Miracle-dz/UniFAR-FTUs huggingface dataset:
Learning Product Graphs From Spectral Templates

Graph Learning (GL) is at the core of leveraging connections in machine learning (ML). By observing a dataset of graph signals and considering specific assumptions, Graph Signal Processing (GSP) provides practical constraints in GL. Inferring a graph with desired frequency signatures, i.e., spectral templates, from stationary graph signals has gained great attention. However, a severe computational burden is a challenging barrier, especially for inference from high-dimensional product graph signals, i.e., graph signals live on the product of smaller factor graphs. Few product GL methods have been proposed for mostly inference with smoothness assumption, while they are limited to learning only two factor graphs, handle only the Cartesian products, and have not addressed GL with desired spectral templates. To bridge the mentioned gaps, we propose a method for learning product graphs from product graph signals in which the product GL problem can be broken into separated optimizations associated with each (significantly smaller) factor graph. Besides, unlike the current approaches, our method can learn from any type of product graph (possibly with more than two factor graphs) without needing to know the type of graph products beforehand, and with significantly reduced complexity than learning directly from product graph signals. In addition to devising theoretical sufficient recovery conditions and validating them numerically, experimental results on synthetic and real-world data, i.e., multi-view image and brain signal analysis, illustrate meaningful factor graphs supported by expert-related research and also superiority over the current methods for learning from spectral templates. The implementation codes are available at https://github.com/ArefEinizade2/ProdSpecTemp
On Minimal Variations for Unsupervised Representation Learning

Unsupervised representation learning aims at describing raw data efficiently to solve various downstream tasks. It has been approached with many techniques, such as manifold learning, diffusion maps, or more recently self-supervised learning. Those techniques are arguably all based on the underlying assumption that target functions, associated with future downstream tasks, have low variations in densely populated regions of the input space. Our main contribution is to unveil minimal variations as a guiding principle behind unsupervised representation learning paves the way to better practical guidelines for self-supervised learning algorithms.
The proper characteristics of frame reference as a 4-invariants

The paper derived 4-dimensional equation for the proper characteristics of the rigid frame of reference. From these conditions it follows the laws of motion of its proper tetrad and inverse kinematics equation, i. e. , differential equations, which solves the problem of recovering the parameters of the motion of rigid frame of reference for their proper acceleration and angular velocity. In particular it is shown that the commission boost the moving frame of reference having Thomas precession for a new laboratory system will have a combination of two rotations: a new self-Thomas precession and rotation Wigner, which combine to give an initial frequency of the Thomas precession.
Hierarchical Feedback Control for Complex Hybrid Models of Multiagent Legged Robotic Systems

This paper presents a hierarchical feedback control strategy for complex hybrid systems that represent collaborative multiagent legged robotic systems with arms for manipulating an object. We develop high-dimensional hybrid models, including continuous- and discrete-time dynamics, for multiagent legged systems. Each agent has its own baseline controller to produce an exponentially stable legged locomotion pattern. For the manipulating purpose of the object, a two-level control strategy is proposed. At the higher level, a model predictive control based convex quadratic programming (QP) computes the required forces to be generated by the end effectors (EEs). The lower-level controllers are then set up based on convex QPs to refine the baseline controllers while generating the prescribed forces at the EEs. Two different strategies for the deployment of the lower-level controllers, including centralized and decentralized algorithms, are proposed. The power of the control algorithms is finally illustrated on an extensive numerical simulation of two quadruped agents (Vision 60 robots) with Kinova arms to steer an object for which the complex hybrid model has 64 continuous-time domains, 132 state variables, and 36 control inputs.
Generalization and Personalization of Mobile Sensing-Based Mood Inference Models

