ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider (discrete time) branching particles in a random environment which is i.i.d. in time and possibly spatially correlated. We prove a representation of the limit process by means of a Brownian snake in random environment.
We study the phase diagram of fully directed lattice animals with nearest-neighbour interactions on the square lattice. This model comprises several interesting ensembles (directed site and bond trees, bond animals, strongly embeddable animals) as special cases and its collapse transition is equivalent to a directed bond percolation threshold. Precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n=17. The crossover region in the vicinity of the collapse transition is analyzed in detail and the crossover exponent $\phi$ is determined directly from the singular part of the free energy. We show using scaling arguments and an exact relation due to Dhar that $\phi$ is equal to the Fisher exponent $\sigma$ governing the size distribution of large directed percolation clusters.
Deep Neural Network (DNN) trained by the gradient descent method is known to be vulnerable to maliciously perturbed adversarial input, aka. adversarial attack. As one of the countermeasures against adversarial attack, increasing the model capacity for DNN robustness enhancement was discussed and reported as an effective approach by many recent works. In this work, we show that shrinking the model size through proper weight pruning can even be helpful to improve the DNN robustness under adversarial attack. For obtaining a simultaneously robust and compact DNN model, we propose a multi-objective training method called Robust Sparse Regularization (RSR), through the fusion of various regularization techniques, including channel-wise noise injection, lasso weight penalty, and adversarial training. We conduct extensive experiments across popular ResNet-20, ResNet-18 and VGG-16 DNN architectures to demonstrate the effectiveness of RSR against popular white-box (i.e., PGD and FGSM) and black-box attacks. Thanks to RSR, 85% weight connections of ResNet-18 can be pruned while still achieving 0.68% and 8.72% improvement in clean- and perturbed-data accuracy respectively on CIFAR-10 dataset, in comparison to its PGD adversarial training baseline.
Inspired by recent measurements on Ba$_3$CuSb$_2$O$_9$, we explore the interplay of spin and orbital degrees of freedom in a triangular lattice for possible spin liquid-like behaviour. Our effective Hamiltonian describes the magnetic Cu layer by considering superexchange paths along the intermediate O's. A mean field study of ordered states reveals an orbitally ordered ground state that isolates the spin degrees of freedom into spin chains. This scenario naturally explains the linear specific heat as $T\to 0$ and, by including the effects of additional defect Cu's sitting off the triangular planes, we find remarkable agreement with the measured magnetic susceptibility.
We report on the interplay of localized and extended degrees of freedom in the metallic state of high-temperature superconductors in a multiband setting. Various ways in which the bare magnetic response may become incommensurate are measured against both phenomenological and theoretical requirements. In particular, the pseudogap temperature is typically much higher than the incommensurability temperature. When microscopic strong-coupling effects with real-time dynamics between copper and oxygen sites are included, they tend to restore commensurability. Quantum transport equations for low-dimensional multiband electronic systems are used to explain the linear doping dependence of the dc conductivity and the doping and temperature dependence of the Hall number in the underdoped LSCO compounds. Coulomb effects of dopands are inferred from the doping evolution of the Hartree-Fock model parameters.
We consider a time inhomogeneous Cox-Ingersoll-Ross diffusion with positive jumps. We exploit a branching property to prove existence of a unique strong solution under a restrictive condition on the jump measure. We give Laplace transforms for the transition probabilities, with an interpretation in terms of limits of mixtures over Gamma laws.
The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape-measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration from simulations. The principal disadvantage of model-fitting for large surveys is the computational time required, but here an algorithm is presented that enables large surveys to be analysed in feasible computation times. The method and algorithm is tested on simulated galaxies from the Shear TEsting Program (STEP).
We present the discovery of 11 new double degenerate systems containing extremely low-mass white dwarfs (ELM WDs). Our radial velocity observations confirm that all of the targets have orbital periods $\leq$ 1 day. We perform spectroscopic fits and provide a complete set of physical and binary parameters. We review and compare recent evolutionary calculations and estimate that the systematic uncertainty in our mass determinations due to differences in the evolutionary models is small ($\approx$ 0.01 M$_{\odot}$). Five of the new systems will merge due to gravitational wave radiation within a Hubble time, bringing the total number of merger systems found in the ELM Survey to 38. We examine the ensemble properties of the current sample of ELM WD binaries, including the period distribution as a function of effective temperature, and the implications for the future evolution of these systems. We also revisit the empirical boundaries of instability strip of ELM WDs and identify new pulsating ELM WD candidates. Finally, we consider the kinematic properties of our sample of ELM WDs and estimate that a significant fraction of the WDs from the ELM Survey are members of the Galactic halo.
