ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study a modified Landau-de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional domains, subject to uniaxial boundary conditions, in the asymptotic regime where the length scale of the defect cores is small compared to the length scale of the domain. We obtain uniform convergence of the minimizers and of their gradients, away from the singularities of the limiting uniaxial map. We also demonstrate the presence of maximally biaxial cores in minimizers on two-dimensional domains, when the temperature is sufficiently low.
The nearly edge-on galaxy NGC4945 is one of the closest galaxies where an AGN and starburst coexist, and is one of the brightest sources at 100 keV. Near and mid-infrared spectroscopy have shown very strong obscuration of its central region, rivaled only in strength by some of the most deeply obscured ULIRGs. We aim to determine the spatial distribution of ISM features in the central 426x426 pc^2 of NGC4945. We map the central region of NGC4945 in three Spitzer-IRS modules (SH, SL and LL). We produce maps of the flux distribution of the starburst tracers [Ne II], [Ne III], [S III] and [S IV] at 12.81, 15.56, 18.71 and 10.51 mum, respectively, and a map of the AGN narrow-line region tracer [Ne V] at 14.32 mum. We also mapped the S(1), S(2) and S(3) pure rotational lines of H2, which trace the distribution of warm molecular hydrogen. We obtained an extinction map (A_V) based on the apparent strength of the 9.7 mum silicate absorption feature. Our A_V map traces the contours of the starburst ring but the highest extinction (A_V(9.85 mum)~60) is found at the nucleus. Within the uncertainty of the astrometry all emission lines are found to peak on the nucleus, except for the warm molecular hydrogen emission which shows a maximum 60-100 pc NW of the nucleus. We favour a scenario in which the lower H2 0-0 S(1) and S(2) rotational lines originate mainly from an unobscured extra-nuclear component associated with the super-wind cone observed in the HST NICMOS map of the H2 1-0 S(1) vibrational line. For the [Ne V] emission we infer an attenuation of a factor 12-160 (A_V=55-112) based on a comparison of the ratio of our [Ne V] flux and the absorption-corrected 14-195 keV Swift-BAT flux to the average [Ne V]/BAT ratio for Seyfert 1 nuclei. The high attenuation indicates that [Ne V] and [O IV] cannot be used as extinction-free tracers of AGN power in galaxies with deeply buried nuclei.
We consider N single server infinite buffer queues with service rate beta. Customers arrive at rate N times alpha,choose L queues uniformly, and join the shortest one. The stability condition is alpha strictly less than beta. We study in equilibrium the sequence of the fraction of queues of length at least k, in the large N limit. We prove a functional central limit theorem on an infinite-dimensional Hilbert space with its weak topology, with limit a stationary Ornstein-Uhlenbeck process. We use ergodicity and justify the inversion of limits of long times and large sizes N by a compactness-uniqueness method. The main tool for proving tightness of the ill-known invariant laws and ergodicity of the limit is a global exponential stability result for the nonlinear dynamical system obtained in the functional law of large numbers limit.
A general discussion of the construction of free fields based on Weinberg anszatz is provided and various applications appearing in the litterature are considered.
With the unequalled INTEGRAL observatory, ESA has provided a unique tool to the astronomical community that has made Europe the world leader in the field of gamma-ray astronomy. INTEGRAL provides an unprecedented survey of the soft gamma-ray sky, revealing hundreds of sources of different kinds, new classes of objects, extraordinary views of antimatter annihilation in our Galaxy, and fingerprints of recent nucleosynthesis processes. While INTEGRAL provides the longly awaited global overview over the soft gamma-ray sky, there is a growing need to perform deeper, more focused investigations of gamma-ray sources, comparable to the step that has been taken in X-rays by going from the ROSAT survey satellite to the more focused XMM-Newton observatory. Technological advances in the past years in the domain of gamma-ray focusing using Laue diffraction techniques have paved the way towards a future European gamma-ray mission, that will outreach past missions by large factors in sensitivity and angular resolution. Such a future Gamma-Ray Imager will allow to study particle acceleration processes and explosion physics in unprecedented depth, providing essential clues on the intimate nature of the most violent and most energetic processes in the Universe.