Mood inference with mobile sensing data has been studied in ubicomp literature over the last decade. This inference enables context-aware and personalized user experiences in general mobile apps and valuable feedback and interventions in mobile health apps. However, even though model generalization issues have been highlighted in many studies, the focus has always been on improving the accuracies of models using different sensing modalities and machine learning techniques, with datasets collected in homogeneous populations. In contrast, less attention has been given to studying the performance of mood inference models to assess whether models generalize to new countries. In this study, we collected a mobile sensing dataset with 329K self-reports from 678 participants in eight countries (China, Denmark, India, Italy, Mexico, Mongolia, Paraguay, UK) to assess the effect of geographical diversity on mood inference models. We define and evaluate country-specific (trained and tested within a country), continent-specific (trained and tested within a continent), country-agnostic (tested on a country not seen on training data), and multi-country (trained and tested with multiple countries) approaches trained on sensor data for two mood inference tasks with population-level (non-personalized) and hybrid (partially personalized) models. We show that partially personalized country-specific models perform the best yielding area under the receiver operating characteristic curve (AUROC) scores of the range 0.78--0.98 for two-class (negative vs. positive valence) and 0.76--0.94 for three-class (negative vs. neutral vs. positive valence) inference. Further, with the country-agnostic approach, we show that models do not perform well compared to country-specific settings, even when models are partially personalized. We also show that continent-specific models outperform multi-country models in the case of Europe. Overall, we uncover generalization issues of mood inference models to new countries and how the geographical similarity of countries might impact mood inference.
Evaluating Novel Mask-RCNN Architectures for Ear Mask Segmentation

The human ear is generally universal, collectible, distinct, and permanent. Ear-based biometric recognition is a niche and recent approach that is being explored. For any ear-based biometric algorithm to perform well, ear detection and segmentation need to be accurately performed. While significant work has been done in existing literature for bounding boxes, a lack of approaches output a segmentation mask for ears. This paper trains and compares three newer models to the state-of-the-art MaskRCNN (ResNet 101 +FPN) model across four different datasets. The Average Precision (AP) scores reported show that the newer models outperform the state-of-the-art but no one model performs the best over multiple datasets.
Scale Invariant Privacy Preserving Video via Wavelet Decomposition

—Video surveillance has become ubiquitous in the modern world. Mobile devices, surveillance cameras, and IoT devices, all can record video that can violate our privacy. One proposed solution for this is privacy-preserving video, which removes identifying information from the video as it is produced. Several algorithms for this have been proposed, but all of them suffer from scale issues: in order to sufﬁciently anonymize near- camera objects, distant objects become unidentiﬁable. In this paper, we propose a scale-invariant method, based on wavelet decomposition. This work was originally published as [1]. Please cite the original paper.
Fano Resonances in All-Dielectric Electromagnetic Metasurfaces

We are interested in the resonant electromagnetic (EM) scattering by all-dielectric metasurfaces made of a two-dimensional lattice of nanoparticles with high refractive indices. In [Ammari et al., Trans. AMS, 376 (2023), 39-90], it has been shown that a single high-index nanoresonator can couple with the incident wave and exhibit a strong magnetic dipole response. Recent physics experiments reveal that when the particles are arranged in certain periodic configurations, they may have different anomalous scattering effects in the macroscopic scale, compared to the single-particle case. In this work, we shall develop a rigorous mathematical framework for analyzing the resonant behaviors of all-dielectric metasurfaces. We start with the characterization of subwavelength scattering resonances in such a periodic setting and their asymptotic expansions in terms of the refractive index of the nanoparticles. Then we show that real resonances always exist below the essential spectrum of the periodic Maxwell operator and that they are the simple poles of the scattering resolvent with the exponentially decaying resonant modes. By using group theory, we discuss the implications of the symmetry of the metasurface on the subwavelength band functions and their associated eigenfunctions. For the symmetric metasurfaces with the normal incidence, we use a variational method to show the existence of embedded eigenvalues (i.e., real subwavelength resonances embedded in the continuous radiation spectrum). Furthermore, we break the configuration symmetry either by introducing a small deformation of particles or by slightly deviating from the normal incidence and prove that Fano-type reflection and transmission anomalies can arise in both of these scenarios.
ON THE NEUTRINO NON-DETECTION OF GRB 130427A

