ShantanuT01/DACTYL-Pretraining huggingface dataset:
For the compressible Euler equations, even when the initial data are uniformly away from vacuum, solution can approach vacuum in infinite time. Achieving sharp lower bounds of density is crucial in the study of Euler equations. In this paper, for the initial value problems of isentropic and full Euler equations in one space dimension, assuming initial density has positive lower bound, we prove that density functions in classical solutions have positive lower bounds in the order of $\textstyle O(1+t)^{-1}$ and $\textstyle O(1+t)^{-1-\delta}$ for any $\textstyle 0<\delta\ll 1$, respectively, where $t$ is time. The orders of these bounds are optimal or almost optimal, respectively. Furthermore, for classical solutions in Eulerian coordinates $(y,t)\in\mathbb{R}\times[0,T)$, we show velocity $u$ satisfies that $u_{y}(y,t)$ is uniformly bounded from above by a constant independent of $T$, although $u_{y}(y,t)$ tends to negative infinity when gradient blowup happens, i.e. when shock forms, in finite time.
We present and study the largest and the most comprehensive catalog of microlensing events ever constructed. The sample of standard microlensing events comprises 3718 unique events from years 2001--2009, with 1409 not detected before in real-time by the Early Warning System of the Optical Gravitational Lensing Experiment (OGLE). The search pipeline makes use of Machine Learning algorithms in order to help find rare phenomena among 150 million objects and derive the detection efficiency. Applications of the catalog can be numerous, from analyzing individual events to large statistical studies for the Galactic mass and kinematics distributions and planetary abundances.   We derive the maps of the mean Einstein ring crossing time of events spanning 31 sq. deg. toward of the Galactic Center and compare the observed distributions with the most recent models. We find good agreement within the observed region and we see the signature of the tilt of the bar in the microlensing data. However, the asymmetry of the mean time-scales seems to rise more steeply than predictions, indicating either a somewhat different orientation of the bar or a larger bar width. The map for the events with sources in the Galactic bulge shows a dependence of the mean time-scale on the Galactic latitude, signaling an increasing contribution from disk lenses closer to the plane, related with the height of the disk. Our data present a perfect set for comparing and enhancing new models of the central parts of the Milky Way and creating the 3D picture of the Galaxy.
We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the $^1S_0$ channel are calculated to subleading order.
The formation time, masses, and location of planets are strongly impacted by the physical mechanisms that disperse protoplanetary disks and the timescale over which protoplanetary material is cleared out. Accretion of matter onto the central star, protostellar winds/jets, magnetic disk winds, and photoevaporative winds operate concurrently. Hence, disentangling their relative contribution to disk dispersal requires identifying diagnostics that trace different star-disk environments. Here, we analyze the low velocity component (LVC) of the Oxygen optical forbidden lines, which is found to be blueshifted by a few km/s with respect to the stellar velocity. We find that the [OI] LVC profiles are different from those of [NeII] at 12.81\mu m and CO at 4.7\mu m lines pointing to different origins for these gas lines. We report a correlation between the luminosity of the [OI] LVC and the accretion luminosity Lacc. We do not find any correlation with the X-ray luminosity, while we find that the higher is the stellar FUV luminosity, the higher is the luminosity of the [OI] LVC. In addition, we show that the [OI]6300\AA/5577\AA\ ratio is low (ranging between 1 and 8). These findings favor an origin of the [OI] LVC in a region where OH is photodissociated by stellar FUV photons and argue against thermal emission from an X-ray-heated layer. Detailed modeling of two spectra with the highest S/N and resolution shows that there are two components within the LVC: a broad, centrally peaked component that can be attributed to gas arising in a warm disk surface in Keplerian rotation (with FWHM between ~40 and ~60 km/s), and a narrow component (with FWHM ~10 km/s and small blueshifts of ~2 km/s) that may arise in a cool (<1,000 K) molecular wind.