Assign to each site of the integer lattice $\Zd$ a real score, sampled according to the same distribution $F$, independently of the choices made at all other sites. A lattice animal is a finite connected set of sites, with its weight being the sum of the scores at its sites. Let $N_n$ be the maximal weight of those lattice animals of size $n$ that contain the origin. Denote by $N$ the almost sure finite constant limit of $n^{-1} N_n$, which exists under a mild condition on the positive tail of $F$. We study certain geometrical aspects of the lattice animal with maximal weight among those contained in an $n$-box where $n$ is large, both in the supercritical phase where $N > 0$, and in the critical case where $N = 0$.
Spectroscopic factors in 10Be, 11Be and 12Be, extracted from (d,p), one neutron knockout, and (p,d) reactions are interpreted within the rotational model. Assuming that the ground state and first excited state of 11Be can be associated with the 1/2[220] and 1/2[101] Nilsson levels, the strong coupling limit gives simple expressions that relate the amplitudes of these wavefunctions (in the spherical basis) with the measured cross-sections and derived spectroscopic factors. We obtain good agreement with both the measured magnetic moment of the ground state in 11Be and the reaction data.
We propose a self-supervised learning framework that uses unlabeled monocular video sequences to generate large-scale supervision for training a Visual Odometry (VO) frontend, a network which computes pointwise data associations across images. Our self-improving method enables a VO frontend to learn over time, unlike other VO and SLAM systems which require time-consuming hand-tuning or expensive data collection to adapt to new environments. Our proposed frontend operates on monocular images and consists of a single multi-task convolutional neural network which outputs 2D keypoints locations, keypoint descriptors, and a novel point stability score. We use the output of VO to create a self-supervised dataset of point correspondences to retrain the frontend. When trained using VO at scale on 2.5 million monocular images from ScanNet, the stability classifier automatically discovers a ranking for keypoints that are not likely to help in VO, such as t-junctions across depth discontinuities, features on shadows and highlights, and dynamic objects like people. The resulting frontend outperforms both traditional methods (SIFT, ORB, AKAZE) and deep learning methods (SuperPoint and LF-Net) in a 3D-to-2D pose estimation task on ScanNet.
The paper comments on a paper by Dawber and Scott published in Appl. Phys. Lett, 76,1060 (2000) and addendum (ibid. p.3655), which addresses an important issue of the physics of ferroelectric thin films - the role of oxygen vacancies in polarization fatigue. It is shown that the content of this paper (starting equations, calculations, parameters used in calculations and the way the obtained results are compared to the experimental data available in the literature) enables questioning the results and conclusions reported in it.
Shape coexistence problems in N=14 isotones are studied with a microscopic method of antisymmetrized molecular dynamics. The present calculations reproduce features of deformation in 28Si, and predict possible shape coexistence of neutron density in neutron-rich nuclei(19B and 24Ne). We also systematically study the structures of the ground and excited states, and the molecular resonances of 28Si. Besides the shape coexistence in the low-energy region, the results indicate the high-lying levels with $\alpha$-cluster and 12C+16O molecular structures in 28Si, which are consistent with the observed spin-assigned resonances. The resonance states above the threshold energies are connected with the low-lying deformed states from a view point of molecular excitation by discussing inter-cluster wave functions.
Magnetization reversal mechanisms and depth-dependent magnetic profile have been investigated in Co/Pd thin films magnetron-sputtered under continuously varying pressure with opposite deposition orders. For samples grown under increasing pressure, magnetization reversal is dominated by domain nucleation, propagation and annihilation; an anisotropy gradient is effectively established, along with a pronounced depth-dependent magnetization profile. However, in films grown under decreasing pressure, disorders propagate vertically from the bottom high-pressure region into the top low-pressure region, impeding domain wall motion and forcing magnetization reversal via rotation; depth-dependent magnetization varies in an inverted order, but the spread is much suppressed.
At high energy, the photoproduction or electroproduction of Vector Mesons allow to prepare a beam of quark-antiquark pairs of a given flavor. At high momentum transfer, the study of the scattering of these pairs on a nucleon opens up an original window on the quark-gluon structure of hadronic matter, which may eventually shed light on its gluonic content, on correlations between quarks and on the van der Walls part of the interaction between hadrons.
A solution to the infinite coupling problem for N=2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E_6 and E_7 SCFTs are found as limits of Lagrangian field theories.
