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The application of Riemannian geometry in the decoding of brain-computer interfaces (BCIs) has swiftly garnered attention because of its straightforwardness, precision, and resilience, along with its aptitude for transfer learning, which has been demonstrated through significant achievements in global BCI competitions. This paper presents a comprehensive review of recent advancements in the integration of deep learning with Riemannian geometry to enhance EEG signal decoding in BCIs. Our review updates the findings since the last major review in 2017, comparing modern approaches that utilize deep learning to improve the handling of non-Euclidean data structures inherent in EEG signals. We discuss how these approaches not only tackle the traditional challenges of noise sensitivity, non-stationarity, and lengthy calibration times but also introduce novel classification frameworks and signal processing techniques to reduce these limitations significantly. Furthermore, we identify current shortcomings and propose future research directions in manifold learning and riemannian-based classification, focusing on practical implementations and theoretical expansions, such as feature tracking on manifolds, multitask learning, feature extraction, and transfer learning. This review aims to bridge the gap between theoretical research and practical, real-world applications, making sophisticated mathematical approaches accessible and actionable for BCI enhancements.

This paper introduces the Pandemic PACT Advanced Categorisation Engine (PPACE) along with its associated dataset. PPACE is a fine-tuned model developed to automatically classify research abstracts from funded biomedical projects according to WHO-aligned research priorities. This task is crucial for monitoring research trends and identifying gaps in global health preparedness and response. Our approach builds on human-annotated projects, which are allocated one or more categories from a predefined list. A large language model is then used to generate `rationales' explaining the reasoning behind these annotations. This augmented data, comprising expert annotations and rationales, is subsequently used to fine-tune a smaller, more efficient model. Developed as part of the Pandemic PACT project, which aims to track and analyse research funding and clinical evidence for a wide range of diseases with outbreak potential, PPACE supports informed decision-making by research funders, policymakers, and independent researchers. We introduce and release both the trained model and the instruction-based dataset used for its training. Our evaluation shows that PPACE significantly outperforms its baselines. The release of PPACE and its associated dataset offers valuable resources for researchers in multilabel biomedical document classification and supports advancements in aligning biomedical research with key global health priorities.

This is the third installment in a series of papers on the subject of derived contact structures. In this paper, we formally introduce Legendrians in the derived context and give a natural example. We then present affine models and prove a Legendrian-Darboux-type theorem for the Legendrians in contact derived schemes., Comment: 23 pages. Comments welcome!

$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the spectral truncation. We focus on kernels whose inputs and outputs are vectors or functions and generalize typical kernels by introducing the noncommutativity of the products appearing in the kernels. The noncommutativity induces interactions along the data function domain. We show that it is a governing factor leading to performance enhancement: we can balance the representation power and the model complexity. We also propose a deep learning perspective to increase the representation capacity of spectral truncation kernels. The flexibility of the proposed class of kernels allows us to go beyond previous commutative kernels, addressing two of the foremost issues regarding learning in vector-valued RKHSs, namely the choice of the kernel and the computational cost.

We report the results of an extensive set of simulations exploring the sensitivity of the BlackCAT CubeSat to long-duration gamma-ray bursts (GRBs). BlackCAT is a NASA APRA-funded CubeSat mission for the detection and real-time sub-arcminute localization of high-redshift ($z\gtrsim 3.5$) GRBs. Thanks to their luminous and long-lived afterglow emissions, GRBs are uniquely valuable probes of high-redshift star-forming galaxies and the intergalactic medium. In addition, each detected GRB with a known redshift serves to localize a region of high-redshift star formation in three dimensions, enabling deep follow-on searches for host galaxies and associated local and large-scale structures. We explore two distinct models for the GRB redshift distribution and luminosity function, both consistent with Swift observations. We find that, for either model, BlackCAT is expected to detect a mean of 42 bursts per year on-orbit, with 6.7% to 10% of these at $z>3.5$. BlackCAT bursts will be localized to $r_{90} \lesssim 55^{\prime\prime}$ precision and reported to the community within seconds. Due to the mission orbit and pointing scheme, bursts will be located in the night sky and well-placed for deep multiwavelength follow-up observations. BlackCAT is on schedule to achieve launch readiness in 2025., Comment: 10 pages, 4 figures, 3 tables; Published in ApJ

Machine learning has a long collaborative tradition with several fields of mathematics, such as statistics, probability and linear algebra. We propose a new direction for machine learning research: $C^*$-algebraic ML $-$ a cross-fertilization between $C^*$-algebra and machine learning. The mathematical concept of $C^*$-algebra is a natural generalization of the space of complex numbers. It enables us to unify existing learning strategies, and construct a new framework for more diverse and information-rich data models. We explain why and how to use $C^*$-algebras in machine learning, and provide technical considerations that go into the design of $C^*$-algebraic learning models in the contexts of kernel methods and neural networks. Furthermore, we discuss open questions and challenges in $C^*$-algebraic ML and give our thoughts for future development and applications., Comment: position paper

In this study, we propose an approach for predicting rare events by exploiting time series in coevolution. Our approach involves a weighted autologistic regression model, where we leverage the temporal behavior of the data to enhance predictive capabilities. By addressing the issue of imbalanced datasets, we establish constraints leading to weight estimation and to improved performance. Evaluation on synthetic and real-world datasets confirms that our approach outperform state-of-the-art of predicting home equipment failure methods.

