Thus
low gas density in magnetized model is in qualitative agreement
with the results of modelling the spectrum 

Flow is convectively stable on average in the model of moving
blobs, where dissipation heat is released homogeneously in volume 
Moving blobs are in radial and perpendicular pressure
equilibriums  They are governed by the same equations as the
medium 

\section{Discussion \& Conclusion}\label{discussion}
The presented accretion study self-consistently treats turbulence
in the averaged model  This model introduces many weak assumptions
instead of few strong ones 

I take dissipation rate to be that of collisional MHD simulations 
But flow in question is rather in collisionless regime 
Observations of collisionless flares in solar corona
\citep{noglik} gives dissipation rate $20$ times smaller than in
collisional simulations \citep{biskamp03}  However, flares in
solar corona may represent a large-scale reconnection event rather
than developed turbulence  It is unclear which dissipation rate is
more realistic for accretion 

Magnetic field presents another caveat  Magnetic field lines
should close, or $\vec{\nabla}\cdot\vec{B}=0$ should hold  Radial
field is much larger than perpendicular in the inner region 
Therefore, characteristic radial scale of the flow is much larger
than perpendicular  If radial turbulence scale is larger than
radius, freezing-in condition does not hold anymore  Matter can
freely slip along radial field lines into the black hole  If
matter slips already at the sonic point, the accretion rate should
be higher than calculated 

Some other assumptions are more likely to be valid  Diffusion
should be weak because of high Mach number that approaches unity
at large radius  Magnetic helicity was found to play very small
dynamical role  Only when the initial turbulence is highly
helical, magnetic helicity conservation may lead to smaller
accretion rate  Neglect of radiative cooling is justified a
posteriori  Line cooling time is about $20$ times larger that
inflow time from outer boundary 

The study is the extension of basic theory, but realistic
analytical models should include more physics  The work is
underway 
\begin{theacknowledgments}
I thank my advisor Prof  Ramesh Narayan for fruitful discussions 
\end{theacknowledgments}

