ShantanuT01/DACTYL-Pretraining huggingface dataset:
A family $\mathcal{A}$ of sets is said to be intersecting if every two sets in $\mathcal{A}$ intersect. Two families $\mathcal{A}$ and $\mathcal{B}$ are said to be cross-intersecting if each set in $\mathcal{A}$ intersects each set in $\mathcal{B}$. For a positive integer $n$, let $[n] = \{1, \dots, n\}$ and $\mathcal{S}_n = \{A \subseteq [n] \colon 1 \in A\}$. In this note, we extend the Erd\H{o}s-Ko-Rado Theorem by showing that if $\mathcal{A}$ and $\mathcal{B}$ are non-empty cross-intersecting families of subsets of $[n]$, $\mathcal{A}$ is intersecting, and $a_0, a_1, \dots, a_n, b_0, b_1, \dots, b_n$ are non-negative real numbers such that $a_i + b_i \geq a_{n-i} + b_{n-i}$ and $a_{n-i} \geq b_i$ for each $i \leq n/2$, then \[\sum_{A \in \mathcal{A}} a_{|A|} + \sum_{B \in \mathcal{B}} b_{|B|} \leq \sum_{A \in \mathcal{S}_n} a_{|A|} + \sum_{B \in \mathcal{S}_n} b_{|B|}.\] For a graph $G$ and an integer $r$, let ${\mathcal{I}_G}^{(r)}$ denote the family of $r$-element independent sets of $G$. Inspired by a problem of Holroyd and Talbot, Feghali, Johnson and Thomas conjectured that if $r < n$ and $G$ is a depth-two claw with $n$ leaves, then $G$ has a vertex $v$ such that $\{A \in {\mathcal{I}_G}^{(r)} \colon v \in A\}$ is a largest intersecting subfamily of ${\mathcal{I}_G}^{(r)}$. They proved this for $r \leq \frac{n+1}{2}$. We use the result above to prove the full conjecture.
We study the precession of accretion disks in the context of gamma-ray burst inner engines. Our aim is to quantitatively estimate the characteristics of gravitational waves produced by the precession of the transient accretion disk in gamma-ray bursts. We evaluate the possible periods of disk precession caused by the Lense-Thirring effect using an accretion disk model that allows for neutrino cooling. Assuming jet ejection perpendicular to the disk plane and a typical intrinsic time-dependence for the burst, we find gamma-ray light curves that have a temporal microstructure similar to that observed in some reported events. The parameters obtained for the precession are then used to evaluate the production of gravitational waves. We find that the precession of accretion disks of outer radius smaller than $10^8$ cm and accretion rates above 1 solar mass per second could be detected by Advanced LIGO if they occur at distances of less than 100 Mpc. We conclude that the precession of a neutrino-cooled accretion disk in long gamma-ray bursts can be probed by gravitational wave astronomy. Precession of the disks in short gamma-ray events is undetectable with the current technology.
We construct Hecke operators acting on Maass waveforms of integer non-zero weight and transforming according to a non-trivial multiplier system on the modular group. Using these Hecke operators we obtain multiplicativity relations for the Fourier coefficients of such Maass waveforms. These relations generalize the usual weight zero relations. We also obtain an unexpected relation between coefficients with positive and negative indices with a constant of proportionality involving the Laplace eigenvalue. Numerical examples of multiplicativity relations are given at the end of the paper.
We obtain a strong renewal theorem with infinite mean beyond regular variation, when the underlying distribution belongs to the domain of geometric partial attraction a semistable law with index $\alpha\in (1/2,1]$. In the process we obtain local limit theorems for both finite and infinite mean, that is for the whole range $\alpha\in (0,2)$. We also derive the asymptotics of the renewal function for $\alpha\in (0,1]$.
Based on first-principles calculations and effective model analysis, we propose that the WC-type HfC, in the absence of spin-orbit coupling (SOC), can host a three-dimensional nodal chain semimetal state. Distinguished from the previous material IrF4 [T. Bzdusek et al., Nature 538, 75 (2016)], the nodal chain here is protected by mirror reflection symmetries of a simple space group, while in IrF4 the nonsymmorphic space group with a glide plane is a necessity. Moreover, in the presence of SOC, the nodal chain in WC type HfC evolves into Weyl points. In the Brillouin zone, a total of 30 pairs of Weyl points in three types are obtained through the first-principles calculations. Besides, the surface states and the pattern of the surface Fermi arcs connecting these Weyl points are studied, which may be measured by future experiments.
