Miracle-dz/UniFAR-FTUs huggingface dataset:
Near-Additive Spanners and Near-Exact Hopsets, A Unified View

Given an {\em unweighted} undirected graph $G = (V,E)$, and a pair of parameters $\epsilon > 0$, $\beta = 1,2,\ldots$, a subgraph $G' =(V,H)$, $H \subseteq E$, of $G$ is a {\em $(1+\epsilon,\beta)$-spanner} (aka, a {\em near-additive spanner}) of $G$ if for every $u,v \in V$, $$d_{G'}(u,v) \le (1+\epsilon)d_G(u,v) + \beta~. $$ It was shown in \cite{EP01} that for any $n$-vertex $G$ as above, and any $\epsilon > 0$ and $\kappa = 1,2,\ldots$, there exists a $(1+\epsilon,\beta)$-spanner $G'$ with $O_{\epsilon,\kappa}(n^{1+1/\kappa})$ edges, with $$\beta = \beta_{EP} = \left({{\log \kappa} \over \epsilon}\right)^{\log \kappa - 2}~. $$ This bound remains state-of-the-art, and its dependence on $\epsilon$ (for the case of small $\kappa$) was shown to be tight in \cite{ABP18}. Given a {\em weighted} undirected graph $G = (V,E,\omega)$, and a pair of parameters $\epsilon > 0$, $\beta = 1,2,\ldots$, a graph $G'= (V,H,\omega')$ is a {\em $(1+\epsilon,\beta)$-hopset} (aka, a {\em near-exact hopset}) of $G$ if for every $u,v \in V$, $$d_G(u,v) \le d_{G\cup G'}^{(\beta)}(u,v) \le (1+\epsilon)d_G(u,v)~,$$ where $ d_{G\cup G'}^{(\beta)}(u,v)$ stands for a $\beta$-(hop)-bounded distance between $u$ and $v$ in the union graph $G \cup G'$. It was shown in \cite{EN16} that for any $n$-vertex $G$ and $\epsilon$ and $\kappa$ as above, there exists a $(1+\epsilon,\beta)$-hopset with $\tilde{O}(n^{1+1/\kappa})$ edges, with $\beta = \beta_{EP}$. Not only the two results of \cite{EP01} and \cite{EN16} are strikingly similar, but so are also their proof techniques. Moreover, Thorup-Zwick's later construction of near-additive spanners \cite{TZ06} was also shown in \cite{EN19,HP17} to provide hopsets with analogous (to that of \cite{TZ06}) properties. In this survey we explore this intriguing phenomenon, sketch the basic proof techniques used for these results, and highlight open questions.
Superresolution in Recovering Embedded Electromagnetic Sources in High Contrast Media

The purpose of this work is to provide a rigorous mathematical analysis of the expected super-resolution phenomenon in the time-reversal imaging of electromagnetic (EM) radiating sources embedded in a high contrast medium. It is known that the resolution limit is essentially determined by the sharpness of the imaginary part of the EM Green's tensor for the associated background. We first establish the close connection between the resolution and the material parameters and the resolvent of the electric integral operator, via the Lippmann-Schwinger representation formula. We then present an insightful characterization of the spectral structure of the integral operator for a general bounded domain and derive the pole-pencil decomposition of its resolvent in the high contrast regime. For the special case of a spherical domain, we provide some quantitative asymptotic behavior of the eigenvalues and eigenfunctions. These mathematical findings shall enable us to provide a concise and rigorous illustration of the super-resolution in the EM source reconstruction in high contrast media. Some numerical examples are also presented to verify our main theoretical results.
Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model

The analysis of level statistics provides a primary method to detect signatures of chaos in the quantum domain. However, for experiments with ion traps and cold atoms, the energy levels are not as easily accessible as the dynamics. In this work, we discuss how properties of the spectrum that are usually associated with chaos can be directly detected from the evolution of the number operator in the one-dimensional, noninteracting Aubry-André model. Both the quantity and the model are studied in experiments with cold atoms. We consider a single-particle and system sizes experimentally reachable. By varying the disorder strength within values below the critical point of the model, level statistics similar to those found in random matrix theory are obtained. Dynamically, these properties of the spectrum are manifested in the form of a dip below the equilibration point of the number operator. This feature emerges at times that are experimentally accessible. This work is a contribution to a special issue dedicated to Shmuel Fishman.
Zero-divisors and idempotents in quandle rings

