ShantanuT01/DACTYL-Pretraining huggingface dataset:
A discrete function of $n$ variables is a mapping $g : X_1 \times \ldots \times X_n \rightarrow A$, where $X_1, \ldots, X_n$, and $A$ are arbitrary finite sets. Function $g$ is called {\em separable} if there exist $n$ functions $g_i : X_i \rightarrow A$ for $i = 1, \ldots, n$, such that for every input $x_1, \ldots ,x_n$ the function $g(x_1, \ldots, x_n)$ takes one of the values $g_1(x_1), \ldots ,g_n(x_n)$. Given a discrete function $g$, it is an interesting problem to ask whether $g$ is separable or not. Although this seems to be a very basic problem concerning discrete functions, the complexity of recognition of separable discrete functions of $n$ variables is known only for $n=2$. In this paper we will show that a slightly more general recognition problem, when $g$ is not fully but only partially defined, is NP-complete for $n \geq 3$. We will then use this result to show that the recognition of fully defined separable discrete functions is NP-complete for $n \geq 4$.   The case $n = 2$ is well-studied in the context of game theory, where (separable) discrete functions of $n$ variables are referred to as (assignable) $n$-person game forms. There is a known sufficient condition for assignability (separability) of two-person game forms (discrete functions of two variables) called (weak) total tightness of a game form. This property can be tested in polynomial time, and can be easily generalized both to higher dimension and to partially defined functions. We will prove in this paper that weak total tightness implies separability for (partially defined) discrete functions of $n$ variables for any $n$, thus generalizing the above result known for $n=2$.   Keywords: separable discrete functions, totally tight and assignable game forms
We study the geometry of a wormhole spacetime filled with anisotropic matter in the context of general relativity. In the course of the study, new static and spherically symmetric solutions, analytic and numerical ones, are found. We specify the existence condition for a wormhole throat. We analyze properties of the solutions after categorizing them based on the spacetime regularity and the signature of energy density. The necessary conditions which allow a wormhole spacetime to be nonsingular are described.
Fluctuations in the statistical model of heavy ion collisions are studied. The role of statistics, relativity, constraints, decaying resonances and branching processes are investigated using this model. Also studied are thermodynamic properties related to these fluctuations with specific concerns centered around the behavior of the specific heat.
We investigate the properties of non-rotating, electrically charged strange quark stars in four-dimensional Einstein-Maxwell theory. For quark matter we adopt the well-motivated quantum chromodynamics (QCD) equation-of-state, while for the charge density we assume it is proportional to the mass density. The system of coupled structure equations are integrated numerically, and we compute the mass, the radius as well as the total electric charge of the stars. Moreover, we perform a detailed numerical study of the effect of electric charge using the interacting quark equation-of-state. We find that stars as heavy as two solar masses can be supported, and that the highest radius and highest mass of the stars increase with the charge density.
In this paper, we derive $C^2$ estimates for a class of mixed Hessian type equations with Dirichlet boundary condition, and obtain the existence theorem of admissible solutions for the classical Dirichlet problem of these mixed Hessian type equations.
The Triple Deck model is a classical high order boundary layer model that has been proposed to describe flow regimes where the Prandtl theory is expected to fail. At first sight the model appears to lose two derivatives through the pressure-displacement relation which links pressure to the tangential slip. In order to overcome this, we split the Triple Deck system into two coupled equations: a Prandtl type system on $\mathbb{H}$ and a Benjamin-Ono type equation on $\mathbb{R}$. This splitting enables us to extract a crucial leading order cancellation at the top of the lower deck. We develop a functional framework to subsequently extend this cancellation into the interior of the lower deck, which enables us to prove the local well-posedness of the model in tangentially real analytic spaces.
The present Thesis covers the subject of the characterization of entangled states by recourse to entropic measures, as well as the description of entanglement related to several issues in quantum mechanics, such as the speed of a quantum evolution or the connections existing between quantum entanglement and quantum phase transitions.