The recent gamma-ray burst GRB 130427A has an isotropic electromagnetic energy Eiso ∼ 1054 erg, suggesting an ample supply of target photons for photo-hadronic interactions, which at its low redshift of z ∼ 0.34 would appear to make it a promising candidate for neutrino detection. However, the IceCube collaboration has reported a null result based on a search during the prompt emission phase. We show that this neutrino non-detection can provide valuable information about this gamma-ray burst's (GRB's) key physical parameters such as the emission radius Rd, the bulk Lorentz factor Γ, and the energy fraction converted into cosmic rays ϵp. The results are discussed both in a model-independent way and in the specific scenarios of an internal shock (IS) model, a baryonic photospheric (BPH) model, and a magnetic photospheric (MPH) model. We find that the constraints are most stringent for the MPH model considered, but the constraints on the IS and the BPH models are fairly modest.
A proof of De Concini-Kac-Procesi conjecture I. Representations of quantum groups at roots of unity and q-W algebras

Let Uε(g) be the standard simply–connected version of the Drinfeld–Jumbo quantum group at an odd m-th root of unity ε. De Concini, Kac and Proicesi observed that isomorphism classes of irreducible representations of Uε(g) are parameterized by the conjugacy classes in the connected simply connected algebraic group G corresponding to the simple complex Lie algebra g. They also conjectured that the dimension of a representation corresponding to a conjugacy class O is divisible by m 1 2 dim O . We show that if O intersects one of special transversal slices Σs to the set of conjugacy classes in G then the dimension of every finite–dimensional irreducible representation of Uε(g) corresponding to O is divisible by m 1 2 codim Σs . This reduces the De Concini–Kac–Proicesi conjecture to constructing appropriate transversal slices Σs such that dim O = codim Σs for conjugacy classes O of exceptional elements in G intersecting Σs. Our result also implies an equivalence between a category of finite–dimensional Uε(g)–modules and a category of finite–dimensional representations of a q-W algebra which can be regarded as a truncation of the quantized algebra of regular functions on Σs. To Michael Arsenyevich Semenov-Tian-Shansky on the occasion of his 65th birthday.
On the density of abelian l-extensions

We derive an asymptotic formula which counts the number of abelian extensions of prime degrees over rational function fields. Specifically, let $\ell$ be a rational prime and $K$ a rational function field $\Bbb F_q(t)$ with $\ell \nmid q$. Let $\textup{Disc}_f\left(F/K\right)$ denote the finite discriminant of $F$ over $K$. Denote the number of abelian $\ell$-extensions $F/K$ with $\textup{deg}\left(\textup{Disc}_f(F/K)\right) = (\ell-1)\alpha n$ by $a_{\ell}(n)$, where $\alpha=\alpha(q, \ell)$ is the order of $q$ in the multiplicative group $\left(\Bbb Z/\ell \Bbb Z\right)^\times$. We give a explicit asymptotic formula for $a_\ell(n)$. In the case of cubic extensions with $q\equiv 2 \pmod 3$, our formula gives an exact analogue of Cohn's classical formula.
Close Encounters of Tight Binary Stars with Stellar-mass Black Holes