This paper presents a novel knowledge distillation based model compression framework consisting of a student ensemble. It enables distillation of simultaneously learnt ensemble knowledge onto each of the compressed student models. Each model learns unique representations from the data distribution due to its distinct architecture. This helps the ensemble generalize better by combining every model's knowledge. The distilled students and ensemble teacher are trained simultaneously without requiring any pretrained weights. Moreover, our proposed method can deliver multi-compressed students with single training, which is efficient and flexible for different scenarios. We provide comprehensive experiments using state-of-the-art classification models to validate our framework's effectiveness. Notably, using our framework a 97% compressed ResNet110 student model managed to produce a 10.64% relative accuracy gain over its individual baseline training on CIFAR100 dataset. Similarly a 95% compressed DenseNet-BC(k=12) model managed a 8.17% relative accuracy gain.
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L=200 rungs (400 spins 1/2) and down to very low temperatures.
Ion bombardment has been shown to be capable of enhancing the interlayer exchange coupling in a trilayer system that exhibits giant magnetoresistance. We demonstrate that this phenomenon can be derived from the phase coherence among scattered paths within the two rough interfaces when their topographies are correlated. In the case of mild corrugations, our method reproduces the predictions by the proximity force approximation which does not consider the interference. When the characteristic Fourier conjugate of the tomography becomes large and comparable to the Fermi momentum, interesting new features arise and can only be captured by our more general approach. Among our findings, the scenario of an enhanced interlayer exchange coupling due to the interface roughness is explained, along with how it depends on the sample parameters. An additional channel for the resonant transmission is identified due to extra scattering paths from the roughness.
Exploiting the peculiar properties of proximity-induced superconductivity on the surface of a topological insulator, we propose a device which allows the creation of a Majorana fermion inside the core of a pinned Abrikosov vortex. The relevant Bogolyubov-de Gennes equations are studied analytically. We demonstrate that in this system the zero-energy Majorana fermion state is separated by a large energy gap, of the order of the zero-temperature superconducting gap $\Delta$, from a band of single-particle non-topological excitations. In other words, the Majorana fermion remains robust against thermal fluctuations, as long as the temperature remains substantially lower than the critical superconducting temperature. Experimentally, the Majorana state may be detected by measuring the tunneling differential conductance at the center of the Abrikosov vortex. In such an experiment, the Majorana state manifests itself as a zero-bias anomaly separated by a gap, of the order of $\Delta$, from the contributions of the nontopological excitations.
We discuss the extent to which photometric measurements alone can be used to identify Type Ia supernovae (SNIa) and to determine redshift and other parameters of interest for cosmological studies. We fit the light curve data of the type expected from a survey such as the one planned with Large Synoptic Survey Telescope (LSST) and also to remove the contamination from the core-collapse supernovae to SNIa samples. We generate 1000 SNIa mock flux data for each of the LSST filters based on existing design parameters, then use a Markov Chain Monte-Carlo (MCMC) analysis to fit for the redshift, apparent magnitude, stretch factor and the phase of the SNIa. We find that the model fitting works adequately well when the true SNe redshift is below 0.5, while at $z < 0.2$ the accuracy of the photometric data is almost comparable with spectroscopic measurements of the same sample. We discuss the contamination of Type Ib/c (SNIb/c) and Type II supernova (SNII) on the SNIa data set. We find it is easy to distinguish the SNII through the large $\chi^2$ mismatch when fitting to photometric data with Ia light curves. This is not the case for SNIb/c. We implement a statistical method based on the Bayesian estimation in order to statistically reduce the contamination from SNIb/c for cosmological parameter measurements from the whole SNe sample. The proposed statistical method also evaluate the fraction of the SNIa in the total SNe data set, which provides a valuable guide to establish the degree of contamination.
Motivated by the descent equation in string theory, we give a new interpretation for the action of the symmetry charges on the BRST cohomology in terms of what we call {\em the Gerstenhaber bracket}. This bracket is compatible with the graded commutative product in cohomology, and hence gives rise to a new class of examples of what mathematicians call a {\em Gerstenhaber algebra}. The latter structure was first discussed in the context of Hochschild cohomology theory \cite{Gers1}. Off-shell in the (chiral) BRST complex, all the identities of a Gerstenhaber algebra hold up to homotopy. Applying our theory to the c=1 model, we give a precise conceptual description of the BRST-Gerstenhaber algebra of this model. We are led to a direct connection between the bracket structure here and the anti-bracket formalism in BV theory \cite{W2}. We then discuss the bracket in string backgrounds with both the left and the right movers. We suggest that the homotopy Lie algebra arising from our Gerstenhaber bracket is closely related to the HLA recently constructed by Witten-Zwiebach. Finally, we show that our constructions generalize to any topological conformal field theory.
