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In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange functions when the orders of the singularities of the radial function's Fourier transforms at zero do not match the parity of the dimension of the space, and therefore new expansions and coefficients are needed to overcome this problem. We develop explicit constructions of infinite Fourier expansions that provide these coefficients and make an extensive comparison of the approximation qualities and - with a particular focus - polynomial precision and uniform approximation order of the various formulae. One of the interesting observations concerns the link between algebraic conditions of expansion coefficients and analytic properties of localness and convergence.

Human emotion recognition plays an important role in human-computer interaction. In this paper, we present our approach to the Valence-Arousal (VA) Estimation Challenge, Expression (Expr) Classification Challenge, and Action Unit (AU) Detection Challenge of the 5th Workshop and Competition on Affective Behavior Analysis in-the-wild (ABAW). Specifically, we propose a novel multi-modal fusion model that leverages Temporal Convolutional Networks (TCN) and Transformer to enhance the performance of continuous emotion recognition. Our model aims to effectively integrate visual and audio information for improved accuracy in recognizing emotions. Our model outperforms the baseline and ranks 3 in the Expression Classification challenge.

In this paper, we propose an effective computational approach to analyze and active control of geometrically nonlinear responses of functionally graded (FG) porous plates with graphene nanoplatelets (GPLs) reinforcement integrated with piezoelectric layers. The key concept behind this work is to utilize isogeometric analysis (IGA) based on B\'ezier extraction technique and $C^0$-type higher-order shear deformation theory ($C^0$-HSDT). By applying B\'ezier extraction, the original Non-Uniform Rational B-Spline (NURBS) control meshes can be transformed into B\'ezier elements which allow us to inherit the standard numerical procedure like the standard finite element method (FEM). In this scenario, the approximation of mechanical displacement field is calculated via $C^0$-HSDT whilst the electric potential field is considered as a linear function across the thickness of each piezoelectric sublayer. The FG plate includes internal pores and GPLs dispersed into metal matrix either uniformly or non-uniformly along plate's thickness. To control responses of structures, the top and bottom surfaces of FG plate are firmly bonded with piezoelectric layers which are considered as sensor and actuator layers. The geometrically nonlinear equations are solved by Newton-Raphson iterative procedure and Newmark's integration. The influence of porosity coefficient, weight fraction of GPLs as well as external electrical voltage on geometrically nonlinear behaviors of plate structures with various distributions of porosity and GPLs are thoroughly investigated. A constant displacement and velocity feedback control approaches are then adopted to actively control geometrically nonlinear static and dynamic responses, where structural damping effect is taken into account, based on a closed-loop control with sensor and actuator layers.

In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the multivariate normals with the same means and covariances. From the total variation bounds, we also derive a comparison of the cumulative distribution functions and quantile coupling inequalities between Pearson's chi-square statistic (written as the normalized quadratic form of a multinomial vector) and its multivariate normal analogue. We apply our results to find confidence intervals for the negative entropy of discrete distributions. Our method can be applied more generally to find confidence intervals for strictly convex functions of the weights of discrete distributions.

In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset.

In this paper, we present a pipeline for image extraction from historical documents using foundation models, and evaluate text-image prompts and their effectiveness on humanities datasets of varying levels of complexity. The motivation for this approach stems from the high interest of historians in visual elements printed alongside historical texts on the one hand, and from the relative lack of well-annotated datasets within the humanities when compared to other domains. We propose a sequential approach that relies on GroundDINO and Meta's Segment-Anything-Model (SAM) to retrieve a significant portion of visual data from historical documents that can then be used for downstream development tasks and dataset creation, as well as evaluate the effect of different linguistic prompts on the resulting detections.

In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption setup. The limit on the multiplication depth of homomorphic encryption circuits is a major challenge for iterative procedures such as gradient descent algorithms. Our analysis not only quantifies these limitations on prototype examples, thus serving as a benchmark for future investigations, but also highlights additional trade-offs like the ones pertaining the choice of gradient descent or accelerated gradient descent methods, opening the road for the use of homomorphic encryption techniques in iterative procedures widely used in optimization based control. In addition, we argue that, among the available homomorphic encryption schemes, the one adopted in this work, namely CKKS, is the only suitable scheme for implementing gradient descent algorithms. The choice of the appropriate step size is crucial to the convergence of the procedure. The paper shows firsthand the feasibility of homomorphically encrypted gradient descent algorithms.

In this paper, we present a transformer architecture for predicting student performance on standardized tests. Specifically, we leverage students historical data, including their past test scores, study habits, and other relevant information, to create a personalized model for each student. We then use these models to predict their future performance on a given test. Applying this model to the RIIID dataset, we demonstrate that using multiple granularities for temporal features as the decoder input significantly improve model performance. Our results also show the effectiveness of our approach, with substantial improvements over the LightGBM method. Our work contributes to the growing field of AI in education, providing a scalable and accurate tool for predicting student outcomes.

In this paper, we address the issue of fairness in preference-based reinforcement learning (PbRL) in the presence of multiple objectives. The main objective is to design control policies that can optimize multiple objectives while treating each objective fairly. Toward this objective, we design a new fairness-induced preference-based reinforcement learning or FPbRL. The main idea of FPbRL is to learn vector reward functions associated with multiple objectives via new welfare-based preferences rather than reward-based preference in PbRL, coupled with policy learning via maximizing a generalized Gini welfare function. Finally, we provide experiment studies on three different environments to show that the proposed FPbRL approach can achieve both efficiency and equity for learning effective and fair policies.