ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate combinatorial properties of a kind of insets we defined in an earlier paper, interpreting them now in terms of restricted ternary words. This allows us to give new combinatorial interpretations of a number of known integer sequences, namely the coefficients of Chebyshev polynomials of both kinds, Fibonacci numbers, Delannoy numbers, asymmetric Delannoy numbers, Sulanke numbers, coordinating sequences for some cubic lattices, crystal ball sequences for some cubic lattices, and others. We also obtain several new properties of said insets. In particular, we derive three generating functions when two of three variables are constant.   At the end, we state 40 combinatorial configurations counted by our words.
We give a preliminary report on one of the tests we have performed of a full non-axisymmetric general relativistic code. The test considered here concerns the numerical evolution of vacuum non-axisymmetric gravitational waves and their comparison at low amplitudes with theoretical waveforms obtained from linearised theory.
We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the different fields is used in order to reduce the classical equations. The system of non-linear partial differential equations obtained becomes a boundary value problem by supplementing a suitable set of boundary conditions. We obtain numerical evidences that the angular excitations of uncharged Q-balls, which exist in flat space-time, get continuously deformed by the Maxwell and the Einstein terms. The electromagnetic and gravitating properties of several solutions, including the spinning Q-balls, are emphasized.
We have developed improved spectral models of relativistic reflection in the lamppost and disc-corona geometries. The models calculate photon transfer in the Kerr metric and give the observed photon-energy spectra produced by either thermal Comptonization or an e-folded power law incident on a cold ionized disc. Radiative processes in the primary X-ray source and in the disc are described with the currently most precise available models. Our implementation of the lamppost geometry takes into account the presence of primary sources on both sides of the disc, which is important when the disc is truncated. We thoroughly discuss the differences between our models and the previous ones.
Convolutional Neural Networks (CNNs) are well established models capable of achieving state-of-the-art classification accuracy for various computer vision tasks. However, they are becoming increasingly larger, using millions of parameters, while they are restricted to handling images of fixed size. In this paper, a quantization-based approach, inspired from the well-known Bag-of-Features model, is proposed to overcome these limitations. The proposed approach, called Convolutional BoF (CBoF), uses RBF neurons to quantize the information extracted from the convolutional layers and it is able to natively classify images of various sizes as well as to significantly reduce the number of parameters in the network. In contrast to other global pooling operators and CNN compression techniques the proposed method utilizes a trainable pooling layer that it is end-to-end differentiable, allowing the network to be trained using regular back-propagation and to achieve greater distribution shift invariance than competitive methods. The ability of the proposed method to reduce the parameters of the network and increase the classification accuracy over other state-of-the-art techniques is demonstrated using three image datasets.
State-of-the-art frame interpolation methods generate intermediate frames by inferring object motions in the image from consecutive key-frames. In the absence of additional information, first-order approximations, i.e. optical flow, must be used, but this choice restricts the types of motions that can be modeled, leading to errors in highly dynamic scenarios. Event cameras are novel sensors that address this limitation by providing auxiliary visual information in the blind-time between frames. They asynchronously measure per-pixel brightness changes and do this with high temporal resolution and low latency. Event-based frame interpolation methods typically adopt a synthesis-based approach, where predicted frame residuals are directly applied to the key-frames. However, while these approaches can capture non-linear motions they suffer from ghosting and perform poorly in low-texture regions with few events. Thus, synthesis-based and flow-based approaches are complementary. In this work, we introduce Time Lens, a novel indicates equal contribution method that leverages the advantages of both. We extensively evaluate our method on three synthetic and two real benchmarks where we show an up to 5.21 dB improvement in terms of PSNR over state-of-the-art frame-based and event-based methods. Finally, we release a new large-scale dataset in highly dynamic scenarios, aimed at pushing the limits of existing methods.
We propose the entropic measurement-induced nonlocality (MIN) as the maximal increment of von Neumann entropy induced by the locally non-disturbing measurement, and study behaviors of it both in the independent and common structured reservoirs. We present schemes for preserving the MIN, and show that for certain initial states the MIN, including the quantum correlations, can even be enhanced by the common reservoir. Additionally, we also show that the different measures of MIN may give different qualitative characterizations of nonlocal properties, i.e., it is rather measure dependent than state dependent.
The light-front distribution amplitudes (LFDAs) and the decay constant of the $K $ pseudoscalar meson are extracted within the framework of the AdS/QCD correspondence. For the LFDAs calculation, we consider a momentum-dependent (dynamical) helicity wave function which contains the dynamical spin effects. We use the LFDAs to predict the transition form factors of the semileptonic $B\to K \ell^{+}\ell^{-}$ decay. With the help of these form factors, the differential branching ratio of the $B\to K\, \mu^+ \mu^-$ on $q^2$ is plotted. A comparison is made between our prediction in AdS/QCD and the results obtained from two models including the light-cons sum rules (LCSR) and lattice QCD as well as the experimental values.
