Miracle-dz/UniFAR-FTUs huggingface dataset:
A Polynomial-Time Algorithm and Applications for Matrix Sampling from Harish-Chandra-Itzykson-Zuber Densities

Given two $n \times n$ Hermitian matrices $Y$ and $\Lambda$, the Harish-Chandra--Itzykson--Zuber (HCIZ) density on the unitary group $\mathrm{U}(n)$ is $e^{\mathrm{Tr}(U \Lambda U^*Y)}d\mu(U)$ where $\mu$ is the Haar measure on $\mathrm{U}(n)$. Random unitary matrices distributed according to the HCIZ density are important in various settings in physics and random matrix theory. However, the basic question of how to sample efficiently from the HCIZ density has remained open. The main contribution of this paper is an algorithm to sample a matrix from a distribution that is $\varepsilon$-close to the given HCIZ density and whose running time depends polylogarithmically on $1/\varepsilon$. Interestingly, HCIZ densities can also be viewed as exponential densities on $\mathrm{U}(n)$-orbits, and in this setting, they have been widely studied. Thus, our result has several direct applications, including polynomial-time algorithms 1) to sample from matrix Langevin distributions studied in statistics, 2) to sample from continuous maximum entropy distributions with applications to quantum inference, and 3) for differentially private low-rank approximation. The key obstacle in sampling from an HCIZ density is that the domain is an algebraic manifold and the entries of the sample matrix are highly correlated. To overcome this, we consider a mapping that sends each Hermitian matrix $X$ to a natural ordering of the eigenvalues of all leading principal minors of $X$. The image of each $\mathrm{U}(n)$-orbit under this map is a convex polytope, and the mapping reveals a recursive structure of $\mathrm{U}(n)$-orbits. Subsequently, we develop efficiently computable determinantal expressions for densities that arise in the intermediate steps of sampling from the polytope. Our proof-technique applies to other compact Lie groups and can be viewed as extending the widely studied notion of self-reducibility.
Asymptotically Optimal Information-Directed Sampling

We introduce a computationally efficient algorithm for finite stochastic linear bandits. The approach is based on the frequentist information-directed sampling (IDS) framework, with an information gain potential that is derived directly from the asymptotic regret lower bound. We establish frequentist regret bounds, which show that the proposed algorithm is both asymptotically optimal and worst-case rate optimal in finite time. Our analysis sheds light on how IDS trades off regret and information to incrementally solve the semi-infinite concave program that defines the optimal asymptotic regret. Along the way, we uncover interesting connections towards a recently proposed two-player game approach and the Bayesian IDS algorithm.
Self-supervised Segmentation via Background Inpainting

While supervised object detection and segmentation methods achieve impressive accuracy, they generalize poorly to images whose appearance significantly differs from the data they have been trained on. To address this when annotating data is prohibitively expensive, we introduce a self-supervised detection and segmentation approach that can work with single images captured by a potentially moving camera. At the heart of our approach lies the observation that object segmentation and background reconstruction are linked tasks, and that, for structured scenes, background regions can be re-synthesized from their surroundings, whereas regions depicting the moving object cannot. We encode this intuition into a self-supervised loss function that we exploit to train a proposal-based segmentation network. To account for the discrete nature of the proposals, we develop a Monte Carlo-based training strategy that allows the algorithm to explore the large space of object proposals. We apply our method to human detection and segmentation in images that visually depart from those of standard benchmarks and outperform existing self-supervised methods.
Non-stoichiometric amorphous magnesium-iron silicates in circumstellar dust shells

Aims. We study the growth of dust in oxygen-rich stellar outflows in order to find out to which extent dust growth models can quantitatively reconcile with the quantities and nature of dust as derived from observations of the infrared emission from circumstellar dust shells. Methods. We use a set of nine well-observed massive supergiants with optically thin dust shells as testbeds because of the relatively simple properties of the outflows from massive supergiants, contrary to the case of AGB stars. Models of the infrared emission from their circumstellar dust shells are compared to their observed infrared spectra to derive the essential parameters that rule dust formation in the extended envelope of these stars. The results are compared with a model for silicate dust condensation. Results. For all objects, the infrared emission in the studied wavelength range, between 6 and 25 μm, can be reproduced rather well by a mixture of non-stoichiometric iron-bearing silicates, alumina, and metallic iron dust particles. For three objects (μ Cep, RW Cyg, and RS Per), the observed spectra can be sufficiently well reproduced by a stationary and (essentially) spherically symmetric outflow in the instantaneous condensation approximation. For these objects, the temperature at the onset of massive silicate dust growth is of the order of 920 K and the corresponding outflow velocity of the order of the sound velocity. This condensation temperature is only somewhat below the vapourisation temperature of the silicate dust and suggests that the silicate dust grows on the corundum dust grains that formed well inside of the silicate dust shell at a much higher temperature. The low expansion velocity at the inner edge of the silicate dust shell further suggests that, for these supergiants, the region inside the silicate dust shell has an only subsonic average expansion velocity, though a high degree of supersonic turbulence is indicated by the widths of spectral lines. Conclusions. Our results suggest that for the two major problems of dust formation in stellar outflows, that is (i) formation of seed nuclei and (ii) their growth to macroscopic dust grains, we are gradually coming close to a quantitative understanding of the second item.
Position-based Scaled Gradient for Model Quantization and Pruning

