ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper first proposes a method of formulating model interpretability in visual understanding tasks based on the idea of unfolding latent structures. It then presents a case study in object detection using popular two-stage region-based convolutional network (i.e., R-CNN) detection systems. We focus on weakly-supervised extractive rationale generation, that is learning to unfold latent discriminative part configurations of object instances automatically and simultaneously in detection without using any supervision for part configurations. We utilize a top-down hierarchical and compositional grammar model embedded in a directed acyclic AND-OR Graph (AOG) to explore and unfold the space of latent part configurations of regions of interest (RoIs). We propose an AOGParsing operator to substitute the RoIPooling operator widely used in R-CNN. In detection, a bounding box is interpreted by the best parse tree derived from the AOG on-the-fly, which is treated as the qualitatively extractive rationale generated for interpreting detection. We propose a folding-unfolding method to train the AOG and convolutional networks end-to-end. In experiments, we build on R-FCN and test our method on the PASCAL VOC 2007 and 2012 datasets. We show that the method can unfold promising latent structures without hurting the performance.
We prove the unconditional security of coherent-state-based differential phase shift quantum key distribution protocol (DPSQKD) with block-wise phase randomization. Our proof is based on the conversion of DPSQKD to an equivalent entanglement-distillation protocol where the estimated phase error rate determines the amount of the privacy amplification. The generated final key has a contribution from events where the sender emits two or more photons, indicating the robustness of DPSQKD against photon-number-splitting attacks.
We use the Fourth Data Release of the Sloan Digital Sky Survey to test the ubiquity of infall patterns around galaxy clusters and measure cluster mass profiles to large radii. We match X-ray cluster catalogs with SDSS, search for infall patterns, and compute mass profiles for a complete sample of X-ray selected clusters. Very clean infall patterns are apparent in most of the clusters, with the fraction decreasing with increasing redshift due to shallower sampling. All 72 clusters in a well-defined sample limited by redshift (ensuring good sampling) and X-ray flux (excluding superpositions) show infall patterns sufficient to apply the caustic technique. This sample is by far the largest sample of cluster mass profiles extending to large radii to date. Similar to CAIRNS, cluster infall patterns are better defined in observations than in simulations. Further work is needed to determine the source of this difference. We use the infall patterns to compute mass profiles for 72 clusters and compare them to model profiles. Cluster scaling relations using caustic masses agree well with those using X-ray or virial mass estimates, confirming the reliability of the caustic technique. We confirm the conclusion of CAIRNS that cluster infall regions are well fit by NFW and Hernquist profiles and poorly fit by singular isothermal spheres. This much larger sample enables new comparisons of cluster properties with those in simulations. The shapes (specifically, NFW concentrations) of the mass profiles agree well with the predictions of simulations. The mass inside the turnaround radius is on average 2.19$\pm$0.18 times that within the virial radius. This ratio agrees well with recent predictions from simulations of the final masses of dark matter haloes.
We prove that the factorization of Appell's generalized hypergeometric series satisfying the so-called quadric property into a product of two Gauss' hypergeometric functions has a geometric origin: we first construct a generalized Kummer variety as minimal nonsingular model for a product-quotient surface with only rational double points from a pair of superelliptic curves of genus $2r-1$ with $r \in \mathbb{N}$. We then show that this generalized Kummer variety is equipped with two fibrations with fibers of genus $2r-1$. When periods of a holomorphic two-form over carefully crafted transcendental two-cycles on the generalized Kummer variety are evaluated using either of the two fibrations, the answer must be independent of the fibration and the aforementioned family of special function identities is obtained. This family of identities can be seen as a multivariate generalization of Clausen's Formula. Interestingly, this paper's finding bridges Ernst Kummer's two independent lines of research, algebraic transformations for the Gauss' hypergeometric function and nodal surfaces of degree four in $\mathbb{P}^3$.
Recent studies have predicted that magnetic EuCd2As2 can host several different topological states depending on its magnetic order, including a single pair of Weyl points. Here we report on the bulk properties and band inversion induced by pressure in the non-magnetic analogs AECd2As2 (AE = Ca, Sr, Ba) as studied with density functional theory calculations. Under ambient pressure we find these compounds are narrow band gap semiconductors, in agreement with experiment. The size of the band gap is dictated by both the increasing ionicity across the AE series which tends to increase the band gap, as well as the larger nearest neighbor Cd-As distance from increasing atomic size which can decrease the band gap because the conduction band edge is an anti-bonding state derived mostly from Cd 5s orbitals. The combination of these two competing effects results in a non-monotonic change of the band gap size across the AE series with SrCd2As2 having the smallest band gap among the three compounds. The application of negative pressure reduces this band gap and causes the band inversion between the Cd 5s and As 4p orbitals along the ${\Gamma}$-A direction to induce a pair of Dirac points. The topological nature of the Dirac points is then confirmed by finding the closed Fermi arcs on the (10-10) surface.
