ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, oppositeness in spherical buildings is used to define an EKR-problem for flags in projective and polar spaces. A novel application of the theory of buildings and Iwahori-Hecke algebras is developed to prove sharp upper bounds for EKR-sets of flags. In this framework, we can reprove and generalize previous upper bounds for EKR-problems in projective and polar spaces. The bounds are obtained by the application of the Delsarte-Hoffman coclique bound to the opposition graph. The computation of its eigenvalues is due to earlier work by Andries Brouwer and an explicit algorithm is worked out. For the classical geometries, the execution of this algorithm boils down to elementary combinatorics. Connections to building theory, Iwahori-Hecke algebras, classical groups and diagram geometries are briefly discussed. Several open problems are posed throughout and at the end.
Higgsino in supersymmetric standard models can play the role of dark matter particle. In conjunction with the naturalness criterion, the higgsino mass parameter is expected to be around the electroweak scale. In this work, we explore the potential of probing the nearly degenerate light higgsinos with machine learning at the LHC. By analyzing jet images and other jet substructure information, we use the Convolutional Neural Network(CNN) to enhance the signal significance. We find that our deep learning jet image method can improve the previous result based on the conventional cut-flow by about a factor of two at the High-Luminosity LHC.
It is now widely accepted that dense filaments of molecular gas are integral to the process of stellar birth. While numerical simulations have succeeded in reproducing filamentary structure in turbulent gas and analytic calculations have predicted the formation of dense gas filaments via radial collapse, the exact process(es) that generate/s such filaments which then form prestellar cores within them, is unclear. In this work we therefore study numerically the formation of a dense filament using a relatively simple set-up of a uniform-density cylinder in pressure equilibrium with its confining medium. In particular, we examine if its propensity to form a dense filament and further, to the formation of prestellar cores within this filament bears on the gravitational state of the initial volume of gas. We report a radial collapse leading to the formation of a dense filamentary cloud is likely when the initial volume of gas is at least critically stable (characterised by the approximate equality between the mass line-density for this volume and its maximum value). Though self-gravitating, this volume of gas, however, is not seen to be in free-fall. This post-collapse filament then fragments along its length due to the growth of a Jeans-like instability to form prestellar cores like \emph{beads on a string}. We suggest, dense filaments in typical star-forming clouds classified as gravitationally super-critical under the assumption of : (i) isothermality when in fact, they are not, and (ii) extended radial profiles as against one that is pressure-truncated, thereby causing significant over-estimation of their mass line-density, are unlikely to experience gravitational free-fall. The radial density and temperature profile derived for this post-collapse filament is consistent with that deduced for typical filamentary clouds mapped in recent surveys of nearby star-forming regions.
We present a 0.72 sq. deg. contiguous 1.1mm survey in the central area of the COSMOS field carried out to a 1sigma ~ 1.26 mJy/beam depth with the AzTEC camera mounted on the 10m Atacama Submillimeter Telescope Experiment (ASTE). We have uncovered 189 candidate sources at a signal-to-noise ratio S/N >= 3.5, out of which 129, with S/N >= 4, can be considered to have little chance of being spurious (< 2 per cent). We present the number counts derived with this survey, which show a significant excess of sources when compared to the number counts derived from the ~0.5 sq. deg. area sampled at similar depths in the Scuba HAlf Degree Extragalactic Survey (SHADES, Austermann et al. 2010). They are, however, consistent with those derived from fields that were considered too small to characterize the overall blank-field population. We identify differences to be more significant in the S > 5 mJy regime, and demonstrate that these excesses in number counts are related to the areas where galaxies at redshifts z < 1.1 are more densely clustered. The positions of optical-IR galaxies in the redshift interval 0.6 < z < 0.75 are the ones that show the strongest correlation with the positions of the 1.1mm bright population (S > 5 mJy), a result which does not depend exclusively on the presence of rich clusters within the survey sampled area. The most likely explanation for the observed excess in number counts at 1.1mm is galaxy-galaxy and galaxy-group lensing at moderate amplification levels, that increases in amplitude as one samples larger and larger flux densities. This effect should also be detectable in other high redshift populations.