We propose the position-based scaled gradient (PSG) that scales the gradient depending on the position of a weight vector to make it more compression-friendly. First, we theoretically show that applying PSG to the standard gradient descent (GD), which is called PSGD, is equivalent to the GD in the warped weight space, a space made by warping the original weight space via an appropriately designed invertible function. Second, we empirically show that PSG acting as a regularizer to a weight vector is favorable for model compression domains such as quantization and pruning. PSG reduces the gap between the weight distributions of a full-precision model and its compressed counterpart. This enables the versatile deployment of a model either as an uncompressed mode or as a compressed mode depending on the availability of resources. The experimental results on CIFAR-10/100 and ImageNet datasets show the effectiveness of the proposed PSG in both domains of pruning and quantization even for extremely low bits. The code is released in Github.
A deep-learning classifier for cardiac arrhythmias

We report on a method that classifies heart beats according to a set of 13 classes, including cardiac arrhythmias. The method localises the QRS peak complex to define each heart beat and uses a neural network to infer the patterns characteristic of each heart beat class. The best performing neural network contains six one-dimensional convolutional layers and four dense layers, with the kernel sizes being multiples of the characteristic scale of the problem, thus resulting a computationally fast and physically motivated neural network. For the same number of heart beat classes, our method yields better results with a considerably smaller neural network than previously published methods, which renders our method competitive for deployment in an internet-of-things solution.
Detecting Adversarial Patches with Class Conditional Reconstruction Networks

Defending against physical adversarial attacks is a rapidly growing topic in deep learning and computer vision. Prominent forms of physical adversarial attacks, such as overlaid adversarial patches and objects, share similarities with digital attacks, but are easy for humans to notice. This leads us to explore the hypothesis that adversarial detection methods, which have been shown to be ineffective against adaptive digital adversarial examples, can be effective against these physical attacks. We use one such detection method based on autoencoder architectures, and perform adversarial patching experiments on MNIST, SVHN, and CIFAR10 against a CNN architecture and two CapsNet architectures. We also propose two modifications to the EM-Routed CapsNet architecture, Affine Voting and Matrix Capsule Dropout, to improve its classification performance. Our investigation shows that the detector retains some of its effectiveness even against adaptive adversarial patch attacks. In addition, detection performance tends to decrease among all the architectures with the increase of dataset complexity.
Regularization of Persistent Homology Gradient Computation

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In order for a given computation to be integrated in such a way, the computation in question must be differentiable. Computing the gradients of persistent homology is an ill-posed inverse problem with infinitely many solutions. Consequently, it is important to perform regularization so that the solution obtained agrees with known priors. In this work we propose a novel method for regularizing persistent homology gradient computation through the addition of a grouping term. This has the effect of helping to ensure gradients are defined with respect to larger entities and not individual points.
Empirical Risk Minimization in the Non-interactive Local Model of Differential Privacy

In this paper, we study the Empirical Risk Minimization (ERM) problem in the non-interactive Local Differential Privacy (LDP) model. Previous research on this problem \citep{smith2017interaction} indicates that the sample complexity, to achieve error $\alpha$, needs to be exponentially depending on the dimensionality $p$ for general loss functions. In this paper, we make two attempts to resolve this issue by investigating conditions on the loss functions that allow us to remove such a limit. In our first attempt, we show that if the loss function is $(\infty, T)$-smooth, by using the Bernstein polynomial approximation we can avoid the exponential dependency in the term of $\alpha$. We then propose player-efficient algorithms with $1$-bit communication complexity and $O(1)$ computation cost for each player. The error bound of these algorithms is asymptotically the same as the original one. With some additional assumptions, we also give an algorithm which is more efficient for the server. In our second attempt, we show that for any $1$-Lipschitz generalized linear convex loss function, there is an $(\epsilon, \delta)$-LDP algorithm whose sample complexity for achieving error $\alpha$ is only linear in the dimensionality $p$. Our results use a polynomial of inner product approximation technique. Finally, motivated by the idea of using polynomial approximation and based on different types of polynomial approximations, we propose (efficient) non-interactive locally differentially private algorithms for learning the set of k-way marginal queries and the set of smooth queries.
A combinatorial translation principle for the general linear group