The high-redshift 21 cm signal from the Epoch of Reionization (EoR) is a promising observational probe of the early universe. Current- and next-generation radio interferometers such as the Hydrogen Epoch of Reionization Array (HERA) and Square Kilometre Array (SKA) are projected to measure the 21 cm auto power spectrum from the EoR. Another observational signal of this era is the kinetic Sunyaev-Zel'dovich (kSZ) signal in the cosmic microwave background (CMB), which will be observed by the upcoming Simons Observatory (SO) and CMB-S4 experiments. The 21 cm signal and the contribution to the kSZ from the EoR are expected to be anti-correlated, the former coming from regions of neutral gas in the intergalactic medium and the latter coming from ionized regions. However, the naive cross-correlation between the kSZ and 21 cm maps suffers from a cancellation that occurs because ionized regions are equally likely to be moving toward or away from the observer and so there is no net correlation with the 21 cm signal. We present here an investigation of the 21 cm-kSZ-kSZ bispectrum, which should not suffer the same cancellation as the simple two-point cross-correlation. We show that there is a significant and non-vanishing signal that is sensitive to the reionization history, suggesting the statistic may be used to confirm or infer the ionization fraction as a function of redshift. In the absence of foreground contamination, we forecast that this signal is detectable at high statistical significance with HERA and SO. The bispectrum we study suffers from the fact that the kSZ signal is sensitive only to Fourier modes with long-wavelength line-of-sight components, which are generally lost in the 21 cm data sets owing to foreground contamination. We discuss possible strategies for alleviating this contamination, including an alternative four-point statistic that may help circumvent this issue.
Inspired by earlier results about proper and polychromatic coloring of hypergraphs, we investigate such colorings of directed hypergraphs, that is, hypergraphs in which the vertices of each hyperedge is partitioned into two parts, a tail and a head. We present a conjecture of D. P\'alv\"olgyi and the author, which states that directed hypergraphs with a certain restriction on their pairwise intersections can be colored with two colors. Besides other contributions, our main result is a proof of this conjecture for $3$-uniform directed hypergraphs. This result can be phrased equivalently such that if a $3$-uniform directed hypergraph avoids a certain directed hypergraph with two hyperedges, then it admits a proper $2$-coloring. Previously, only extremal problems regarding the maximum number of edges of directed hypergraphs that avoid a certain hyperedge were studied.
We measured the electronic properties and gas sensing response of nanowires containing segments of poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT/PSS) that were synthesized using anodic aluminum oxide (AAO) membranes. The nanowires have a "striped" structure of gold-PEDOT/PSS-gold and are typically 8 um long (1 um-6 um-1 um for each section, respectively) and 220 nm in diameter. Dielectrophoretic assembly was used to position single nanowires on pre-fabricated gold electrodes. A polymer conductivity of 11.5 +/- 0.7 S/cm and a contact resistance of 27.6 +/- 4 kOhm were inferred from resistance measurements of nanowires of varying length and diameter. When used as gas sensors, the wires showed a resistance change of 10.5%, 9%, and 4% at the saturation vapor pressure of acetone, methanol and ethanol, respectively. Sensor response and recovery were rapid (seconds) with excellent reproducibility in time and across devices. "Striped" template-grown nanowires are thus intriguing candidates for use in electronic nose vapor sensing systems.
We consider the subsonic moving point source problem for the scalar wave equation in $\pmb{R}^3$, proving a regularity result for the direct problem, and uniqueness and stability results for the inverse problem. We then present and investigate numerically a Bayesian framework for the inference of the source trajectory and intensity from wave field measurements. The framework employs Gaussian process priors, the pre-conditioned Crank-Nicholson scheme with Markov Chain Monte Carlo sampling, and conditioning on functionals to include prior information on the source trajectory.
Feature preserving image interpolation is an active area in image processing field. In this paper a new direct edge directed image super-resolution algorithm based on structure tensors is proposed. Using an isotropic Gaussian filter, the structure tensor at each pixel of the input image is computed and the pixels are classified to three distinct classes; uniform region, corners and edges, according to the eigenvalues of the structure tensor. Due to application of the isotropic Gaussian filter, the classification is robust to noise presented in image. Based on the tangent eigenvector of the structure tensor, the edge direction is determined and used for interpolation along the edges. In comparison to some previous edge directed image interpolation methods, the proposed method achieves higher quality in both subjective and objective aspects. Also the proposed method outperforms previous methods in case of noisy and JPEG compressed images. Furthermore, without the need for optimization in the process, the algorithm can achieve higher speed.