\bibliographystyle{aipproc}


Context 2: The future of mobile CPUs, part 1: Today’s fork in the road | Ars Technica
2013 may be a big year for the evolution of smartphones and tablets 
Mobile computing's rise from niche market to the mainstream is among the most significant technological trends in our lifetimes  And to a large extent, it's been driven by the bounty of Moore’s Law—the rule that transistor density doubles every 24 months  Initially, most mobile devices relied on highly specialized hardware to meet stringent power and size budgets  But with so many transistors available, devices inevitably grew general-purpose capabilities  Most likely, that wasn't even the real motivation  The initial desire was probably to reduce costs by creating a more flexible software ecosystem with better re-use and faster time to market  As such, the first smartphones were very much a novelty, and it took many years before the world realized the potential of such devices  Apple played a major role by creating innovative smartphones that consumers craved and quickly adopted 
To some extent, this is where we still stand today  Smartphones are still (relatively) expensive and primarily interesting to the developed world  But over the next 10 years, this too will change  As Moore’s Law rolls on, the cost of a low-end smartphone will decline  At some point, the incremental cost will be quite minimal and many feature phones of today will be supplanted by smartphones  A $650 unsubsidized phone is well beyond the reach of most of the world compared to a $20 feature phone, but a $30 to $40 smartphone would naturally be very popular 
In this grand progression, 2013 will certainly be a significant milestone for mobile devices, smartphones and beyond  It's likely to be the first year in which tablets out-ship notebooks in the US  And in the coming years, this will lead to a confluence of high-end tablets and ultra-mobile notebooks as the world figures out how these devices co-exist, blend, hybridize, and/or merge 
Against this backdrop, in this two-part series, we'll explore the major trends and evolution for mobile SoCs  More importantly, we'll look to where the major vendors are likely going in the next several years 
Tablet and phone divergence
While phones and tablets are mobile devices that often share a great deal of software, it's becoming increasingly clear the two are very different products  These two markets have started to diverge and will continue doing so over time 
From a technical perspective, smartphones are far more compact and power constrained  Smartphone SoCs are limited to around 1W, both by batteries and by thermal dissipation  The raison d’etre of a smartphone is connectivity, so a cellular modem is an absolute necessity  For the cost sensitive-models that make up the vast majority of the market, the modem is integrated into the SoC itself  High-end designs favor discrete modems with a greater power budget instead  The main smartphone OSes today are iOS and Android, though Windows is beginning to make an appearance (perhaps with Linux or BlackBerry on the horizon)  Just as importantly, phone vendors like HTC must pass government certification and win the approval of carriers  There is very much a walled-garden aspect, where carriers control which devices can be attached to their networks, and in some cases devices can only be sold through a certain carrier  The business model places consumers quite far removed from the actual hardware 
In contrast, tablets are far more akin to the PC both technically and economically  The power budget for tablet SoCs is much greater, up to 4W for a passively cooled device and as high as 7-8W for systems with fans  This alone means there is a much wider range of tablet designs than smartphones  Moreover, the default connectivity for tablets is Wi-Fi rather than a cellular modem  The vast majority of tablets do not have cellular modems, and even fewer customers actually purchase a wireless data plan  As a result, cellular modems are almost always optional discrete components of the platform  The software ecosystem is relatively similar, with Microsoft, Apple, and Google OSes available  Because tablets eschew cellular modems, the time to market is faster, and they are much more commonly sold directly to consumers rather than through carriers  In terms of usage models, tablets are much more PC-like, with reasonable-sized screens that make games and media more attractive 
Looking forward, these distinctions will likely become more pronounced  Many tablets today use high-end smartphone SoCs, but the difference in power targets and expected performance is quite large  As the markets grow in volume, SoCs will inevitably bifurcate to focus on one market or the other  Even today, Apple is doing so, with the A6 for phones and the larger A6X for tablets  Other vendors may need to wait a few years to have the requisite volume, but eventually the two markets will be clearly separate 
Horizontal business model evolution
Another aspect of the mobile device market that is currently in flux and likely to change in the coming years is the business model for the chip and system vendors  Currently, Apple is the only company truly pursuing a vertically integrated model, where all phones and tablets are based on Apple’s own SoC designs and iOS  The tight integration between hardware and software has been a huge boon for Apple, and it has yielded superb products 
Samsung is one of the few others companies that takes a vertically integrated approach to phones and tablets, although in truth its strategy seems to be ambivalent on that point  Unlike Apple, Samsung’s SoCs are readily available to third parties, and some Samsung devices, such as the S7562 Galaxy S Duos, use SoCs from competitors  More recently though, there has been a trend of Samsung devices using Samsung SoCs, at least for the premier products  For the moment, Samsung’s approach is best characterized as a hybrid, particularly as the company lacks a bespoke OS 
The rest of the major SoC vendors (e g , Intel, Qualcomm, Nvidia, TI, Mediatek, etc ) have stayed pretty far away from actual mobile devices  These companies tend to focus on horizontal business models that avoid competing with customers or suppliers 
In the long term, mobile devices are likely to evolve similarly to the PC and favor a horizontal business model  The real advantage is one of flexibility; as costs drop and the market expands, it will be increasingly necessary for vendors like HTC to offer a wide range of phones based on radically different SoCs  While a vertically integrated company like Apple can focus and maintain leadership in a specific (and highly lucrative) niche, it would be very difficult to expand in many growing areas of the market  The differences between an iPhone 6 and a $20 feature phone are tremendous and would be very difficult for a single company to bridge 
However, SoC vendors will attempt to reap the benefits of vertical integration by providing complete reference platforms to OEMs  Conceptually, this is a form of "optional" system integration, where the phone vendor or carrier can get the entire platform from the SoC supplier  This has the principal advantages of reducing time to market while also providing a baseline quality and experience for consumers  Currently, this approach has mostly been tested in emerging markets, but it's likely to become more common over time  There is a crucial distinction between reference platforms and vertical integration  Namely, OEMs can always choose to customize a platform to differentiate, and the SoC vendor avoids dealing with consumers directly  Typically, most of the customization is in terms of software on top of a base operating system 
Quote:Moreover, that will make the transition to a 10nm node even more difficult, as the foundries will have to move from 20nm interconnects to 10nm interconnects and skip a generation The advances in technology lately allowing components on such a small scale to even be envisioned, much less planned for, are truly amazing 
Off topic: show
I present the first generation 'non-technical' rock:
I don't think your horizontal market development theory is supported by facts  Samsung and Apple are more vertically oriented than their competition, for starters  I know this article is narrowly focused on the hardware, but MS and Intel getting into hardware, Amazon getting into hardware, Google buying Moto, this is all vertical integration  How can you support the idea that this trend will be reversed with no real justification? I'm sure mobile chips will continue to specialize, but I don't think this means what you think it means  Automobile companies started making their own engines and with rare exceptions, never went back to being more horizontal  Same with retail and their store brands  Same with cloud companies and their servers  Same with mobile companies and their OSs  The horizontal market of PCs created by long-lasting standards and loose hegemony is the exception, not the norm 
Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?
I'm not so sure about several things:1- Moore's law's relevance  Moore's Law is about ICs  ICs are not as big a part of mobile computers as they are of desktops, even of laptops: screens, batteries, radios are a huge part of tablets' and phones' costs, as opposed to the bare SoC + RAM 2- The tablet vs phone dichotomy  For some reason (probably price insensitivity due to subsidies), Phones have a tendency to be more powerful than Tablets, ie phone SoCs are more than good enough for tablets  Since the OS and peripherals are the same, it makes more sense to design and build just one type of SoC, and just disable the phone-modem part of it (even the other radios are still required: BT, Wifi, GPS   ), same as Intel disable cache and cores for their entry-level CPUs  Once you're fabbing a SoC, it makes more sense to make more of the same than to setup a separate run of a cut-down SoC on an older process, unless volumes are huge  We might still be getting previous-generation, well amortized SoCs in cheaper tablets, though 3- On the contrary, I see a tablet and phone convergence (the ugly phablet)  I'm patiently waiting for the new 6"+ phones to replace my Nook Color and Galaxy Note 1 with a single device 4- The advantage of diversity ? Software is becoming ever more important than hardware  Multiplying SoCs means multiplying product development costs, making support and updates more difficult    Again, unless volumes are huge, OEMs are probaly better off going the way of the car industry and using modular "platforms" housed in different chassis with various screen sizes, keyboards, radios, digitizers   I'm wondering why the "single device" trend does not figure in your analysis  Is it stillborn ? Does it have no impact nor dependency on/with SoCs ?
Samsung has its own bespoke OS: Bada and it is used on an extensive line of devices  I think there are numbers somewhere that it outsold Windows Phone 7 for a time 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?First mover advantage 
SoC? System on a Chip I guess?
You're way off on the Moore's Law/cost of smartphones point  The processors used in today's high-end smartphones are already cheap, around $25  And there are less expensive options if you want a lower end product  In fact, the hardware in the whole smartphone is relatively cheap  Analyst's estimate the Z10's materials cost around $160, the iPhone 5 around $140  They're using expensive glass and metals, then there's the battery, memory, etc  which means the processor is a small factor of the cost And then there's the jump from $140 in materials to the unsubsidized costs  The reason these phones cost $650 is because of the high margins these companies are able to get and the high cost of hardware design and/or software development  But the point is that making the processors 4 times better/cheaper isn't going to change the economics of the smartphone  What will change the economics is commoditized designs and software and cheaper materials all around  Then you'll have a $50 smartphone that's decent 
Last edited by ggeezz on Wed Feb 13, 2013 9:17 am
bigterp wrote:SoC? System on a Chip I guess?Yup 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries 
Quote:Currently, the only products using 3D integration are FPGAs from Xilinx,Doesn't Sony use it in the PS Vita? I thought I read somewhere that they had the CPU, main memory (2 dies) and video memory, so 4 dies in total, sitting on top of each other all on the same chip 
renoX wrote:gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries Exactly and I would clarify that it's all about margins, the difference between what it costs to make a chip and what it sells for  The margins for desktop and server processors is huge because a) the whole product is expensive so $200 to $1000 for the chip is acceptable, and b) Intel has huge advantages in that space and little competition So Intel can afford to do the R&D to stay ahead of the curve and keep their position  When your smartphone chip sells for $25 you can't do the R&D to leapfrog a company that sells Xeons for $1000 and Core i5's for $200 
I am happy to see Kanter here at Ars, I like his writing and he maintains Real World Tech, where Linus Torvalds often shows up to comment on CPU arch and other interesting topics 
ggeezz wrote:renoX wrote:gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries Exactly and I would clarify that it's all about margins, the difference between what it costs to make a chip and what it sells for  The margins for desktop and server processors is huge because a) the whole product is expensive so $200 to $1000 for the chip is acceptable, and b) Intel has huge advantages in that space and little competition So Intel can afford to do the R&D to stay ahead of the curve and keep their position  When your smartphone chip sells for $25 you can't do the R&D to leapfrog a company that sells Xeons for $1000 and Core i5's for $200 Spot on Intel are able to piggyback other development efforts off the highly lucrative mainstream x86 market which generates the huge sums of money to fund their amazing fab technology The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art 
solomonrex wrote:I don't think your horizontal market development theory is supported by facts  Samsung and Apple are more vertically oriented than their competition, for starters  I know this article is narrowly focused on the hardware, but MS and Intel getting into hardware, Amazon getting into hardware, Google buying Moto, this is all vertical integration  How can you support the idea that this trend will be reversed with no real justification? I'm sure mobile chips will continue to specialize, but I don't think this means what you think it means  Automobile companies started making their own engines and with rare exceptions, never went back to being more horizontal  Same with retail and their store brands  Same with cloud companies and their servers  Same with mobile companies and their OSs  The horizontal market of PCs created by long-lasting standards and loose hegemony is the exception, not the norm Yea, each year Amazon, MS, Apple and Google look more and more the same 
Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Intel's called Chipzilla for a reason up
Lagrange wrote:The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art I think the processing is a bigger advantage than many realize  If Intel can stay ahead in process design - which this article seems to indicate - they should have a major advantage  All else being equal a 14nm chip should be significantly faster and more efficient than the same chip at 22nm  Add in the fact that yields increase geometrically - you can fit a lot more 14nm chips on a given wafer size vs 22nm (or 32nm for the other manufacturers ) and you have a very appealing proposition  And then add in the fact that Intel actually has a pretty good graphics stack and IP  It's not a sure thing by any means, but I suspect ARM may have just prodded a sleeping giant edit: Also worth noting, Intel, TSMC, and Samsung are the only manufacturers who are building out 450nm wafers  This will increase yields dramatically  Of course Samsung and TSMC will build ARM out, but it definitely puts quite a bit of pressure on all other manufacturers  As the article mentions Intel and Samsung are the only ones who control production top to bottom, and Samsung must share some of the benefits with ARM 
As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP 
Last edited by paul5ra on Wed Feb 13, 2013 11:06 am
introiboad wrote:I am happy to see Kanter here at Ars, I like his writing and he maintains Real World Tech, where Linus Torvalds often shows up to comment on CPU arch and other interesting topics Indeed  Most tech writing in this area is atrocious  This piece is one of the few well informed articles I've read in a long time 
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The word you're looking for is Haswell, as far as I know 
Mabsark
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Probably a mix of a lot of things  One big thing was during this recession, Intel was the ONLY fab company that didn't scale back their R&D  That alone gave Intel a large advantage Intel has almost always been ahead  One of the reasons could be that Intel works with much higher margins than many of the commodity companies like Samsung and TSMC Outside of the P4 flop and some of the monopolistic abuses, Intel has typically been selling to high end customers that are willing to pay a premium for "the best" Intel has a large benefit of having a relatively "good name" when it comes to CPUs, so they can effectively charge a brand-name premium I'm sure there are other reasons, and probably better reasons, but these are the main ones that I think of 
Mabsark wrote:Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well
Context 3: Paper Info