Let k be an algebraically closed field of characteristic p>0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under the assumption that p is bigger than the greatest hook length in the partitions involved. Then we introduce and study the rational Schur functor from a category of GL_n-modules to the category of modules for the walled Brauer algebra. As a corollary we obtain the decomposition numbers for the walled Brauer algebra when $p$ is bigger than the greatest hook length in the partitions involved. This is a sequel to an earlier paper on the symplectic group and the Brauer algebra.
Evidence for Hierarchical Black Hole Mergers in the Second LIGO–Virgo Gravitational Wave Catalog

We study the population properties of merging binary black holes in the second LIGO–Virgo Gravitational-Wave Transient Catalog assuming they were all formed dynamically in gravitationally bound clusters. Using a phenomenological population model, we infer the mass and spin distribution of first-generation black holes, while self-consistently accounting for hierarchical mergers. Considering a range of cluster masses, we see compelling evidence for hierarchical mergers in clusters with escape velocities ≳100 km s−1. For our most probable cluster mass, we find that the catalog contains at least one second-generation merger with 99% credibility. We find that the hierarchical model is preferred over an alternative model with no hierarchical mergers (Bayes factor >1400 ) and that GW190521 is favored to contain two second-generation black holes with odds >700 , and GW190519, GW190602, GW190620, and GW190706 are mixed-generation binaries with >10 . However, our results depend strongly on the cluster escape velocity, with more modest evidence for hierarchical mergers when the escape velocity is ≲100 km s−1. Assuming that all binary black holes are formed dynamically in globular clusters with escape velocities on the order of tens of km s−1, GW190519 and GW190521 are favored to include a second-generation black hole with odds >1 . In this case, we find that 99% of black holes from the inferred total population have masses that are less than 49M ⊙, and that this constraint is robust to our choice of prior on the maximum black hole mass.
Subtle connection between shape coexistence and quantum phase transition: The Zr case

Background: Zr region is characterized by very rapid changes in the ground state structure of the nuclei. In particular, the onset of deformation when passing from $^{98}$Zr to $^{100}$Zr is one of the fastest ever observed in the nuclear chart. It has been probed both experimental and theoretically that certain low-lying excited states of Zr isotopes own different shapes than the ground state. Purpose: We intend to disentangle the interplay between the sudden changes in the ground state shape, i.e., the existence of a quantum phase transition, and the presence in the spectra of coexisting states with very different deformation, i.e., the presence of shape coexistence. Method: We rely on a previous calculation using the Interacting Boson Model with Configuration Mixing (IBM-CM) which reproduces in detail the spectroscopic properties of $^{96-110}$Zr. This IBM-CM calculation allows to compute mean-field energy surfaces, wave functions and any other observable related with the presence of shape coexistence or with a quantum phase transition. Results: We obtain energy surfaces and the equilibrium value of the deformation parameter $\beta$, the U(5) decomposition of the wave functions and the density of states. Conclusions: We confirm that Zr is a clear example of quantum phase transition that originates from the crossing of two configurations with a very different degree of deformation. Moreover, we observe how the intruder configuration exhibits its own evolution which resembles a quantum phase transition too.
The Role of the Crowd in Countering Misinformation: A Case Study of the COVID-19 Infodemic

Fact checking by professionals is viewed as a vital defense in the fight against misinformation. While fact checking is important and its impact has been significant, fact checks could have limited visibility and may not reach the intended audience, such as those deeply embedded in polarized communities. Concerned citizens (i.e., the crowd), who are users of the platforms where misinformation appears, can play a crucial role in disseminating fact-checking information and in countering the spread of misinformation. To explore if this is the case, we conduct a data-driven study of misinformation on the Twitter platform, focusing on tweets related to the COVID-19 pandemic, analyzing the spread of misinformation, professional fact checks, and the crowds response to popular misleading claims about COVID-19.In this work, we curate a dataset of false claims and statements that seek to challenge or refute them. We train a classifier to create a novel dataset of 155,468 COVID-19-related tweets, containing 33,237 false claims and 33,413 refuting arguments. Our findings show that professional fact-checking tweets have limited volume and reach. In contrast, we observe that the surge in misinformation tweets results in a quick response and a corresponding increase in tweets that refute such misinformation. More importantly, we find contrasting differences in the way the crowd refutes tweets, some tweets appear to be opinions, while others contain concrete evidence, such as a link to a reputed source. Our work provides insights into how misinformation is organically countered in social platforms by some of their users and the role they play in amplifying professional fact checks. These insights could lead to development of tools and mechanisms that can empower concerned citizens in combating misinformation. The code and data can be found in this link.1
Flavor mixing and renormalization in a perturbation theory