In d=2+1 dimensions, there exist field theories which are non-relativistic and superconformal. These theories describe two species of anyons, whose spins differ by 1/2, interacting in a harmonic trap. We compute the dimensions of chiral primary operators. These operators receive large anomalous dimensions which are related to the unusual angular momentum properties of anyons. Surprisingly, we find that the dimensions of some chiral primary operators violate the unitarity bound and we trace this to the fact that the associated wavefunctions become non-normalisable. We also study BPS non-perturbative states in this theory: these are Jackiw-Pi vortices. We show that these emerge at exactly the point where perturbative operators hit the unitarity bound. To describe the low-energy dynamics of these vortices, we construct a novel type of supersymmetric gauged linear sigma model.
In this paper, we construct a class of spin-1/2 antiferromagnetic (AFM) two-chain ladder models consisting of blocks of n-spin tetrahedral clusters alternating with two-spin rungs. For n=4 and 6 and in extended parameter regimes, the exact ground state of the ladder is shown to be a product of the ground states of the rungs and the n-spin blocks, in both zero and finite magnetic fields. In the latter case, magnetization/site (m) versus magenetic field (h) plot exhibits well-defined magnetization plateaus.
In some problems of fluid mechanics, it is possible to be confronted with data that are not regular, that is why we are interested here in the search for the so-called very weak solutions for the stationary Stokes problem with Navier-type boundary conditions in a three-dimensional exterior domain. The problem describes the flow of a viscous and incompressible fluid past an obstacle where we assume that the fluid may slip on the boundary of the obstacle. Because the flow domain is unbounded, we set the problem in weighted Sobolev spaces in order to control the behavior at infinity of the solutions. Our purpose is to prove the existence and the uniqueness of a very weak solution in a Hilbertian framework.
The technique of determining the acoustic location of layers of sharp changes in the sound speed inside a star from the oscillatory signal in its frequencies is applied on a solar-type star, the CoRoT target, HD49933. We are able to determine the acoustic depth of the second helium ionisation zone of HD49933 to be 794 +55/-68 seconds. The acoustic depth of the base of the convective zone is found to be 1855 +173/-412 seconds where the large error bars reflect the ambiguity in the result, which is difficult to determine with present precision on the frequencies because of the intrinsically weak nature of the signal. The positions of both these layers are consistent with those in a representative stellar model of HD49933.
The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible measurements be used in order to demonstrate Bell inequality violation? Our main result is to construct a local hidden variable model for an incompatible set of qubit measurements. Specifically, we show that if Alice uses this set of measurements, then for any possible shared entangled state, and any possible dichotomic measurements performed by Bob, the resulting statistics are local. This represents significant progress towards proving that measurement incompatibility does not imply Bell nonlocality in general.
In this study we prove the existence-uniqueness of a coupled non-linear elliptic PDE system using Lax-Milgram theorem, Galerkin Method, Brouwer's fixed point theorem. Later we derive the finite element scheme for the numerical solution of the PDE system and also carry out the convergence analysis for the derived scheme. Further successfully apply the scheme to an application related to free convection phenomena.
Steady state properties of a driven tracer moving in a narrow two dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one dimensional SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean field theory and exact solution in the limit where no exchange is allowed, gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.
We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for bosonization at the level of quantum states. Thus, we use the TNO to provide an explicit algorithm for bosonizing fermionic projected entangled pair states (fPEPs). A key step in the algorithm is to account for a choice of spin-structure, encoded in a set of bonds of the bosonized fPEPS. This enables our tensor network approach to bosonization to be applied to systems on arbitrary triangulations of orientable 2D manifolds.
(abridged) We utilize existing imaging and spectroscopic data for the galaxy clusters MS2137-23 and Abell 383 to present improved measures of the distribution of dark and baryonic material in the clusters' central regions. Our method, based on the combination of gravitational lensing and dynamical data, is uniquely capable of separating the distribution of dark and baryonic components at scales below 100 kpc. We find a variety of strong lensing models fit the available data, including some with dark matter profiles as steep as expected from recent simulations. However, when combined with stellar velocity dispersion data for the brightest member, shallower inner slopes than predicted by numerical simulations are preferred. For Abell 383, the preferred shallow inner slopes are statistically a good fit only when the multiple image position uncertainties associated with our lens model are assumed to be 0\farcs5, to account for unknown substructure. No statistically satisfactory fit was obtained matching both the multiple image lensing data and the velocity dispersion profile of the brightest cluster galaxy in MS2137-23. This suggests that the mass model we are using, which comprises a pseudo-elliptical generalized NFW profile and a brightest cluster galaxy component may inadequately represent the inner cluster regions. This may plausibly arise due to halo triaxiality or by the gravitational interaction of baryons and dark matter in cluster cores. However, the progress made via this detailed study highlights the key role that complementary observations of lensed features and stellar dynamics offer in understanding the interaction between dark and baryonic matter on non-linear scales in the central regions of clusters.