We present the results of neutron diffraction studies on polycrystals of a metallic kagome lattice, Tb3Ru4Al12, reported recently to undergo reentrant magnetism, with the onset of long range antiferromagnetic order below (TN=) 22 K and spin-glass features below about 17 K. The present results reveal long-range antiferromagnetic order of an incommensurate type with the moments oriented along c-axis at all temperatures below TN. There are however notable changes in the T dependence of propagation vector along b-axis across 17 K. An observation of interest is that there is no decrease of intensity of magnetic Bragg peaks on entrance into the glassy phase (that is, below 17 K). This finding suggests that the magnetism of this compound is an exotic one and we wonder whether this compound is an example for dynamical spin-glass freezing phenomenon, as a consequence of geometrical frustration.
We present high spatial resolution observations of Giant Molecular Clouds (GMCs) in the eastern part of the nearby spiral galaxy NGC 6946 obtained with the Combined Array for Research in Millimeter-wave Astronomy (CARMA). We have observed 12CO(1-0), 12CO(2-1) and 13CO(1-0), achieving spatial resolutions of 5.4" x 5.0", 2.5" x 2.0" and 5.6" x 5.4" respectively over a region of 6 x 6 kpc. This region extends from 1.5 kpc to 8 kpc galactocentric radius, thus avoiding the intense star formation in the central kpc. We have recovered short-spacing u-v components by using single dish observations from the Nobeyama 45m and IRAM 30m telescopes. Using the automated CPROPS algorithm we identified 44 CO cloud complexes in the 12CO(1-0) map and 64 GMCs in the 12CO(2-1) maps. The sizes, line widths, and luminosities of the GMCs are similar to values found in other extragalactic studies. We have classified the clouds into on-arm and inter-arm clouds based on the stellar mass density traced by the 3.6 um map. On-arm clouds present in general higher star formation rates than clouds located on inter-arm regions. Although the star formation efficiency shows no systematic trend with galactocentric radius, some on-arm clouds -- which are more luminous and more massive compared to inter-arm GMCs -- are also forming stars more efficiently than the rest of the identified GMCs. These structures appear to be located on two specific regions in the spiral arms. One of them shows a strong gradient, suggesting that this region of high star formation efficiency may be the result of gas flow convergence.
We develop some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete lightcone quantization (DLCQ). After preparing the consistency conditions of the twisted boundary conditions for Annulus/M\"obius/Klein Bottle amplitudes in generic non-abelian orbifold, we classify the most general solutions of the constraints when the discrete group is $S_N$. We calculate the corresponding orbifold amplitudes from two viewpoints -- from the boundary state formalism and from the trace over the open string Hilbert space. It is shown that the topology of the world sheet for the short string and that of the long string in general do not coincide. For example the annulus sector for the short string contains all the sectors (torus, annulus, Klein bottle, M\"obius strip) of the long strings. The boundary/cross-cap states of the short strings are classified into three categories in terms of the long string, the ordinary boundary and the cross-cap states, and the ``joint'' state which describes the connection of two short strings. We show that the sum of the all possible boundary conditions is equal to the exponential of the sum of the irreducible amplitude -- one body amplitude of long open (closed) strings. This is typical structure of DLCQ partition function. We examined that the tadpole cancellation condition in our language and derived the well-known gauge group $SO(2^{13})$.
The perfect physical and geometrical parameters of the main-sequence close visual binary system (CVBS), HIP\,105947, are explicitly presented. These parameters have been constructed conclusively using Al-Wardat's complex method for analyzing CVBSs, which is a method for constructing a synthetic spectral energy distribution (SED) for the entire binary system using individual SED for each component star. Which in its turn built using Kurucz ({\fontfamily{cmtt}\selectfont ATLAS9}) line-blanketed plane-parallel models. At the same time, the orbital parameters for the system are calculated using Tokovinin's dynamical method for constructing the best orbits of the interferometric binary system. Henceforth, the mass-sum of the components, the $\triangle\theta $ and $\triangle\rho $ residuals for the system are introduced. The combination of Al-Wardat's and Tokovinin's methods yields the estimation of the physical and geometrical parameters to their best values. The positions of the components of the system on the evolutionary tracks and isochrones are plotted, and their formation and evolution are discussed.