Title: An CUSUM Test with Observation-Adjusted Control Limits in Change Detection
Publish Date: March 9, 2023
Author List: Fuquan Tang (from Department of Statistics, Shanghai Jiao Tong University), Dong Han (from Department of Statistics, Shanghai Jiao Tong University)

Figure

exp{−cg(µ)(θ − x Hv (θ) + o(1))} for 1 ≤ k ≤ ac − 1, bc ≤ n ≤ m, where Zi = −g ′ (µ)(Z i − µ)/a and Hv (θ) = ln hv (θ) + ( ac k − 1) ln ĥv (θ), ĥv (θ) = E v (e θ Zi ) 
i < cg(µ)(1 + o(1))) exp{−cg(µ)θ * v (1 + o(1))} (A  5) for ac ≤ k ≤ bc − 1, bc ≤ n ≤ m,andP v (
i + g ′ (µ)a −1 Tc(g)−1 i=Tc(g)−ac (Z i − µ)] −→ µas c → ∞ By the uniform integrability of {T c (g)/c} and using Theorem A 1 1 in Gut's book(1988), we haveE v (T c (g)) = (1 + o(1)) cg(µ) µfor a large c This completes the proof of Theorem 2 Proof of Theorem 4  Since g(x) < 0 for x > a * , a * ≤ µ * and µ * ≥ 0, it follows thatP v m Ẑm < cg( Ẑm ), Ẑm > a * ≤ P v ( Ẑm < µ * )andP v (T c (g) > m) = P v n i=n−k+1 Z i < cg( Ẑn ), 1 ≤ k ≤ n, 1 ≤ n ≤ m ≤ P v m Ẑm < cg( Ẑm ) = P v m Ẑm < cg( Ẑm ), Ẑm ≤ a * + P v m Ẑm < cg( Ẑm ), Ẑm > a * ≤ 2P v ( Ẑm < µ * ) Furthermore,P v ( Ẑm < µ * ) = P v ( m i −Z i > −mµ * ) = P v ( m i (µ − Z i ) > m(µ − µ * )) = P v (e θ m i (µ−Z i ) > e θm(µ−µ * ) ) ≤ e −m[θ(µ−µ * )−ln M (θ)] ,whereM(θ) = E v (e θ(µ−Z 1 )) and the last inequality follows from Chebychev's inequality Note thath(θ) = θ(µ − µ * ) − ln M(θ) attains its maximum value h(θ * ) = θ * (µ − µ * ) − ln M(θ * ) > 0 at θ = θ * > 0, where h ′ (θ * ) = 0  So, E v (T c (g)) = 1 + ∞ m=1 P v (T c (g) > m) ≤ 1 + m=1 −m[θ * (µ−µ * )−ln M (θ * )] = e θ * (µ−µ * )−ln M (θ * ) + 1 e θ * (µ−µ * )−ln M (θ * ) − Let k > 1 It follows that E vk (T c (g) − k + 1) + = ∞ m=1 P vk (T c (g) > m + k − 1, T c (g) > k − 1) ≤ (a 0 + 1)(k − 1)P 0 (T c (g) > k − 1) + ∞ m≥(a 0 +1)(k−1) P vk (T c (g) > m + k − 1) Similarly, we haveP vk (T c (g) > m + k − 1) = P vk n i=n−k+1 Z i < cg( Ẑn ), 1 ≤ k ≤ n, 1 ≤ n ≤ m + k − 1 ≤ 2P vk ( Ẑm+k−1 < µ * ) − Z i ) > m(µ − µ * ) + (k − 1)(µ 0 − µ * ) ≤ 2 exp{−m θ * (µ − µ * ) − ln M(θ * ) + k − 1 m [µ 0 − µ * − ln M 0 (θ * )] } ≤ e −mb for m ≥ (a 0 + 1)(k − 1), since θ * (µ − µ * ) − ln M(θ * ) + k − 1 m [µ 0 − µ * − ln M 0 (θ * )] ≥ b for m ≥ (a 0 + 1)(k−1) Thus, E vk (T c (g) − k + 1) + ≤ (a 0 + 1)(k − 1)P 0 (T c (g) ≥ k) + m≥(a 0 +1)(k−1) e −mb ≤ (a 0 + 1)(k − 1)P 0 (T c (g) >≥ k) + 2e −(a 0 +1)(k−1)b 1 − e −b  
Simulation of E τ i ,v and J ACE for detecting two mean shifts v = 0 1, v = 1 The parameters for T * M are k1=1, k2=150, r 1 = 5 2 * 10 −5 , r 2 = 1 1 * 10 −5 , and the expectation and standard deviation in both cases are 1717 06with 13459 80 and 3918 33 with 16893 25,respectively 

abstract

In this paper, we not only propose an new optimal sequential test of sum of logarithmic likelihood ratio (SLR) but also present the CUSUM sequential test (control chart, stopping time) with the observation-adjusted control limits (CUSUM-OAL) for monitoring quickly and adaptively the change in distribution of a sequential observations 
Two limiting relationships between the optimal test and a series of the CUSUM-OAL tests are established  Moreover, we give the estimation of the in-control and the out-of-control average run lengths (ARLs) of the CUSUM-OAL test  The theoretical results are illustrated by numerical simulations in detecting mean shifts of the observations sequence 