We suggest here a mechanism for the seeding of the primordial density fluctuations. We point out that a process like reheating at the end of inflation will inevitably generate perturbations, even on superhorizon scales, by the local diffusion of energy. Provided that the reheating temperature is of order the GUT scale, the density contrast $\delta_R$ for spheres of radius $R$ will be of order $10^{-5}$ at horizon entry, consistent with the values measured by \texttt{WMAP}. If this were a purely classical process, $\delta_R^2$ would fall as $1/R^4$ beyond the horizon, and the resulting primordial density power spectrum would be $P(k) \propto k^n$ with $n=4$. However, as shown by Gabrielli et al, a quantum diffusion process can generate a power spectrum with any index in the range $0<n\leq 4$, including values close to the observed $n=1$ ($\delta_R^2$ will then be $\propto 1/R^{3+n}$ for $n<1$ and $1/R^4$ for $n>1$). Thus, the two characteristic parameters that determine the appearance of present day structures could be natural consequences of this mechanism. These are in any case the minimum density variations that must have formed if the universe was rapidly heated to GUT temperatures by the decay of a `false vacuum'. There is then no \emph{a priori} necessity to postulate additional (and fine tuned) quantum fluctuations in the `false vacuum', nor a pre-inflationary period. Given also the very stringent pre-conditions required to trigger a satisfactory period of inflation, altogether it seems at least as natural to assume that the universe began in a flat and homogeneously expanding phase.
We present a direct measurement of the mean halo occupation distribution (HOD) of galaxies taken from the eleventh data release (DR11) of the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey (BOSS). The HOD of BOSS low-redshift (LOWZ: $0.2 < z < 0.4$) and Constant-Mass (CMASS: $0.43 <z <0.7$) galaxies is inferred via their association with the dark-matter halos of 174 X-ray-selected galaxy clusters drawn from the XMM Cluster Survey (XCS). Halo masses are determined for each galaxy cluster based on X-ray temperature measurements, and range between ${\rm log_{10}} (M_{180}/M_{\odot}) = 13-15$. Our directly measured HODs are consistent with the HOD-model fits inferred via the galaxy-clustering analyses of Parejko et al. for the BOSS LOWZ sample and White et al. for the BOSS CMASS sample. Under the simplifying assumption that the other parameters that describe the HOD hold the values measured by these authors, we have determined a best-fit alpha-index of 0.91$\pm$0.08 and $1.27^{+0.03}_{-0.04}$ for the CMASS and LOWZ HOD, respectively. These alpha-index values are consistent with those measured by White et al. and Parejko et al. In summary, our study provides independent support for the HOD models assumed during the development of the BOSS mock-galaxy catalogues that have subsequently been used to derive BOSS cosmological constraints.
Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap' methodology. In this approach, operator expectation values are related by symmetries -- such as time translation and $SU(N)$ gauge invariance -- and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator. We then reproduce the known solution of large $N$ single matrix quantum mechanics. Finally, we present new results on the ground state of large $N$ two matrix quantum mechanics.
