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Modern robotic systems sense the environment geometrically, through sensors like cameras, lidar, and sonar, as well as semantically, often through visual models learned from data, such as object detectors. We aim to develop robots that can use all of these sources of information for reliable navigation, but each is corrupted by noise. Rather than assume that object detection will eventually achieve near perfect performance across the lifetime of a robot, in this work we represent and cope with the semantic and geometric uncertainty inherent in methods like object detection. Specifically, we model data association ambiguity, which is typically non-Gaussian, in a way that is amenable to solution within the common nonlinear Gaussian formulation of simultaneous localization and mapping (SLAM). We do so by eliminating data association variables from the inference process through max-marginalization, preserving standard Gaussian posterior assumptions. The result is a max-mixture-type model that accounts for multiple data association hypotheses as well as incorrect loop closures. We provide experimental results on indoor and outdoor semantic navigation tasks with noisy odometry and object detection and find that the ability of the proposed approach to represent multiple hypotheses, including the "null" hypothesis, gives substantial robustness advantages in comparison to alternative semantic SLAM approaches. | Probabilistic Data Association via Mixture Models for Robust Semantic SLAM |
Foundation models have shown outstanding performance and generalization capabilities across domains. Since most studies on foundation models mainly focus on the pretraining phase, a naive strategy to minimize a single task-specific loss is adopted for fine-tuning. However, such fine-tuning methods do not fully leverage other losses that are potentially beneficial for the target task. Therefore, we propose MEta Loss TRansformer (MELTR), a plug-in module that automatically and non-linearly combines various loss functions to aid learning the target task via auxiliary learning. We formulate the auxiliary learning as a bi-level optimization problem and present an efficient optimization algorithm based on Approximate Implicit Differentiation (AID). For evaluation, we apply our framework to various video foundation models (UniVL, Violet and All-in-one), and show significant performance gain on all four downstream tasks: text-to-video retrieval, video question answering, video captioning, and multi-modal sentiment analysis. Our qualitative analyses demonstrate that MELTR adequately `transforms' individual loss functions and `melts' them into an effective unified loss. Code is available at https://github.com/mlvlab/MELTR. | MELTR: Meta Loss Transformer for Learning to Fine-tune Video Foundation Models |
First indications of the warm/hot intergalactic medium, tracing out the large scale structure of the universe, have been obtained in sensitive Chandra and XMM-Newton high resolution absorption line spectroscopy of bright blazars. High resolution X-ray spectroscopy and imaging also provides important new constraints on the physical condition of the cooling matter in the centers of clusters, requiring major modifications to the standard cooling flow models. XMM-Newton and Chandra low resolution spectroscopy detected significant Fe K_alpha absorption features in the spectrum of the ultraluminous, high redshift lensed broad absorption line QSO APM 08279+5255, yielding new insights in the outflow geometry indicating a supersolar Fe/O ratio. Chandra high resolution imaging spectroscopy of the nearby ULIRG/obscured QSO NGC 6240 for the first time gave evidence of two active supermassive black holes in the same galaxy, likely bound to coalesce in the course of the ongoing major merger in this galaxy. Deep X-ray surveys have shown that the cosmic X-ray background (XRB) is largely due to the accretion onto supermassive black holes, integrated over the cosmic time. These surveys have resolved more than 80% of the X-ray background into discrete sources. Optical spectroscopic identifications show that the sources producing the bulk of the X-ray background are a mixture of obscured (type-2) and unobscured (type-1) AGNs, as predicted by the XRB population synthesis models. A class of highly luminous type-2 AGN, so called QSO-2s, has been detected in the deepest Chandra and XMM-Newton surveys. The new Chandra AGN redshift distribution peaks at much lower redshifts (z~0.7) than that based on ROSAT data, indicating that the evolution of Seyfert galaxies occurs at significantly later cosmic time than that of QSOs. | Studying the Evolving Universe with XMM-Newton and Chandra |
An important application of intelligent vehicles is advance detection of dangerous events such as collisions. This problem is framed as a problem of optimal alarm choice given predictive models for vehicle location and motion. Techniques for real-time collision detection are surveyed and grouped into three classes: random Monte Carlo sampling, faster deterministic approximations, and machine learning models trained by simulation. Theoretical guarantees on the performance of these collision detection techniques are provided where possible, and empirical analysis is provided for two example scenarios. Results validate Monte Carlo sampling as a robust solution despite its simplicity. | Optimal Alarms for Vehicular Collision Detection |
We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients of the canonical coherent states by a specific generalized factorial depending on a parameter gamma. These states are superposition of eigenstates of the Hamiltonian with a symmetric Poschl-Teller potential depending on a parameter nu > 1. The associated Bargmann-type transform is defined for equal parameters. Some results on the infinite square well potential are also derived. For some different values of gamma, we discuss two sets of orthogonal polynomials that are naturally attached to these coherent states. | Orthogonal polynomials attached to coherent states for the symmetric Poschl-Teller oscillator |
We study several aspects of charged dilaton black holes with planar symmetry in $(d+2)$-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schr\"{o}dinger equation and find that the AC conductivity behaves like $\omega^{\delta}$, where the exponent $\delta$ is determined by the dilaton coupling $\alpha$ and the spacetime dimension parameter $d$. Moreover, we also study the Gauss-Bonnet corrections to $\eta/s$ in a five-dimensional finite-temperature background. | Holography of Charged Dilaton Black Holes in General Dimensions |
It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the $q$-Morris constant term identity. This conjecture was proved and extended by K\'{a}rolyi, Nagy, Petrov and Volkov in 2015. In this paper, we obtain two symmetric function generalizations of the $q$-Baker--Forrester ex-conjecture. These includes: (i) a $q$-Baker--Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV's result. | Symmetric function generalizations of the $q$-Baker--Forrester ex-conjecture and Selberg-type integrals |
Three very different algorithms have been proposed for solution of the Rayleigh-Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow, which serve to complete these underspecified equations by selection of the physically relevant solution from among the many otherwise nonunique solutions of these equations. The disputed physical principle is the admissibility condition which selects the physically meaningful solution from among the myriad of nonphysical solutions. The three different algorithms, expressing the three physical admissibility principles, are formulated alternately in terms of the energy dissipation rate or the entropy production rate. The three alternatives are zero, minimal or maximal rates. The solutions are markedly different. We find strong validation evidence that supports the solution with the maximum rate of dissipated energy, based on a review of prior results and new results presented here. Our verification reasoning, consisting of mathematical analysis based on physics assumptions, also supports the maximum energy dissipation rate and reasons against the other two. The zero dissipation solution is based on claims of direct numerical simulation. We dispute these claims and introduce analysis indicating that such simulations are far from direct numerical simulations. Recommendations for the numerical modeling of the deflagration to detonation transition in type Ia supernova are discussed. | A crisis for the V&V of turbulence simulations |
In this paper we continue our analysis of the stationary flows of $M$ component, coupled KdV (cKdV) hierarchies and their modifications. We describe the general structure of the $t_1$ and $t_2$ flows, using the case $M=3$ as our main example. One of our stationary reductions gives $N$ degrees of freedom, superintegrable systems. When $N=1$ (for $t_1$) and $N=2$ (for $t_2$), we have Poisson maps, which give multi-Hamiltonian representations of the flows. We discuss the general structure of these Poisson tensors and give explicit forms for the case $M=3$. In this case there are 3 modified hierarchies, each with 4 Poisson brackets. The stationary $t_2$ flow (for $N=2$) is separable in parabolic coordinates. Each Poisson bracket has rank 4, with $M+1$ Casimirs. The $4\times 4$ ``core'' of the Poisson tensors are nonsingular and related by a ``recursion operator''. The remaining part of each tensor is built out of the two commuting Hamiltonian vector fields, depending upon the specific Casimirs. The Poisson brackets are generalised to include the entire class of potential, separable in parabolic coordinates. The Jacobi identity imposes specific dependence on some parameters, representing the Casimirs of the extended canonical bracket. This general case is no longer a stationary cKdV flow, with Lax representation. We give a recursive procedure for constructing the Lax representation of the stationary flow for all values of $M$, {\em without} having to go through the stationary reduction. | Stationary Coupled KdV Hierarchies and Related Poisson Structures |
This paper introduces WaveGrad, a conditional model for waveform generation which estimates gradients of the data density. The model is built on prior work on score matching and diffusion probabilistic models. It starts from a Gaussian white noise signal and iteratively refines the signal via a gradient-based sampler conditioned on the mel-spectrogram. WaveGrad offers a natural way to trade inference speed for sample quality by adjusting the number of refinement steps, and bridges the gap between non-autoregressive and autoregressive models in terms of audio quality. We find that it can generate high fidelity audio samples using as few as six iterations. Experiments reveal WaveGrad to generate high fidelity audio, outperforming adversarial non-autoregressive baselines and matching a strong likelihood-based autoregressive baseline using fewer sequential operations. Audio samples are available at https://wavegrad.github.io/. | WaveGrad: Estimating Gradients for Waveform Generation |
We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of disorder degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical point, solutions of the statistical problem can be written as a Landau-de Gennes expansion for the free energy. If the disorder degrees of freedom are quenched, we confirm the existence of a biaxial nematic strucure. If orientational and disorder degrees of freedom are allowed to thermalize, this biaxial solution becomes thermodynamically unstable. Also, we use a two-temperature formalism to mimic the presence of two distinct relaxation times, and show that a slight departure from complete thermalization is enough to stabilize a biaxial nematic phase. | Biaxial nematic phase in the Maier-Saupe model for a mixture of discs and cylinders |