We construct a continuous family of exchangeable pairs by perturbing the random variable through diffusion processes on manifold in order to apply Stein method to certain geometric settings. We compare our perturbation by diffusion method with other approaches of building exchangeable pairs and show that our perturbation scheme cooperates with the infinitesimal version of Stein's method harmoniously. More precisely, our exchangeable pairs satisfy a key condition in the infinitesimal Stein's method in general. Based on the exchangeable pairs, we are able to extend the approximate normality of eigenfunctions of Laplacian on compact manifold to eigenfunctions of Witten Laplacian, which is of the form:$\Delta_w = \Delta - \nabla H$. We then apply our abstract theorem to recover a central limit result of linear statistics on sphere. Finally, we prove an an infinitesimal version of Stein's method for exponential distribution and combine it with our continuous family of exchangeable pairs to extend an approximate exponentiality result of $|Tr U|^2$, where $Tr U$ is the trace of the first power of a matrix $U$ sampled from the Haar measure of unitary group, to arbitrary power and its analog for general circular ensemble.
Recently, high-precision optical 2~min cadence light curves obtained with \emph{TESS} for targets located in the mission's defined first four sectors have been released. The majority of these high-cadence and high-precision measurements currently span $\sim28\,{\rm d}$, thereby allowing periodic variability occurring on timescales $\lesssim14\,{\rm d}$ to potentially be detected. Magnetic chemically peculiar (mCP) A-type stars are well known to exhibit rotationally modulated photometric variability that is produced by inhomogeneous chemical abundance distributions in their atmospheres. While mCP stars typically exhibit rotation periods that are significantly longer than those of non-mCP stars, both populations exhibit typical periods $\lesssim10\,{\rm d}$; therefore, the early \emph{TESS} releases are suitable for searching for rotational modulation of the light curves of both mCP and non-mCP stars. We present the results of our search for A-type stars that exhibit variability in their \emph{TESS} light curves that is consistent with rotational modulation based on the first two data releases obtained from sectors 1 to 4. Our search yielded $134$ high-probability candidate rotational variables -- $60$ of which have not been previously reported. Approximately half of these stars are identified in the literature as Ap (mCP) stars. Comparisons between the subsample of high-probability candidate rotationally variable Ap stars and the subsample of stars that are not identified as Ap reveal that the latter subsample exhibits statistically (i) shorter rotation periods and (ii) significantly lower photometric amplitudes.
Manifestly consistent Fock representations of non-central (but ``core-central'') extensions of the $Z^N$-graded algebras of functions and vector fields on the $N$-dimensional torus $T^N$ are constructed by a kind of renormalization procedure. These modules are of lowest-energy type, but the energy is not a linear function of the momentum. Modulo a technical assumption, reducibility conditions are proved for the extension of $vect(T^N)$, analogous to the discrete series of Virasoro representations.
We provide formulas for the degrees of the projections of the locus of square matrices with given rank from linear spaces spanned by a choice of matrix entries. The motivation for these computations stem from applications to `matrix rigidity'; we also view them as an excellent source of examples to test methods in intersection theory, particularly computations of Segre classes. Our results are generally expressed in terms of intersection numbers in Grassmannians, which can be computed explicitly in many cases. We observe that, surprisingly (to us), these degrees appear to match the numbers of Kekul\'e structures of certain `benzenoid hydrocarbons', and arise in many other contexts with no apparent direct connection to the enumerative geometry of rank conditions.
We report the discovery of water vapour toward the carbon star V Cygni. We have used Herschel's HIFI instrument, in dual beam switch mode, to observe the 1(11) - 0(00) para-water transition at 1113.3430 GHz in the upper sideband of the Band 4b receiver. The observed spectral line profile is nearly parabolic, but with a slight asymmetry associated with blueshifted absorption, and the integrated antenna temperature is 1.69 \pm 0.17 K km/s. This detection of thermal water vapour emission, carried out as part of a small survey of water in carbon-rich stars, is only the second such detection toward a carbon-rich AGB star, the first having been obtained by the Submillimeter Wave Astronomy Satellite toward IRC+10216. For an assumed ortho-to-para ratio of 3 for water, the observed line intensity implies a water outflow rate ~ (3 - 6) E-5 Earth masses per year and a water abundance relative to H2 of ~ (2-5) E-6. This value is a factor of at least 1E+4 larger than the expected photospheric abundance in a carbon-rich environment, and - as in IRC+10216 - raises the intriguing possibility that the observed water is produced by the vapourisation of orbiting comets or dwarf planets. However, observations of the single line observed to date do not permit us to place strong constraints upon the spatial distribution or origin of the observed water, but future observations of additional transitions will allow us to determine the inner radius of the H2O-emitting zone, and the H2O ortho-to-para ratio, and thereby to place important constraints upon the origin of the observed water emission.