Accurate pedestrian classification and localization have received considerable attention due to their wide applications such as security monitoring, autonomous driving, etc. Although pedestrian detectors have made great progress in recent years, the fixed Intersection over Union (IoU) based assignment-regression manner still limits their performance. Two main factors are responsible for this: 1) the IoU threshold faces a dilemma that a lower one will result in more false positives, while a higher one will filter out the matched positives; 2) the IoU-based GT-Proposal assignment suffers from the inconsistent supervision problem that spatially adjacent proposals with similar features are assigned to different ground-truth boxes, which means some very similar proposals may be forced to regress towards different targets, and thus confuses the bounding-box regression when predicting the location results. In this paper, we first put forward the question that \textbf{Regression Direction} would affect the performance for pedestrian detection. Consequently, we address the weakness of IoU by introducing one geometric sensitive search algorithm as a new assignment and regression metric. Different from the previous IoU-based \textbf{one-to-one} assignment manner of one proposal to one ground-truth box, the proposed method attempts to seek a reasonable matching between the sets of proposals and ground-truth boxes. Specifically, we boost the MR-FPPI under R$_{75}$ by 8.8\% on Citypersons dataset. Furthermore, by incorporating this method as a metric into the state-of-the-art pedestrian detectors, we show a consistent improvement.
We discuss processes in galactic cosmic ray (GCR) acceleration sites - supernova remnants, compact associations of young massive stars, and superbubbles. Mechanisms of efficient conversion of the mechanical power of the outflows driven by supernova shocks and fast stellar winds of young stars into magnetic fields and relativistic particles are discussed. The high efficiency of particle acceleration in the sources implies the importance of nonlinear feedback effects in a symbiotic relationship where the magnetic turbulence required to accelerate the CRs is created by the accelerated CRs themselves. Non-thermal emission produced by relativistic particles (both those confined in and those that escape from the cosmic accelerators) can be used to constrain the basic physical models of the GCR sources. High resolution X-ray synchrotron imaging, combined with GeV-TeV gamma ray spectra, is a powerful tool to probe the maximum energies of accelerated particles. Future MeV regime spectroscopy will provide unique information on the composition of accelerated particles.
How to describe a black hole embedded in an expanding universe is an important topic. Some models about this issue are suggested by assuming that the metric is a conformal transformation of the Schwarzschild metric or of the isotropic black hole metric. However, there exists naked singularities in the two metrics. Recently, it is argued that the singularity in the Sultana-Dyer space-time is covered by an apparent horizon surface. But we find that such an apparent horizon does not exist if the null energy condition holds.
We study the spectrum of the scalar Laplacian on the five-dimensional toric Sasaki-Einstein manifolds Y^{p,q}. The eigenvalue equation reduces to Heun's equation, which is a Fuchsian equation with four regular singularities. We show that the ground states, which are given by constant solutions of Heun's equation, are identified with BPS states corresponding to the chiral primary operators in the dual quiver gauge theories. The excited states correspond to non-trivial solutions of Heun's equation. It is shown that these reduce to polynomial solutions in the near BPS limit.
We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The nonlinear conductance is computed by explicitly evaluating the various partial density of states, the sensitivity and the characteristic potential. Interesting spatial structure of these quantities are revealed. We present detailed results concerning the crossover behavior of the second order nonlinear conductance when the conductor changes from geometrically symmetrical to asymmetrical. Other issues of interests such as the gauge invariance are also discussed.