The importance of microphysical inputs from laboratory nuclear experiments and theoretical nuclear structure calculations in the understanding of the core collapse dynamics, and the subsequent supernova explosion, is largely recognized in the recent literature. In this work, we analyze the impact of the masses of very neutron rich nuclei on the matter composition during collapse, and the corresponding electron capture rate. To this aim, we introduce an empirical modification of the popular Duflo-Zuker mass model to account for possible shell quenching far from stability, and study the effect of the quenching on the average electron capture rate. We show that the preeminence of the $N=50$ and $N=82$ closed shells in the collapse dynamics is considerably decreased if the shell gaps are reduced in the region of $^{78}$Ni and beyond. As a consequence, local modifications of the overall electron capture rate up to 30\% can be expected, with integrated values strongly dependent on the stiffness of magicity quenching and progenitor mass and potential important consequences on the entropy generation, the neutrino emissivity, and the mass of the core at bounce. Our work underlines the importance of new experimental measurements in this region of the nuclear chart, the most crucial information being the nuclear mass and the Gamow-Teller strength. Reliable microscopic calculations of the associated elementary rate, in a wide range of temperatures and electron densities, optimized on these new empirical information, will be additionally needed to get quantitative predictions of the collapse dynamics.
In this work we prove sharp $L^p$ versions of multipolar Hardy inequalities in the case of a bipolar potential and $p\geq 2$, which were first developed in the case $p=2$ by Cazacu (CCM 2016) and Cazacu&Zuazua (Studies in phase space analysis with applications to PDEs, 2013). Our results are sharp and minimizers do exist in the energy space. New features appear when $p>2$ compared to the linear case $p=2$ at the level of criticality of the p-Laplacian $-\Delta_p$ perturbed by a singular Hardy bipolar potential.
To explore the role of titanium- and calcium-dust depletion in gas in and around galaxies we systematically study Ti/Ca abundance ratios in intervening absorption-line systems at low and high redshift. We investigate high-resolution optical spectra obtained by the UVES instrument at the Very Large Telescope and spectroscopically analyze 34 absorption-line systems at z<=0.5 to measure column densities (or limits) for CaII and TiII. We complement our UVES data set with previously published absorption-line data on Ti/Ca for redshifts up to z~3.8. Our absorber sample contains 110 absorbers (DLAs, sub-DLAs & LLSs). We compare our Ti/Ca findings with results from the Milky Way and the Magellanic Clouds and discuss the properties of Ti/Ca absorbers in the general context of quasar absorption-line systems.Our analysis indicates that there are two distinct populations of absorbers with either high or low Ti/Ca ratios with a separation at [Ti/Ca}]~1. While the calcium dust depletion in most of the absorbers appears to be severe, the titanium depletions are mild in systems with high Ti/Ca ratios. The derived trend indicates that absorbers with high Ti/Ca ratios have dust-to-gas ratios that are substantially lower than in the Milky Way. We characterize the overall nature of the absorbers by correlating Ti/Ca with other observables (e.g., metallicity, velocity-component structure) and by modeling the ionization properties of singly-ionized Ca and Ti in different environments. We conclude that CaII and TiII bearing absorption-line systems trace predominantly neutral gas in the disks and inner halo regions of galaxies, where the abundance of Ca and Ti reflects the local metal and dust content of the gas. Our study suggests that the Ti/Ca ratio represents a useful measure for the gas-to-dust ratio and overall metallicity in intervening absorption-line systems.
The Modified Horizontal Bridgman (MHB) process produces Cadmium Zinc Telluride (CZT) crystals with high yield and excellent homogeneity. Various groups,including our own, previously reported on the test of 2x2x0.5 cm3 MHB CZT detectors grown by the company Orbotech and read out with 8x8 pixels. In this contribution, we describe the optimization of the photolithographic process used for contacting the CZT detector with pixel contacts. The optimized process gives a high yield of good pixels down to pixel diameters/pitches of 50 microns. Furthermore, we discuss the performance of 0.5 cm and 0.75 cm thick detectors contacted with 64 and 225 pixel read out with the RENA-3 ASICs from the company NOVA R&D.