This paper presents the 2nd place solution to the Google Landmark Retrieval 2021 Competition on Kaggle. The solution is based on a baseline with training tricks from person re-identification, a continent-aware sampling strategy is presented to select training images according to their country tags and a Landmark-Country aware reranking is proposed for the retrieval task. With these contributions, we achieve 0.52995 mAP@100 on private leaderboard. Code available at https://github.com/WesleyZhang1991/Google_Landmark_Retrieval_2021_2nd_Place_Solution
Many machine learning models operate on images, but ignore the fact that images are 2D projections formed by 3D geometry interacting with light, in a process called rendering. Enabling ML models to understand image formation might be key for generalization. However, due to an essential rasterization step involving discrete assignment operations, rendering pipelines are non-differentiable and thus largely inaccessible to gradient-based ML techniques. In this paper, we present {\emph DIB-R}, a differentiable rendering framework which allows gradients to be analytically computed for all pixels in an image. Key to our approach is to view foreground rasterization as a weighted interpolation of local properties and background rasterization as a distance-based aggregation of global geometry. Our approach allows for accurate optimization over vertex positions, colors, normals, light directions and texture coordinates through a variety of lighting models. We showcase our approach in two ML applications: single-image 3D object prediction, and 3D textured object generation, both trained using exclusively using 2D supervision. Our project website is: https://nv-tlabs.github.io/DIB-R/
Abridged: The giant radio galaxy M 87 with its proximity, famous jet, and very massive black hole provides a unique opportunity to investigate the origin of very high energy (VHE; E>100 GeV) gamma-ray emission generated in relativistic outflows and the surroundings of super-massive black holes. M 87 has been established as a VHE gamma-ray emitter since 2006. The VHE gamma-ray emission displays strong variability on timescales as short as a day. In this paper, results from a joint VHE monitoring campaign on M 87 by the MAGIC and VERITAS instruments in 2010 are reported. During the campaign, a flare at VHE was detected triggering further observations at VHE (H.E.S.S.), X-rays (Chandra), and radio (43 GHz VLBA). The excellent sampling of the VHE gamma-ray light curve enables one to derive a precise temporal characterization of the flare: the single, isolated flare is well described by a two-sided exponential function with significantly different flux rise and decay times. While the overall variability pattern of the 2010 flare appears somewhat different from that of previous VHE flares in 2005 and 2008, they share very similar timescales (~day), peak fluxes (Phi(>0.35 TeV) ~= (1-3) x 10^-11 ph cm^-2 s^-1), and VHE spectra. 43 GHz VLBA radio observations of the inner jet regions indicate no enhanced flux in 2010 in contrast to observations in 2008, where an increase of the radio flux of the innermost core regions coincided with a VHE flare. On the other hand, Chandra X-ray observations taken ~3 days after the peak of the VHE gamma-ray emission reveal an enhanced flux from the core. The long-term (2001-2010) multi-wavelength light curve of M 87, spanning from radio to VHE and including data from HST, LT, VLA and EVN, is used to further investigate the origin of the VHE gamma-ray emission. No unique, common MWL signature of the three VHE flares has been identified.
Most of PNe are not spherical. The loss of spherical symmetry occurs somewhere between the AGB and PN phase. The cause of this change of morphology is not yet well known, but magnetic fields are one of the possible agents. Its origin remains to be determined, and potentially requires the presence of a massive companion to the AGB star. Therefore, further detections of the magnetic field around evolved stars (in particular those thought to be part of a binary system) are crucial to improve our understanding of the origin and role of magnetism on evolved stars. One such binaries is the pre-PN OH231.8, around which a magnetic field was detected in the OH maser region of the outer circumstellar envelope. We aim to detect and infer the properties of the magnetic field of this source in the water maser region.   We observed the 6_{1,6}-5_{2,3} water maser rotational transition to determine its linear and circular polarization. These emissions are located within the inner regions of OH231.8 (at few tens of AU). We detected 30 water maser features, which occur in two distinct regions that are moving apart with a velocity on the sky of 2.3 mas/year. Taking into account the inclination angle of the source, this corresponds to an average separation velocity of 21 km/s. Based on the velocity gradient of the maser emission, the masers appear to be dragged along the direction of the nebula jet. Linear polarization is present in 3 of the features, and circular polarization was detected in the 2 brightest ones. We found that the strength of the magnetic field is |B_{||}|~45 mG which, when assuming a toroidal magnetic field, implies B~2.5 G on the stellar surface. The morphology of the field is not yet determined, but the high scatter found on the directions of the linear polarization vectors could indicate that the masers occur near the tangent points of a toroidal field.
This paper is devoted to investigate the thermodynamic stability of a generic cosmological fluid known as Van der Waals fluid in the context of flat FRW universe. It is treated as a perfect fluid that obeys the equation of state $P=\frac{\gamma\rho}{1-\beta\rho}-\alpha\rho^{2}, 0\leq\gamma<1$, where $\rho$ stands for energy density and $P$ stands for pressure of the fluid. In this regard, we discuss the behavior of physical parameters to analyze the evolution of the universe. We investigate whether the cosmological scenario fulfills the third law of thermodynamics using specific heat formalism. Next we discuss the thermal equation of state and by means of adiabatic, specific heat and isothermal conditions from classical thermodynamics we examine the thermal stability.