We study the generic problem of the escape of a classical particle over a fluctuating barrier under the influence of non-Gaussian noise mimicking the effects of not-fully equilibrated bath. Our attention focuses on the effect of the stable noises on the mean escape time and on the phenomenon of resonant activation (RA). Possible physical interpretation of the occurrence of L\'evy noises in the system of interest is discussed and the connection between the Tsallis statistics and the Fractional Fokker Planck Equation is addressed.
We study the Coulomb branches of the rank-one 4d $\mathcal{N} = 2$ quantum field theories, including the KK theories obtained from the circle compactification of the 5d $\mathcal{N}= 1$ $E_n$ Seiberg theories. The focus is set on the relation between their Seiberg-Witten geometries and rational elliptic surfaces, with more attention being given to the modular surfaces, which we completely classify using the classification of subgroups of the modular group ${\rm PSL}(2,\mathbb{Z})$. We derive closed-form expressions for the modular functions for all congruence and some of the non-congruence subgroups associated with these geometries. Moreover, we show how the BPS quivers of these theories can be determined directly from the fundamental domains of the monodromy groups and study how changes of these domains can be interpreted as quiver mutations. This approach can also be generalized to theories whose Coulomb branches contain `undeformable' singularities, leading to known quivers of such theories.
The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov-Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrangian flow. An a priori estimate on the smallness of the superlevels of the flow in three dimensions is established in order to control the characteristics.
We study the spin-resolved transport properties of T-shaped double quantum dots coupled to ferromagnetic leads. Using the numerical renormalization group method, we calculate the linear conductance and the spin polarization of the current for various model parameters and at different temperatures. We show that an effective exchange field due to the presence of ferromagnets results in different conditions for Fano destructive interference in each spin channel. This spin dependence of the Fano effect leads to perfect spin polarization, the sign of which can be changed by tuning the dots' levels. Large spin polarization occurs due to Coulomb correlations in the dot, which is not directly coupled to the leads, while finite correlations in the directly-coupled dot can further enhance this effect. Moreover, we complement accurate numerical results with a simple qualitative explanation based on analytical expressions for the zero-temperature conductance. The proposed device provides a prospective example of an electrically-controlled, fully spin-polarized current source, which operates without an external magnetic field.
We establish a formula which decomposes the cohomologies of various sheaves on a simple normal crossings divisor (SNC) $D$ in terms of the simplicial cohomologies of the dual complex $\Delta(D)$ with coefficients in a presheaf of vector spaces. This presheaf consists precisely of the corresponding cohomology data on the components of $D$ and on their intersections. We use this formula to give a Hodge decomposition for SNC divisors and investigate the toric setting. We also conjecture the existence of such a formula for effective non-reduced divisors with SNC support, and show that this would imply the vanishing of the higher simplicial cohomologies of the dual complex associated to a resolution of an isolated rational singularity.
The magnetorotational instability(MRI) in the Kerr spacetime is studied on a 3+1 viewpoint. The Maxwell's equations are expressed in a circularly orbiting observer's frame that co-rotates with matter in Keplerian orbits. There exist large proper growth rates in MRI around a rapidly rotating black hole. The large "centrifugal force" and the rapid variations of magnetic fields are caused by the rotation of spacetime geometry. As the result, in the extreme Kerr case the maximum proper growth rate at $r=r_{ms}$ becomes about twelve times as large as that in Schwartzshield case.
Let $X$ be an $n$-dimensional random centered Gaussian vector with independent but not identically distributed coordinates and let $T$ be an orthogonal trasformation of $\mathbb R^n$. We show that the random vector $Y=T(X)$ satisfies $$\mathbb E\sum\limits_{j=1}^k j\mbox{-}\min_{i\leq n}{X_{i}}^2 \leq C\mathbb E\sum\limits_{j=1}^k j\mbox{-}\min_{i\leq n}{Y_{i}}^2$$ for all $k<n$, where "$j\mbox{-}\min$" denotes the $j$-th smallest component of corresponding vector and $C>0$ is a universal constant. This resolves (up to a multiplicative constant) an old question of S.Mallat and O.Zeitouni regarding optimality of the Karhunen-Loeve basis for the nonlinear signal approximation. As a by-product we obtain some relations for order statistics of random vectors (not only Gaussian) which are of independent interest.
We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kaehler fourfold studied by Beauville and Donagi, and the hyper-Kaehler fourfold constructed by Debarre and Voisin. We exhibit an analog of the notion of "triangle" for these varieties and prove that the 6-dimensional variety of "triangles" is a Lagrangian subvariety in the cube of the constructed hyper-Kaehler fourfold.
The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to $\a'^3$. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.