The paper deals with a theoretical model for interacting dark energy. The interaction between the cold dark matter (dust) and the dark energy has been assumed to be non-gravitational in nature. Exact analytic cosmological solutions are obtained both for constant and variable equation of state for dark energy. It is found that, for very small value of the coupling parameter (in the interaction term), the model asymptotically extends up to $\Lambda$CDM, while the model can enter into the phantom domain asymptotically, if the coupling parameter is not so small. Both the solutions are then analyzed with 194 Supernovae Type Ia data. The best fit parameters are shown with 1$\sigma$ and 2$\sigma$ confidence intervals. Finally, we have discussed the cosmographic parameters for both the cases.
An analytical solution for the out-of-equilibrium quasi-stationary states of the paradigmatic Hamiltonian Mean Field (HMF) model can be obtained from a maximum entropy principle. The theory has been so far tested with reference to a specific class of initial condition, the so called (single-level) water-bag type. In this paper a step forward is taken by considering an arbitrary number of overlapping water bags. The theory is benchmarked to direct microcanonical simulations performed for the case of a two-levels water-bag. The comparison is shown to return an excellent agreement.
We study the multipartite correlations of the multi-atom dark states, which are characterized by the atomic squeezing beyond the pairwise entanglement. It is shown that, in the photon storage process with atomic ensemble via electromagnetically induced transparency (EIT) mechanism, the atomic squeezing and the pairwise entanglement can be created by adiabatically manipulating the Rabi frequency of the classical light field on the atomic ensemble. We also consider the sudden death for the atomic squeezing and the pairwise entanglement under various decoherence channels. An optimal time for generating the greatest atomic squeezing and pairwise entanglement is obtained by studying in details the competition between the adiabatic creation of quantum correlation in the atomic ensemble and the decoherence that we describe with three typical decoherence channels.
We present spectroscopic observations of 182 disk galaxies (96 in the cluster and 86 in the field environment) in the region of the Abell 901/902 multiple cluster system, which is located at a redshift of $z\sim 0.165$. The presence of substructures and non-Gaussian redshift distributions indicate that the cluster system is dynamically young and not in a virialized state. We find evidence for two important galaxy populations. \textit{Morphologically distorted galaxies} are probably subject to increased tidal interactions. They show pronounced rotation curve asymmetries at intermediate cluster-centric radii and low rest-frame peculiar velocities. \textit{Morphologically undistorted galaxies} show the strongest rotation curve asymmetries at high rest-frame velocities and low cluster-centric radii. Supposedly, this group is strongly affected by ram-pressure stripping due to interaction with the intra-cluster medium. Among the morphologically undistorted galaxies, dusty red galaxies have particularly strong rotation curve asymmetries, suggesting ram pressure is an important factor in these galaxies. Furthermore, dusty red galaxies on average have a bulge-to-total ratio higher by a factor of two than cluster blue cloud and field galaxies. The fraction of kinematically distorted galaxies is 75% higher in the cluster than in the field environment. This difference mainly stems from morphological undistorted galaxies, indicating a cluster-specific interaction process that only affects the gas kinematics but not the stellar morphology. Also the ratio between gas and stellar scale length is reduced for cluster galaxies compared to the field sample. Both findings could be best explained by ram-pressure effects.
Using unreliable or noisy components for reliable communication requires error correction. But which noise processes can support information transmission, and which are too destructive? For classical systems any channel whose output depends on its input has the capacity for communication, but the situation is substantially more complicated in the quantum setting. We find a generic test for incapacity based on any suitable forbidden transformation---a protocol for communication with a channel passing our test would also allow us to implement the associated forbidden transformation. Our approach includes both known quantum incapacity tests---positive partial transposition (PPT) and antidegradability (no cloning)---as special cases, putting them both on the same footing. We also find a physical principle explaining the nondistillability of PPT states: Any protocol for distilling entanglement from such a state would also give a protocol for implementing the forbidden time-reversal operation.
In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we characterize the value function of a finite horizon stochastic control problem with unbounded controls as the unique viscosity solution of the corresponding dynamic programming equation.
I present a systematic study of all possible four leptons final states from $\gamma\gamma$ collisions. It is given a detailed account of fermion masses effects which are sizable since several collinear and $t$ channel enancements occur. The effects of angular cuts on the final charged leptons are also discussed. To perform the computation I have used the recently developed ALPHA algorithm (and the resulting code) for the automatic computation of scattering amplitudes.