INTRODUCTION

In order to quickly detect a change in distribution of observations sequence without exceeding a certain false alarm rate, a great variety of sequential tests have been proposed, developed and applied to various fields since proposed a control chart method, see, for example, , , One of popular used sequential tests is the following upper-sided CUSUM test which was proposed by  
where c > 0 is a constant control limit, Z i = log[p v 1 (X i )/p v 0 (X i )], p v 0 (x) and p v 1 (x) are prechange and post-change probability density functions respectively for a sequence of mutually independent observations {X i , i ≥ 1}, that is, there is a unknown change-point τ ≥ 1 such that X 1 ,    , X τ −1 have the probability density function p v 0 , whereas, X τ , X τ +1 ,     have the probability density function p v 1  
By the renewal property of the CUSUM test T C we have , where E 1 (T C ) is the out-of-control average run length (ARL 1 ), P k and E k denote the probability and expectation respectively when the change from p v 0 to p v 1 occurs at the change-point τ = k for k ≥ 1  Though we know that the CUSUM test is optimal under Lorden's measure (see Moustakides 1986 and Ritov 1990), the out-of-control ARL 1 of the CUSUM test is not small, especially in detecting small mean shifts ( see Table in Section 4) 
In other words, the CUSUM test is insensitive in detecting small mean shifts  Then, how to increase the sensitivity of the CUSUM test ? Note that the control limit in the CUSUM test is a constant c which does not depend on the observation samples  Intuitively, if the control limit of the CUSUM test can become low as the samples mean of the observation sequence increases, then the alarm time of detecting the increasing mean shifts will be greatly shortened 
Based on this idea, by selecting a decreasing function g(x) we may define the ( upper-sided ) CUSUM chart T C (cg) with the observation-adjusted control limits cg( Ẑn ) ( abbreviated to the CUSUM-OAL chart ) in the following where c > 0 is a constant and Ẑn = n i=1 Z i /n  In other words, the control limits cg( Ẑn ) of the CUSUM-OAL test can be adjusted adaptively according to the observation information { Ẑn } 
Note that the control limits cg( Ẑn ) may be negative  In the special case, the CUSUM-OAL chart T C (cg) becomes into the conventional CUSUM chart T C (c) in (1) when g ≡ 1  Similarly, we can define a down-sided CUSUM-OAL test  In this paper, we consider only the upper-sided CUSUM-OAL test since the properties of the down-sided CUSUM-OAL test can be obtained by the similar method 
The main purpose of the present paper is to show the good detection performance of the CUSUM-OAL test and to give the estimation of its the in-control and out-of-control ARLs  The paper is organized as follows  In Section 2, we first present an optimal SLR sequential test, then define two sequences of the CUSUM-OAL tests and prove that one of the two sequences of CUSUM-OAL tests converges to the optimal test, another sequences of CUSUM-OAL tests converges to a combination of the optimal test and the CUSUM test 
The estimation of the in-control and out-of-control ARLs of the CUSUM-OAL tests and their comparison are given in Section 3  The detection performances of the three CUSUM-OAL tests and the conventional CUSUM test are illustrated in Section 4 by comparing their numerical out-ofcontrol ARLs  Section 5 provides some concluding remarks 
Proofs of the theorems are given in the Appendix



ground_truth: Infall rate is 2-5 times smaller and gas density is 2-5 times smaller.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How are smartphones and tablets different from a technical perspective?

Read the following text and answer briefly.