The paper develops further the theory of quandle rings which was introduced by the authors in a recent work. Orderability of quandles is defined and many interesting examples of orderable quandles are given. It is proved that quandle rings of left or right orderable quandles which are semi-latin have no zero-divisors. Idempotents in quandle rings of certain interesting quandles are computed and used to determine sets of maximal quandles in these rings. Understanding of idempotents is further applied to determine automorphism groups of these quandle rings. Also, commutator width of quandle rings is introduced and computed in a few cases. The paper conclude by commenting on relation of quandle rings with other well-known non-associative algebras.
The Incentives that Shape Behaviour

Which variables does an agent have an incentive to control with its decision, and which variables does it have an incentive to respond to? We formalise these incentives, and demonstrate unique graphical criteria for detecting them in any single decision causal influence diagram. To this end, we introduce structural causal influence models, a hybrid of the influence diagram and structural causal model frameworks. Finally, we illustrate how these incentives predict agent incentives in both fairness and AI safety applications.
Structural analysis of an L-infinity variational
problem and relations to distance functions

In this work we analyse the functional ${\cal J}(u)=\|\nabla u\|_\infty$ defined on Lipschitz functions with homogeneous Dirichlet boundary conditions. Our analysis is performed directly on the functional without the need to approximate with smooth $p$-norms. We prove that its ground states coincide with multiples of the distance function to the boundary of the domain. Furthermore, we compute the $L^2$-subdifferential of ${\cal J}$ and characterize the distance function as unique non-negative eigenfunction of the subdifferential operator. We also study properties of general eigenfunctions, in particular their nodal sets. Furthermore, we prove that the distance function can be computed as asymptotic profile of the gradient flow of ${\cal J}$ and construct analytic solutions of fast marching type. In addition, we give a geometric characterization of the extreme points of the unit ball of ${\cal J}$. Finally, we transfer many of these results to a discrete version of the functional defined on a finite weighted graph. Here, we analyze properties of distance functions on graphs and their gradients. The main difference between the continuum and discrete setting is that the distance function is not the unique non-negative eigenfunction on a graph.
Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications

The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning, sparse blind deconvolution, and many other problems in signal processing and machine learning. However, in contrast to the classical sparse recovery problem, the most natural formulation for finding the sparsest vector in a subspace is usually nonconvex. In this paper, we overview recent advances on global nonconvex optimization theory for solving this problem, ranging from geometric analysis of its optimization landscapes, to efficient optimization algorithms for solving the associated nonconvex optimization problem, to applications in machine intelligence, representation learning, and imaging sciences. Finally, we conclude this review by pointing out several interesting open problems for future research.
Gated Path Selection Network for Semantic Segmentation

Semantic segmentation is a challenging task that needs to handle large scale variations, deformations, and different viewpoints. In this paper, we develop a novel network named Gated Path Selection Network (GPSNet), which aims to adaptively select receptive fields while maintaining the dense sampling capability. In GPSNet, we first design a two-dimensional SuperNet, which densely incorporates features from growing receptive fields. And then, a Comparative Feature Aggregation (CFA) module is introduced to dynamically aggregate discriminative semantic context. In contrast to previous works that focus on optimizing sparse sampling locations on regular grids, GPSNet can adaptively harvest free form dense semantic context information. The derived adaptive receptive fields and dense sampling locations are data-dependent and flexible which can model various contexts of objects. On two representative semantic segmentation datasets, i.e., Cityscapes and ADE20K, we show that the proposed approach consistently outperforms previous methods without bells and whistles.
Chaotic D1-D5 Black Hole Dynamics through Networks