Entropy in nonequilibrium statistical mechanics is investigated theoretically so as to extend the well-established equilibrium framework to open nonequilibrium systems. We first derive a microscopic expression of nonequilibrium entropy for an assembly of identical bosons/fermions interacting via a two-body potential. This is performed by starting from the Dyson equation on the Keldysh contour and following closely the procedure of Ivanov, Knoll and Voskresensky [Nucl. Phys. A {\bf 672} (2000) 313]. The obtained expression is identical in form with an exact expression of equilibrium entropy and obeys an equation of motion which satisfies the $H$-theorem in a limiting case. Thus, entropy can be defined unambiguously in nonequilibrium systems so as to embrace equilibrium statistical mechanics. This expression, however, differs from the one obtained by Ivanov {\em et al}., and we show explicitly that their ``memory corrections'' are not necessary. Based on our expression of nonequilibrium entropy, we then propose the following principle of maximum entropy for nonequilibrium steady states: ``The state which is realized most probably among possible steady states without time evolution is the one that makes entropy maximum as a function of mechanical variables, such as the total particle number, energy, momentum, energy flux, etc.'' During the course of the study, we also develop a compact real-time perturbation expansion in terms of the matrix Keldysh Green's function.
This paper presents a basic enhancement to the DeSTIN deep learning architecture by replacing the explicitly calculated transition tables that are used to capture temporal features with a simpler, more scalable mechanism. This mechanism uses feedback of state information to cluster over a space comprised of both the spatial input and the current state. The resulting architecture achieves state-of-the-art results on the MNIST classification benchmark.
It is well known that, for bright gamma-ray pulsars with high statistics above a few GeV, the phase averaged spectral energy distribution (SED) is harder than a simple exponential cutoff above the break. We perform phase-resolved spectral analyses of bright gamma-ray pulsars and demonstrate that, even over narrow phase ranges, the SEDs of gamma-ray pulsars above the break energy are harder than a simple exponential cutoff. We argue within a radiation-reaction limited curvature framework that this is indicative of non-stationary emission or emission from multiple zones. Further, we address a common problem faced when fitting hard spectral tails with a power-law times a sub-exponential function. Namely, that the sub-exponent parameter does not describe any parameters of physical models of pulsar emission. We introduce a simple analytical fit function to solve this problem.
We study light ray transform of symmetric 2-tensor fields defined on a bounded time-space domain in $\mathbb{R}^{1+n}$ for $n\geq 3$. We prove a uniqueness result for such light ray transforms. More precisely, we characterize the kernel of the light ray transform vanishing near a fixed direction at each point in the time-space domain.
For each positive integer n this paper considers a one-parameter family of complex-valued measures on the symmetric group S_n, depending on a complex parameter z. For parameter values z=p^f a prime power, this measure describes splitting probabilities for monic degree n polynomials over the finite field with p^f elements, conditioned on being square-free. It studies these measure in the special case z=1, and shows they have an interesting internal structure having a representation theoretic interpretation. These measures may provide data relevant to the hypothetical "field with one element ${\mathbb F_1}$". It additionally studies the case z=-1, which also has a representation-theoretic interpretation
Single channel, single energy partial wave analyses (SE_PWA) are from the first principles non-unique in the inelastic region if only data from elastic channels are used, so we in details discuss mechanisms how the problem is eliminated in pion-nucleon scattering. The "continuum ambiguities" puzzle has been extensively discussed since early 1970es, and two major mechanisms for solving the problem have been suggested: either to ensure the continuity of Argand diagrams by imposing the T-matrix t-channel analyticity (Karlsruhe-Helsinki, VPI/GWU) or to restore the unitarity loss in the kinematical regime where the inelastic channels are successively opened by replacing the standard single channel PWA by the coupled channel formalism (CMB, Zagreb, Kent, Pittsburgh/ANL, Giessen). In both approaches the insufficiency of the single channel data is eliminated by introducing additional constraints using the data from other channels. The importance and physical meaning of the second approach is presented in details, and the significance of inelastic channels for the uniqueness of the partial wave analysis is discussed. The outline of the procedure for utilizing the coupled channel formalism to perform the search for the minimal number/full set of T-matrix poles in the complex energy plane, which connect the quark model predictions to experimental reality, is proposed. The appearance of new, additional resonances unneeded in the sole elastic channel is demonstrated.