Context 2:  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product That's true as long as most people are still buying both a tablet and a laptop when each needs to be replaced  I think the assumption is that, as you say, the tablet market will saturate, with people just replacing existing ones, but the desktop/laptop market could decrease much farther than that, if most people stop replacing them at all  I'm not sure of the likelihood of that, but I think that's where this idea comes from 
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The upcoming Haswell chip is showing to consume 1/3 the power of IvyBridge at peak, consumes 1/20th the power at idle, all the while maintaining Identical or better performance This chip should actually compete with ARM CPUs on both power/performance and idle I am expecting a large war 
Apple once again is dictating the performance in the mobile industry  Nice to see others being able to keep the pace, as well 
paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple evolutionary path by the SoC providers since then Yeah, and most of the innovation in the automobile industry came about before Henry Ford came into the business  Doesn't change the fact that cars would probably have been an asterisk in the history books under "toys for rich people" if it weren't for him The same applies to to mobile computing for Apple, Samsung, et al 
SheldonRoss wrote:Lagrange wrote:The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art I think the processing is a bigger advantage than many realize  If Intel can stay ahead in process design - which this article seems to indicate - they should have a major advantage  All else being equal a 14nm chip should be significantly faster and more efficient than the same chip at 22nm  Add in the fact that yields increase geometrically - you can fit a lot more 14nm chips on a given wafer size vs 22nm (or 32nm for the other manufacturers ) and you have a very appealing proposition  And then add in the fact that Intel actually has a pretty good graphics stack and IP  My point was that Intel might have a one or two process advantage over the rest of the industry at the cutting edge but that doesn't mean that they can afford to manufacture on those processes for very low margin parts  If the SoC market becomes increasingly commoditised, there isn't going to be the money to justify making them in a state of the art fab Remember that one of the big selling points of Itanium was that it would make use of process advantages that were effectively paid for by the mainstream x86 market  That didn't quite work out in practice and Itanium processors were often well behind Xeons in process technology 
paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM 
Last edited by melgross on Wed Feb 13, 2013 11:13 am
Mark Havel wrote:ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The word you're looking for is Haswell, as far as I know If tablets move into the $100-200 range, is there going to be room for Haswell?So long as there is a higher-end tablet market, then Haswell will be able to shine, but it's going to be a much more powerful and costly part than the sort of ARM based hardware that often runs tablets  If we see a race to the bottom where price is the dominant motivator behind purchases, then a high performance SoC will struggle to make its mark 
melgross wrote:paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM Of course I realise ARM IP has indeed been a major driving factor too (though only one if several architectures before ARM became dominant), though I see ARM's influence on the mobile industry as having nothing to do with modern day Apple and only one small piece of the puzzle  My point is that the hard electrical engineering, mathematics, DSP, semiconductor physics/chemistry, RF engineering, analogue design, CAD etc  that make modern telecommunications possible has very little to do with the fashion companies who consumers (and unfortunately much of the tech media) associate with it and give the credit (though in this respect Samsung does deserve a bit more credit for their work on NAND flash and displays)  The industry simply would not exist TODAY without the overwhelming horizontal integration that already dominates 
Quote:In the long term, mobile devices are likely to evolve similarly to the PC and favor a horizontal business model  The real advantage is one of flexibility; as costs drop and the market expands, it will be increasingly necessary for vendors like HTC to offer a wide range of phones based on radically different SoCs  You don't mention in the article that each SoC necessarily requires a bit of parallel dev work unlike the PC  In the PC world there is a standard BIOS and HW architecture that allows for pluggable designs  On a highly integrated SoC this is untrue  HTC suffers because it has to support radically different SoCs, their drivers and boot loaders, etc  Quote:While a vertically integrated company like Apple can focus and maintain leadership in a specific (and highly lucrative) niche, it would be very difficult to expand in many growing areas of the market  The differences between an iPhone 6 and a $20 feature phone are tremendous and would be very difficult for a single company to bridge It's only difficult because Apple chooses to ignore that market, not because they can't  If they can release a $99 Apple TV, they can surely cobble together a $20 feature phone if they chose to eschew 8GB of NAND, BT, WiFi, a specialized dock connector, LTE, and their specialized processors  In other words, build the equivalent of an iPod shuffle with a horrible screen and no OS to speak of 
paul5ra wrote:melgross wrote:paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM Of course I realise ARM IP has indeed been a major driving factor too (though only one if several architectures before ARM became dominant), though I see ARM's influence on the mobile industry as having nothing to do with modern day Apple and only one piece of the puzzle  My point is that the hard electrical engineering, mathematics, DSP, semiconductor physics/chemistry, RF engineering, analogue design,etc  that make modern telecommunications possible has very little to do with the fashion companies who consumers (and unfortunately much of the tech media) associate with it and give the credit (though in this respect Samsung does deserve a bit more credit for their work on NAND flash and displays)  The industry simply would not exist TODAY without the overwhelming horizontal integration that already dominates Yes the efforts of these companies getting cellular communications standardized were immense  And the technology matured  And then they didn't do much with it  It took some youngin's to look at the problem fresh and add the UI that make today's smartphones work  As we have all seen, the moment your technology has matured is the moment you are screwed because someone else now has the opportunity to look at it as a black box and make something new  Each of those manufacturers knew that smartphones would eventually be awesome, but none of them had the UI and software design to make a truly breakout product  Imagine if Motorola would have been smart enough to buy the Android guys instead of Google  Instead, Google bought a bunch of patents on that cellular black box to try to defend it's platform And when you think about it, which consumes more man years of engineering effort per year at this point     iterating that cellular black box or developing the OS, services and apps that power today's smartphones?
Intel had better decide that they are competing in this space "for real", or they are screwed  They've already let the Atom languish for five years, during which ARM has completely caught up in performance Just like Tim Cook said, if you don't cannibalize your own markets someone else will do it for you Whether Intel will embrace that concept in time remains to be seen  Personally, I hope they don't; if Intel transforms into a chipless Fab company (like TSMC) everyone benefits 
I still think Samsung has the advantage long term because they have both the SOC and the memory products  As mentioned in the article, TSV's (Through Silicon Via's) are going to be quite a disruption  Today, people normally stack an LPDDR2 package on top of their SOC package (POP or Package On Package)  Within the LPDDR2 package, you could have a stack of DRAM die typically with wire bonding connecting the die within the package Once you more to TSV's, you can have a LOT more connections between the SOC and its DRAM's  While this is being standardized through JEDEC (http://www jedec org/category/technolog     a/3d-ics-0), Samsung has all the pieces in house to do whatever they want  You could see a 512 bit or higher bus from the SOC to the memory  The trick is that the memory and the SOC need to line up with each other when you stack them  This gives Samsung an inherent advantage This isn't just going to impact mobile either  Take a look at that JEDEC link  It also lists High Bandwidth Memory (HBM)  This is a 1024 bit bus that provides 128GBytes/s to 256GBytes/s of bandwidth to a stack of up to 8 DRAM's  Here is your processor that includes 8-16 cores and 4GBytes of really, really, fast DRAM    No DIMMs required  How many of them do you want in your server rack?If I was Intel or Apple, I would be thinking seriously about making some investments in Micron to guarantee they make some compelling DRAM's to integrate with their SOC's and processors    otherwise Samsung is going to blow them out of the water on bandwidth 
Great_Scott wrote:Intel had better decide that they are competing in this space "for real", or they are screwed  They've already let the Atom languish for five years, during which ARM has completely caught up in performance Just like Tim Cook said, if you don't cannibalize your own markets someone else will do it for you Whether Intel will embrace that concept in time remains to be seen  Personally, I hope they don't; if Intel transforms into a chipless Fab company (like TSMC) everyone benefits It's true that Atom has stood still for too long, but honestly it's pretty amazing how Atom is still competitive with current ARM chips  The Z2760 is even 32nm vs 28nm of the latest Krait and A15 chips But that's all changing with Atom moving to the tick tock schedule this year  It wouldn't even surprise me to see Apple move to Intel chips for IOS And I don't see how Intel moving to a chipless Fab company would help everyone  It certainly wouldn't help Intel 
Mabsark wrote:ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product Yes and no  I'm not sure the tablet market will saturate in a "couple of years " It may be more like 5 years  But that's a quibble Here's the real issue  Right now Apple wants you to own an iPhone AND iPad AND Macbook AND iWatch AND Apple TV  Microsoft, OTOH, is making the Surface so that you could ditch your laptop and just use a Surface  Not everyone, but some people If 5 years from now, we're in a world where a significant number of people use a Surface-type device instead of a laptop, then the PC market is going to contract significantly  Maybe some of the tablet-like devices will use moderately expensive Intel chips, but some of them are going to use cheaper chips 
GravyGraphics wrote:I still think Samsung has the advantage long term because they have both the SOC and the memory products  As mentioned in the article, TSV's (Through Silicon Via's) are going to be quite a disruption  Today, people normally stack an LPDDR2 package on top of their SOC package (POP or Package On Package)  Within the LPDDR2 package, you could have a stack of DRAM die typically with wire bonding connecting the die within the package Once you more to TSV's, you can have a LOT more connections between the SOC and its DRAM's  While this is being standardized through JEDEC (http://www jedec org/category/technolog     a/3d-ics-0), Samsung has all the pieces in house to do whatever they want  You could see a 512 bit or higher bus from the SOC to the memory  The trick is that the memory and the SOC need to line up with each other when you stack them  This gives Samsung an inherent advantage This isn't just going to impact mobile either  Take a look at that JEDEC link  It also lists High Bandwidth Memory (HBM)  This is a 1024 bit bus that provides 128GBytes/s to 256GBytes/s of bandwidth to a stack of up to 8 DRAM's  Here is your processor that includes 8-16 cores and 4GBytes of really, really, fast DRAM    No DIMMs required  How many of them do you want in your server rack?If I was Intel or Apple, I would be thinking seriously about making some investments in Micron to guarantee they make some compelling DRAM's to integrate with their SOC's and processors    otherwise Samsung is going to blow them out of the water on bandwidth Why not AMD? Last I checked they still made memory   and processors/GPUs 
Context 3: 