Betweenness centrality quantifies the importance of a vertex for the information flow in a network. We propose a flexible definition of betweenness for temporal multiplexes, where geodesics are determined accounting for the topological and temporal structure and the duration of paths. We propose an algorithm to compute the new metric via a mapping to a static graph. We show the importance of considering the temporal multiplex structure and an appropriate distance metric comparing the results with those obtained with static or single-layer metrics on a dataset of $\sim 20$k European flights. | Betweenness centrality for temporal multiplexes |
We establish recurrences formulas of the order of the classical groups that allow us to find a generalization of Euler's angles for classical groups and the invariant measures of these groups. We find the generating function for the SU(2) subset of SU(3) basis in the Fock-Bargmann space and a new basis of SU(3). This new basis is eigenfunction of the square of kinetic moment in product spaces of spherical harmonics. We generalize the generating function of SU (2) and we find invariant polynomials of SU (3) which are elements of the basis of SU (6). Using the above results we deduce the method of calculation isoscalar factors. We expose this method and we give the generating function for a particular case. Finally we determine the generating function of the elements of the representation matrix of SU(3) and we derive the analytical expression of these elements. | On the Euler angles for the classical groups, Schwinger approach and Isoscalar factors for SU (3) |
Existing zero-shot learning (ZSL) methods usually learn a projection function between a feature space and a semantic embedding space(text or attribute space) in the training seen classes or testing unseen classes. However, the projection function cannot be used between the feature space and multi-semantic embedding spaces, which have the diversity characteristic for describing the different semantic information of the same class. To deal with this issue, we present a novel method to ZSL based on learning class label autoencoder (CLA). CLA can not only build a uniform framework for adapting to multi-semantic embedding spaces, but also construct the encoder-decoder mechanism for constraining the bidirectional projection between the feature space and the class label space. Moreover, CLA can jointly consider the relationship of feature classes and the relevance of the semantic classes for improving zero-shot classification. The CLA solution can provide both unseen class labels and the relation of the different classes representation(feature or semantic information) that can encode the intrinsic structure of classes. Extensive experiments demonstrate the CLA outperforms state-of-art methods on four benchmark datasets, which are AwA, CUB, Dogs and ImNet-2. | Class label autoencoder for zero-shot learning |
This is an attempt to build Banach space valued theory for certain singular integrals on Hamming cube. Of course all estimates below are dimension independent, and we tried to find ultimate sharp assumptions on the Banach space for a corresponding operators to be bounded. In certain cases we succeeded, although there are still many open questions, some of them are listed in the last Section. Using the approach of \cite{IVHV} and also quantum random variables approach of \cite{ELP} we generalize several theorems of Pisier \cite{P} and Hyt\"onen-Naor \cite{HN}. We also improve the constant in $L^1$-Poincar\'e inequality on Hamming cube, the previous results are due to Talagrand and Ben Efraim--Lust-Piquard. | Banach space valued Pisier and Riesz type inequalities on discrete cube |
In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function $f$ has on the entropy solution. More precisely, if the set $\{w:f''(w)\ne 0\}$ is dense, the regularity of the solution can be expressed in terms of $\mathrm{BV}^\Phi$ spaces, where $\Phi$ depends on the nonlinearity of $f$. If moreover the set $\{w:f''(w)=0\}$ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that $f'\circ u(t)\in \mathrm{BV}_{\mathrm{loc}}(\mathrm{R})$ for every $t>0$ and that this can be improved to $\mathrm{SBV}_{\mathrm{loc}}(\mathbb{R})$ regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces. | Regularity estimates for scalar conservation laws in one space dimension |
An analytical formula for the contributions of the trend leftovers in DFA method is presented, based upon which the crossovers in DFA are investigated in detail. This general formula can explain the calculated results with DFA method for some examples in literature very well. | A Brief Discussion on the Crossovers in Detrended Fluctuation Analysis |
Topological defects in elastic media may be described by a geometric field akin to three-dimensional gravity. From this point of view, disclinations are line defects of zero width corresponding to a singularity of the curvature in an otherwise flat background. On the other hand, in two dimensions, the Frank free energy of a nematic liquid crystal may be interpreted as an Abelian Higgs Lagrangian. In this work, we construct an Abelian Higgs model coupled to "gravity" for the nematic phase, with the perspective of finding more realistic disclinations. That is, a cylindrically symmetric line defect of finite radius, invariant under translations along its axis. Numerical analysis of the equations of motion indeed yield a $+1$ winding number "thick" disclination. The defect is described jointly by the gauge and the Higgs fields, that compose the director field, and the background geometry. Away from the defect, the geometry is conical, associated to a dihedral deficit angle. The gauge field, confined to the defect, gives a structure to the disclination while the Higgs field, outside, represents the nematic order. | An Abelian Higgs model for disclinations in nematics |
The symmetrized Density-Matrix-Renormalization-Group (DMRG) method is used to study linear and nonlinear optical properties of Free base porphine and metallo-porphine. Long-range interacting model, namely, Pariser-Parr-Pople (PPP) model is employed to capture the quantum many body effect in these systems. The non-linear optical coefficients are computed within correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modelled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have $D_{4h}$ symmetry and hence have more degenerate excited states. The ground state of Metalloporphines show 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients. | A Density Matrix Renormalization Group Method Study of Optical Properties of Porphines and Metalloporphines |
To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach. | Safe Learning of Quadrotor Dynamics Using Barrier Certificates |
We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient S^n/rho is a manifold that is homotopically equivalent but not diffeomorphic to RP^n. We use these formulas for constructing explicit non-trivial elements in pi_1 Diff(S^5) and pi_1 Diff(S^13) and to provide explicit formulas for non-cancellation phenomena in group actions. | Wiedersehen metrics and exotic involutions of Euclidean spheres |
We find that AdS spacetime with a non-trivial linear dilaton field is an exact solution in the effective action of string theory, which is described by gravity with the Gauss-Bonnet curvature terms coupled to a dilaton field in the string frame. The AdS radius is determined by the spacetime dimensions and the coupling constants of curvature corrections. We also construct the asymptotically AdS black hole solutions with a linear dilaton field numerically. We discuss the thermodynamical properties of those solutions. Extending the model to the case with the even-order higher Lovelock curvature terms, we also find the exact AdS spacetime with non-trivial dilaton. We further find a cosmological solution with a bounce of three space and a solitonic solution with a non-trivial dilaton field, which is regular everywhere and approaches an asymptotically AdS spacetime. | AdS Black Hole Solution in Dilatonic Einstein-Gauss-Bonnet Gravity |
We prove that the degree $r(2p-3)$ cohomology of any finite group of Lie type over $\mathbb{F}_{p^r}$, with coefficients in characteristic $p$, is nonzero as long as its Coxeter number is at most $p$. We do this by providing a simple explicit construction of a nonzero element. | Nonvanishing cohomology classes on finite groups of Lie type with Coxeter number at most p |
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying the semi-implicit Euler scheme. The solution of the equation is only H\"older continuous in time, which is disadvantageous to improve the temporal convergence rate. Firstly, the system is transformed into an equivalent form having better regularity than the original one in time. But the regularity of nonlinear term remains unchanged. Then, combining Lagrange mean value theorem and independent increments of Brownian motion leads to a higher accuracy discretization of nonlinear term which ensures the implementation of the proposed time discretization scheme without loss of convergence rate. Our scheme can improve the convergence rate from ${\min\{\frac{\gamma}{2\alpha},\frac{1}{2}\}}$ to ${\min\{\frac{\gamma}{\alpha},1\}}$ in the sense of mean-squared $L^2$-norm. The theoretical error estimates are confirmed by extensive numerical experiments. | High-accuracy time discretization of stochastic fractional diffusion equation |
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structures. By utilizing category algebras and states on categories instead of simply considering categories, we can directly integrate relativity as a category theoretic structure and quantumness as a noncommutative probabilistic structure. Conceptual relationships with conventional approaches to quantum fields, including Algebraic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT), are also discussed. | Quantum Fields as Category Algebras |
We introduce the notion of a stationary random manifold and develop the basic entropy theory for it. Examples include manifolds admitting a compact quotient under isometries and generic leaves of a compact foliation. We prove that the entropy of an ergodic stationary random manifold is zero if and only if the manifold satisfies the Liouville property almost surely, and is positive if and only if it admits an infinite dimensional space of bounded harmonic functions almost surely. Upper and lower bounds for the entropy are provided in terms of the linear drift of Brownian motion and average volume growth of the manifold. Other almost sure properties of these random manifolds are also studied. | Brownian motion on stationary random manifolds |
The effect of resonant tunneling on magnetoresistance (MR) is studied theoretically in a double junction system. We have found that the ratio of the MR of the resonant peak current is reduced more than that of the single junction, whereas that of the valley current is enhanced depending on the change of the discrete energy-level under the change of magnetic field. We also found that the peak current-valley current (PV) ratio decreases when the junction conductance increases. | The Effects of Resonant Tunneling on Magnetoresistance through a Q uantum Dot |
To improve the ability of particle identification of the RIBLL2 separator at the HIRFL-CSR complex, a new high-performance detector for measuring fragment starting time and position at the F1 dispersive plane has been constructed and installed, and a method for achieving precise B\r{ho} determination has been developed using the experimentally derived ion-optical transfer matrix elements from the measured position and ToF information. Using the high-performance detectors and the precise B\r{ho} determination method, the fragments produced by the fragmentation of 78Kr at 300 MeV/nucleon were identified clearly at the RIBLL2-ETF under full momentum acceptance. The atomic number Z resolution of {\sigma}Z~0.19 and the mass-to-charge ratio A/Q resolution of {\sigma}A/Q~5.8e-3 were obtained for the 75As33+ fragment. This great improvement will increase the collection efficiency of exotic nuclei, extend the range of nuclei of interest from the A<40 mass region up to the A~80 mass region, and promote the development of radioactive nuclear beam experiments at the RIBLL2 separator. | Improving the particle identification of radioactive isotope beams at the RIBLL2 separator |