Relaxation schemes for finding normal modes of nonlinear excitations are described, and applied to the vortex-spinwave scattering problem in classical two-dimensional easy-plane Heisenberg models. The schemes employ the square of an effective Hamiltonian to ensure positive eigenvalues, together with an evolution in time or a self-consistent Gauss-Seidel iteration producing diffusive relaxation. We find some of the lowest frequency spinwave modes in a circular system with a single vortex present. The method is used to describe the vortex-spinwave scattering (S-matrix and phase shifts) and other dynamical properties of vortices in ferromagnets and antiferromagnets, for systems larger than that solvable by diagonalization methods. The lowest frequency modes associated with translation of the vortex center are used to estimate the vortex mass.
Soft-phonon modes of an undistorted phase encode a material's preference for symmetry lowering. However, the evidence is sparse for the relationship between an unstable phonon wavevector's reciprocal and the number of formula units in the stable distorted phase. This "1/q*-criterion" holds great potential for the first-principles design of materials, especially in low-dimension. We validate the approach on the Q1D materials space containing 1199 ring-metal units and identify candidates that are stable in undistorted (1 unit), Peierls (2 units), charge density wave (3-5 units), or long wave (>5 units) phases. We highlight materials exhibiting gap-opening as well as an uncommon gap-closing Peierls transition, and discuss an example case stabilized as a charge density wave insulator. We present the data generated for this study through an interactive publicly accessible Big Data analytics platform (http://moldis.tifrh.res.in/data/rmq1d) facilitating limitless and seamless data-mining explorations.
We consider the torus compactifications with flux of a class of $6d$ $(1,0)$ SCFTs that can be engineered as the low-energy theories on M$5$-branes near an M$9$-plane on a $C^2/Z_2$ singularity. Specifically, we concentrate on the two SCFTs where the $Z_2$ orbifold action acts non-trivially on the $E_8$ global symmetry. We analyze this problem by compactifying to $5d$, where we can exploit the relation to $5d$ duality domain walls. By a suitable guess of the domain wall theories, the resulting $4d$ theories can be conjectured. These can then be tested by comparing their properties, notably anomalies and symmetries, against the $6d$ expectations. These constructions lead to various interesting $4d$ phenomena like dualities and symmetry enhancements.
Detecting image correspondences by feature matching forms the basis of numerous computer vision applications. Several detectors and descriptors have been presented in the past, addressing the efficient generation of features from interest points (keypoints) in an image. In this paper, we investigate eight binary descriptors (AKAZE, BoostDesc, BRIEF, BRISK, FREAK, LATCH, LUCID, and ORB) and eight interest point detector (AGAST, AKAZE, BRISK, FAST, HarrisLapalce, KAZE, ORB, and StarDetector). We have decoupled the detection and description phase to analyze the interest point detectors and then evaluate the performance of the pairwise combination of different detectors and descriptors. We conducted experiments on a standard dataset and analyzed the comparative performance of each method under different image transformations. We observed that: (1) the FAST, AGAST, ORB detectors were faster and detected more keypoints, (2) the AKAZE and KAZE detectors performed better under photometric changes while ORB was more robust against geometric changes, (3) in general, descriptors performed better when paired with the KAZE and AKAZE detectors, (4) the BRIEF, LUCID, ORB descriptors were relatively faster, and (5) none of the descriptors did particularly well under geometric transformations, only BRISK, FREAK, and AKAZE showed reasonable resiliency.
We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of the critical group of a graph. We show how to realize these critical groups explicitly as cokernels of reduced Laplacians, and prove that they are finite, with orders given by weighted enumerators of simplicial spanning trees. We describe how the critical groups of a complex represent flow along its faces, and sketch another potential interpretation as analogues of Chow groups.