AN OPTIMAL SLR TEST, TWO CUSUM-OAL TESTS AND THEIR LIMITING RELATIONSHIPS

Let P 0 and E 0 denote the probability and the expectation respectively with the probability density p v 0 when there is no change for all the time  It is known that It follows from Proposition 2 38 in and (5 8)-(5 9) in Chow et al, P 108) that the following sequence test of sum of logarithmic likelihood ratio (SLR)
for B > 1, is optimal in the following sense min for P 0 (T SLR < ∞) = α, where c = log B and 0 < α < 1  In particular, if P 0 is the standard normal distribution with mean shift µ > 0 after changepoint, we have Z j − µ 0 = µX j , where µ 0 = −µ 2 /2  It follows from proposition 4 in that the SLR test T SLR in (4) is also optimal (minimal ARL 1 ) with the same false alarm probability P 0 (T < τ ) 
It can be seen that the in-control average run length of T SLR is infinite, that is, ARL 0 = E 0 (T SLR ) = ∞  However, the minimal ARL 1 with finite ARL 0 is a widely used optimality criterion in statistical quality control (see ) and detection of abrupt changes (see   In order to get finite ARL 0 for T SLR , we replace the constant control limit c of T SLR in (3) or (4) with the dynamic control limit n(µ 0 − r) and obtain a modified SLR test T SLR (r) in the following
for r ≥ 0  For comparison, the in-control ARL 0 of all candidate sequential tests are constrained to be equal to the same desired level of type I error, the test with the lowest out-of-control ARL v has the highest power or the fastest monitoring (detection) speed  In the following example 1, the numerical simulations of the out-of-control ARLs of the CUSUM-OAL tests T C (cg u,0 ) in detecting the mean shifts of observations with normal distribution will be compared with that of the SLR tests T * (r) and T * (0), and that of the CUSUM-SLR test T C (c) ∧ T * (0) := min{T C (c), T * (0)} in the following Table  
These comparisons lead us to guess that there are some limiting relationships between T C (cg u,r ) and T * (r), and T C (c g u ) and T C (c) ∧ T * (0), respectively  Example 1  Let X 1 , X 2 ,      be mutually independent following the normal distribution N(0, 1) if there is no change  After the change-point τ = 1, the mean E µ (X k ) ( k ≥ 1 ) will change from v 0 = 0 to v = 0 1, 0 25, 0 5, 0 75, 1, 1 25, 1 5, 3  Here, we let
, where v 1 = 1 is a given reference value which for the CUSUM test is the magnitude of a shift in the process mean to be detected quickly  We conducted the numerical simulation based on 1,000,000 repetitions  The following Table lists the simulation results of the ARLs of the tests T C (c), T C (c g u ) for u = 1, 10, 10 2 , 10 3 , 10 4 , T * (0 0007), T C (c) ∧ T * (0) and T * (0) for detecting the mean shifts, where the mean shift 0 0 means that there is no change which corresponds to the in-control ARL 0 and all tests have the common ARL 0 ≈ 1000 except the test T * (0) which has ARL 0 = ∞ 
The values in the parameters are the standard deviations of the tests  From the last row in Table , it's a little surprising that though the ARL 0 of T * (0) is infinite, that is, E 0 (T * (0)) = ∞, the detection speed of T * (0) is faster than that of the CUSUM chart T C for all mean shifts, in particular, for detecting the small mean shift 0 1, the speed of T * (0) is only 7 47 which is very faster than the speed, 439, of the CUSUM test 
Moreover, both control charts T * (0 0007) and T C (11 9271) ∧ T * (0) not only have the nearly same detection performance as T * (0) but also can have the finite in-control ARL 0   Note particularly that when the number u in g u is taken from 0 to 1, 10, 10 2 , 10 3 , 10 4 , the detection speed of T C (c g u ) is getting faster and faster, approaching to that of T C (c) ∧ T * (0) 
This inspires us to prove the following theoretic results  Let τ = 1 and {X k , k ≥ 1} be an i i d  observations sequence with Theorem 2 shows that when the constant control limit c of the CUSUM test T C (c) is replaced with the observation-adjusted control limits {cg u,r ( Ẑn )} and {c g u ( Ẑn )} respectively, the corresponding two CUSUM-OAL tests {T C (cg u,r )} and {T C (c g u )} will converge to the optimal SLR test T * (r) and the CUSUM-SLR test T C (c) ∧ T * (0) as u → ∞, respectively 
In other words, the fastest alarm times that {T C (cg u,r )} and {T C (c g u )} can be reached are T * (r) and T C (c) ∧ T * (0), respectively  u ≥ 0} can be seen as two "long bridges" connecting T C (c) and T * (r), and T C (c) and T C (c) ∧ T * (0), respectively 

ESTIMATION AND COMPARISON OF ARL OF THE CUSUM-OAL TEST

In this section we will give an estimation of the ARLs of the following CUSUM-OAL test that can be written as where g( ) is a decreasing function, Ẑn (ac x] denotes the smallest integer greater than or equal to x  Here Ẑn (ac) is a sliding average of the statistics, Next we discuss on the the post-change probability distribution in order to estimate the ARLs of T C (cg) 
Usually we rarely know the post-change probability distribution P v of the observation process before it is detected  But the possible change domain and its boundary (including the size and form of the boundary) about v may be determined by engineering knowledge, practical experience or statistical data 
So we may assume that the region of parameter space V and a probability distribution Q on V are known  If we have no prior knowledge of the possible value of v after the change time τ , we may assume that v occurs equally on V , that is, the probability distribution Q is an equal probability distribution (or uniform distribution ) on V 



ground_truth: Smartphones are more compact and power constrained.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What are the three subsets into which the parameter space V is divided?