We establish a conjecture of Graham and Lov\'asz that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal; we also prove they are log-concave.
In the present work the so-called Higher Tamm-Dancoff Apporximation method is presented for the generalized case of isovector and isoscalar residual interactions treated simultaneously. The role of different particle-hole excitations and of proton-neutron pairing correlations in the ground state of the self-conjugate 64Ge nucleus is discussed.
We derive necessary and sufficient conditions for there to exist a latin square of order $n$ containing two subsquares of order $a$ and $b$ that intersect in a subsquare of order $c$. We also solve the case of two disjoint subsquares. We use these results to show that: (a) A latin square of order $n$ cannot have more than $\frac nm{n \choose h}/{m\choose h}$ subsquares of order $m$, where $h=\lceil(m+1)/2\rceil$. Indeed, the number of subsquares of order $m$ is bounded by a polynomial of degree at most $\sqrt{2m}+2$ in $n$. (b) For all $n\ge5$ there exists a loop of order $n$ in which every element can be obtained as a product of all $n$ elements in some order and with some bracketing.
The role of the dense matter properties on the tidal deformability and gravitational waveforms of binary neutron stars is studied using a set of unified equations of state. Based on the nuclear energy-density functional theory, these equations of state provide a thermodynamically consistent treatment of all regions of the stars and were calculated using functionals that were precision fitted to experimental and theoretical nuclear data.
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
We present new formulae for the mass functions of the clusters and the isolated clusters with non Gaussian initial conditions. For this study, we adopt the Extended Zel'dovich (EZL) model as a basic framework, focusing on the case of primordial non-Gaussianity of the local type whose degree is quantified by a single parameter $f_{nl}$. By making a quantitative comparison with the N-body results, we first demonstrate that the EZL formula with the constant values of three fitting parameters still works remarkably well for the local $f_{nl}$ case. We also modify the EZL formula to find an analytic expression for the mass function of isolated clusters which turns out to have only one fitting parameter other than the overall normalization factor and showed that the modified EZL formula with a constant value of the fitting parameter matches excellently the N-body results with various values of $f_{nl}$ at various redshifts. Given the simplicity of the generalized EZL formulae and their good agreements with the numerical results, we finally conclude that the EZL mass functions of the massive clusters and isolated clusters should be useful as an analytic guideline to constrain the scale dependence of the primordial non-Gaussianity of the local type.
Observations of neutral hydrogen can provide a wealth of information about the distribution and kinematics of galaxies. To detect HI beyond the ionisation edge of galaxy disks, column density sensitivities have to be achieved that probe the regime of Lyman limit systems. Typically HI observations are limited to a brightness sensitivity of NHI~10^19 cm-2 but this has to be improved by at least an order of magnitude. In this paper, reprocessed data is presented that was originally observed for the HI Parkes All Sky Survey (HIPASS). HIPASS provides complete coverage of the region that has been observed for the Westerbork Virgo Filament HI Survey (WVFS), presented in accompanying papers, and thus is an excellent product for data comparison. The region of interest extends from 8 to 17 hours in right ascension and from -1 to 10 degrees in declination. Although the original HIPASS product already has good flux sensitivity, the sensitivity and noise characteristics can be significantly improved with a different processing method. The newly processed data has an 1sigma RMS flux sensitivity of ~10 mJy beam-1 over 26 km s-1, corresponding to a column density sensitivity of ~3\cdot10^17 cm-2. While the RMS sensitivity is improved by only a modest 20%, the more substantial benefit is in the reduction of spectral artefacts near bright sources by more than an order of magnitude. In the reprocessed region we confirm all previously catalogued HIPASS sources and have identified 29 additional sources of which 14 are completely new HI detections. Extended emission or companions were sought in the nearby environment of each discrete detection. With the improved sensitivity after reprocessing and its large sky coverage, the HIPASS data is a valuable resource for detection of faint HI emission.(Abridged)
Based on an equation for the rank of an elliptic surface over $\mathbb{Q}$ which appears in the work of Nagao, Rosen, and Silverman, we conjecture that 100% of elliptic surfaces have rank $0$ when ordered by the size of the coefficients of their Weierstrass equations, and present a probabilistic heuristic to justify this conjecture. We then discuss how it would follow from either understanding of certain $L$-functions, or from understanding of the local behaviour of the surfaces. Finally, we make a conjecture about ranks of elliptic surfaces over finite fields, and highlight some experimental evidence supporting it.