The Event Horizon Telescope (EHT) Collaboration recently published the first images of the supermassive black holes in the cores of the Messier 87 and Milky Way galaxies. These observations have provided a new means to study supermassive black holes and probe physical processes occurring in the strong-field regime. We review the prospects of future observations and theoretical studies of supermassive black hole systems with the next-generation Event Horizon Telescope (ngEHT), which will greatly enhance the capabilities of the existing EHT array. These enhancements will open up several previously inaccessible avenues of investigation, thereby providing important new insights into the properties of supermassive black holes and their environments. This review describes the current state of knowledge for five key science cases, summarising the unique challenges and opportunities for fundamental physics investigations that the ngEHT will enable., Comment: To be submitted to journal. Comments are welcome

Background and objectives: Dynamic handwriting analysis, due to its non-invasive and readily accessible nature, has recently emerged as a vital adjunctive method for the early diagnosis of Parkinson's disease. In this study, we design a compact and efficient network architecture to analyse the distinctive handwriting patterns of patients' dynamic handwriting signals, thereby providing an objective identification for the Parkinson's disease diagnosis. Methods: The proposed network is based on a hybrid deep learning approach that fully leverages the advantages of both long short-term memory (LSTM) and convolutional neural networks (CNNs). Specifically, the LSTM block is adopted to extract the time-varying features, while the CNN-based block is implemented using one-dimensional convolution for low computational cost. Moreover, the hybrid model architecture is continuously refined under ablation studies for superior performance. Finally, we evaluate the proposed method with its generalization under a five-fold cross-validation, which validates its efficiency and robustness. Results: The proposed network demonstrates its versatility by achieving impressive classification accuracies on both our new DraWritePD dataset ($96.2\%$) and the well-established PaHaW dataset ($90.7\%$). Moreover, the network architecture also stands out for its excellent lightweight design, occupying a mere $0.084$M of parameters, with a total of only $0.59$M floating-point operations. It also exhibits near real-time CPU inference performance, with inference times ranging from $0.106$ to $0.220$s. Conclusions: We present a series of experiments with extensive analysis, which systematically demonstrate the effectiveness and efficiency of the proposed hybrid neural network in extracting distinctive handwriting patterns for precise diagnosis of Parkinson's disease.

This is a sequel of our previous work, arXiv:2209.09686, on the development of derived contact geometry, in which we formally introduced shifted contact structures on derived stacks and proved some results for $k$-shifted contact derived schemes, with $k<0$. In this paper, we extend these results from derived schemes to derived Artin stacks. In brief, we first show that for $k<0$, every $k$-shifted contact derived Artin stack admits a contact Darboux atlas. Secondly, we canonically describe the symplectification of a derived Artin stack equipped with a $k$-shifted contact structure, where $k<0$. Lastly, we give several constructions of contact derived stacks using certain cotangent stacks and shifted prequantization structures., Comment: V02: 25 Pages; a new section on examples added; minor edits; Comments welcome!

We present a new catalog of Kepler planet candidates that prioritizes accuracy of planetary dispositions and properties over uniformity. This catalog contains 4376 transiting planet candidates, including 1791 residing within 709 multi-planet systems, and provides the best parameters available for a large sample of Kepler planet candidates. We also provide a second set of stellar and planetary properties for transiting candidates that are uniformly-derived for use in occurrence rates studies. Estimates of orbital periods have been improved, but as in previous catalogs, our tabulated values for period uncertainties do not fully account for transit timing variations (TTVs). We show that many planets are likely to have TTVs with long periodicities caused by various processes, including orbital precession, and that such TTVs imply that ephemerides of Kepler planets are not as accurate on multi-decadal timescales as predicted by the small formal errors (typically 1 part in $10^6$ and rarely $ > 10^{-5}$) in the planets' measured mean orbital periods during the Kepler epoch. Analysis of normalized transit durations implies that eccentricities of planets are anti-correlated with the number of companion transiting planets. Our primary catalog lists all known Kepler planet candidates that orbit and transit only one star; for completeness, we also provide an abbreviated listing of the properties of the two dozen non-transiting planets that have been identified around stars that host transiting planets discovered by Kepler., Comment: 62 pages, 32 figures, 5 tables. Published in The Planetary Science Journal, volume 5, #6 (2024). The first table appears in abbreviated form in the main manuscript and is provided in full as a separate file. A standard resolution version of Figure 32 appears within the manuscript; a high-resolution version of Figure 32 is also provided separate file

Random features have been introduced to scale up kernel methods via randomization techniques. In particular, random Fourier features and orthogonal random features were used to approximate the popular Gaussian kernel. The former is performed by a random Gaussian matrix and leads exactly to the Gaussian kernel after averaging. In this work, we analyze the bias and the variance of the kernel approximation based on orthogonal random features which makes use of Haar orthogonal matrices. We provide explicit expressions for these quantities using normalized Bessel functions and derive sharp exponential bounds supporting the view that orthogonal random features are more informative than random Fourier features.