Read the following text and answer briefly.

Context 3: 
For example, let P v be the normal distribution and v = (µ, σ), where µ and σ denote the mean and standard deviation respectively, we can take the set V = {(µ, σ) : and Q is subject to the uniform distribution U(V ) on V if v occurs equally on V , where the numbers µ 1 , µ 2 , σ 1 and σ 2 are known  It means that we know the domain of the possible post-change distributions, P v , v ∈ V , i e , the boundary ∂V of the parameter space V is known 
Next we shall divide the parameter space V into three subsets V + , V 0 and V − by the Kullback-Leibler information distance  Let and are two Kullblak-Leibler information distances between P v , P v 0 and P v , P v 1   Since I(p|q) = 0 if and only if p = q, where p and q are two probability measures, it follows that
, it means that P v is closer to P v 0 than to P v 1 according to the Kullblak-Leibler information distance  There is a similar explanation for v ∈ V + or ∈ V 0   Suppose the post-change distribution P v and the function g(x) satisfy the following conditions: (I) The probability P v is not a point mass at E v (Z 1 ) and P v (Z 1 > 0) > 0 
(II) The moment-generating function h v (θ) = E v (e θZ 1 ) satisfies h v (θ) < ∞ for some θ > 0  (III) The function g(x) is decreasing, its second order derivative function g ′′ (x) is continuous and bounded, and there is a positive number x * such that g(x * ) = 0  ) and and therefore, Θ ′ (θ(u)) = −H(θ(u)) = −H(θ * v ) = 0, Θ ′ (θ(1/x)) > 0 for x > 1/u and Θ ′ (θ(1/x)) < 0 for x > 1/u 
Hence, there exists a positive number b defined in (??)  It can be seen, the main part of ARL v (T c (g)) will be an exponential function, square function, and linear function of c when the process {Z k : k ≥ 0} has no change or a "small change", a "medium change" and a "large change" from P v 0 to P v , respectively 
Here, the "small change" (v ∈ V − ) means that P v is closer to P v 0 than to P v 1 , i e , I(P v |P v 0 ) < I(P v |P v 1 ), and the "large change" is just the opposite  The "medium change" (v ∈ V 0 ) corresponds to In this paper, we will use another method to prove Theorem 3 since Wald's identity and the martingale method do not hold or can not work for showing the ARLs estimation of the test T c (g) when g is not constant 
Next we compare the detection performance of the CUSUM-OAL test (ARL v (T c ′ (g))) with that of the CUSUM test (ARL v (T C (c))) by using (??) in Theorem 4 1  ) when µ 0 < µ < 0 and for θ * v 0 > g(µ)/g(µ 0 ) when µ ≥ 0  This means that ARL v (T c (g)) can be smaller than ARL v (T C (c)) as long as g(µ)/g(µ 0 ) is small for all µ > µ 0  

NUMERICAL SIMULATION AND A REAL EX-AMPLE ILLUSTRATION

4 1 Numerical Simulation of ARLs for τ ≥ 1 By the simulation results of ARLs in Table , we see that the detection performance of T * (r), T C (c)∧T * (0), T * (0) and T C (c g u ) for large u is much better than that of the conventional CUSUM test T C for τ = 1  The following Table illustrates the simulation values of E τ i ,v and J ACE of nine tests in detecting two mean shifts v = 0 1 and v = 1 after six change-points, τ i , 1 ≤ i ≤ 6 with ARL 0 (T ) = E 0 (T ) ≈ 500 
Note that H v (θ) is a convex function and H ′ v (0) = µ < 0  This means that there is a unique positive number   It follows from (A 9) that for a large c  Taking θ ց θ * v and u ′ ց u, we have for a large c  Thus, by (A 11) we have as c → ∞  By the properties of exponential distribution, we have for a large c 
To prove the downward inequality of (A 10), let where b is defined in (??) and without loss of generality, we assume that b > a  Obviously, Let k = xcg(µ)  By Chebyshev's inequality, we have Since Hv (θ) and H v (θ) are two convex functions and Let m = tcg(µ)θ * v /bc for t > 0  By (A 13), (A 14), (A 15) and Theorem 5 1 in Esary, Proschan and Walkup (1967) we have
Finally, as c → +∞, where θ 0 > 0 satisfies h v (θ 0 ) = 1  Thus as c → ∞  This implies that for a large c  This completes the proof of (A 10)  Let v ∈ V 0   Let m 1 = (cg(0)) 2 /σ 2   It follows that Note that for a large c, where A = |g ′ (0)|/a, and , where Φ( ) is the standard normal distribution  Let m 2 = (cg(0)) 2 /(8σ 2 ln c) 
Note that as c → ∞, where the third inequality comes from Theorem 5 1 in Esary, Proschan and Walkup (1967)  Thus, we have Let v ∈ V + and let The uniform integrability of {T c (g)/c} for c ≥ 1, follows from the well-known uniform integrability of {T 0 /c} (see Gut (1988)) 



ground_truth: The three subsets are V+, V0, and V-, determined by the Kullback-Leibler information distance.