For $N\geq 4$, we let $\Omega$ to be a smooth bounded domain of $\mathbb{R}^N$, $\Gamma$ a smooth closed submanifold of $\Omega$ of dimension $k$ with $1\leq k \leq N-2$ and $h$ a continuous function defined on $\Omega$. We denote by $\rho_\Gamma\left(\cdot\right):=\dist_g\left(\cdot, \Gamma\right)$ the distance function to $\Gamma$. For $\sigma\in (0,2)$, we study existence of positive solutions $u \in H^1_0\left(\Omega\right)$ to the nonlinear equation $$ -\Delta u+h u=\rho_\Gamma^{-\sigma} u^{2^*(\sigma)-1} \qquad \textrm{in } \Omega, $$ where $2^*(\sigma):=\frac{2(N-\sigma)}{N-2}$ is the critical Hardy-Sobolev exponent. In particular, we provide existence of solution under the influence of the local geometry of $\G$ and the potential $h$.
3D topological insulators are a new state of quantum matter which exhibits both a bulk band structure with an insulating energy gap as well as metallic spin-polarized Dirac fermion states when interfaced with a topologically trivial material. There have been various attempts to tune the Dirac point to a desired energetic position for exploring its unusual quantum properties. Here we show a direct experimental proof by angle-resolved photoemission of the realization of a vertical topological p-n junction made of a heterostructure of two different binary 3D TI materials $\mathrm{Bi_2Te_3}$ and $\mathrm{Sb_2Te_3}$ epitaxially grown on Si(111). We demonstrate that the chemical potential is tunable by about 200 meV when decreasing the upper $\mathrm{Sb_2Te_3}$ layer thickness from 25 to 6 quintuple layers without applying any external bias. These results make it realistic to observe the topological exciton condensate and pave the way of exploring other exotic quantum phenomena in the near future.
In 1997 Richard Pink has clarified the concept of Hodge structures over function fields in positive characteristic, which today are called Hodge-Pink structures. They form a neutral Tannakian category over the underlying function field. He has defined Hodge realization functors from the uniformizable abelian $t$-modules and $t$-motives of Greg Anderson to Hodge-Pink structures. This allows one to associate with each uniformizable $t$-motive a Hodge-Pink group, analogous to the Mumford-Tate group of a smooth projective variety over the complex numbers. It further enabled Pink to prove the analog of the Mumford-Tate Conjecture for Drinfeld modules. Moreover, based on unpublished work of Pink and the first author, the second author proved in her Diploma thesis that the Hodge-Pink group equals the motivic Galois group of the $t$-motive as defined by Papanikolas and Taelman. This yields a precise analog of the famous Hodge Conjecture, which is an outstanding open problem for varieties over the complex numbers.   In this report we explain Pink's results on Hodge structures and the proof of the function field analog of the Hodge conjecture. The theory of $t$-motives has a variant in the theory of dual $t$-motives. We clarify the relation between $t$-motives, dual $t$-motives and $t$-modules. We also construct cohomology realizations of abelian $t$-modules and (dual) $t$-motives and comparison isomorphisms between them generalizing Gekeler's de Rham isomorphism for Drinfeld modules.
We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to normal approximation for the combined weights of subgraphs in the Erd\H{o}s-R\'enyi random graph, extending the graph counting results of [1] to the setting of graph weighting. Our approach relies on a general stochastic analytic framework for functionals of independent random sequences.