Subject: In this article, convolutional networks of one, two, and three dimensions are compared with respect to their ability to distinguish between the drawing tests produced by Parkinson's disease patients and healthy control subjects. Motivation: The application of deep learning techniques for the analysis of drawing tests to support the diagnosis of Parkinson's disease has become a growing trend in the area of Artificial Intelligence. Method: The dynamic features of the handwriting signal are embedded in the static test data to generate one-dimensional time series, two-dimensional RGB images and three-dimensional voxelized point clouds, and then one-, two-, and three-dimensional CNN can be used to automatically extract features for effective diagnosis. Novelty: While there are many results that describe the application of two-dimensional convolutional models to the problem, to the best knowledge of the authors, there are no results based on the application of three-dimensional models and very few using one-dimensional models. Main result: The accuracy of the one-, two- and three-dimensional CNN models was 62.50%, 77.78% and 83.34% in the DraWritePD dataset (acquired by the authors) and 73.33%, 80.00% and 86.67% in the PaHaW dataset (well known from the literature), respectively. For these two data sets, the proposed three-dimensional convolutional classification method exhibits the best diagnostic performance.

The directed Oberwolfach problem OP$^\ast(m_1,\ldots,m_k)$ asks whether the complete symmetric digraph $K_n^\ast$, assuming $n=m_1+\ldots +m_k$, admits a decomposition into spanning subdigraphs, each a disjoint union of $k$ directed cycles of lengths $m_1,\ldots,m_k$. We hereby describe a method for constructing a solution to OP$^\ast(m_1,\ldots,m_k)$ given a solution to OP$^\ast(m_1,\ldots,m_\ell)$, for some $\ell

In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the probability density function and the cumulative distribution function of Maximum Exponentiated Exponential distribution. These functions are used to determine an exact expression of the probability density function, the cumulative function, reliability function, and hazard function of our Exponentiated Hypoexponential Distribution. We discuss estimation of the parameters by maximum likelihood estimators. The distribution has been fitted to a real life data set and the fit has been found to be a serious competitor to the others., Comment: 26 pages, 5 figures

In the frame of shallow water model the influence of free surface action on nonlinear propagation of planetary ULF magnetized Rossby waves in the weakly ionized ionospheric D-, E-, and F-layers is revealed. Relevant nonlinear dynamic equations satisfying several conservation laws are obtained and investigated. The role of Hall and Pedersen conductivities is investigated explicitly. It is shown that while potential vorticity is conserved in the ionospheric D-,and E-layer it is broken by Pedersen conductivity in the ionospheric F-layer. Similar to KdV nonlinearity two new scalar nonlinearities due to Pedersen conductivity are revealed in the F-layer. Obtained results extend and complement known theoretical investigations and are especially relevant for nonlinear vortical propagation of magnetized Rossby waves in the weakly ionized ionospheric plasma., Comment: 15 pages

Liquid nanofilms are ubiquitous in nature and technology, and their equilibrium and out-of-equilibrium dynamics are key to a multitude of phenomena and processes. We numerically study the evolution and rupture of viscous nanometric films, incorporating the effects of surface tension, van der waals forces, thermal fluctuations and viscous shear. We show that thermal fluctuations create perturbations that can trigger film rupture, but they do not significantly affect the growth rate of the perturbations. The film rupture time can be predicted from a linear stability analysis of the governing thin film equation, by considering the most unstable wavelength and the thermal roughness. Furthermore, applying a sufficiently large unidirectional shear can stabilise large perturbations, creating a finite-amplitude travelling wave instead of film rupture. In contrast, in three dimensions, unidirectional shear does not inhibit rupture, as perturbations are not suppressed in the direction perpendicular to the applied shear. However, if the direction of shear varies in time, the growth of large perturbations is prevented in all directions, and rupture can hence be impeded.

The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in large-scale scenarios. We provide an efficient Frank-Wolfe-based algorithm to approximately seek the nearest separable density matrix and derive a systematic way for labeling density matrices as separable or entangled, allowing us to treat quantum separability as a classification problem. Our method is applicable to any two-qudit mixed states. Numerical experiments with quantum states of 3- and 7-dimensional qudits validate the efficiency of the proposed procedure, and demonstrate that it scales up to thousands of density matrices with a high quantum entanglement detection accuracy. This takes a step towards benchmarking quantum separability to support the development of more powerful entanglement detection techniques.