In this paper we complete the determination of the index of factoriality of moduli spaces of semistable sheaves on an abelian or projective K3 surface $S$. If $v=2w$ is a Mukai vector, $w$ is primitive, $w^{2}=2$ and $H$ is a generic polarization, let $M_{v}(S,H)$ be the moduli space of $H-$semistable sheaves on $S$ with Mukai vector $v$. First, we describe in terms of $v$ the pure weight-two Hodge structure and the Beauville form on the second integral cohomology of the symplectic resolutions of $M_{v}(S,H)$ (when $S$ is K3) and of the fiber $K_{v}(S,H)$ of the Albanese map of $M_{v}(S,H)$ (when $S$ is abelian). Then, if $S$ is K3 we show that $M_{v}(S,H)$ is either locally factorial or $2-$factorial, and we give an example of both cases. If $S$ is abelian, we show that $M_{v}(S,H)$ and $K_{v}(S,H)$ are $2-$factorial.
The orthovanadates are useful as host matrices for immobilization of radioactive wastes. The thermodynamic stability of these materials is crucial for their applications in high pressure and temperatures environment. It is necessary to investigate the phonons in the entire Brillouin zone, beyond the zone-centre phonons accessible in previous Raman and infrared experiments. We have carried out extensive neutron inelastic scattering experiments to derive the phonon dispersion relation of YVO4 up to high energy transfer of 65 meV using a single crystal, which are perhaps reported for the first time in any orthovanadate compound. The measured phonon dispersion relation is in good agreement with our first principles density functional theory as well as shell model calculations. The calculated pressure dependence of phonon modes in the zircon and scheelite phases shows unstable modes and violation of the Born stability criteria at high pressure, which may be lead to instability in YVO4 at high pressures. We also calculate large anisotropy in the thermal expansion behavior which arises from difference in anisotropic elasticity and mode Gr\"uneisen parameters.
Using R\'enyi-$\alpha$ entropy to quantify bipartite entanglement, we prove monogamy of entanglement in multi-qubit systems for $\alpha \geq 2$. We also conjecture a polygamy inequality of multi-qubit entanglement with strong numerical evidence for $0.83-\epsilon \leq \alpha \leq 1.43+\epsilon$ with $0<\epsilon<0.01$.
Where, and how, does energy dissipation of electrical energy take place in a ballistic wire? Fully two decades after the advent of the transmissive phenomenology of electrical conductance, this deceptively simple query remains unanswered. We revisit the quantum kinetic basis of dissipation and show its power to give a definitive answer to our query. Dissipation leaves a clear, quantitative trace in the non-equilibrium current noise of a quantum point contact; this signature has already been observed in the laboratory. We then highlight the current state of accepted understandings in the light of well-known yet seemingly contradictory measurements. The physics of mesoscopic transport rests not in coherent carrier transmission through a perfect and dissipationless metallic channel, but explicitly in their dissipative inelastic scattering at the wire's interfaces and adjacent macroscopic leads.
We fix a maximal order $\mathcal O$ in $\F=\R,\C$ or $\mathbb{H}$, and an $\F$-hermitian form $Q$ of signature $(n,1)$ with coefficients in $\mathcal O$. Let $k\in\N$. By applying a lattice point theorem on the $\F$-hyperbolic space, we give an asymptotic formula with an error term, as $t\to+\infty$, for the number $N_t(Q,-k)$ of integral solutions $x\in\mathcal O^{n+1}$ of the equation $Q[x]=-k$ satisfying $|x_{n+1}|\leq t$.