We consider d=10 N=1 supersymmetry algebra with maximal number of tensor charges Z and introduce a class of orbits of Z, invariant w.r.t. the $T_8$ subgroup of massless particles' little group $T_8\ltimes SO(8)$. For that class of orbits we classify all possible orbits and little groups, which appear to be semidirect products of $T_8\ltimes SO(k_1)\times ... SO(k_n)$ form, with $k_1+...+k_n=8$, where compact factor is embedded into SO(8) by triality map. We define actions of little groups on supercharge Q and construct corresponding supermultiplets. In some particular cases we show the existence of supermultiplets with both Fermi and Bose sectors consisting of the same representations of tensorial Poincare. In addition, complete classification of supermultiplets (not restricted to $T_8$-invariant orbits) with rank-2 matrix of supersymmetry charges anticommutator, is given.
Gamma-ray observations give us a direct view into the most extreme environments of the universe. They help us to study astronomical particle accelerators as supernovae remnants, pulsars, active galaxies or gamma-ray bursts and help us to understand the propagation of cosmic rays through our Milky Way. This article summarizes the status of gamma-ray observations from space; it is the write-up of a rapporteur talk given at the 34th ICRC in The Hague, The Netherlands. The primary instrument used in the presented studies is the Large Area Telescope on-board the Fermi Spacecraft, which images the whole gamma-ray sky at photon energies between 20 MeV and 2 TeV. The Fermi mission is currently in its 8th year of observations. This article will review many of the exciting discoveries made in this time, focusing on the most recent ones.
Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations combines Stein's method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. In the last decade, Malliavin-Stein techniques have allowed researchers to establish new quantitative limit theorems in a variety of domains of theoretical and applied stochastic analysis. The aim of this survey is to illustrate some of the latest developments of the Malliavin-Stein method, with specific emphasis on extensions and generalisations in the framework of Markov semigroups and of random point measures.
We establish sufficient conditions for the appearance of apparent horizons in spherically symmetric initial data when spacetime is foliated extrinsically. Let $M$ and $P$ be respectively the total material energy and the total material current contained in some ball of radius $\ell$. Suppose that the dominant energy condition is satisfied. We show that if $M- P \ge \ell$ then the region must possess a future apparent horizon for some non -trivial closed subset of such gauges. The same inequality holds on a larger subset of gauges but with a larger constant of proportionality which depends weakly on the gauge. This work extends substantially both our joint work on moment of time symmetry initial data as well as the work of Bizon, Malec and \'O Murchadha on a maximal slice.
Thickness is one of the fundamental parameters that define the electronic, optical, and thermal properties of two-dimensional (2D) crystals. Phonons in molybdenum disulfide (MoS2) were recently found to exhibit unique thickness dependence due to interplay between short and long range interactions. Here we report Raman spectra of atomically thin sheets of WS2 and WSe2 in the mono- to few-layer thickness regime. We show that, similar to the case of MoS2, the characteristic and modes exhibit stiffening and softening with increasing number of layers, respectively, with a small shift of less than 3 cm-1 due to large mass of the atoms. Thickness dependence is also observed in a series of multiphonon bands arising from overtone, combination, and zone edge phonons, whose intensity exhibit significant enhancement in excitonic resonance conditions. Some of these multiphonon peaks are found to be absent only in monolayers. These features provide a unique fingerprint and rapid identification for monolayer flakes.
Abelian covers of $\mathbb{CP}^{1}$, with fixed Galois group $A$, are classified, as a first step, by a discrete set of parameters. Any such cover $X$, of genus $g\geq1$ say, carries a finite set of $A$-invariant divisors of degree $g-1$ on $X$ that produce non-zero theta constants on $X$. We show how to define a quotient involving a power of the theta constant on $X$ that is associated with such a divisor $\Delta$, some polynomial in the branching values, and a fixed determinant on $X$ that does not depend on $\Delta$, such that the quotient is constant on the moduli space of $A$-covers with the given discrete parameters. This generalizes the classical formula of Thomae, as well as all of its known extensions by various authors.
In this paper, we examine the application of an ideal phonon-hydrodynamic material as the heat transfer medium between two non-hydrodynamic contacts with a finite temperature difference. We use the integral-equation approach to solve a modified phonon Boltzmann transport equation with the displaced Bose-Einstein distribution as the equilibrium distribution between two boundaries perpendicular to the heat transfer direction. When the distance between the boundaries is smaller than the phonon normal scattering mean free path, our solution converges to the ballistic limit as expected. In the other limit, we find that, although the local thermal conductivity in the bulk of the hydrodynamic material approaches infinity, the thermal boundary resistance at the hydrodynamic/non-hydrodynamic interfaces becomes dominant. Our study provides insights to both the steady-state thermal characterization of phonon-hydrodynamic materials and the practical application of phonon-hydrodynamic materials for thermal management.