We extend the analysis of the conductance fluctuations in disordered metals by Altshuler, Kravtsov, and Lerner (AKL) to disordered superconductors with broken time-reversal symmetry in $d=(2+\epsilon)$ dimensions (symmetry classes C and D of Altland and Zirnbauer). Using a perturbative renormalization group analysis of the corresponding non-linear sigma model (NL$\sigma$M) we compute the anomalous scaling dimensions of the dominant scalar operators with $2s$ gradients to one-loop order. We show that, in analogy with the result of AKL for ordinary, metallic systems (Wigner-Dyson classes), an infinite number of high-gradient operators would become relevant (in the renormalization group sense) near two dimensions if contributions beyond one-loop order are ignored. We explore the possibility to compare, in symmetry class D, the $\epsilon=(2-d)$ expansion in $d<2$ with exact results in one dimension. The method we use to perform the one-loop renormalization analysis is valid for general symmetric spaces of K\"ahler type, and suggests that this is a generic property of the perturbative treatment of NL$\sigma$Ms defined on Riemannian symmetric target spaces. | Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions |
Very recently neural implicit rendering techniques have been rapidly evolved and shown great advantages in novel view synthesis and 3D scene reconstruction. However, existing neural rendering methods for editing purposes offer limited functionality, e.g., rigid transformation, or not applicable for fine-grained editing for general objects from daily lives. In this paper, we present a novel mesh-based representation by encoding the neural implicit field with disentangled geometry and texture codes on mesh vertices, which facilitates a set of editing functionalities, including mesh-guided geometry editing, designated texture editing with texture swapping, filling and painting operations. To this end, we develop several techniques including learnable sign indicators to magnify spatial distinguishability of mesh-based representation, distillation and fine-tuning mechanism to make a steady convergence, and the spatial-aware optimization strategy to realize precise texture editing. Extensive experiments and editing examples on both real and synthetic data demonstrate the superiority of our method on representation quality and editing ability. Code is available on the project webpage: https://zju3dv.github.io/neumesh/. | NeuMesh: Learning Disentangled Neural Mesh-based Implicit Field for Geometry and Texture Editing |
In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work we use this fact to derive in an unified way old and new properties concerning the sieved ultraspherical polynomials of the first and second kind. In particular we derive ordinary differential equations for these polynomials. As an application, we use the differential equation for sieved ultraspherical polynomials of the first kind to deduce that the zeros of these polynomials mark the locations of a set of particles that are in electrostatic equilibrium with respect to a particular external field. | An electrostatic interpretation of the zeros of sieved ultraspherical polynomials |
Hierarchical coordination of controllers often uses symbolic state representations that fully abstract their underlying low-level controllers, treating them as "black boxes" to the symbolic action abstraction. This paper proposes a framework to realize robust behavior, which we call Feasibility-based Control Chain Coordination (FC$^3$). Our controllers expose the geometric features and constraints they operate on. Based on this, FC$^3$ can reason over the controllers' feasibility and their sequence feasibility. For a given task, FC$^3$ first automatically constructs a library of potential controller chains using a symbolic action tree, which is then used to coordinate controllers in a chain, evaluate task feasibility, as well as switching between controller chains if necessary. In several real-world experiments we demonstrate FC$^3$'s robustness and awareness of the task's feasibility through its own actions and gradual responses to different interferences. | FC$^3$: Feasibility-Based Control Chain Coordination |
This is the first in a series of papers on an attempt to understand quantum field theory mathematically. In this paper we shall introduce and study BV QFT algebra and BV QFT as the proto-algebraic model of quantum field theory by exploiting Batalin-Vilkovisky quantization scheme. We shall develop a complete theory of obstruction (anomaly) to quantization of classical observables and propose that expectation value of quantized observable is certain quantum homotopy invariant. We shall, then, suggest a new method, bypassing Feynman's path integrals, of computing quantum correlation functions when there is no anomaly. An exact solution for all quantum correlation functions shall be presented provided that the number of equivalence classes of observables is finite for each ghost numbers. Such a theory shall have its natural family parametrized by a smooth-formal moduli space in quantum coordinates, which notion generalize that of flat or special coordinates in topological string theories and shall be interpreted as an example of quasi-isomorphism of general QFT algebra. | Algebraic Principles of Quantum Field Theory I: Foundation and an exact solution of BV QFT |
Regression test case prioritization (RTCP) aims to improve the rate of fault detection by executing more important test cases as early as possible. Various RTCP techniques have been proposed based on different coverage criteria. Among them, a majority of techniques leverage code coverage information to guide the prioritization process, with code units being considered individually, and in isolation. In this paper, we propose a new coverage criterion, code combinations coverage, that combines the concepts of code coverage and combination coverage. We apply this coverage criterion to RTCP, as a new prioritization technique, code combinations coverage based prioritization (CCCP). We report on empirical studies conducted to compare the testing effectiveness and efficiency of CCCP with four popular RTCP techniques: total, additional, adaptive random, and search-based test prioritization. The experimental results show that even when the lowest combination strength is assigned, overall, the CCCP fault detection rates are greater than those of the other four prioritization techniques. The CCCP prioritization costs are also found to be comparable to the additional test prioritization technique. Moreover, our results also show that when the combination strength is increased, CCCP provides higher fault detection rates than the state-of-the-art, regardless of the levels of code coverage. | Regression Test Case Prioritization by Code Combinations Coverage |
Stephan's Quintet (SQ), discovered more than 100 years ago, is the most famous and well studied compact galaxy group. It has been observed in almost all wavebands, with the most advanced instruments including Spitzer, GALEX, HST, Chandra, VLA, and various large mm/submm telescopes/arrays such as the IRAM 30m and BIMA. The rich multi-band data reveal one of the most fascinating pictures in the universe, depicting a very complex web of interactions between member galaxies and various constituents of the intragroup medium (IGM), which in turn trigger some spectacular activities such as a 40 kpc large scale shock and a strong IGM starburst. In this talk I will give a review on these observations. | Stephan's Quintet: A Multi-galaxy Collision |
We study the first-order formalism of pure four-dimensional ${\rm SU}(2)$ Yang--Mills theory with theta-term. We describe the Green functions associated to electric and magnetic flux operators \`a la 't~Hooft by means of gauge-invariant non-local operators. These Green functions are related to Witten's invariants of four-manifolds. | The Donaldson-Witten Invariants in Pure QCD with Order and Disorder 't Hooft-like Operators |
We present the Lyman-$\alpha$ flux power spectrum measurements of the XQ-100 sample of quasar spectra obtained in the context of the European Southern Observatory Large Programme "Quasars and their absorption lines: a legacy survey of the high redshift universe with VLT/XSHOOTER". Using $100$ quasar spectra with medium resolution and signal-to-noise ratio we measure the power spectrum over a range of redshifts $z = 3 - 4.2$ and over a range of scales $k = 0.003 - 0.06\,\mathrm{s\,km^{-1}}$. The results agree well with the measurements of the one-dimensional power spectrum found in the literature. The data analysis used in this paper is based on the Fourier transform and has been tested on synthetic data. Systematic and statistical uncertainties of our measurements are estimated, with a total error (statistical and systematic) comparable to the one of the BOSS data in the overlapping range of scales, and smaller by more than $50\%$ for higher redshift bins ($z>3.6$) and small scales ($k > 0.01\,\mathrm{s\,km^{-1}}$). The XQ-100 data set has the unique feature of having signal-to-noise ratios and resolution intermediate between the two data sets that are typically used to perform cosmological studies, i.e. BOSS and high-resolution spectra (e.g. UVES/VLT or HIRES). More importantly, the measured flux power spectra span the high redshift regime which is usually more constraining for structure formation models. | The Lyman-alpha forest power spectrum from the XQ-100 Legacy Survey |
Electrostatic doping into an $n$-type Mott insulator Sm$_{2}$CuO$_{4}$ has been successfully achieved with use of the heterojunction with an $n$-type band semiconductor Nb-doped SrTiO$_{3}$. The junction exhibits rectifying current-voltage characteristics due to the interface band discontinuity and the formation of depleted region. The application of reverse bias electric field on this junction enables the field-effect electron doping (presumably up to 6% per Cu atom) to the Mott insulator. The electro-modulation absorption spectroscopy could clearly show a large modification of the Mott-gap state accompanying the spectral weight transfer to the lower-energy region, reminiscent of formation of a metallic state. | Optical probe of electrostatic doping in an n-type Mott insulator |
A fluid flow in a simple dense liquid, passing an obstacle in a two-dimensional thin film geometry, is simulated by Molecular Dynamics (MD) computer simulation and compared to results of Lattice Boltzmann (LB) simulations. By the appropriate mapping of length and time units from LB to MD, the velocity field as obtained from MD is quantitatively reproduced by LB. The implications of this finding for prospective LB-MD multiscale applications are discussed. | Lattice Boltzmann versus Molecular Dynamics simulation of nano-hydrodynamic flows |
This paper considers human activity classification for an indoor radar system. Human motions generate nonstationary radar returns which represent Doppler and micro-Doppler signals. The time-frequency (TF) analysis of micro-Doppler signals can discern subtle variations on the motion by precisely revealing velocity components of various moving body parts. We consider radar for activity monitoring using TF-based machine learning approach exploiting both temporal and spatial degrees of freedom. The proposed approach captures different human motion representations more vividly in joint-variable data domains achieved through beamforming at the receiver. The radar data is collected using real time measurements at 77 GHz using four receive antennas, and subsequently micro-Doppler signatures are analyzed through machine learning algorithm for classifications of human walking motions. We present the performance of the proposed multi antenna approach in separating and classifying two closely walking persons moving in opposite directions. | Radar Human Motion Classification Using Multi-Antenna System |