Strong dynamical interactions among stars and compact objects are expected in a variety of astrophysical settings, such as star clusters and the disks of active galactic nuclei. Via a suite of 3D hydrodynamics simulations using the moving-mesh code AREPO, we investigate the formation of transient phenomena and their properties in close encounters between an 2M⊙ or 20M⊙ equal-mass circular binary star and single 20M⊙ black hole (BH). Stars can be disrupted by the BH during dynamical interactions, naturally producing electromagnetic transient phenomena. Encounters with impact parameters smaller than the semimajor axis of the initial binary frequently lead to a variety of transients whose electromagnetic signatures are qualitatively different from those of ordinary disruption events involving just two bodies. These include the simultaneous or successive disruptions of both stars and one full disruption of one star accompanied by successive partial disruptions of the other star. On the other hand, when the impact parameter is larger than the semimajor axis of the initial binary, the binary is either simply tidally perturbed or dissociated into bound and unbound single stars (“micro-Hills” mechanism). The dissociation of 20M⊙ binaries can produce a runaway star and an active BH moving away from one another. Also, the binary dissociation can either produce an interacting binary with the BH, or a non-interacting, hard binary; both could be candidates of BH high- and low-mass X-ray binaries. Hence our simulations especially confirm that strong encounters can lead to the formation of the (generally difficult to form) BH low-mass X-ray binaries.
Higher order degrees of affine plane curve complements

We study finiteness (and vanishing) properties of the higher order degrees associated to complements of complex affine plane curves with mild singularities at infinity. Our results impose new obstructions on the class of groups that can be realized as fundamental groups of affine plane curve complements. We also clarify the relationship between the higher order degrees and the multivariable Alexander polynomial of a non-irreducible plane curve.
K-theoretic boson–fermion correspondence and melting crystals

We study non-Hermitian integrable fermion and boson systems from the perspectives of Grothendieck polynomials. The models considered in this article are the five-vertex model as a fermion system and the non-Hermitian phase model as a boson system. Both models are characterized by different solutions satisfying the same Yang–Baxter relation. From our previous works on the identification between the wavefunctions of the five-vertex model and Grothendieck polynomials, we introduce skew Grothendieck polynomials and derive the addition theorem among them. Using these relations, we derive the wavefunctions of the non-Hermitian phase model as a determinant form, which can also be expressed as Grothendieck polynomials. Namely, we establish a K-theoretic boson–fermion correspondence at the level of wavefunctions. As a by-product, the partition function of the statistical mechanical model of a three-dimensional (3D) melting crystal is exactly calculated by use of the scalar products of the wavefunctions of the phase model. The resultant expression can be regarded as a K-theoretic generalization of the MacMahon function describing the generating function of the plane partitions, which interpolates the generating functions of two-dimensional (2D) and (3D) Young diagrams.
The baker’s map with a convex hole

We consider the baker’s map B on the unit square X and an open convex set which we regard as a hole. The survivor set is defined as the set of all points in X whose B-trajectories are disjoint from H. The main purpose of this paper is to study holes H for which (dimension traps) as well as those for which any periodic trajectory of B intersects (cycle traps). We show that any H which lies in the interior of X is not a dimension trap. This means that, unlike the doubling map and other one-dimensional examples, we can have for H whose Lebesgue measure is arbitrarily close to one. Also, we describe holes which are dimension or cycle traps, critical in the sense that if we consider a strictly convex subset, then the corresponding property in question no longer holds. We also determine such that for all convex H whose Lebesgue measure is less than δ. This paper may be seen as a first extension of our work begun in Clark (2016 Discrete Continuous Dyn. Syst. A 6 1249–69; Clark 2016 PhD Dissertation The University of Manchester; Glendinning and Sidorov 2015 Ergod. Theor. Dynam. Syst. 35 1208–28; Hare and Sidorov 2014 Mon.hefte Math. 175 347–65; Sidorov 2014 Acta Math. Hung. 143 298–312) to higher dimensions.
On modeling Maze solving ability of slime mold via a hyperbolic model of chemotaxis

Many studies have shown that Physarum polycephalum slime mold is able to find the shortest path in a maze. In this paper we study this behavior in a network, using a hyperbolic model of chemotaxis. Suitable transmission and boundary conditions at each node are considered to mimic the behavior of such an organism in the feeding process. Several numerical tests are presented for special network geometries to show the qualitative agreement between our model and the observed behavior of the mold.
On algebras of three-dimensional quaternionic harmonic fields