The comparison of the kinematic properties of different Vector Boson Scattering (VBS) and Vector Boson Fusion (VBF) processes using multivariate discriminator is presented. The search is performed to identify common features in the the polarized $W^{\pm}W^{\pm}jj$ channel, mainly central and forward region jets kinematic variables such as eta, phi, mass and transverse energy, in order to determine some universal cuts. Traditionally boosted decision trees (BDT) are used as multivariate discriminator. The presented results are based on proton-proton collision Monte Carlo (MC) simulation samples center-of-mass energy 14 TeV and corresponding to an integrated luminosity of 3000 $fb^{-1}$. MC samples are generated using MADGRAPH and PYTHIA.

Reproducing kernel Hilbert $C^*$-module (RKHM) is a generalization of reproducing kernel Hilbert space (RKHS) by means of $C^*$-algebra, and the Perron-Frobenius operator is a linear operator related to the composition of functions. Combining these two concepts, we present deep RKHM, a deep learning framework for kernel methods. We derive a new Rademacher generalization bound in this setting and provide a theoretical interpretation of benign overfitting by means of Perron-Frobenius operators. By virtue of $C^*$-algebra, the dependency of the bound on output dimension is milder than existing bounds. We show that $C^*$-algebra is a suitable tool for deep learning with kernels, enabling us to take advantage of the product structure of operators and to provide a clear connection with convolutional neural networks. Our theoretical analysis provides a new lens through which one can design and analyze deep kernel methods.

Analyzing the observations obtained by the LIGO and the Virgo Collaborations, a new era has begun in binary black hole (BBH) merger processes and black hole physics studies. The fact that very massive stars that will become black holes at the end of their evolution are in binary or multiple states adds particular importance to BBH studies. In this study, using the SEOBNRv4$\_opt$ gravitational waveform model developed for compact binary systems, many ($\sim 10^6$) models were produced under different initial conditions, and the pre- and post-merge parameters were compared. In the models, it is assumed that the initial total mass (M$_{\rm{tot}}$) of the binary systems varies between 12-130 $\rm{M}_\odot$ with step interval 1$\rm{M}_\odot$, the mass ratios ($q = \rm{m}_{1i}/\rm{m}_{2i}$) vary between 1 and 2 with step interval 0.004, and the initial spin ($\abs{\rchi_{1i}} = \abs{\rchi_{2i}}$) value varies between $-0.83$ and $+0.83$ with step interval 0.017. Final spin ($\rchi_{f}$), fractional mass loss (M$_{FL}$), and the maximum gravitational wave amplitude (h$_{\rm{max}}$) obtained during the merger were compared with appropriate tables and figures obtained from the results of the relativistic numeric model obtained according to the initial parameters. Our results show that M$_{\rm{FL}}$ in generated BBH coalescences varied about 2.7 to 9.2\%, and $\rchi_{\rm{f}}$ between 0.29 and 0.91. In most of the BBHs we have modeled, we found that M$_{\rm{FL}}$ varies inversely with $q$. However, it has been found that M$_{\rm{FL}}$ values are not always inversely varied to the $q$ parameter in systems of opposite initial spin, where the large mass black hole component is positively oriented. Accordingly, it is understood that the values of M$_{\rm{FL}}$ decrease to a certain point of $q$ and then increase according to the increasing direction of $q$., Comment: 29 pages, 5 figure, 5 tables, submitted for publication

In recent years, deep learning methods have achieved great success in various fields due to their strong performance in practical applications. In this paper, we present a light-weight neural network for Parkinson's disease diagnostics, in which a series of hand-drawn data are collected to distinguish Parkinson's disease patients from healthy control subjects. The proposed model consists of a convolution neural network (CNN) cascading to long-short-term memory (LSTM) to adapt the characteristics of collected time-series signals. To make full use of their advantages, a multilayered LSTM model is firstly used to enrich features which are then concatenated with raw data and fed into a shallow one-dimensional (1D) CNN model for efficient classification. Experimental results show that the proposed model achieves a high-quality diagnostic result over multiple evaluation metrics with much fewer parameters and operations, outperforming conventional methods such as support vector machine (SVM), random forest (RF), lightgbm (LGB) and CNN-based methods.

Almost a hundred compact binary mergers have been detected via gravitational waves by the LIGO-Virgo-KAGRA collaboration in the past few years providing us with a significant amount of new information on black holes and neutron stars. In addition to observations, numerical simulations using newly developed modern codes in the field of gravitational wave physics will guide us to understand the nature of single and binary degenerate systems and highly energetic astrophysical processes. We here presented a set of new fully general relativistic hydrodynamic simulations of high-mass binary neutron star systems using the open-source Einstein Toolkit and LORENE codes. We considered systems with total baryonic masses ranging from 2.8 $M_\odot$ to 4.0 $M_\odot$ and used the SLy equation of state. We analyzed the gravitational wave signal for all models and reported potential indicators of systems undergoing rapid collapse into a black hole that could be observed by future detectors like the Einstein Telescope and the Cosmic Explorer. The properties of the post-merger black hole, the disk and ejecta masses, and their dependence on the binary parameters were also extracted. We also compared our numerical results with recent analytical fits presented in the literature and provided parameter-dependent semi-analytical relations between the total mass and mass ratio of the systems and the resulting black hole masses and spins, merger frequency, BH formation time, ejected mass, disk mass, and radiated gravitational wave energy., Comment: 12 pages, 6 figures, 5 tables, Accepted for publication in MNRAS