We investigate how radiative feedback from the first stars affects the assembly of the first dwarf galaxies. We perform cosmological zoomed SPH simulations of a dwarf galaxy assembling inside a halo of virial mass 10^9 solar at z = 10. The simulations follow the non-equilibrium chemistry/cooling of primordial gas and the conversion of the gas into metal-free stars. To quantify the radiative feedback, we compare a simulation in which stars emit both molecular hydrogen dissociating and hydrogen/helium ionizing radiation with a simulation in which stars emit only dissociating radiation, and with a simulation in which stars remain dark. Photodissociation and -ionization exert a strong negative feedback on the assembly of the simulated galaxy. Gas condensation is strongly impeded, and star formation is strongly suppressed in comparison with the simulation in which stars remain dark. The feedback on the gas implies a suppression of the central dark matter densities in the minihalo progenitor by factors of up to a few, which is a significant deviation from the singular isothermal density profile characterizing the dark matter distribution in the absence of radiative feedback. The evolution of gas densities, star formation rates, and the distribution of dark matter becomes insensitive to the inclusion of dissociating radiation in the late stages of the minihalo assembly, and it becomes insensitive to the inclusion of ionizing radiation once the minihalo turns into an atomically cooling galaxy. The formation of an extended disk inside the dwarf galaxy is a robust outcome not affected by the inclusion of radiation. We estimate that dwarf galaxies such as simulated here will be among the faintest galaxies the upcoming James Webb Space Telescope will detect. Our conclusions are subject to our neglect of feedback from supernovae and chemical enrichment as well as to cosmic variance. [abridged]
We make a change of field variables in the J formulation of self-dual Yang--Mills theory. The field equations for the resulting algebra valued field are derivable from a simple cubic action. The cubic interaction vertex is different from that considered previously from the N=2 string, however, perturbation theory with this action shows that the only non-vanishing connected scattering amplitude is for three external particles just as for the string.
We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a bijection that allows us to determine some notable features of these permutations, such as the distribution of the statistics "number of ascents", "number of left-to-right maxima", "first element", and "position of the maximum element"
We forecast the scientific capabilities to improve our understanding of cosmic inflation of CORE, a proposed CMB space satellite submitted in response to the ESA fifth call for a medium-size mission opportunity. The CORE satellite will map the CMB anisotropies in temperature and polarization in 19 frequency channels spanning the range 60-600 GHz. CORE will have an aggregate noise sensitivity of $1.7 \mu$K$\cdot \,$arcmin and an angular resolution of 5' at 200 GHz. We explore the impact of telescope size and noise sensitivity on the inflation science return by making forecasts for several instrumental configurations. This study assumes that the lower and higher frequency channels suffice to remove foreground contaminations and complements other related studies of component separation and systematic effects, which will be reported in other papers of the series "Exploring Cosmic Origins with CORE." We forecast the capability to determine key inflationary parameters, to lower the detection limit for the tensor-to-scalar ratio down to the $10^{-3}$ level, to chart the landscape of single field slow-roll inflationary models, to constrain the epoch of reheating, thus connecting inflation to the standard radiation-matter dominated Big Bang era, to reconstruct the primordial power spectrum, to constrain the contribution from isocurvature perturbations to the $10^{-3}$ level, to improve constraints on the cosmic string tension to a level below the presumptive GUT scale, and to improve the current measurements of primordial non-Gaussianities down to the $f_{NL}^{\rm local} < 1$ level. For all the models explored, CORE alone will improve significantly on the present constraints on the physics of inflation. Its capabilities will be further enhanced by combining with complementary future cosmological observations.
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations, then the solution is approximated by the scaled Gaussian of the corresponding linear parabolic problem. The proof is based on the scaling variables and energy estimates.