This work studies dynamics controlling the transition between different microstates of two charge D1-D5 black holes by network methods, in which microstates of the system are defined as network nodes, while transitions between them are defined as edges. It is found that the eigenspectrum of this network's Laplacian matrix, which is identified with Hamiltonians of the microstate system, has completely the same Nearest-Neighbor Spacing Distribution as that of general Gaussian Orthogonal Ensemble of Random Matrices. According to the BGS, i.e. Bohigas, Giannoni and Schmit conjecture, this forms evidence for chaotic features of the D1-D5 microstate dynamics. This evidence is further strengthened by observations that inverse of the first/minimal nonzero eigenvalue of the Laplacian matrix is proportional to logarithms of the microstate number of the system. By Sekino and Susskind, this means that dynamics of the D1-D5 black hole microstates are not only chaotic, but also the fastest scrambler in nature.
A proof of Sørensen’s conjecture on Hermitian surfaces

<p>In this article we prove a conjecture formulated by A. B. Sørensen in 1991 on the maximal number of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="double-struck upper F Subscript q squared"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">F</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">\mathbb {F}_{q^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-rational points on the intersection of a non-degenerate Hermitian surface and a surface of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="d less-than-or-equal-to q period"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≤<! -- ≤ --></mml:mo> <mml:mi>q</mml:mi> <mml:mo>. </mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">d \le q. </mml:annotation> </mml:semantics> </mml:math> </inline-formula></p>
Prevalence and Trends of HIV, Syphilis, and HCV in Migrant and Resident Men Who Have Sex with Men in Shandong, China: Results from a Serial Cross-Sectional Study

Background Migrant men who have sex with men (MSM) have a higher predisposition for HIV transmission. We aimed to determine and compare the prevalence and trends of HIV, Syphilis, and HCV between migrant and resident MSM in Shandong, China. Methods A serial cross-sectional study was conducted in eight cities in Shandong, China from 2010 to 2014. The surveys collected information on demographics, HIV-related knowledge, and HIV-related behaviors including the serologic status of HIV, syphilis, and HCV. Bivariate and multivariable logistic regressions were used to determine differences between migrant and resident MSM. Results The overall prevalence of HIV among the 15,705 MSM (14120 were resident, 1580 were migrant and 5 were missing) was 2.6%, with an increase of 1.0% in 2010 to 4.4% in 2014. Prevalence of HIV was higher among migrant MSMs (5.5%) compared to resident MSMs (2.3%). Compared to residents, migrants also had higher prevalence of syphilis (7.5% vs 4.9%) and HCV (1.1% vs 0.6%). We found that there was an increase in the proportion of migrant MSM engaging in anal sex [adjusted OR (AOR) = 1.41 in migrants vs 1.12 in residents], condom use during last anal sex (AOR = 1.14 in residents, P for trend = 0.32), consistent condom use (AOR = 1.04 residents, P for trend = 0.11) and drug use (AOR = 1.51 in migrants and 1.29 among residents). Except in the year 2011, receiving some health services in last year was significant for people who were HIV-positive compared to negative. (P for trend <0.05). Conclusions Prevalence of HIV increased in resident as well as migrant MSMs. The migrant MSMs had higher STIs compared to resident MSMs and therefore, should be targeted for effective interventions aimed at reducing their risk behaviors. Deeper understanding of the role of migration in health issues is required for combating the persistently high and gradually increasing HIV burden in MSM in China.
Discrete Variational Methods and Symplectic Generalized Additive Runge-Kutta Methods

We consider a Lagrangian system $L(q,\dot q) = \sum_{l=1}^{N}L^{\{l\}}(q,\dot q)$, where the $q$-variable is treated by a Generalized Additive Runge--Kutta (GARK) method. Applying the technique of discrete variations, we show how to construct symplectic schemes. Assuming the diagonal methods for the GARK given, we present some techinques for constructing the transition matrices. We address the problem of the order of the methods and discuss some semi-separable and separable problems, showing some interesting constructions of methods with non-square coefficient matrices.
A Trend in the Effective Spin Distribution of LIGO Binary Black Holes with Mass