The `Internal Linear Combination' (ILC) component separation method has been extensively used on the data of the WMAP space mission, to extract a single component, the CMB, from the WMAP multifrequency data. We extend the ILC approach for reconstructing millimeter astrophysical emissions beyond the CMB alone. In particular, we construct a Constrained ILC to extract clean maps of both the CMB or the thermal Sunyaev Zeldovich (SZ) effect, with vanishing contamination from the other. The performance of the Constrained ILC is tested on simulations of Planck mission observations, for which we successfully reconstruct independent estimates of the CMB and of the thermal SZ.
In this paper, we defined three kinds of measures depending on the given finite directed graphs. For the given finite directed graph, we can construct the free semigroupoid, the diagram set and the reduced diagram set, as algebraic structures determined by the admissibility on the graph. The power sets of such structures are sigma algebras of them, respectively. On them, we can define a measure. The pain purpose of this paper is to introduce those three measures and observe some properties of them. Moreover, we consider Measure Theory on them
We develop a robust and versatile platform to define nanostructures at oxide interfaces via patterned top gates. Using LaAlO$_3$/SrTiO$_3$ as a model system, we demonstrate controllable electrostatic confinement of electrons to nanoscale regions in the conducting interface. The excellent gate response, ultra-low leakage currents, and long term stability of these gates allow us to perform a variety of studies in different device geometries from room temperature down to 50 mK. Using a split-gate device we demonstrate the formation of a narrow conducting channel whose width can be controllably reduced via the application of appropriate gate voltages. We also show that a single narrow gate can be used to induce locally a superconducting to insulating transition. Furthermore, in the superconducting regime we see indications of a gate-voltage controlled Josephson effect.
We investigate the effects of AGN feedback on the colour evolution of galaxies found in local (z<0.2) groups and clusters. Galaxies located within the lobes of powerful Fanaroff-Riley type II (edge-brightened) sources show much redder colours than neighbouring galaxies that are not spatially coincident with the radio source. By contrast, no similar effect is seen near Fanaroff-Riley type I (core-dominated) radio sources. We show that these colours are consistent with FR-IIs truncating star formation as the expanding bow shock overruns a galaxy. We examine a sample of clusters with no detectable radio emission and show that galaxy colours in these clusters carry an imprint of past AGN feedback. AGN activity in the low-redshift Universe is predominantly driven by low-luminosity radio sources with short duty cycles. Our results show that, despite their rarity, feedback from powerful radio sources is an important driver of galaxy evolution even in the local volume.
We present an estimate of the bolometric X-ray luminosity - velocity dispersion L_x - sigma_v relation measured from a new, large and homogeneous sample of 171 low redshift, X-ray selected galaxy clusters. The linear fitting of log(L_x) - log(sigma_v) gives L_x = 10^{32.72 \pm 0.08} sigma^{4.1 \pm 0.3}_v erg s^{-1} h^{-2}_{50}. Furthermore, a study of 54 clusters, for which the X-ray temperature of the intracluster medium T is available, allows us to explore two other scaling relations, L_x -T and sigma_v -T. From this sample we obtain L_x \propto T^{3.1 \pm 0.2} and sigma_v \propto T^{1.00 \pm 0.16}, which are fully consistent with the above result for the L_x-sigma_v. The slopes of L_x -T and sigma_v -T are incompatible with the values predicted by self-similarity (L_x \propto T^{2} \propto \sigma_v^4), thus suggesting the presence of non-gravitational energy sources heating up the intracluster medium, in addition to the gravitational collapse, in the early stages of cluster formation. On the other hand, the result on log(L_x) - log(sigma_v) supports the self-similar model.