Modified gravity theories with a screening mechanism have acquired much interest recently in the quest for a viable alternative to General Relativity on cosmological scales, given their intrinsic property of being able to pass Solar System scale tests and, at the same time, to possibly drive universe acceleration on much larger scales. Here, we explore the possibility that the same screening mechanism, or its breaking at a certain astrophysical scale, might be responsible of those gravitational effects which, in the context of general relativity, are generally attributed to Dark Matter. We consider a recently proposed extension of covariant Galileon models in the so-called "beyond Horndeski" scenario, where a breaking of the Vainshtein mechanism is possible and, thus, some peculiar observational signatures should be detectable and make it distinguishable from general relativity. We apply this model to a sample of clusters of galaxies observed under the \textit{CLASH} survey, using both new data from gravitational lensing events and archival data from X-ray intra-cluster hot gas observations. In particular, we use the latter to model the gas density, and then use it as the only ingredient in the matter clusters' budget to calculate the expected lensing convergence map. Results show that, in the context of this extended Galileon, the assumption of having only gas and no Dark Matter at all in the clusters is able to match observations. We also obtain narrow and very interesting bounds on the parameters which characterize this model. In particular, we find that, at least for one of them, the general relativity limit is excluded at $2\sigma$ confidence level, thus making this model clearly statistically different and competitive with respect to general relativity.
We study the dynamical Mahler measure of multivariate polynomials and present dynamical analogues of various results from the classical Mahler measure as well as examples of formulas allowing the computation of the dynamical Mahler measure in certain cases. We discuss multivariate analogues of dynamical Kronecker's Lemma and present some improvements on the result for two variables due to Carter, Lal\'in, Manes, Miller, and Mocz.
With the rapid development of self-supervised learning (e.g., contrastive learning), the importance of having large-scale images (even without annotations) for training a more generalizable AI model has been widely recognized in medical image analysis. However, collecting large-scale task-specific unannotated data at scale can be challenging for individual labs. Existing online resources, such as digital books, publications, and search engines, provide a new resource for obtaining large-scale images. However, published images in healthcare (e.g., radiology and pathology) consist of a considerable amount of compound figures with subplots. In order to extract and separate compound figures into usable individual images for downstream learning, we propose a simple compound figure separation (SimCFS) framework without using the traditionally required detection bounding box annotations, with a new loss function and a hard case simulation. Our technical contribution is four-fold: (1) we introduce a simulation-based training framework that minimizes the need for resource extensive bounding box annotations; (2) we propose a new side loss that is optimized for compound figure separation; (3) we propose an intra-class image augmentation method to simulate hard cases; and (4) to the best of our knowledge, this is the first study that evaluates the efficacy of leveraging self-supervised learning with compound image separation. From the results, the proposed SimCFS achieved state-of-the-art performance on the ImageCLEF 2016 Compound Figure Separation Database. The pretrained self-supervised learning model using large-scale mined figures improved the accuracy of downstream image classification tasks with a contrastive learning algorithm. The source code of SimCFS is made publicly available at https://github.com/hrlblab/ImageSeperation.
With the advance in computational resources, Bayesian inference is increasingly becoming the standard tool of practise in GW astronomy. However, algorithms such as Markov Chain Monte Carlo (MCMC) require a large number of iterations to guarantee convergence to the target density. Each chain demands a large number of evaluations of the likelihood function, and in the case of a Hessian MCMC, calculations of the Fisher information matrix for use as a proposal distribution. As each iteration requires the generation of at least one gravitational waveform, we very quickly reach a point of exclusion for current Bayesian algorithms, especially for low mass systems where the length of the waveforms is large and the waveform generation time is on the order of seconds. This suddenly demands a timescale of many weeks for a single MCMC. As each likelihood and Fisher information matrix calculation requires the evaluation of noise-weighted scalar products, we demonstrate that by using the linearity of integration, and the fact that more than 90% of the generation time is spent at frequencies less that one third of the maximum, we can construct composite integrals that speed up the MCMCs for comparable mass binaries by a factor of between 3.5 and 5.5, depending on the waveform length. This method is both source and detector type independent, and can be applied to any waveform that displays significant frequency evolution, such as stellar mass binaries with Advanced LIGO/Virgo, as well as supermassive black holes with eLISA
Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${\cal L}$ is given in terms of a function of the salar curvature $R$ as ${\cal L}=\sqrt{-\det g_{\mu\nu}}f(R)$. The local Hamiltonian is obtained by a canonical transformation which interchanges a pair of the generalized coordinate and its canonical momentum coming from the higher derivative of the metric.
Silicon metal-oxide-semiconductor (MOS) spin qubits have become a promising platform for quantum information processing, with recent demonstrations of high-fidelity single and two-qubit gates. To move beyond a few qubits, however, more scalable designs that reduce the fabrication complexity and electrode density are needed. Here, we introduce a two-metal-layer MOS quantum dot device in which tunnel barriers are naturally formed by gaps between electrodes and controlled by adjacent accumulation gates. The accumulation gates define the electron reservoirs and provide tunability of the tunnel rate of nearly 8.5 decades/V, determined by a combination of charge sensor electron counting measurements and by direct transport. The valley splitting in the few-electron regime is probed by magneto-spectroscopy up to a field of 6 T, providing an estimate for the ground-state gap of 290 $\mu$eV. We show preliminary characterization of a double quantum dot, demonstrating that this design can be extended to linear dot arrays that should be useful in applications like electron shuttling. These results motivate further innovations in MOS quantum dot design that can improve the scalability prospects for spin qubits.