Binary black holes (BBHs) detected by gravitational wave (GW) observations could be broadly divided into two formation channels: those formed through field binary evolution and those assembled dynamically in dense stellar systems. Each of these formation channels, and their subchannels, populate a distinct region in the effective spin–mass ( ) plane. Depending on the branching ratio of different channels, an ensemble of BBHs could show a trend in this plane. Here we fit a mass-dependent distribution for to the GWTC-1 BBHs from the first and second observing runs of Advanced LIGO and Advanced Virgo. We find a negative correlation between mass and the mean effective spin ( ), and positive correlation with its dispersion ( ) at 75% and 80% confidence. This trend is robust against the choice of mass variable, but most pronounced when the mass variable is taken to be the chirp mass of the binary. The result is consistent with significant contributions from both dynamically assembled and field binaries in the GWTC-1 catalog. The upcoming LIGO O3a data release will critically test this interpretation.
Convolutional Neural Networks as a Model of the Visual System: Past, Present, and Future

Abstract Convolutional neural networks (CNNs) were inspired by early findings in the study of biological vision. They have since become successful tools in computer vision and state-of-the-art models of both neural activity and behavior on visual tasks. This review highlights what, in the context of CNNs, it means to be a good model in computational neuroscience and the various ways models can provide insight. Specifically, it covers the origins of CNNs and the methods by which we validate them as models of biological vision. It then goes on to elaborate on what we can learn about biological vision by understanding and experimenting on CNNs and discusses emerging opportunities for the use of CNNs in vision research beyond basic object recognition.
A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications

Generative adversarial networks (GANs) have recently become a hot research topic; however, they have been studied since 2014, and a large number of algorithms have been proposed. Nevertheless, few comprehensive studies explain the connections among different GAN variants and how they have evolved. In this paper, we attempt to provide a review of the various GAN methods from the perspectives of algorithms, theory, and applications. First, the motivations, mathematical representations, and structures of most GAN algorithms are introduced in detail, and we compare their commonalities and differences. Second, theoretical issues related to GANs are investigated. Finally, typical applications of GANs in image processing and computer vision, natural language processing, music, speech and audio, the medical field, and data science are discussed.
Single photon emission from droplet epitaxial quantum dots in the standard telecom window around a wavelength of 1.55 μm

We study the luminescence dynamics of telecom wavelength InAs quantum dots grown on InP(111)A by droplet epitaxy. The use of the ternary alloy InAlGaAs as a barrier material leads to photon emission in the 1.55 μm telecom C-band. The luminescence decay is well described in terms of the theoretical interband transition strength without the impact of nonradiative recombination. The intensity autocorrelation function shows clear anti-bunching photon statistics. The results suggest that our quantum dots are useful for constructing a practical source of single photons and quantum entangled photon pairs.
A Multiwavelength Study of the γ-Ray Binary Candidate HESS J1832–093

We investigate the nature of the unidentified very-high-energy γ-ray object, HESS J1832–093, in a multiwavelength context. Based on X-ray variability and spectral index ( ), and its broadband spectrum, which was remarkably similar to that of HESS J0632+057—a confirmed γ-ray binary—HESS J1832–093 has been considered a strong γ-ray binary candidate in previous works. In this work, we provide further evidence for this scenario. We obtained a spectrum of its IR counterpart using Gemini/Flamingo, finding absorption lines that are usually seen in massive stars, in particular O stars. We also obtained a rather steep ATCA spectrum ( ), which is consistent with a γ-ray binary. Based on spatial-spectral analysis and variability search, we found that 4FGL J1832.9-0913 is possibly associated with SNR G22.7-0.2 rather than with HESS J1832–093 only.
Robust skyrmion-bubble textures in 
SrRuO3
 thin films stabilized by magnetic anisotropy