We study the chemistry of small hydrocarbons in the photon-dominated regions (PDRs) associated with the ultra-compact HII region Mon R2. Our goal is to determine the variations of the abundance of small hydrocarbons in a high-UV irradiated PDR and investigate their chemistry. We present an observational study of CH, CCH and c-C$_3$H$_2$ in Mon R2 combining data obtained with the IRAM 30m telescope and Herschel. We determine the column densities of these species, and compare their spatial distributions with that of polycyclic aromatic hydrocarbon (PAH). We compare the observational results with different chemical models to explore the relative importance of gas-phase, grain-surface and time-dependent chemistry in these environments. The emission of the small hydrocarbons show different patterns. The CCH emission is extended while CH and c-C$_3$H$_2$ are concentrated towards the more illuminated layers of the PDR. The ratio of the column densities of c-C$_3$H$_2$ and CCH shows spatial variations up to a factor of a few, increasing from $N(c-C$_3$H$_2$)/N(CCH)\approx0.004$ in the envelope to a maximum of $\sim0.015-0.029$ towards the 8$\mu$m emission peak. Comparing these results with other galactic PDRs, we find that the abundance of CCH is quite constant over a wide range of G$_0$, whereas the abundance of c-C$_3$H$_2$ is higher in low-UV PDRs. In Mon R2, the gas-phase steady-state chemistry can account relatively well for the abundances of CH and CCH in the most exposed layers of the PDR, but falls short by a factor of 10 to reproduce c-C$_3$H$_2$.   In the molecular envelope, time-dependent effects and grain surface chemistry play a dominant role in determining the hydrocarbons abundances. Our study shows that CCH and c-C$_3$H$_2$ present a complex chemistry in which UV photons, grain-surface chemistry and time dependent effects contribute to determine their abundances.
Neurofibromatosis type 1 (NF1) is an autosomal dominant tumor predisposition syndrome that involves the central and peripheral nervous systems. Accurate detection and segmentation of neurofibromas are essential for assessing tumor burden and longitudinal tumor size changes. Automatic convolutional neural networks (CNNs) are sensitive and vulnerable as tumors' variable anatomical location and heterogeneous appearance on MRI. In this study, we propose deep interactive networks (DINs) to address the above limitations. User interactions guide the model to recognize complicated tumors and quickly adapt to heterogeneous tumors. We introduce a simple but effective Exponential Distance Transform (ExpDT) that converts user interactions into guide maps regarded as the spatial and appearance prior. Comparing with popular Euclidean and geodesic distances, ExpDT is more robust to various image sizes, which reserves the distribution of interactive inputs. Furthermore, to enhance the tumor-related features, we design a deep interactive module to propagate the guides into deeper layers. We train and evaluate DINs on three MRI data sets from NF1 patients. The experiment results yield significant improvements of 44% and 14% in DSC comparing with automated and other interactive methods, respectively. We also experimentally demonstrate the efficiency of DINs in reducing user burden when comparing with conventional interactive methods. The source code of our method is available at \url{https://github.com/Jarvis73/DINs}.
We study the problem of closing the detection loophole in three-qubit Bell tests, the experimentally most relevant case beyond the usual bipartite scenario, and show that the minimal detection efficiencies required can be considerably lowered compared to the two-qubit case. The lowest reported detection efficiency thresholds for two and three qubits so far are $\sim66.7\%$ and $60\%$, respectively. Using the three-qubit W state and a 3-setting Bell inequality, we beat these thresholds and with an 8-setting Bell inequality we reach $50.13\%$. We also investigate generic three-qubit states which allow us to attain a detection efficiency of $50\%$ in a 4-setting Bell test. We conjecture that the limit of $50\%$ is unbeatable using three-qubit states and any number of measurements.