The search for specific objects or motifs is essential to art history as both assist in decoding the meaning of artworks. Digitization has produced large art collections, but manual methods prove to be insufficient to analyze them. In the following, we introduce an algorithm that allows users to search for image regions containing specific motifs or objects and find similar regions in an extensive dataset, helping art historians to analyze large digitized art collections. Computer vision has presented efficient methods for visual instance retrieval across photographs. However, applied to art collections, they reveal severe deficiencies because of diverse motifs and massive domain shifts induced by differences in techniques, materials, and styles. In this paper, we present a multi-style feature fusion approach that successfully reduces the domain gap and improves retrieval results without labelled data or curated image collections. Our region-based voting with GPU-accelerated approximate nearest-neighbour search allows us to find and localize even small motifs within an extensive dataset in a few seconds. We obtain state-of-the-art results on the Brueghel dataset and demonstrate its generalization to inhomogeneous collections with a large number of distractors.
We extend the investigation of the gravitational collapse of a spherically symmetric Yang-Mills field in Einstein gravity and show that, within the black hole regime, a new kind of critical behavior arises which separates black holes formed via Type I collapse from black holes formed through Type II collapse. Further, we provide evidence that these new attracting critical solutions are in fact the previously discovered colored black holes with a single unstable mode.
We study the stability of thin-shell wormholes in Einstein-Maxwell-Gauss-Bonnet gravity. The equation of state of the thin shell wormhole is considered first to obey a generalized Chaplygin gas and then we generalize it to an arbitrary state function which covers all known cases studied so far. In particular we study the modified Chaplygin gas and give an assessment for a general parotropic fluid. Our study is in d-dimensions and with numerical analysis in d=5 we show the effect of the GB parameter in the stability of thin-shell wormholes against the radial perturbations.
We prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform boundedness assumption on the operator norm. We can relax the operator norm assumption to an estimate on sums associated to graphs of matrices, further extending the range of applications (for example, to Wigner matrices with exploding moments and so the sparse regime of the Erd\H{o}s-R\'{e}nyi model). The result still holds even if the matrices are multiplied entrywise by bounded random variables (for example, as in the case of matrices with a variance profile and percolation models).
We study the decay rate for the energy of solutions of a damped wave equation in a situation where the Geometric Control Condition is violated. We assume that the set of undamped trajectories is a flat torus of positive codimension and that the metric is locally flat around this set. We further assume that the damping function enjoys locally a prescribed homogeneity near the undamped set in traversal directions. We prove a sharp decay estimate at a polynomial rate that depends on the homogeneity of the damping function. Our method relies on a refined microlocal analysis linked to a second microlocalization procedure to cut the phase space into tiny regions respecting the uncertainty principle but way too small to enter a standard semi-classical analysis localization. Using a multiplier method, we obtain the energy estimates in each region and we then patch the microlocal estimates together.
We analyze a system of cross-diffusion equations that models the growth of an avascular-tumor spheroid. The model incorporates two nonlinear diffusion effects, degeneracy type and super diffusion. We prove the global existence of weak solutions and justify the convergence towards the free boundary problem of the Hele-Shaw type when the pressure gets stiff. We also investigate the convergence rate of the solutions in $L^1-$Lebesgue spaces.
This paper is devoted to probabilistic cellular automata (PCA) on $\mathbb{N}$, $\mathbb{Z}$ or $\mathbb{Z}/n\mathbb{Z}$, depending of two neighbors, with a general alphabet $E$ (finite or infinite, discrete or not). We study the following question: under which conditions does a PCA possess a Markov chain as invariant distribution? Previous results in the literature give some conditions on the transition matrix (for positive rate PCA) when the alphabet $E$ is finite. Here we obtain conditions on the transition kernel of PCA with a general alphabet $E$. In particular, we show that the existence of an invariant Markov chain is equivalent to the existence of a solution to a cubic integral equation.   One of the difficulties to pass from a finite alphabet to a general alphabet comes from some problems of measurability, and a large part of this work is devoted to clarify these issues.