Gravitational redshifts and other relativistic effects are beginning to be studied in the context of galaxy clustering. Distortions consistent with those expected in General Relativity have been measured in galaxy cluster redshift profiles by Wojtak et al. and others and in the the cross-correlation function of galaxy populations by Alam et al. On scales below ~20 Mpc/$h$ simulations have shown that gravitational redshift dominates over other effects. However, this signal is related to the shape and depth of gravitational potentials, and therefore the matter density in galaxies and galaxy clusters that is responsible for them. We investigate the effects of baryonic physics on the gravitational redshift profiles of massive (group and cluster-sized) halos. We compare the profiles of different components in halos taken from the MassiveBlack-II cosmological hydrodynamic simulation and a dark matter-only version of the same simulation. We find that inclusion of baryons, cooling, star formation and feedback significantly alters the relevant inner density profiles. These baryonic effects lead to overall increases in both gravitational redshifts and the transverse relativistic Doppler effects by up to ~50% for group size halos. We show how modified Navarro Frenk White halo profiles can be used to parametrize these differences, and provide relevant halo profile fits.
We investigate hadron formation in high energy electroproduction off complex nuclei in the framework of a BUU transport model. Our approach combines a quantum mechanical treatment of the photon's initial state interactions with a semi-classical coupled channel simulation of the (pre)hadronic final-state interactions (FSI). This allows us to study the hadron attenuation observed at HERMES and to get information on the space-time picture of hadron formation separately for $\pi^{\pm}$, $\pi^0$, $K^\pm$, $p$ and $\bar{p}$.
The globular cluster (GC) systems of low-mass late-type galaxies, such as NGC 2403, have been poorly studied to date. As a low mass galaxy (M$_{\ast}$ = 7 $\times$ 10$^{9}$ M$_{\odot}$), cosmological simulations predict NGC 2403 to contain few, if any, accreted GCs. It is also isolated, with a remarkably undisturbed HI disk. Based on candidates from the literature, Sloan Digital Sky Survey and Hyper Suprime-Cam imaging, we selected several GCs for follow-up spectroscopy using the Keck Cosmic Web Imager. From their radial velocities, and other properties, we identify 8 bona-fide GCs associated with either the inner halo or the disk of this bulgeless galaxy. A stellar population analysis suggests a wide range of GC ages from shortly after the Big Bang until the present day. We find all of the old GCs to be metal-poor with [Fe/H] $\le$ --1. The age--metallicity relation for the observed GCs suggests that they were formed over many Gyr from gas with a low effective yield, similar to that observed in the SMC. Outflows of enriched material may have contributed to the low yield. With a total system of $\sim$50 GCs expected, our study is the first step in fully mapping the star cluster history of NGC 2403 in both space and time.
For a plane curve, a point in the projective plane is said to be Galois when the point projection induces a Galois extension of function fields. We give a new characterization of a Fermat curve whose degree minus one is a power of $p$ in characteristic $p>2$, which is sometimes called Hermitian, by the number of Galois points lying on the curve.
We have applied the coupled-channel complex scaling method (ccCSM) to K^{bar}N-\pi Y system. One advantage of ccCSM is that resonant states as well as scattering states can be treated in the same framework. For the interactions in the system, we have constructed a meson-baryon potential-matrix by basing on the chiral SU(3) theory and respecting the K^{bar}N scattering length obtained in the Martin's analysis. For future purpose to apply it more complicated system such as K^{bar}NN, we adopt a local Gaussian form in the r-space. We have investigated both the non-relativistic (NR) and the semi-relativistic (SR) kinematics. In the SR case, two types of the potentials are obtained. To test the constructed potentials, we have calculated scattering amplitudes and searched resonances. One resonance pole, corresponding to \Lambda(1405), is found in isospin I=0 system around (1419, -20) MeV ((1425, -25) or (1419, -13) MeV) on complex-energy plane with the NR (SR) kinematics. Mean distance between meson and baryon in the resonant state is 1.3 - i0.3 fm (1.2 - i0.5 fm) for NR (SR), in which the states are treated as Gamow states. In addition, we have observed a signature of another pole in lower-energy region involving large decay width, although they are unstable against the change of scaling angle \theta. This may correspond to the lower pole of the double-pole of \Lambda(1405) discussed in literature to date.