We show that there are models of MA where the boldface $\Sigma^1_3$-uniformization property holds. Further we show that BPFA and the assertion $\aleph_1$ is accessible to reals outright implies that the boldface $\Sigma^1_3$-uniformization property is true. | Forcing Axioms, the Uniformization and the Basis Property |
A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the sam distance. A Finsler space $(M, F)$ is called Clifford-Wolf homogeneous if for any two point $x_1, x_2\in M$ there is a Clifford-Wolf translation $\rho$ such that $\rho(x_1)=x_2$. In this paper, we study Clifford-Wolf translations of left invariant Randers metrics on compact Lie groups. The mian result is that a left invariant Randers metric on a connected compact simple Lie group is Clifford-Wolf homogeneous if and only if the indicatrix of the metric is a round sphere with respect to a bi-invariant Riemannian metric. This presents a large number of examples of non-reversible Finsler metrics which are Clifford-Wolf homogeneous. | Clifford-Wolf translations of left invariant Randers metrics on compact Lie groups |
Given any asymptotically flat 3-manifold $(M,g)$ with smooth, non-empty, compact boundary $\Sigma$, the conformal conjecture states that for every $\delta>0$, there exists a metric $g' = u^4 g$, with $u$ a harmonic function, such that the area of outermost minimal area enclosure $\tilde{\Sigma}_{g'}$ of $\Sigma$ with respect to $g'$ is less than $\delta$. Recently, the conjecture was used to prove the Riemannian Penrose inequality for black holes with zero horizon area, and was proven to be true under the assumption of existence of only a finite number of minimal area enclosures of boundary $\Sigma$, and boundedness of harmonic function $u$. We prove the conjecture assuming only the boundedness of $u$. | Proof of the bounded conformal conjecture |
We analyze in detail supersymmetry breaking by compactification of the fifth dimension in M-theory in the compactification pattern $11d \to 5d \to 4d$ and find that a superpotential is generated for the complex fields coming from $5d$ hypermultiplets, namely the dilaton $S$ and the complex structure moduli. Using general arguments it is shown that these fields are always stabilized such that they don't contribute to supersymmetry breaking, which is completely saturated by the K\"ahler moduli coming from vector multiplets. It is shown that this mechanism is the strong-coupling analog of the Rohm-Witten quantization of the antisymmetric tensor field strength of string theories. The effect of a gaugino condensate on one of the boundaries is also considered. | Supersymmetry breaking in M-theory and quantization rules |
We consider wireless communication systems with compact planar arrays having densely spaced antenna elements in conjunction with one-bit analog-to-digital and digital-to-analog converters (ADCs/DACs). We provide closed-form expressions for the achievable rates with simple linear processing techniques for the uplink as well as the downlink scenarios while taking into account the effects of antenna mutual coupling. In the downlink case, we introduce the concept of non-radiating dithering to combat correlations of the quantization errors. Under higher antenna element density, we show that the performance of the quantized system can be made close to the ideal performance regardless of the operating signal-to-noise ratio. | Massive MIMO with Dense Arrays and 1-bit Data Converters |
Analyses of a 3D simulation of the upper layers of a solar convective envelope provide constraints on the physical quantities which enter the theoretical formulation of a stochastic excitation model of solar p modes, for instance the convective velocities and the turbulent kinetic energy spectrum. These constraints are then used to compute the acoustic excitation rate for solar p modes, P. The resulting values are found ~5 times larger than the values resulting from a computation in which convective velocities and entropy fluctuations are obtained with a 1D solar envelope model built with the time-dependent, nonlocal Gough (1977) extension of the mixing length formulation for convection (GMLT). This difference is mainly due to the assumed mean anisotropy properties of the velocity field in the excitation region. The 3D simulation suggests much larger horizontal velocities compared to vertical ones than in the 1D GMLT solar model. The values of P obtained with the 3D simulation constraints however are still too small compared with the values inferred from solar observations. Improvements in the description of the turbulent kinetic energy spectrum and its depth dependence yield further increased theoretical values of P which bring them closer to the observations. It is also found that the source of excitation arising from the advection of the turbulent fluctuations of entropy by the turbulent movements contributes ~ 65-75 % to the excitation and therefore remains dominant over the Reynolds stress contribution. The derived theoretical values of P obtained with the 3D simulation constraints remain smaller by a factor ~3 compared with the solar observations. This shows that the stochastic excitation model still needs to be improved. | Numerical constraints on the model of stochastic excitation of solar-type oscillations |
We study the topological susceptibility, chi, in two flavour lattice QCD. We find clear evidence for the expected suppression of chi at small quark mass. The estimate of the pion decay constant, f_pi = 105 +/-5 +18/-10 MeV, is consistent with the experimental value of approximately 93 MeV. We compare chi to the large-N_c prediction and find consistency over a large range of quark masses. | The topological susceptibility and pion decay constant from lattice QCD |
Recent works that revealed the vulnerability of dialogue state tracking (DST) models to distributional shifts have made holistic comparisons on robustness and qualitative analyses increasingly important for understanding their relative performance. We present our findings from standardized and comprehensive DST diagnoses, which have previously been sparse and uncoordinated, using our toolkit, CheckDST, a collection of robustness tests and failure mode analytics. We discover that different classes of DST models have clear strengths and weaknesses, where generation models are more promising for handling language variety while span-based classification models are more robust to unseen entities. Prompted by this discovery, we also compare checkpoints from the same model and find that the standard practice of selecting checkpoints using validation loss/accuracy is prone to overfitting and each model class has distinct patterns of failure. Lastly, we demonstrate how our diagnoses motivate a pre-finetuning procedure with non-dialogue data that offers comprehensive improvements to generation models by alleviating the impact of distributional shifts through transfer learning. | Know Thy Strengths: Comprehensive Dialogue State Tracking Diagnostics |
The specific heat, magnetic susceptibility and ESR signals of a Na-deficient vanadate Na_xV_2O_5 (x=1.00 - 0.90) were studied in the temperature range 0.07 - 10 K, well below the transition point to a spin-gap state. The contribution of defects provided by sodium vacancies to the specific heat was observed. It has a low temperature part which does not tend to zero till at least 0.3 K and a high temperature power-like tail appears above 2 K. Such dependence may correspond to the existence of local modes and correlations between defects in V-O layers. The magnetic measurements and ESR data reveal S=1/2 degrees of freedom for the defects, with their effective number increasing in temperature and under magnetic field. The latter results in the nonsaturating magnetization at low temperature. No long-range magnetic ordering in the system of defects was found. A model for the defects based on electron jumps near vacancies is proposed to explain the observed effects. The concept of a frustrated two-dimensional correlated magnet induced by the defects is considered to be responsible for the absence of magnetic ordering. | Investigation of thermal and magnetic properties of defects in a spin-gap compound NaV2O5 |
In this review articel we study the gaugings of extended supergravity theories in various space-time dimensions. These theories describe the low-energy limit of non-trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so-called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half-maximal (N=4) supergravities in d=4 and d=5 and to the maximal supergravities in d=2 and d=7. Examples of particular gaugings are given. Whenever possible, the higher-dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor. | Gauged Supergravities in Various Spacetime Dimensions |
This paper presents a nonequilibrium, first-principles, thermodynamic-ensemble based model for the relaxation process of interacting non-equilibrium systems. This model is formulated using steepest-entropy-ascent quantum thermodynamics (SEAQT) and its equation of motion for a grand canonical ensemble and is applied to a many particle system of classical or indistinguishable particles. Two kinds of interactions are discussed, including pure heat diffusion and heat and mass diffusion together. Since no local equilibrium assumption is made, the conjugate fluxes and forces are intrinsic to the subspaces of the state space of one system and/or of the state space of the two interacting systems. They are derived via the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space of a single system and/or of the state space of the two interacting systems. The Onsager relations are shown to be thermodynamic kinematic features of the system and are found without knowledge of the detailed mechanics of the dynamic process. A fundamental thermodynamic explanation for the measurement of each intensive property of a system in a nonequilibrium state is given. The fundamental thermodynamic definition of reservoir is also discussed. Finally, the equation of motion for a system undergoing multiple interactions is provided, which permits the modeling of a network of local systems in nonequilibrium at any spatial and temporal scale. | Steepest-entropy-ascent quantum thermodynamic modeling of the far-from-equilibrium interactions between nonequilibrium systems of indistinguishable particle ensembles |
Xiao and Zhu has shown that if $\cal C$ is a locally finite triangulated category, then the Auslander-Reiten triangles generate the relations for the Grothendieck group of $\cal C$. The notion of $(d +2)$-angulated categories is a "higher dimensional" analogue of triangulated categories. In this article, we show that if A $(d+2)$-angulated category $\cal C$ is locally finite if and only if the Auslander-Reiten $(d+2)$-angles generate the relations for the Grothendieck group of $\cal C$. This extends the result of Xiao and Zhu, and gives the converse of Xiao and Zhu's result is also true. | Grothendieck groups and Auslander-Reiten (d+2)-angles |
Mantaci et al. [TCS 2007] defined the eBWT to extend the definition of the BWT to a collection of strings, however, since this introduction, it has been used more generally to describe any BWT of a collection of strings and the fundamental property of the original definition (i.e., the independence from the input order) is frequently disregarded. In this paper, we propose a simple linear-time algorithm for the construction of the original eBWT, which does not require the preprocessing of Bannai et al. [CPM 2021]. As a byproduct, we obtain the first linear-time algorithm for computing the BWT of a single string that uses neither an end-of-string symbol nor Lyndon rotations. We combine our new eBWT construction with a variation of prefix-free parsing to allow for scalable construction of the eBWT. We evaluate our algorithm (pfpebwt) on sets of human chromosomes 19, Salmonella, and SARS-CoV2 genomes, and demonstrate that it is the fastest method for all collections, with a maximum speedup of 7.6x on the second best method. The peak memory is at most 2x larger than the second best method. Comparing with methods that are also, as our algorithm, able to report suffix array samples, we obtain a 57.1x improvement in peak memory. The source code is publicly available at https://github.com/davidecenzato/PFP-eBWT. | Computing the original eBWT faster, simpler, and with less memory |