We consider a cantilevered (clamped-free) beam in an axial potential flow. Certain flow velocities may bring about a bounded-response instability in the structure, termed {\em flutter}. As a preliminary analysis, we employ the theory of {\em large deflections} and utilize a piston-theoretic approximation of the flow for appropriate parameters, yielding a nonlinear (Berger/Woinowsky-Krieger) beam equation with a non-dissipative RHS. As we obtain this structural model via a simplification, we arrive at a nonstandard nonlinear boundary condition that necessitates careful well-posedness analysis. We account for rotational inertia effects in the beam and discuss technical issues that necessitate this feature.   We demonstrate nonlinear semigroup well-posedness of the model with the rotational inertia terms. For the case with no rotational inertia, we utilize a Galerkin approach to establish existence of weak, possibly non-unique, solutions. For the former, inertial model, we prove that the associated non-gradient dynamical system has a compact global attractor. Finally, we study stability regimes and {\em post-flutter} dynamics (non-stationary end behaviors) using numerical methods for models with, and without, the rotational inertia terms.
Currently, a plethora of saliency models based on deep neural networks have led great breakthroughs in many complex high-level vision tasks (e.g. scene description, object detection). The robustness of these models, however, has not yet been studied. In this paper, we propose a sparse feature-space adversarial attack method against deep saliency models for the first time. The proposed attack only requires a part of the model information, and is able to generate a sparser and more insidious adversarial perturbation, compared to traditional image-space attacks. These adversarial perturbations are so subtle that a human observer cannot notice their presences, but the model outputs will be revolutionized. This phenomenon raises security threats to deep saliency models in practical applications. We also explore some intriguing properties of the feature-space attack, e.g. 1) the hidden layers with bigger receptive fields generate sparser perturbations, 2) the deeper hidden layers achieve higher attack success rates, and 3) different loss functions and different attacked layers will result in diverse perturbations. Experiments indicate that the proposed method is able to successfully attack different model architectures across various image scenes.
Some atomic decays of elementary particles with pionium ($\pi^+\pi^-$-dimesoatom) in the final state are considered. Only for K-meson atomic decays are the corresponding branching ratios big enough to make their experimental study realistic. The $O(\alpha)$ order corrections to the lifetime of pionium are also calculated.
We study the Pauli--Schr\"odinger equation in a uniformly rotating frame of reference to describe a coupling of spins and mechanical rotations. The explicit form of the spin-orbit interaction (SOI) with the inertial effects due to the mechanical rotation is presented. We derive equations of motion for a wavepacket of electrons in two-dimensional planes subject to the SOI. The solution is a superposition of two cyclotron motions with different frequencies and a circular spin current is created by the mechanical rotation.
Nuclear energy released by splitting Uranium and Thorium isotopes into two, three, four, up to eight fragments with nearly equal size are studied. We found that the energy released come from equally splitting the $^{235,238}$U and $^{230,232}$Th nuclei into to three fragments is largest. The statistical multifragmentation model is employed to calculate the probability of different breakup channels for the excited nuclei. Weighing the the probability distributions of fragments multiplicity at different excitation energies for the $^{238}$U nucleus, we found that an excitation energy between 1.2 and 2 MeV/u is optimal for the $^{235}$U, $^{238}$U, $^{230}$Th and $^{232}$Th nuclei to release nuclear energy of about 0.7-0.75 MeV/u.
We argue that Josephson junction networks may be engineered to allow for the emergence of new and robust quantum coherent states. We provide a rather intuitive argument showing how the change in topology may affect the quantum properties of a bosonic particle hopping on a network. As a paradigmatic example, we analyze in detail the quantum and thermodynamic properties of non-interacting bosons hopping on a comb graph. We show how to explicitly compute the inhomogeneities in the distribution of bosons along the comb's fingers, evidencing the effects of the topology induced spatial Bose-Einstein condensation characteristic of the system. We propose an experiment enabling to detect the spatial Bose-Einstein condensation for Josephson networks built on comb graphs.