A quaternionic field is a pair p = {α, u} of function α and vector field u given on a 3d Riemannian maifold Ω with the boundary. The field is said to be harmonic if ∇α = rot u in Ω. The linear space of harmonic fields is not an algebra w.r. t. quaternion multiplication. However, it may contain the commutative algebras, what is the subject of the paper. Possible application of these algebras to the impedance tomography problem is touched on.
The Hitting Times of A Stochastic Epidemic Model

In this paper, we focus on the hitting times of a stochastic epidemic model presented by \cite{Gray}. Under the help of the auxiliary stopping times, we investigate the asymptotic limits of the hitting times by the variations of calculus and the large deviation inequalities when the noise is sufficiently small. It can be shown that the relative position between the initial state and the hitting state determines the scope of the hitting times greatly.
A Proximal Operator for Multispectral Phase Retrieval Problems

Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval problem commonly refers to the task of recovering a target signal based on the magnitude of linear projections of that signal onto known vectors, usually under the presence of noise. A more general problem is the multispectral phase retrieval problem, where sums of these magnitudes are observed instead. In this paper we study the proximal operator for this problem, which appears in applications like X-ray solution scattering. We show that despite its non-convexity, all local minimizers are global minimizers, guaranteeing the optimality of simple descent techniques. An efficient linear time exact Newton method is proposed based on the structure of the problem's Hessian. Initialization criteria are discussed and the computational performance of the proposed algorithm is compared to that of traditional descent methods. The studied proximal operator can be used in a distributed and parallel scenarios using an ADMM scheme and allows for exploiting the spectral characteristics of the problem's measurement matrices, known in many physical sensing applications, in a way that is not possible with non-splitted optimization algorithms. The dependency of the proximal operator on the rank of these matrices, instead of their dimension, can greatly reduce the memory and computation requirements for problems of moderate to large size (N>10000) when these measurement matrices admit a low-rank representation.
Local study of stable module categories via tensor triangulated geometry

We investigate the particular properties of the stable category of modules over a finite dimensional cocommutative graded connected Hopf algebra $A$, via tensor-triangulated geometry. This study requires some mild conditions on the Hopf algebra $A$ under consideration (satisfied for example by all finite sub-Hopf-algebras of the modulo $2$ Steenrod algebra). In particular, we study some particular covers of its spectrum of prime ideals $\mathrm{Spc}(A)$, which are related to Margolis' Work. We then exploit the existence of Margolis' Postnikov towers in this situation to show that the localization at an open subset $U$ of $\mathrm{Spc}(A)$, for various $U$, assembles in an $\infty$-stack. Finally, we turn to applications in the study of Picard groups of Hopf algebras and localizations in the stable categories of modules.
Relations between positive definite functions and irreducible representations on a locally compact groupoid

If G is a locally compact groupoid with a Haar system λ , then a positive deﬁnite function p on G has a form p ( x ) = h L ( x ) ξ ( d ( x )) ,ξ ( r ( x )) i , where L is a representation of G on a Hilbert bundle H = ( G 0 , { H u } , µ ), µ is a quasi invariant measure on G 0 and ξ ∈ L ∞ ( G 0 , H ). [10]. In this paper ﬁrt we prove that if µ is a quasi invariant ergodic measure on G 0 , then two corresponding representations of G and C c ( G ) are irreducible in the same time. Then by using the theory of positive linear functionals on C ∗ ( G ) we show that when µ is an ergodic quasi invariant measure on G 0 , for a positive deﬁnite function p which is an extreme point of P µ 1 ( G ) the corresponding representation L is irreducible and conversely, every irreducible representation L of G on a Hilbert bundle H = ( G 0 , { H u } , µ ) and every section ξ ∈ H ( µ ) with norm one, deﬁne an extreme point of P µ 1 ( G ).
Topological Entropy, Entropy points and shadowing

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having shadowing property.