It is a classic result that the geometry of the total space of a principal bundle with reference to the action of the bundle's structure group is codified in the bundle's operation, a collection of derivations comprising the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and obeying the six Cartan relations. In particular, connections and gauge transformations can be defined through the way they are acted upon by the operation's derivations. In this paper, the first of a series of two extending the ordinary theory, we construct an operational total space theory of strict principal 2--bundles with regard to the action of the structure strict 2--group. Expressing this latter via a crossed module $(\mathsans{E},\mathsans{G})$, the operation is based on the derived Lie group $\mathfrak{e}[1]\rtimes\mathsans{G}$. In the second paper, an original formulation of the theory of $2$--connections and $1$-- and $2$--gauge transformations based on the operational framework worked out here will be provided. | Operational total space theory of principal 2--bundles I: operational geometric framework |
We study the birational geometry of some moduli spaces of abelian varieties with extra structure: in particular, with a symmetric theta structure and an odd theta characteristic. For a $(d_1,d_2)$-polarized abelian surface, we show how the parities of the $d_i$ influence the relation between canonical level structures and symmetric theta structures. For certain values of $d_1$ and $d_2$, a theta characteristic is needed in order to define Theta-null maps. We use these Theta-null maps and preceding work of other authors on the representations of the Heisenberg group to study the birational geometry and the Kodaira dimension of these moduli spaces. | Moduli of abelian surfaces, symmetric theta structures and theta characteristics |
Hydrogen trapping ability of various metal - ethylene complexes has been studied at the B3LYP and MP2 level of theory using the 6-311+G(d,p) basis set. Different global and local reactivity descriptors and the associated electronic structure principles provide important insights into the associated interactions. There exist two distinct classes of bonding patterns, viz., a Kubas-type interaction between the metal and the H2 molecule behaving as a {\eta}2-ligand and an electrostatic interaction between the metal and the atomic hydrogens. | Analyzing the Efficiency of Mn-(C2H4) (M = Sc, Ti, Fe, Ni; n = 1, 2) Complexes as Effective Hydrogen Storage Materials |
Timing side-channels represent an insidious security challenge for cloud computing, because: (a) massive parallelism in the cloud makes timing channels pervasive and hard to control; (b) timing channels enable one customer to steal information from another without leaving a trail or raising alarms; (c) only the cloud provider can feasibly detect and report such attacks, but the provider's incentives are not to; and (d) resource partitioning schemes for timing channel control undermine statistical sharing efficiency, and, with it, the cloud computing business model. We propose a new approach to timing channel control, using provider-enforced deterministic execution instead of resource partitioning to eliminate timing channels within a shared cloud domain. Provider-enforced determinism prevents execution timing from affecting the results of a compute task, however large or parallel, ensuring that a task's outputs leak no timing information apart from explicit timing inputs and total compute duration. Experiments with a prototype OS for deterministic cloud computing suggest that such an approach may be practical and efficient. The OS supports deterministic versions of familiar APIs such as processes, threads, shared memory, and file systems, and runs coarse-grained parallel tasks as efficiently and scalably as current timing channel-ridden systems. | Determinating Timing Channels in Compute Clouds |
Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised of different parts, it is common to describe the dynamics of a subsystem of interest by making an adiabatic elimination of the remaining components of the system. This procedure often leads to an effective master equation for the subsystem that is not in the well-known Gorini-Kossakowski-Lindblad-Sudarshan form (here called standard Lindblad form). Instead, it has a more general structure (here called generalized Lindblad form), which explicitly reveals the dissipative coupling between the various components of the subsystem. Moreover, for systems weakly coupled to a reservoir, the presence of counter-rotating terms in the interaction Hamiltonian or the nonstationarity of the reservoir state guarantees that the master equation describing the system of interest will be of the generalized Lindblad form. In this work, we present a set of dynamical equations for the first and second moments of the canonical variables for linear systems, bosonic and fermionic, described by generalized Lindblad master equations. Our method is efficient and allows one to obtain analytical solutions for the steady state. Further, we include as a review some covariance matrix methods for which our results are particularly relevant, paying special attention to those related to the measurement of entanglement. Finally, we prove that the Duan criterion for entanglement is also applicable to fermionic systems. | Generalized Lindblad master equations in quantum reservoir engineering |
A two-step, two-color laser spectroscopy technique has been used to measure the hyperfine splitting of the 7p$_{1/2}$ excited state in $^{203}$Tl and $^{205}$Tl, as well as the isotope shift within the 7s$_{1/2}$ - 7p$_{1/2}$ transition. Our measured values for the hyperfine splittings, 2153.2(7) MHz (in $^{203}$Tl) and 2173.3(8) MHz (in $^{205}$Tl), each differ by 20 MHz from previously published values which quoted comparable precision. The transition isotope shift of $^{203}$Tl relative to $^{205}$Tl was measured to be 534.4(9) MHz. In our experiment, one laser was locked to the thallium ground-state 6p$_{1/2}$ - 7s$_{1/2}$ 378 nm transition, while the second, spatially overlapping laser was scanned across the 7s$_{1/2}$(F=1) - 7p$_{1/2}$(F=0,1) hyperfine transitions. To facilitate accurate frequency calibration, radio-frequency modulation of the laser was used to create sidebands in the absorption spectrum. | Measurement of 7p$_{1/2}$-state hyperfine structure and 7s$_{1/2}$-7p$_{1/2}$ transition isotope shift in $^{203}$Tl and $^{205}$Tl |
We show that the apolar ideal to the determinant of a generic symmetric matrix is generated in degree two, and the apolar ideal to the permanent of a generic symmetric matrix is generated in degrees two and three. In each case we specify the generators of the apolar ideal. As a consequence, using a result of K. Ranestad and F. O. Schreyer we give lower bounds to the cactus rank and rank of each of these polynomials. We compare these bounds with those obtained by J. Landsberg and Z. Teitler. | Apolarity for determinants and permanents of generic symmetric matrices |
A polar decomposition of mutual information between a complex-valued channel's input and output is proposed for a input whose amplitude and phase are independent of each other. The mutual information is symmetrically decomposed into three terms: an amplitude term, a phase term, and a cross term, whereby the cross term is negligible at high signal-to-noise ratio. Theoretical bounds of the amplitude and phase terms are derived for additive white Gaussian noise channels with Gaussian inputs. This decomposition is then applied to the recently proposed amplitude phase shift keying with product constellation (product-APSK) inputs. It shows from an information theoretical perspective that coded modulation schemes using product-APSK are able to outperform those using conventional quadrature amplitude modulation (QAM), meanwhile maintain a low complexity. | Polar Decomposition of Mutual Information over Complex-Valued Channels |
Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this work we show that a multipartite entanglement measure recently proposed in the context of holography, the Markov gap, provides a universal diagnostic of ungappable edge states. Defined as a difference of the reflected entropy and mutual information $h(A:B) = S_R(A:B) - I(A:B)$ between two parties, we argue that for $A,B$ being adjacent subregions in the bulk, $h=\frac{c_+}{3}\log 2$, where $c_+$ is the minimal total central charge of the boundary theory. As evidence, we prove that $h=0$ for string-net models, and numerically verify that $h=\frac{|C|}{3}\log 2$ for a Chern-$C$ insulator. Our work establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary. | A universal tripartite entanglement signature of ungappable edge states |
The Web is ubiquitous, increasingly populated with interconnected data, services, people, and objects. Semantic web technologies (SWT) promote uniformity of data formats, as well as modularization and reuse of specifications (e.g., ontologies), by allowing them to include and refer to information provided by other ontologies. In such a context, multi-agent system (MAS) technologies are the right abstraction for developing decentralized and open Web applications in which agents discover, reason and act on Web resources and cooperate with each other and with people. The aim of the project is to propose an approach to transform "Agent and artifact (A&A) meta-model" into a Web-readable format with ontologies in line with semantic web formats and to reuse already existing ontologies in order to provide uniform access for agents to things. | Semantic Web Environments for Multi-Agent Systems: Enabling agents to use Web of Things via semantic web |
Open-set object detection (OSOD) has recently gained attention. It is to detect unknown objects while correctly detecting known objects. In this paper, we first point out that the recent studies' formalization of OSOD, which generalizes open-set recognition (OSR) and thus considers an unlimited variety of unknown objects, has a fundamental issue. This issue emerges from the difference between image classification and object detection, making it hard to evaluate OSOD methods' performance properly. We then introduce a novel scenario of OSOD, which considers known and unknown classes within a specified super-class of object classes. This new scenario has practical applications and is free from the above issue, enabling proper evaluation of OSOD performance and probably making the problem more manageable. Finally, we experimentally evaluate existing OSOD methods with the new scenario using multiple datasets, showing that the current state-of-the-art OSOD methods attain limited performance similar to a simple baseline method. The paper also presents a taxonomy of OSOD that clarifies different problem formalizations. We hope our study helps the community reconsider OSOD problems and progress in the right direction. | Rectifying Open-set Object Detection: A Taxonomy, Practical Applications, and Proper Evaluation |
We present a simple model for the non-thermal emission from the historical supernova remnant SN 1006. We constrain the synchrotron parameters of the model with archival radio and hard X-ray data. Our stationary emission model includes two populations of electrons, which is justified by multi-frequency images of the object. From the set of parameters that predict the correct synchrotron flux we select those which are able to account, either partly or entirely, for the gamma-ray emission of the source as seen by HESS. We use the results from this model as well as the latest constraints imposed by the Fermi observatory and conclude that the TeV emission cannot be accounted for by neutral pion decay produced by high-energy cosmic rays with a single "soft" power-law distribution (i.e., with a particle index greater than 2 or so). | On the Nature of the TeV Emission from the SNR SN 1006 |