Through viewing out the literature, many generated distributions took a new special form of probability density function (PDF) in which it is written as a linear combination of n other distributions. Therefore, we define in this paper a new type of distributions called "The New Mixed Distribution" form in which a distribution is written as a linear combination of n others and derive its characteristics. Second we construct "The New Mixed T-G family" a family of distributions following another new defined type "The New Mixed T-G Distribution". Third, we generate "The New Mixed Hypoexponential G-Family" out of 6 new mixed distributions with characterizing their PDFs, CDFs, hazard rate and reliability functions, MGF, and nth moment, and studying their maximum likelihood estimator and method of moments.

Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist to this rich literature by generalizing supervised learning in RKHS and vvRKHS to reproducing kernel Hilbert $C^*$-module (RKHM), and show how to construct effective positive-definite kernels by considering the perspective of $C^*$-algebra. Unlike the cases of RKHS and vvRKHS, we can use $C^*$-algebras to enlarge representation spaces. This enables us to construct RKHMs whose representation power goes beyond RKHSs, vvRKHSs, and existing methods such as convolutional neural networks. Our framework is suitable, for example, for effectively analyzing image data by allowing the interaction of Fourier components., Comment: We corrected errors in the experiments in Section 6.2

Regularized Maximum Likelihood (RML) techniques are a class of image synthesis methods that achieve better angular resolution and image fidelity than traditional methods like CLEAN for sub-mm interferometric observations. To identify best practices for RML imaging, we used the GPU-accelerated open source Python package MPoL, a machine learning-based RML approach, to explore the influence of common RML regularizers (maximum entropy, sparsity, total variation, and total squared variation) on images reconstructed from real and synthetic ALMA continuum observations of protoplanetary disks. We tested two different cross-validation (CV) procedures to characterize their performance and determine optimal prior strengths, and found that CV over a coarse grid of regularization strengths easily identifies a range of models with comparably strong predictive power. To evaluate the performance of RML techniques against a ground truth image, we used MPoL on a synthetic protoplanetary disk dataset and found that RML methods successfully resolve structures at fine spatial scales present in the original simulation. We used ALMA DSHARP observations of the protoplanetary disk around HD 143006 to compare the performance of MPoL and CLEAN, finding that RML imaging improved the spatial resolution of the image by up to a factor of 3 without sacrificing sensitivity. We provide general recommendations for building an RML workflow for image synthesis of ALMA protoplanetary disk observations, including effective use of CV. Using these techniques to improve the imaging resolution of protoplanetary disk observations will enable new science, including the detection of protoplanets embedded in disks., Comment: 27 pages, 12 figures, accepted for publication in PASP

In this paper, we formally define the concept of $k$-shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry. In this regard, for $k$-shifted contact derived $\mathbb{K}$-schemes, we develop a Darboux-like theorem and formulate the notion of symplectification., Comment: V03: 24 pages; improved by the suggestions of an anonymous referee; to appear in the Annales de la Faculte des Sciences de Toulouse: Math\'ematiques. Comments are welcome!

We study the implicit regularization effects of deep learning in tensor factorization. While implicit regularization in deep matrix and 'shallow' tensor factorization via linear and certain type of non-linear neural networks promotes low-rank solutions with at most quadratic growth, we show that its effect in deep tensor factorization grows polynomially with the depth of the network. This provides a remarkably faithful description of the observed experimental behaviour. Using numerical experiments, we demonstrate the benefits of this implicit regularization in yielding a more accurate estimation and better convergence properties., Comment: Accepted to ICML 2022

This note is a survey on the basic aspects of moduli theory along with some examples. In that respect, one of the purposes of this current document is to understand how the introduction of stacks circumvents the non-representability problem of the corresponding moduli functor $\mathcal{F}$ by using the 2-category of stacks. To this end, we shall briefly revisit the basics of 2-category theory and present a 2-categorical version of Yoneda's lemma., Comment: 17 pages, 2 figures

We contribute to fulfil the long-lasting gap in the understanding of the spatial search with multiple marked vertices. The theoretical framework is that of discrete-time quantum walks (QW), \textit{i.e.} local unitary matrices that drive the evolution of a single particle on the lattice. QW based search algorithms are well understood when they have to tackle the fundamental problem of finding only one marked element in a $d-$dimensional grid and it has been proven they provide a quadratic advantage over classical searching protocols. However, once we consider to search more than one element, the behaviour of the algorithm may be affected by the spatial configuration of the marked elements and even the quantum advantage is no longer guaranteed. Here our main contribution is threefold~: (i)~we provide \textit{sufficient conditions for optimality} for a multi-items QWSearch algorithm~; (ii)~we provide analytical evidences that \textit{almost, but not all} spatial configurations with multiple marked elements are optimal; and (iii)~we numerically show that the computational advantage with respect to the classical counterpart is not always certain and it does depend on the proportion of searched elements over the total number of grid points.