Humans recognize the visual world at multiple levels: we effortlessly categorize scenes and detect objects inside, while also identifying the textures and surfaces of the objects along with their different compositional parts. In this paper, we study a new task called Unified Perceptual Parsing, which requires the machine vision systems to recognize as many visual concepts as possible from a given image. A multi-task framework called UPerNet and a training strategy are developed to learn from heterogeneous image annotations. We benchmark our framework on Unified Perceptual Parsing and show that it is able to effectively segment a wide range of concepts from images. The trained networks are further applied to discover visual knowledge in natural scenes. Models are available at \url{https://github.com/CSAILVision/unifiedparsing}.
We study the full stable pair theory --- with descendents --- of the Calabi-Yau 3-fold $X=K_S$, where $S$ is a surface with a smooth canonical divisor $C$.   By both $\mathbb C^*$-localisation and cosection localisation we reduce to stable pairs supported on thickenings of $C$ indexed by partitions. We show that only strict partitions contribute, and give a complete calculation for length-1 partitions. The result is a surprisingly simple closed product formula for these "vertical" thickenings.   This gives all contributions for the curve classes $[C]$ and $2[C]$ (and those which are not an integer multiple of the canonical class). Here the result verifies, via the descendent-MNOP correspondence, a conjecture of Maulik-Pandharipande, as well as various results about the Gromov-Witten theory of $S$ and spin Hurwitz numbers.
We report on the search for electromagnetic counterparts to the nine gravitational-wave events with a $>$60\% probability of containing a neutron star during the third (O3) LIGO-Virgo Collaboration (LVC) observing run with the All-Sky Automated Survey for SuperNovae (ASAS-SN). No optical counterparts associated with a gravitational wave event was found. However, thanks to its network of telescopes, the average area visible to at least one ASAS-SN site during the first 10 hours after the trigger contained $\sim$30\% of the integrated source location probability. Through a combination of normal operations and target-of-opportunity observations, ASAS-SN observations of the highest probability fields began within one hour of the trigger for four of the events. After 24 hours, ASAS-SN observed $>$60\% of total probability for three events and $>$40\% for all but one of the events. This is the largest area coverage to a depth of $g = 18.5$ mag from any survey with published coverage statistics for seven of the nine events. With its observing strategy, five sites around the world, and a large field of view, ASAS-SN will be one of the leading surveys to optically search for nearby neutron star mergers during LVC O4.
We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent diffeomorphisms, $L_p$-maximal regularity theory, and the implicit function theorem.
In this paper, we consider the convergence problem of Schr\"odinger equation. Firstly, we show the almost everywhere pointwise convergence of Schr\"odinger equation in Fourier-Lebesgue spaces $\hat{H}^{\frac{1}{p},\frac{p}{2}}(\mathbb{R})(4\leq p<\infty),$ $\hat{H}^{\frac{3 s_{1}}{p},\frac{2p}{3}}(\mathbb{R}^2)(s_{1}>\frac{1}{3},3\leq p<\infty),$ $\hat{H}^{\frac{2 s_{1}}{p},p}(\mathbb{R}^n)(s_{1}>\frac{n}{2(n+1)},2\leq p<\infty,n\geq3)$ with rough data. Secondly, we show that the maximal function estimate related to one Schr\"odinger equation can fail with data in $\hat{H}^{s,\frac{p}{2}}(\mathbb{R})(s<\frac{1}{p})$. Finally, we show the stochastic continuity of Schr\"odinger equation with random data in $\hat{L}^{r}(\mathbb{R}^n)(2\leq r<\infty)$ almost surely. The main ingredients are Lemmas 2.4, 2.5, 3.2-3.4.