We prove modularity of certain residually reducible ordinary 2-dimensional $p$-adic Galois representations with determinant a finite order odd character $\chi$. For certain non-quadratic $\chi$ we prove an $R=T$ result for $T$ the weight 1 specialisation of the Hida Hecke algebra acting on non-classical weight 1 forms, under the assumption that no two Hida families congruent to an Eisenstein series cross in weight 1. For quadratic $\chi$ we prove that the quotient of $R$ corresponding to deformations split at $p$ is isomorphic to the Hecke algebra acting on classical CM weight 1 modular forms. | $R=T$ theorems for weight one modular forms |
Matrices associated with graphs, such as the Laplacian, lead to numerous interesting graph problems expressed as linear systems. One field where Laplacian linear systems play a role is network analysis, e. g. for certain centrality measures that indicate if a node (or an edge) is important in the network. One such centrality measure is current-flow closeness. To allow network analysis workflows to profit from a fast Laplacian solver, we provide an implementation of the LAMG multigrid solver in the NetworKit package, facilitating the computation of current-flow closeness values or related quantities. Our main contribution consists of two algorithms that accelerate the current-flow computation for one node or a reasonably small node subset significantly. One sampling-based algorithm provides an unbiased estimation of the related electrical farness, the other one is based on the Johnson-Lindenstrauss transform. Our inexact algorithms lead to very accurate results in practice. Thanks to them one is now able to compute an estimation of current-flow closeness of one node on networks with tens of millions of nodes and edges within seconds or a few minutes. From a network analytical point of view, our experiments indicate that current-flow closeness can discriminate among different nodes significantly better than traditional shortest-path closeness and is also considerably more resistant to noise -- we thus show that two known drawbacks of shortest-path closeness are alleviated by the current-flow variant. | Estimating Current-Flow Closeness Centrality with a Multigrid Laplacian Solver |
Recent advances have shown that implicit bias of gradient descent on over-parameterized models enables the recovery of low-rank matrices from linear measurements, even with no prior knowledge on the intrinsic rank. In contrast, for robust low-rank matrix recovery from grossly corrupted measurements, over-parameterization leads to overfitting without prior knowledge on both the intrinsic rank and sparsity of corruption. This paper shows that with a double over-parameterization for both the low-rank matrix and sparse corruption, gradient descent with discrepant learning rates provably recovers the underlying matrix even without prior knowledge on neither rank of the matrix nor sparsity of the corruption. We further extend our approach for the robust recovery of natural images by over-parameterizing images with deep convolutional networks. Experiments show that our method handles different test images and varying corruption levels with a single learning pipeline where the network width and termination conditions do not need to be adjusted on a case-by-case basis. Underlying the success is again the implicit bias with discrepant learning rates on different over-parameterized parameters, which may bear on broader applications. | Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization |
Based upon kinetic Monte Carlo simulations of crystallization in a simple polymer model we present a new picture of the mechanism by which the thickness of lamellar polymer crystals is constrained to a value close to the minimum thermodynamically stable thickness, l_{min}. The free energetic costs of the polymer extending beyond the edges of the previous crystalline layer and of a stem being shorter than l_{min} provide upper and lower constraints on the length of stems in a new layer. Their combined effect is to cause the crystal thickness to converge dynamically to a value close to l_{min} where growth with constant thickness then occurs. This description contrasts with those given by the two dominant theoretical approaches. However, at small supercoolings the rounding of the crystal profile does inhibit growth as suggested in Sadler and Gilmer's entropic barrier model. | Kinetic Monte Carlo simulations of the growth of polymer crystals |
Let X be a smooth projective curve of genus g \geq 2 over an algebraically closed field k of characteristic p > 0. Let M_X be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map F: X \to X_1 induces by pull-back a rational map V: M_{X_1} \to M_{X}. In this paper we show the following results. 1) For any line bundle L over X, the rank-p vector bundle F_*L is stable. 2) The rational map V has base points, i.e., there exist stable bundles E over X_1 such that F^* E is not semistable. 3) Let B \subset M_{X_1} denote the scheme-theoretical base locus of V. If g=2, p>2 and X ordinary, then B is a 0-dimensional local complete intersection of length {2/3}p(p^2 -1) and the degree of V equals {1/3}p(p^2 +2). | On Frobenius-destabilized rank-2 vector bundles over curves |
We consider a scenario for the longest duration gamma ray bursts, resulting from the collapse of a massive rotating star in a close binary system with a companion black hole. The primary black hole born during the core collapse is first being spun up and increases its mass during the fallback of the stellar envelope just after its birth. As the companion black hole enters the outer envelope, it provides an additional angular momentum to the gas. After the infall and spiral-in towards the primary, the two black holes merge inside the circumbinary disk. The second episode of mass accretion and high final spin of the post-merger black hole prolongs the gamma ray burst central engine activity. The observed events should have two distinct peaks in the electromagnetic signal, separated by the gravitational wave emission. The gravitational recoil of the burst engine is also possible. | Long Gamma Ray Bursts from binary black holes |
Frequency-encoded quantum information offers intriguing opportunities for quantum communications and networking, with the quantum frequency processor paradigm -- based on electro-optic phase modulators and Fourier-transform pulse shapers -- providing a path for scalable construction of quantum gates. Yet all experimental demonstrations to date have relied on discrete fiber-optic components that occupy significant physical space and impart appreciable loss. In this article, we introduce a model for the design of quantum frequency processors comprising microring resonator-based pulse shapers and integrated phase modulators. We estimate the performance of single and parallel frequency-bin Hadamard gates, finding high fidelity values that extend to frequency bins with relatively wide bandwidths. By incorporating multi-order filter designs as well, we explore the limits of tight frequency spacings, a regime extremely difficult to obtain in bulk optics. Overall, our model is general, simple to use, and extendable to other material platforms, providing a much-needed design tool for future frequency processors in integrated photonics. | Design Methodologies for Integrated Quantum Frequency Processors |
One of the most elusive features of Gamma Ray Bursts (GRBs) is the sporadic emission prior to the main prompt event observed in at least $\sim 15\%$ of cases. These precursors have spectral and temporal properties similar to the main prompt emission, and smaller, but comparable, energetics. They are separated from the main event by a quiescent time that may be extremely long and, in some cases, more than one precursor has been observed in the same burst. Precursors are still a puzzle: despite many attempts none of the proposed models can account for all the observed features. Based on the complete sample of bright long GRBs observed by Swift (BAT6), we propose a new scenario for which precursors are explained by assuming that the central GRB engine is a newly born magnetar. In this model the precursor and the prompt emission arise from accretion of matter onto the surface of the magnetar. The accretion process can be halted by the centrifugal drag exerted by the rotating magnetosphere onto the in-falling matter, allowing for multiple precursors and very long quiescent times. | How to switch on and off a Gamma-ray burst through a magnetar |
Virus binding to a surface results at least locally, at the contact area, in stress and potential structural perturbation of the virus cage. Here we address the question of the role of substrate-induced deformation in the overall virus mechanical response to the adsorption event. This question may be especially important for the broad category of viruses that have their shells stabilized by weak, non-covalent interactions. We utilize atomic force microscopy to measure the height change distributions of the brome mosaic virus upon adsorption from liquid on atomically flat substrates and present a continuum model which captures well the behavior. Height data fitting according the model provides, without recourse to indentation, estimates of virus elastic properties and of the interfacial energy. | Contact Mechanics of a Small Icosahedral Virus |
In this work we report a systematic study of electrical current effects on superconducting properties of granular Y$_{1-x}$Pr$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ samples with x close to the critical Pr concentration above which the superconductivity vanishes. The results indicate the occurrence of superconductor-insulator quantum phase transition (SIT) driven by the applied electrical current, and suggest that the current-induced SIT can be considered as the dynamical counterpart of the magnetic-field- tuned SIT. | Current-Induced Superconductor-Insulator Transition in Granular High-T_c Superconductors |
A new method which allows one to study multiple coherent reflection/transmissions by partially transparent interfaces, (e.g., in multi-layer mesoscopic structures or grain boundaries in high-Tc's), in the framework of the quasiclassical theory of superconductivity is suggested. It is argued that in the presence of interfaces, a straight-line trajectory transforms to a simple connected 1-dimensional tree (graph) with knots, i.e. the points where the interface scattering events occur and pieces of the trajectories are coupled. For the 2-component trajectory "wave function" which factorizes the matrix Gor'kov Green's function, a linear boundary condition on the knot is formulated for an arbitrary interface, specular or diffusive (in the many channel model). From the new boundary condition, we derive: (i) the excitation scattering amplitude for the multi-channel Andreev/ordinary reflection/transmission processes; (ii) the boundary conditions for the Riccati equation; (iii) the transfer matrix which couples the trajectory Green's function before and after the interface scattering. To show the usage of the method, the cases of a film separated from a bulk superconductor by a partially transparent interface, and a SIS' sandwich with finite thickness layers, are considered. The electric current response to the vector potential (the superfluid density $\rho_s$) with the $\pi $ phase difference in S and S' is calculated for the sandwich. It is shown that the model is very sensitive to imperfection of the SS' interface: the low temperature response being paramagnetic ($\rho_s <0$) in the ideal system case, changes its sign and becomes diamagnetic ($\rho_s > 0$) when the probability of reflection is as low as a few percent. | Quasiclassical theory of superconductivity: a multiple interface geometry(II) |
Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and retailing limited-time availability products. In this paper, we consider a set of sequential decision problems in which the decision-maker must not only balance holding and shortage costs but discard all inventory before a fixed number of decision epochs, with the option for an early inventory reset. Finding optimal policies using dynamic programming for these problems is particularly challenging since the resulting value functions are non-convex. Moreover, this structure cannot be easily analyzed using existing extended definitions, such as $K$-convexity. Our key contribution is to present sufficient conditions that ensure the optimal policy has an easily interpretable structure that generalizes the well-known $(s, S)$ policy from the operations literature. Furthermore, we demonstrate that the optimal policy has a four-threshold structure under these rather mild conditions. We then conclude with computational experiments, thereby illustrating the policy structures that can be extracted in several inventory management scenarios. | Optimal Policy for Inventory Management with Periodic and Controlled Resets |
For $n\in\{2^t-3,2^t-2,2^t-1\}$ ($t\ge3$) we study the cohomology algebra $H^*(\widetilde G_{n,3};\mathbb Z_2)$ of the Grassmann manifold $\widetilde G_{n,3}$ of oriented $3$-dimensional subspaces of $\mathbb R^n$. A complete description of $H^*(\widetilde G_{n,3};\mathbb Z_2)$ is given in the cases $n=2^t-3$ and $n=2^t-2$, while in the case $n=2^t-1$ we obtain a description complete up to a coefficient from $\mathbb Z_2$. | On the mod 2 cohomology algebra of oriented Grassmannians |
Populations of mammalian stem cells commonly exhibit considerable cell-cell variability. However, the functional role of this diversity is unclear. Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. We propose an information-theoretic interpretation of these results that views cellular multipotency as an instance of maximum entropy statistical inference. | Entropy, Ergodicity and Stem Cell Multipotency |
We studied low temperature (T=50mK) in-plane magnetoresistance of a dilute two-dimensional hole system in GaAs/AlGaAs heterostructure that exhibits an apparent metal-insulator transition. We found an anisotropic magnetoresistance, which changes dramatically at high in-plane fields ($B_{\parallel}\agt$5T) as the hole density is varied. At high densities where the system behaves metallic at $B_{\parallel}=0$, the transverse magnetoresistance is larger than the longitudinal magnetoresistance. With decreasing the hole density the difference becomes progressively smaller, and at densities near the "critical" density and lower, the longitudinal magnetoresistance becomes larger than the transverse magnetoresistance. | Non-monotonic magnetic field and density dependence of in-plane magnetoresistance in dilute two-dimensional holes in GaAs/AlGaAs |
In this paper, we address the problem of conditional scene decoration for 360-degree images. Our method takes a 360-degree background photograph of an indoor scene and generates decorated images of the same scene in the panorama view. To do this, we develop a 360-aware object layout generator that learns latent object vectors in the 360-degree view to enable a variety of furniture arrangements for an input 360-degree background image. We use this object layout to condition a generative adversarial network to synthesize images of an input scene. To further reinforce the generation capability of our model, we develop a simple yet effective scene emptier that removes the generated furniture and produces an emptied scene for our model to learn a cyclic constraint. We train the model on the Structure3D dataset and show that our model can generate diverse decorations with controllable object layout. Our method achieves state-of-the-art performance on the Structure3D dataset and generalizes well to the Zillow indoor scene dataset. Our user study confirms the immersive experiences provided by the realistic image quality and furniture layout in our generation results. Our implementation will be made available. | Conditional 360-degree Image Synthesis for Immersive Indoor Scene Decoration |
Identity management systems (IDMSs) are widely used to provision user identities while managing authentication, authorization, and data sharing within organizations and on the web. Traditional identity systems typically suffer from single points of failure, lack of interoperability, and privacy issues, such as enabling mass data collection and user tracking. Blockchain technology has the potential to alleviate these concerns: it can support the ability for users to control the custody of their own identifiers and credentials, enabling novel data ownership and governance models with built-in control and consent mechanisms. Hence, blockchain-based IDMSs, which could benefit both users and businesses, are beginning to proliferate. This work categorizes these systems into a taxonomy based on differences in blockchain architectures, governance models, and other salient features. Context is provided for the taxonomy through the description of related terms, emerging standards, and use cases while highlighting relevant security and privacy considerations. | A Taxonomic Approach to Understanding Emerging Blockchain Identity Management Systems |
Multi-turn Injection scheme with gaseous stripper is usually used in high intensity and super heavy ion injection process. With its advantage of long lifetime and uniformity, a gaseous stripper is proposed based on the under construction hadrontherapy facility HIMM (Heavy Ion Medical Machine). In this paper, the physical process between the injecting beam and the gaseous target is studied, and a simulation work is conducted based on the former developed code. | A gaseous stripper proposal based on hadrontherapy facility HIMM |
We present results of a global survey of single-pixel intensity power spectra from a 12-hour time period on 26 June 2013 in a 1600x1600 pixel region from four channels of the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA) instrument. We extract single-pixel time series from a derotated image sequence, fit models to the power spectra of these time series, and study the spatial dependence of the model parameters. Two power spectra models are considered: i) a three-parameter power-law + tail model and ii) a power-law + tail model + three-parameter localized Lorentzian, the latter to model periodicity. Spectra are well-described by at least one of these models for all pixel locations, with the spatial distribution of best-fit model parameters shown to provide new and unique insights into turbulent, quiescent and periodic features in the EUV corona and upper photosphere. Findings include: individual model parameters correspond clearly and directly to visible solar features; detection of numerous quasi-periodic three- and five-minute oscillations; observational identification of concentrated magnetic flux as regions of largest power-law indices [n]; identification of unique spectral features of coronal holes and filaments; identification of sporadic and pervasive five-minute oscillations throughout the corona; detection of the known global ~4.0-minute chromospheric oscillation; "coronal bullseyes" appearing as radially decaying periodicities over sunspots and sporadic foot-point regions; and "penumbral periodic voids" appearing as broad rings around sunspots in 1600 and 1700 {\AA} in which spectra contain no statistically significant periodic component. | A Global Survey of EUV Corona Power Spectra |
The computer-aided diagnosis of focal liver lesions (FLLs) can help improve workflow and enable correct diagnoses; FLL detection is the first step in such a computer-aided diagnosis. Despite the recent success of deep-learning-based approaches in detecting FLLs, current methods are not sufficiently robust for assessing misaligned multiphase data. By introducing an attention-guided multiphase alignment in feature space, this study presents a fully automated, end-to-end learning framework for detecting FLLs from multiphase computed tomography (CT) images. Our method is robust to misaligned multiphase images owing to its complete learning-based approach, which reduces the sensitivity of the model's performance to the quality of registration and enables a standalone deployment of the model in clinical practice. Evaluation on a large-scale dataset with 280 patients confirmed that our method outperformed previous state-of-the-art methods and significantly reduced the performance degradation for detecting FLLs using misaligned multiphase CT images. The robustness of the proposed method can enhance the clinical adoption of the deep-learning-based computer-aided detection system. | Robust End-to-End Focal Liver Lesion Detection using Unregistered Multiphase Computed Tomography Images |
We give a status report on the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment from the Dyson-Schwinger approach. We discuss novel, model-independent properties of the light-by-light amplitude: we give its covariant decomposition in view of electromagnetic gauge invariance and Bose symmetry, and we identify the relevant kinematic regions that are probed under the integral. The decomposition of the amplitude at the quark level and the importance of its various diagrams are discussed and related to model approaches. | The muon g-2: Dyson-Schwinger status on hadronic light-by-light scattering |
Using the framework of supersymmetric non-linear $\sigma$-model we develop a general non-perturbative characterisation of universal features of the density $\rho(\Gamma)$ of the imaginary parts (``width'') for $S$-matrix poles (``resonances'') describing waves incident and reflected from a disordered medium via $M$-channel waveguide/lead. Explicit expressions for $\rho(\Gamma)$ are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels ($M\sim 1$) the most salient features are tails $\rho(\Gamma)\sim \Gamma^{-1}$ for narrow resonances reflecting exponential localization and $\rho(\Gamma)\sim \Gamma^{-2}$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with $M\gg 1$, an intermediate asymptotics $\rho(\Gamma)\sim \Gamma^{-3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts. | Resonances in a single-lead reflection from a disordered medium: $\sigma$-model approach |
Microscopic studies of nuclear matter under diverse conditions of density and asymmetry are of great contemporary interest. Concerning terrestrial applications, they relate to future experimental facilities that will make it possible to study systems with extreme neutron-to-proton ratio. In this talk, I will review recent efforts of my group aimed at exploring nuclear interactions in the medium through the nuclear equation of state (EoS). The approach we take is microscopic and relativistic, with the predicted EoS properties derived from realistic nucleon-nucleon potentials. I will also discuss work in progress. Most recently, we completed a DBHF calculation of the $\Lambda$ hyperon binding energy in nuclear matter. | In-Medium Hadronic Interactions and the Nuclear Equation of State |
It is well known that observing CP violation in many-body decays could provide strong evidence for physics beyond the Standard Model. Many searches have been carried out; however, no 5sigma evidence for CP violation has yet been found in these types of decays. A novel model-independent method for observing CP violation in many-body decays is presented in this paper. It is shown that the sensitivity of this method is significantly larger than those used to-date. | Observing CP Violation in Many-Body Decays |
Unsupervised object discovery (UOD) refers to the task of discriminating the whole region of objects from the background within a scene without relying on labeled datasets, which benefits the task of bounding-box-level localization and pixel-level segmentation. This task is promising due to its ability to discover objects in a generic manner. We roughly categorise existing techniques into two main directions, namely the generative solutions based on image resynthesis, and the clustering methods based on self-supervised models. We have observed that the former heavily relies on the quality of image reconstruction, while the latter shows limitations in effectively modeling semantic correlations. To directly target at object discovery, we focus on the latter approach and propose a novel solution by incorporating weakly-supervised contrastive learning (WCL) to enhance semantic information exploration. We design a semantic-guided self-supervised learning model to extract high-level semantic features from images, which is achieved by fine-tuning the feature encoder of a self-supervised model, namely DINO, via WCL. Subsequently, we introduce Principal Component Analysis (PCA) to localize object regions. The principal projection direction, corresponding to the maximal eigenvalue, serves as an indicator of the object region(s). Extensive experiments on benchmark unsupervised object discovery datasets demonstrate the effectiveness of our proposed solution. The source code and experimental results are publicly available via our project page at https://github.com/npucvr/WSCUOD.git. | Weakly-supervised Contrastive Learning for Unsupervised Object Discovery |