The generalized group of units of the ring modulo $n$ was first introduced by El-Kassar and Chehade, written as $U^k(Z_n)$. This allows us to formulate a new generalization to the Euler phi function $\varphi(n)$, that represents the order of $% U^k(Z_n)$ and it is denoted by $\varphi ^{k}(n).$ In this paper, we introduce this newly defined function, where we compute its explicit form and examine some of its properties similar to that of $\varphi (n)$. In addition, we study some generalized equations involving $\varphi ^{k}(n)$ where complete solution is given for some equations by considering the general case and others for some particular cases.

Traditionally, kernel methods rely on the representer theorem which states that the solution to a learning problem is obtained as a linear combination of the data mapped into the reproducing kernel Hilbert space (RKHS). While elegant from theoretical point of view, the theorem is prohibitive for algorithms' scalability to large datasets, and the interpretability of the learned function. In this paper, instead of using the traditional representer theorem, we propose to search for a solution in RKHS that has a pre-image decomposition in the original data space, where the elements don't necessarily correspond to the elements in the training set. Our gradient-based optimisation method then hinges on optimising over possibly sparse elements in the input space, and enables us to obtain a kernel-based model with both primal and dual sparsity. We give theoretical justification on the proposed method's generalization ability via a Rademacher bound. Our experiments demonstrate a better scalability and interpretability with accuracy on par with the traditional kernel-based models.

The objective of this work is to study the role of shear on the rupture of ultrathin polymer films. To do so, a finite-difference numerical scheme for the resolution of the thin film equation was set up taking into account capillary and van der Waals (vdW) forces. This method was validated by comparing the dynamics obtained from an initial harmonic perturbation to established theoretical predictions. With the addition of shear, three regimes have then been evidenced as a function of the shear rate. In the case of low shear rates the rupture is delayed when compared to the no-shear problem, while at higher shear rates it is even suppressed: the perturbed interface goes back to its unperturbed state over time. In between these two limiting regimes, a transient one in which shear and vdW forces balance each other, leading to a non-monotonic temporal evolution of the perturbed interface, has been identified. While a linear analysis is sufficient to describe the rupture time in the absence of shear, the nonlinearities appear to be essential otherwise.

Earth's magnetosphere is vital for today's technologically dependent society. To date, numerous design studies have been conducted and over a dozen science missions have own to study the magnetosphere. However, a majority of these solutions relied on large monolithic satellites, which limited the spatial resolution of these investigations, as did the technological limitations of the past. To counter these limitations, we propose the use of a satellite swarm carrying numerous and distributed payloads for magnetospheric measurements. Our mission is named APIS (Applications and Potentials of Intelligent Swarms), which aims to characterize fundamental plasma processes in the Earth's magnetosphere and measure the effect of the solar wind on our magnetosphere. We propose a swarm of 40 CubeSats in two highly-elliptical orbits around the Earth, which perform radio tomography in the magnetotail at 8-12 Earth Radii (RE) downstream, and the subsolar magnetosphere at 8-12RE upstream. In addition, in-situ measurements of the magnetic and electric fields, plasma density will be performed by on-board instruments. In this article, we present an outline of previous missions and designs for magnetospheric studies, along with the science drivers and motivation for the APIS mission. Furthermore, preliminary design results are included to show the feasibility of such a mission. The science requirements drive the APIS mission design, the mission operation and the system requirements. In addition to the various science payloads, critical subsystems of the satellites are investigated e.g., navigation, communication, processing and power systems. We summarize our findings, along with the potential next steps to strengthen our design study., Comment: Accepted in Acta Astronautica

Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a quadratic improvement over the classical perceptron algorithm using Grover's search have been proposed by Wiebe et al. arXiv:1602.04799 . While the first model reduces the complexity with respect to the size of the training set, the second one improves the bound on the number of mistakes made by the perceptron. In this paper, we introduce a hybrid quantum-classical perceptron algorithm with lower complexity and better generalization ability than the classical perceptron. We show a quadratic improvement over the classical perceptron in both the number of samples and the margin of the data. We derive a bound on the expected error of the hypothesis returned by our algorithm, which compares favorably to the one obtained with the classical online perceptron. We use numerical experiments to illustrate the trade-off between computational complexity and statistical accuracy in quantum perceptron learning and discuss some of the key practical issues surrounding the implementation of quantum perceptron models into near-term quantum devices, whose practical implementation represents a serious challenge due to inherent noise. However, the potential benefits make correcting this worthwhile., Comment: 13 pages, 4 figures, Published at the Conference on Uncertainty in Artificial Intelligence (UAI) 2022

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying that a paradigm shift is required and that dynamics has to be taken into account. In the present work we address the more general setup of tensor completion by leveraging two popularized tensor factorization, namely Tucker and TensorTrain (TT). We track relevant quantities such as tensor nuclear norm, effective rank, generalized singular values and we introduce deep Tucker and TT unconstrained factorization to deal with the completion task. Experiments on both synthetic and real data show that gradient descent promotes solution with low-rank, and validate the conjecture saying that the phenomenon has to be addressed from a dynamical perspective.