In this paper we discuss the connection between the geometric and tetrad approaches in the quantum affine-metric gravity. The corresponding transition formulas are obtained at the one-loop level. As an example, the one-loop counterterms are calculated in the tetrad formalism in the theory with terms quadratic in the torsion field. This model possesses the extra local symmetries connected with transformation of the connection field. It is shown that the special gauge can be chosen so that the corresponding additional ghosts do not contribute to the one-loop divergent terms.
The goal of this work is give a precise numerical description of the K\"ahler cone of a compact K\"ahler manifold. Our main result states that the K\"ahler cone depends only on the intersection form of the cohomology ring, the Hodge structure and the homology classes of analytic cycles: if $X$ is a compact K\"ahler manifold, the K\"ahler cone $\cK$ of $X$ is one of the connected components of the set $\cP$ of real $(1,1)$ cohomology classes $\{\alpha\}$ which are numerically positive on analytic cycles, i.e. $\int_Y\alpha^p>0$ for every irreducible analytic set $Y$ in $X$, \hbox{$p=\dim Y$}. This result is new even in the case of projective manifolds, where it can be seen as a generalization of the well-known Nakai-Moishezon criterion, and it also extends previous results by Campana-Peternell and Eyssidieux. The principal technical step is to show that every nef class $\{\alpha\}$ which has positive highest self-intersection number $\int_X\alpha^n>0$ contains a K\"ahler current; this is done by using the Calabi-Yau theorem and a mass concentration technique for Monge-Amp\`ere equations. The main result admits a number of variants and corollaries, including a description of the cone of numerically effective $(1,1)$ classes and their dual cone. Another important consequence is the fact that for an arbitrary deformation $\cX\to S$ of compact K\"ahler manifolds, the K\"ahler cone of a very general fibre $X_t$ is ``independent'' of $t$, i.e.\ invariant by parallel transport under the $(1,1)$-component of the Gauss-Manin connection.
We find soft X-ray emission lines from the X-ray binary Swift J1858.6-0814 in data from XMM-Newton-RGS: N VII, O VII and O VIII, as well as notable residuals short of a detection at Ne IX and other higher ionisation transitions. These could be associated with the disc atmosphere, as in accretion disc corona sources, or with a wind, as has been detected in Swift J1858.6-0814 in emission lines at optical wavelengths. Indeed, the N VII line is redshifted, consistent with being the emitting component of a P-Cygni profile. We find that the emitting plasma has an ionisation parameter $\log(\xi)=1.35\pm0.2$ and a density $n>1.5\times10^{11}$ cm$^{-3}$. From this, we infer that the emitting plasma must be within $10^{13}$ cm of the ionising source, $\sim5\times10^{7}r_{\rm g}$ for a $1.4M_{\odot}$ neutron star, and from the line width that it is at least $10^4r_{\rm g}$ away ($2\times10^{9}(M/1.4M_{\odot})$ cm). We compare this with known classes of emission line regions in other X-ray binaries and active galactic nuclei.
We present cosmological simulations of galaxy clusters, with focus on the cluster outskirts. We show that large-scale cosmic accretion and mergers produce significant internal gas motions and inhomogeneous gas distribution ("clumpiness") in the intracluster medium (ICM) and introduce biases in measurements of the ICM profiles and the cluster mass. We also show that non-thermal pressure provided by the gas motions is one of the dominant sources of theoretical uncertainties in cosmic microwave background secondary anisotropies. We briefly discuss implications for cluster cosmology and future prospects for understanding the physics of cluster outskirts using computer simulations and multi-wavelength cluster surveys.
We investigate the measurement uncertainties of a triple of positive operator-valued measures (POVMs) based on statistical distance, and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms of triple-wise joint measurability. Particularly, uncertainty inequalities for three unbiased qubit measurements are presented with analytical lower bounds which relates to the necessary and sufficient condition of the triple-wise joint measurability of the given triple. We show that the measurement uncertainties for a triple measurement are essentially different from the ones obtained by pair wise measurement uncertainties by comparing the lower bounds of different measurement uncertainties.