The renormalization of theories with flavor mixing is discussed, and it is shown that the physical unstable particles should be interpreted as quasiparticles which cannot be regarded as external states. Several popular beliefs on renormalization are disproved accordingly, and the limitations of physical renormalization schemes are discussed. In addition, the properties of unstable particles with flavor mixing such as decay widths are studied from scattering mediated by them.
New measurements of the cyclotron line energy in Cen X-3

We report results from the analysis of data from two observations of the accreting binary X-ray pulsar Cen X-3 carried out with the broadband X-ray observatories Suzaku and NuSTAR. The pulse profile is dominated by a broad single peak and show some energy dependence with two additional weak pulse peaks at energies below 15 and 25 keV respectively. The broadband X-ray spectrum for 0.8-60.0 keV for Suzaku and 3.0-60.0 keV for NuSTAR is fitted well with high energy cut-off power-law model along with soft-excess, multiple iron emission lines and a cyclotron absorption. The cyclotron line energy is found to be $30.29^{+0.68}_{-0.61}$ keV and $29.22^{+0.28}_{-0.27}$ keV respectively in the Suzaku and NuSTAR spectra. We make a comparison of these two measurements with four previous measurements of CRSF in Cen X-3 obtained with Ginga, BeppoSAX and RXTE. We find no evidence for a dependence of the CRSF on luminosity. Except for one CRSF measurement with BeppoSAX, the remaining measurements are consistent with a CRSF energy in the range of 29.5 - 30.0 keV over a luminosity range of 1.1-5.4 $\times 10^{37}$ ergs s$^{-1}$ different from several other sources that show considerable CRSF variation in the same luminosity range.
On a general matrix valued unbalanced optimal transport and its fully discretization: dynamic formulation and convergence framework

In this work, we present a rather general class of transport distances over the space of positive semidefinite matrix valued Radon measures, called the weighted Wasserstein Bures distance, and consider the convergence property of their fully discretized counterparts. These distances are defined via a generalization of Benamou Brenier formulation of the quadratic optimal transport, based on a new weighted action functional and an abstract matricial continuity equation. It gives rise to a convex optimization problem. We shall give a complete characterization of its minimizer (i.e., the geodesic) and discuss some topological and geometrical properties of these distances. Some recently proposed models: the interpolation distance by Chen et al. [18] and the Kantorovich Bures distance by Brenier et al. [11], as well as the well studied Wasserstein Fisher Rao distance [43, 19, 40], fit in our model. The second part of this work is devoted to the numerical analysis of the fully discretization of the new transport model. We reinterpret the convergence framework proposed very recently by Lavenant [41] for the quadratic optimal transport from the perspective of Lax equivalence theorem and extend it to our general problem. In view of this abstract framework, we suggest a concrete fully discretized scheme inspired by the finite element theory, and show the unconditional convergence under mild assumptions. In particular, these assumptions are removed in the case of Wasserstein Fisher Rao distance due to the existence of a static formulation.
Deep Transfer Learning-Assisted Signal Detection for Ambient Backscatter Communications

Existing tag signal detection algorithms inevitably suffer from a high bit error rate (BER) due to the difficulties in estimating the channel state information (CSI). To eliminate the requirement of channel estimation and to improve the system performance, in this paper, we adopt a deep transfer learning (DTL) approach to implicitly extract the features of communication channel and directly recover tag symbols. Inspired by the powerful capability of convolutional neural networks (CNN) in exploring the features of data in a matrix form, we design a novel covariance matrix aware neural network (CMNet)-based detection scheme to facilitate DTL for tag signal detection, which consists of offline learning, transfer learning, and online detection. Specifically, a CMNet-based likelihood ratio test (CMNet-LRT) is derived based on the minimum error probability (MEP) criterion. Taking advantage of the outstanding performance of DTL in transferring knowledge with only a few training data, the proposed scheme can adaptively fine-tune the detector for different channel environments to further improve the detection performance. Finally, extensive simulation results demonstrate that the BER performance of the proposed method is comparable to that of the optimal detection method with perfect CSI.