Patient no-shows is a major burden for health centers leading to loss of revenue, increased waiting time and deteriorated health outcome. Developing machine learning (ML) models for the prediction of no -shows could help addressing this important issue. It is crucial to consider fair ML models for no-show prediction in order to ensure equality of opportunity in accessing healthcare services. In this wo rk, we are interested in developing deep learning models for no-show prediction based on tabular data while ensuring fairness properties. Our baseline model, TabNet, uses on attentive feature transforme rs and has shown promising results for tabular data. We propose Fair-TabNet based on representation learning that disentangles predictive from sensitive components. The model is trained to jointly min imize loss functions on no-shows and sensitive variables while ensuring that the sensitive and prediction representations are orthogonal. In the experimental analysis, we used a hospital dataset of 210, 000 appointments collected in 2019. Our preliminary results show that the proposed Fair-TabNet improves the predictive, fairness performance and convergence speed over TabNet for the task of appointment no-show prediction. The comparison with the state-of-the art models for tabular data shows promising results and could be further improved by a better tuning of hyper-parameters.

We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and entanglement, we propose a new view on operator-valued kernels and define a general family of kernels that encompasses previously known operator-valued kernels, including separable and transformable kernels. Within this framework, we introduce another novel class of operator-valued kernels called entangled kernels that are not separable. We propose an efficient two-step algorithm for this framework, where the entangled kernel is learned based on a novel extension of kernel alignment to operator-valued kernels. We illustrate our algorithm with an application to supervised dimensionality reduction, and demonstrate its effectiveness with both artificial and real data for multi-output regression.

Let $R$ be a finite commutative ring with identity and $U(R)$ be its group of units. In 2005, El-Kassar and Chehade presented a ring structure for $U(R)$ and as a consequence they generalized this group of units to the generalized group of units $U^{k}\left( R\right) $ defined iteratively as the group of the units of $U^{k-1}(R)$, with $U^{1}\left( R\right) =U(R) $. In this paper, we examine the structure of this group, when $R=\mathbb{Z}_{n}.$ We find a decomposition of $U^{k}\left(\mathbb{Z}_{n}\right)$ as a direct product of cyclic groups for the general case of any $k$, and we study when these groups are boolean and trivial. We also show that this decomposition structure is directly related to the Pratt Tree primes.

This regional dossier aims to provide a concise description of the European minority language, Võro in Estonia, in education. Aspects that are addressed include features of the education system, recent educational policies, main actors, legal arrangements and support structures, as well as quantitative aspects such as the number of schools, teachers, pupils, and financial investments. This information serves several purposes and are relevant for policymakers, researchers, teachers, students and journalists who wish to explore developments in minority language schooling in Europe. They can also serve as a first orientation towards further research, or function as a source of ideas for improving educational provisions in their own region. Every Regional dossier begins with an introduction about the region concerned, followed by six sections that each deals with a specific level of the education system (e.g. primary education). Sections eight and nine cover the main lines of research into education of the concerned minority language, the prospects for the minority language in general and for education in particular. The tenth section gives a summary of statistics. Lists of regulations, publications and useful addresses concerning the minority language, are given at the end of the dossier. [This Regional dossier was originally compiled by Kadri Koreinik. Kara D. Brown, Sulev Iva, and Kadri Koreinik updated the dossier in 2018. Unless otherwise stated educational/academic data refer to the 2017/2018 school year.]

The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps. We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems.

Rapid testing of appropriate specimens from patients suspected for a disease during an epidemic, such as the current Coronavirus outbreak, is of a great importance for the disease management and control. We propose a method to enhance processing large amounts of collected samples. The method is based on mixing samples in testing tubes in a specific configuration, as opposed to testing single samples in each tube, and accounting for natural virus amounts in infected patients from variation of positiveness in test tubes. To illustrate the efficiency of the suggested method we carry out numerical tests for actual scenarios under various tests. Applying the proposed method enhances the number of tests by order of magnitudes, where all positives are identified with no false negatives, and the effective testing time can be reduced drastically even when the uncertainty in the test is relatively high.