In the present paper, we investigate the Sahlqvist-type correspondence theory for instantial neighbourhood logic (INL), which can talk about existential information about the neighbourhoods of a given world and is a mixture between relational semantics and neighbourhood semantics. We have two proofs of the correspondence results, the first proof is obtained by using standard translation and minimal valuation techniques directly, the second proof follows [4] and [6], where we use bimodal translation method to reduce the correspondence problem in instantial neighbourhood logic to normal bimodal logics in classical Kripke semantics. We give some remarks and future directions at the end of the paper. | Sahlqvist Correspondence Theory for Instantial Neighbourhood Logic |
The d-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean field theory for a two dimensional t-J model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no double occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\delta$ and $U$ are studied. Using the standard value of $t/J=3.0$ and in the large $U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\delta\sim0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\delta\sim0.15$. In the small $U$ limit, only the dSC order survives while the AF order disappears. As $U$ increased to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half filing, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean field approach, We show that the ground state energy of the coexistent state is always lower than that of the pure dSC state. | Study of gossamer superconductivity and antiferromagnetism in the t-J-U model |
We study the growth of dark matter halos in the concordance LCDM cosmology using several N-body simulations of large cosmological volumes. We build merger trees from the Millennium and Millennium-II simulations, covering a range 10^9-10^15 Msun in halo mass and 1-10^5 in merger mass ratio. Our algorithm takes special care of halo fragmentation and ensures that the mass contribution of each merger to halo growth is only counted once. This way the integrated merger rate converges and we can consistently determine the contribution of mergers of different mass ratios to halo growth. We find that all resolved mergers, up to mass ratios of 10^5, contribute only ~60% of the total halo mass growth, while major mergers are subdominant, e.g. mergers with mass ratios smaller than 3:1 (10:1) contribute only ~20% (~30%). This is verified with an analysis of two additional simulation boxes, where we follow all particles individually throughout cosmic time. Our results are also robust against using several halo definitions. Under the assumption that the power-law behaviour of the merger rate at large mass ratios can be extrapolated to arbitrarily large mass ratios, it is found that, independently of halo mass, ~40% of the mass in halos comes from genuinely smooth accretion of dark matter that was never bound in smaller halos. We discuss possible implications of our findings for galaxy formation. One implication, assuming as is standard that the pristine intergalactic medium is heated and photoionized by UV photons, is that all halos accrete >40% of their baryons in smooth "cold" T>~10^4K gas, rather than as warm, enriched or clumpy gas or as stars. | The growth of dark matter halos: evidence for significant smooth accretion |
Motivated by the striking ability of transformers for in-context learning, several works demonstrate that transformers can implement algorithms like gradient descent. By a careful construction of weights, these works show that multiple layers of transformers are expressive enough to simulate gradient descent iterations. Going beyond the question of expressivity, we ask: Can transformers learn to implement such algorithms by training over random problem instances? To our knowledge, we make the first theoretical progress toward this question via analysis of the loss landscape for linear transformers trained over random instances of linear regression. For a single attention layer, we prove the global minimum of the training objective implements a single iteration of preconditioned gradient descent. Notably, the preconditioning matrix not only adapts to the input distribution but also to the variance induced by data inadequacy. For a transformer with $k$ attention layers, we prove certain critical points of the training objective implement $k$ iterations of preconditioned gradient descent. Our results call for future theoretical studies on learning algorithms by training transformers. | Transformers learn to implement preconditioned gradient descent for in-context learning |
In this paper we consider the steepest descent L2-gradient flow of the entropy functional. The flow expands convex curves, with the radius of an initial circle growing like the square root of time. Our main result is that, for any initial curve (either immersed locally strictly convex of class $C^2$ or embedded of class $W^{2,2}$ bounding a strictly convex body), the flow converges smoothly to a round expanding multiply-covered circle. | The gradient flow for entropy on closed planar curves |
This paper deals with certain estimation problems involving the covariance matrix in large dimensions. Due to the breakdown of finite-dimensional asymptotic theory when the dimension is not negligible with respect to the sample size, it is necessary to resort to an alternative framework known as large-dimensional asymptotics. Recently, Ledoit and Wolf (2015) have proposed an estimator of the eigenvalues of the population covariance matrix that is consistent according to a mean-square criterion under large-dimensional asymptotics. It requires numerical inversion of a multivariate nonrandom function which they call the QuEST function. The present paper explains how to numerically implement the QuEST function in practice through a series of six successive steps. It also provides an algorithm to compute the Jacobian analytically, which is necessary for numerical inversion by a nonlinear optimizer. Monte Carlo simulations document the effectiveness of the code. | Numerical Implementation of the QuEST Function |
Object tracking becomes critical especially when similar objects are present in the same area. Recent state-of-the-art (SOTA) approaches are proposed based on taking a matching network with a heavy structure to distinguish the target from other objects in the area which indeed drastically downgrades the performance of the tracker in terms of speed. Besides, several candidates are considered and processed to localize the intended object in a region of interest for each frame which is time-consuming. In this article, a special architecture is proposed based on which in contrast to the previous approaches, it is possible to identify the object location in a single shot while taking its template into account to distinguish it from the similar objects in the same area. In brief, first of all, a window containing the object with twice the target size is considered. This window is then fed into a fully convolutional neural network (CNN) to extract a region of interest (RoI) in a form of a matrix for each of the frames. In the beginning, a template of the target is also taken as the input to the CNN. Considering this RoI matrix, the next movement of the tracker is determined based on a simple and fast method. Moreover, this matrix helps to estimate the object size which is crucial when it changes over time. Despite the absence of a matching network, the presented tracker performs comparatively with the SOTA in challenging situations while having a super speed compared to them (up to $120 FPS$ on 1080ti). To investigate this claim, a comparison study is carried out on the GOT-10k dataset. Results reveal the outstanding performance of the proposed method in fulfilling the task. | Single Object Tracking through a Fast and Effective Single-Multiple Model Convolutional Neural Network |
This paper addresses the problem of very large-scale image retrieval, focusing on improving its accuracy and robustness. We target enhanced robustness of search to factors such as variations in illumination, object appearance and scale, partial occlusions, and cluttered backgrounds - particularly important when search is performed across very large datasets with significant variability. We propose a novel CNN-based global descriptor, called REMAP, which learns and aggregates a hierarchy of deep features from multiple CNN layers, and is trained end-to-end with a triplet loss. REMAP explicitly learns discriminative features which are mutually-supportive and complementary at various semantic levels of visual abstraction. These dense local features are max-pooled spatially at each layer, within multi-scale overlapping regions, before aggregation into a single image-level descriptor. To identify the semantically useful regions and layers for retrieval, we propose to measure the information gain of each region and layer using KL-divergence. Our system effectively learns during training how useful various regions and layers are and weights them accordingly. We show that such relative entropy-guided aggregation outperforms classical CNN-based aggregation controlled by SGD. The entire framework is trained in an end-to-end fashion, outperforming the latest state-of-the-art results. On image retrieval datasets Holidays, Oxford and MPEG, the REMAP descriptor achieves mAP of 95.5%, 91.5%, and 80.1% respectively, outperforming any results published to date. REMAP also formed the core of the winning submission to the Google Landmark Retrieval Challenge on Kaggle. | REMAP: Multi-layer entropy-guided pooling of dense CNN features for image retrieval |
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical Bayes. The plug-in posterior squared-$L^2$ norm is shown to converge at the minimax rate for the euclidean norm for appropriate choices of spike and slab distributions. Possible choices include standard spike and slab with heavy tailed slab, and the spike and slab LASSO of Rockov\'a and George with heavy tailed slab. Surprisingly, the popular Laplace slab is shown to lead to a suboptimal rate for the full empirical Bayes posterior. This provides a striking example where convergence of aspects of the empirical Bayes posterior does not entail convergence of the full empirical Bayes posterior itself. | Empirical Bayes analysis of spike and slab posterior distributions |
The extragalactic background light (EBL) is the diffuse radiation with the second highest energy density in the Universe after the cosmic microwave background. The aim of this study is the measurement of the imprint of the EBL opacity to gamma-rays on the spectra of the brightest extragalactic sources detected with the High Energy Stereoscopic System (H.E.S.S.). The originality of the method lies in the joint fit of the EBL optical depth and of the intrinsic spectra of the sources, assuming intrinsic smoothness. Analysis of a total of ~10^5 gamma-ray events enables the detection of an EBL signature at the 8.8 std dev level and constitutes the first measurement of the EBL optical depth using very-high energy (E>100 GeV) gamma-rays. The EBL flux density is constrained over almost two decades of wavelengths (0.30-17 microns) and the peak value at 1.4 micron is derived as 15 +/- 2 (stat) +/- 3 (sys) nW / m^2 sr. | Measurement of the extragalactic background light imprint on the spectra of the brightest blazars observed with H.E.S.S |