Topological spin textures in an itinerant ferromagnet, SrRuO$_3$ is studied combining Hall transport measurements and numerical simulations. We observe characteristic signatures of the Topological Hall Effect associated with skyrmions. A relatively large thickness of our films and absence of heavy metal layers make the interfacial Dzyaloshinskii-Moriya interaction an unlikely source of these topological spin textures. Additionally, the transport anomalies exhibit an unprecedented robustness to magnetic field tilting and temperature. Our numerical simulations suggest that this unconventional behavior results from magnetic bubbles with skyrmion topology stabilized by magnetodipolar interactions in an unexpected region of parameter space.
Towards Stabilizing Batch Statistics in Backward Propagation of Batch Normalization

Batch Normalization (BN) is one of the most widely used techniques in Deep Learning field. But its performance can awfully degrade with insufficient batch size. This weakness limits the usage of BN on many computer vision tasks like detection or segmentation, where batch size is usually small due to the constraint of memory consumption. Therefore many modified normalization techniques have been proposed, which either fail to restore the performance of BN completely, or have to introduce additional nonlinear operations in inference procedure and increase huge consumption. In this paper, we reveal that there are two extra batch statistics involved in backward propagation of BN, on which has never been well discussed before. The extra batch statistics associated with gradients also can severely affect the training of deep neural network. Based on our analysis, we propose a novel normalization method, named Moving Average Batch Normalization (MABN). MABN can completely restore the performance of vanilla BN in small batch cases, without introducing any additional nonlinear operations in inference procedure. We prove the benefits of MABN by both theoretical analysis and experiments. Our experiments demonstrate the effectiveness of MABN in multiple computer vision tasks including ImageNet and COCO.
Čech cohomology, homoclinic trajectories and robustness of non-saddle sets

In this paper we study flows $\varphi:M\times\mathbb{R}\longrightarrow M$ having an isolated non-saddle set. We see that the complexity of the region of influence of an isolated non-saddle set $K$ depends on the way in which $K$ sits on the phase space at the cohomological level. We construct flows in surfaces having isolated non-saddle sets with a prescribed structure for its region of influence. We also study parametrized families of smooth flows and continuations of non-saddle sets.
Generalizable Adversarial Attacks with Latent Variable Perturbation Modelling

Adversarial attacks on deep neural networks traditionally rely on a constrained optimization paradigm, where an optimization procedure is used to obtain a single adversarial perturbation for a given input example. In this work we frame the problem as learning a distribution of adversarial perturbations, enabling us to generate diverse adversarial distributions given an unperturbed input. We show that this framework is domain-agnostic in that the same framework can be employed to attack different input domains with minimal modification. Across three diverse domains---images, text, and graphs---our approach generates whitebox attacks with success rates that are competitive with or superior to existing approaches, with a new state-of-the-art achieved in the graph domain. Finally, we demonstrate that our framework can efficiently generate a diverse set of attacks for a single given input, and is even capable of attacking \textit{unseen} test instances in a zero-shot manner, exhibiting attack generalization.
Gravity in the infrared and effective nonlocal models

We provide a systematic and updated discussion of a research line carried out by our group over the last few years, in which gravity is modified at cosmological distances by the introduction of nonlocal terms, assumed to emerge at an effective level from the infrared behavior of the quantum theory. The requirement of producing a viable cosmology turns out to be very stringent and basically selects a unique model, in which the nonlocal term describes an effective mass for the conformal mode. We discuss how such a specific structure could emerge from a fundamental local theory of gravity, and we perform a detailed comparison of this model with the most recent cosmological datasets, confirming that it fits current data at the same level as ΛCDM. Most notably, the model has striking predictions in the sector of tensor perturbations, leading to a very large effect in the propagation of gravitational wave (GWs) over cosmological distances. At the redshifts relevant for the next generation of GW detectors such as Einstein Telescope, Cosmic Explorer and LISA, this leads to deviations from GR that could be as large as 80%, and could be verified with the detection of just a single coalescing binary with electromagnetic counterpart. This would also have potentially important consequences for the search of the counterpart since, for a given luminosity distance to the source, as inferred through the GW signal, the actual source redshift could be significantly different from that predicted by ΛCDM. At the redshifts relevant for advanced LIGO/Virgo/Kagra the effect is smaller, but still potentially observable over a few years of runs at target sensitivity.