This document summarises the talks and discussions happened during the VBSCan Mid-Term Scientific Meeting workshop. The VBSCan COST action is dedicated to the coordinated study of vector boson scattering (VBS) from the phenomenological and experimental point of view, for the best exploitation of the data that will be delivered by existing and future particle colliders., Comment: Editors: I.Brivio, C.Charlot, R.Covarelli, R.L.Delgado, K.Lohwasser, M.Pellen, M.Slawinska, G.Ortona, K.Ozdemir, C.Petridou, I.Puljak, M.Zaro. Proceedings for the VBSCan Mid-Term Scientific Meeting of the VBSCan COST action

In neuroscience, understanding inter-individual differences has recently emerged as a major challenge, for which functional magnetic resonance imaging (fMRI) has proven invaluable. For this, neuroscientists rely on basic methods such as univariate linear correlations between single brain features and a score that quantifies either the severity of a disease or the subject's performance in a cognitive task. However, to this date, task-fMRI and resting-state fMRI have been exploited separately for this question, because of the lack of methods to effectively combine them. In this paper, we introduce a novel machine learning method which allows combining the activation-and connectivity-based information respectively measured through these two fMRI protocols to identify markers of individual differences in the functional organization of the brain. It combines a multi-view deep autoencoder which is designed to fuse the two fMRI modalities into a joint representation space within which a predictive model is trained to guess a scalar score that characterizes the patient. Our experimental results demonstrate the ability of the proposed method to outperform competitive approaches and to produce interpretable and biologically plausible results.

Multilingualism is a cultural cornerstone of Europe and firmly anchored in the European treaties including full language equality. However, language barriers impacting business, cross-lingual and cross-cultural communication are still omnipresent. Language Technologies (LTs) are a powerful means to break down these barriers. While the last decade has seen various initiatives that created a multitude of approaches and technologies tailored to Europe's specific needs, there is still an immense level of fragmentation. At the same time, AI has become an increasingly important concept in the European Information and Communication Technology area. For a few years now, AI, including many opportunities, synergies but also misconceptions, has been overshadowing every other topic. We present an overview of the European LT landscape, describing funding programmes, activities, actions and challenges in the different countries with regard to LT, including the current state of play in industry and the LT market. We present a brief overview of the main LT-related activities on the EU level in the last ten years and develop strategic guidance with regard to four key dimensions., Comment: Proceedings of the 12th Language Resources and Evaluation Conference (LREC 2020). To appear

We consider the quantum version of the bandit problem known as {\em best arm identification} (BAI). We first propose a quantum modeling of the BAI problem, which assumes that both the learning agent and the environment are quantum; we then propose an algorithm based on quantum amplitude amplification to solve BAI. We formally analyze the behavior of the algorithm on all instances of the problem and we show, in particular, that it is able to get the optimal solution quadratically faster than what is known to hold in the classical case., Comment: All your comments are very welcome!

We present results of a long-term photometric multicolor optical monitoring project of selected low-mass and high-mass X-ray binaries carried out at the T\"UB\.ITAK National Observatory (TUG). New long-term $VRI$ multicolor observations of three selected X-ray binaries with neutron star components (HZ Her, ScoX-1, SAX J2103.5+4545) were observed between 2015 and 2019 with the TUG 60-cm telescope. The light variations of the systems are presented and discussed., Comment: 5 pages, 8 figures, accepted for publication in the CAOSP

We obtained new multicolour photometry of close binary stars in the young open cluster M35, the solar-age open cluster M67, and the globular cluster M71. New observations have been carried out at the T\"{U}B\.{I}TAK National Observatory (TUG) by using the 100cm (T100) telescope. We present observational results for eclipsing binary systems in the selected Galactic clusters. New accurate light curves for 2MASS J19532554 + 1851175, 2MASS J19533427 + 1844047, 2MASS J06092044 + 2415155, and AH Cnc were obtained. The light curves were analysed and we derived some of the orbital parameters of the systems., Comment: 5 pages, 4 figures, accepted for publication in CAOSP

This paper proposes an energy management framework for cellular heterogeneous networks (HetNets) supported by dynamic solar powered drones. A HetNet composed of a macrocell base station (BS), micro cell BSs, and drone small cell BSs are deployed to serve the networks' subscribers. The drones can land at pre-planned locations defined by the mobile operator and at the macrocell BS site where they can charge their batteries. The objective of the framework is to jointly determine the optimal trips of the drones and the MBSs that can be safely turned off in order to minimize the total energy consumption of the network. This is done while considering the cells' capacities and the minimum receiving power guaranteeing successful communications. To do so, an integer linear programming problem is formulated and optimally solved for three cases based on the knowledge level about future renewable energy statistics of the drones. A low complex relaxed solution is also developed. Its performances are shown to be close to those of the optimal solutions. However, the gap increases as the network becomes more congested. Numerical results investigate the performance of the proposed drone-based approach and show notable improvements in terms of energy saving and network capacity.

Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional architectures with an approximation of a kernel function by relying on the Nystr{\"o}m approximation. Our approach is easy and highly flexible. It is compatible with any kernel function and it allows exploiting multiple kernels. We show that our architecture has the same performance than standard architecture on datasets like SVHN and CIFAR100. One benefit of the method lies in its limited number of learnable parameters which makes it particularly suited for small training set sizes, e.g. from 5 to 20 samples per class.