Fast and accurate measurement is a highly desirable, if not vital, feature of quantum computing architectures. In this work we investigate the usefulness of adaptive measurements in improving the speed and accuracy of qubit measurement. We examine a particular class of quantum computing architectures, ones based on qubits coupled to well controlled harmonic oscillator modes (reminiscent of cavity-QED), where adaptive schemes for measurement are particularly appropriate. In such architectures, qubit measurement is equivalent to phase discrimination for a mode of the electromagnetic field, and we examine adaptive techniques for doing this. In the final section we present a concrete example of applying adaptive measurement to the particularly well-developed circuit-QED architecture.
We study numerically in the time domain the linearized gravitational waves emitted from a plunge into a nearly extremal Kerr black hole by solving the inhomogeneous Teukolsky equation. We consider spinning black holes for which the specific spin angular momentum $a/M=1-\epsilon$, and we consider values of $\epsilon\geq 10^{-6}$. We find an effective transient behavior for the quasi-normal ringdown: the early phase of the quasi-normal ringdown is governed by a decay according to inverse time, with frequency equaling twice the black hole's horizon frequency. The smaller $\epsilon$ the later the transition from this transient inverse time decay to exponential decay. Such sources, if exist, may be interesting potential sources for terrestrial or space borne gravitational wave observatories.
Water plays a crucial role both in the interstellar medium and on Earth. To constrain its formation mechanisms and its evolution through the star formation process, the determination of the water deuterium fractionation ratios is particularly suitable. Previous studies derived HDO/H$_2$O ratios in the warm inner regions of low-mass protostars. We here report a detection of the D$_2$O 1$_{1,0}$-1$_{0,1}$ transition toward the low-mass protostar NGC1333 IRAS2A with the Plateau de Bure interferometer: this represents the first interferometric detection of D$_2$O - and only the second solar-type protostar for which this isotopologue is detected. Using the observations of the HDO 5$_{4,2}$-6$_{3,3}$ transition simultaneously detected and three other HDO lines previously observed, we show that the HDO line fluxes are well reproduced with a single excitation temperature of 218$\pm$21 K and a source size of $\sim$0.5 arcsec. The D$_2$O/HDO ratio is $\sim$(1.2$\pm$0.5) $\times$ 10$^{-2}$, while the use of previous H$_2^{18}$O observations give an HDO/H$_2$O ratio of $\sim$(1.7$\pm$0.8) $\times$ 10$^{-3}$, i.e. a factor of 7 lower than the D$_2$O/HDO ratio. These results contradict the predictions of current grain surface chemical models and indicate that either the surface deuteration processes are poorly understood or that both sublimation of grain mantles and water formation at high temperatures ($\gtrsim$230 K) take place in the inner regions of this source. In the second scenario, the thermal desorption of the grain mantles would explain the high D$_2$O/HDO ratio, while water formation at high temperature would explain significant extra production of H$_2$O leading to a decrease of the HDO/H$_2$O ratio.
The paper [J. Balogh, B. Bollob\'{a}s, D. Weinreich, A jump to the Bell number for hereditary graph properties, J. Combin. Theory Ser. B 95 (2005) 29--48] identifies a jump in the speed of hereditary graph properties to the Bell number $B_n$ and provides a partial characterisation of the family of minimal classes whose speed is at least $B_n$. In the present paper, we give a complete characterisation of this family. Since this family is infinite, the decidability of the problem of determining if the speed of a hereditary property is above or below the Bell number is questionable. We answer this question positively by showing that there exists an algorithm which, given a finite set $\mathcal{F}$ of graphs, decides whether the speed of the class of graphs containing no induced subgraphs from the set $\mathcal{F}$ is above or below the Bell number. For properties defined by infinitely many minimal forbidden induced subgraphs, the speed is known to be above the Bell number.
We give a classification of the log canonical models of elliptic surface pairs consisting of an elliptic fibration, a section, and a weighted sum of marked fibers. In particular, we show how the log canonical models depend on the choice of the weights. We describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes. In addition, we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers. This is the first step in constructing compactifcations of moduli spaces of elliptic surfaces using the minimal model program.