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Large language models (LLMs) play a vital role in almost every domain in today's organizations. In the context of this work, we highlight the use of LLMs for sentiment analysis (SA) and explainability. Specifically, we contribute a novel technique to leverage LLMs as a post-hoc model-independent tool for the explainability of SA. We applied our technique in the financial domain for currency-pair price predictions using open news feed data merged with market prices. Our application shows that the developed technique is not only a viable alternative to using conventional eXplainable AI but can also be fed back to enrich the input to the machine learning (ML) model to better predict future currency-pair values. We envision our results could be generalized to employing explainability as a conventional enrichment for ML input for better ML predictions in general., Comment: 7 pages, 3 figures, AIFin@ECAI 2024

This paper addresses two primary objectives in the realm of classical multiple orthogonal polynomials with an arbitrary number of weights. Firstly, it establishes new and explicit hypergeometric expressions for type I Hahn multiple orthogonal polynomials. Secondly, applying the residue theorem and the Mellin transform, the paper derives contour integral representations for several families of orthogonal polynomials. Specifically, it presents contour integral formulas for both type I and type II multiple orthogonal polynomials in the Laguerre of the first kind, Jacobi-Pi\~neiro, and Hahn families. The evaluation of these integrals leads to explicit hypergeometric representations., Comment: 21 pages

We consider a Maxwell system on $\mathbb{R}^3$ with periodic and highly oscillating coefficients. It is known that the solutions converge in the weak-$\ast$ topology of $L^\infty(0,T;\,L^2(\mathbb{R}^3))$ to the solution of a similar problem with constant coefficients given as the $H$-limits of the electric permittivity and the magnetic permeability respectively, i.e. the limit in the sense of the homogenization of linear elliptic equations with varying coefficients. However, it is not true that the elliptic corrector also provides a corrector for the solution of the Maxwell system, i.e. an approximation of the solutions in the strong topology of $L^2$. We shall prove that the oscillations in the space variable also produce oscillations in the time variable. We get a corrector consisting of adding to the elliptic corrector the sum of infinitely plane waves in the fast variable. Note that related results have been previously proved for the wave equation. Our proof is based on the two-scale convergence theory for almost periodic functions. One of the novelties is to show how this contains the classical Block decomposition.

This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Pi\~neiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for nearest-neighbor recurrence coefficients, as well as the step line case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials.

We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a long-range memory term. Our aim is not only to get this limit problem but also to study its main properties. Using the micro-structure variables it is simple to check that it satisfies an energy conservation law assuring in particular the existence and uniqueness of solution. The difficulty is to characterize these properties using only the macroscopic system. We prove that the nonlocal term is given through a convolution kernel which exponentially decreases to zero and satisfies some positive conditions which we write in terms of the Laplace transform. These conditions can be used to directly prove the existence and uniqueness of solution. The results apply to modeling the mechanical behavior of skin as an indicator of what kind of models we should use. In a naive interpretation the fluid inclusions represent the cells and the elastic medium the extracellular matrix.

The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in $L^N(\Omega)$, with $N$ the dimension of the space. It is known that there exists a unique solution for each of these problems in the Sobolev space $H^1_0(\Omega)$. However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in \cite{boc1}, and a regularization obtained by adding a small nonlinear first order term, to pass to the limit in these problems.

We introduce a DeGroot-based model for opinion dynamics in social networks. A community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. The model is formalized using labeled transition systems, henceforth called opinion transition systems (OTS), whose states represent the agents' opinions and whose actions are the edges of the influence graph. If a transition labeled $(i,j)$ is performed, agent $j$ updates their opinion taking into account the opinion of agent $i$ and the influence $i$ has over $j$. We study (convergence to) opinion consensus among the agents of strongly-connected graphs with influence values in the interval $(0,1)$. We show that consensus cannot be guaranteed under the standard strong fairness assumption on transition systems. We derive that consensus is guaranteed under a stronger notion from the literature of concurrent systems; bounded fairness. We argue that bounded-fairness is too strong of a notion for consensus as it almost surely rules out random runs and it is not a constructive liveness property. We introduce a weaker fairness notion, called $m$-bounded fairness, and show that it guarantees consensus. The new notion includes almost surely all random runs and it is a constructive liveness property. Finally, we consider OTS with dynamic influence and show convergence to consensus holds under $m$-bounded fairness if the influence changes within a fixed interval $[L,U]$ with $0

For a general number $p\geq 2$ of measures, we provide explicit expressions for the Jacobi-Pi\~neiro and Laguerre of the first kind multiple orthogonal polynomials of type I, presented in terms of multiple hypergeometric functions.

Perception systems for ornithopters face severe challenges. The harsh vibrations and abrupt movements caused during flapping are prone to produce motion blur and strong lighting condition changes. Their strict restrictions in weight, size, and energy consumption also limit the type and number of sensors to mount onboard. Lightweight traditional cameras have become a standard off-the-shelf solution in many flapping-wing designs. However, bioinspired event cameras are a promising solution for ornithopter perception due to their microsecond temporal resolution, high dynamic range, and low power consumption. This paper presents an experimental comparison between frame-based and an event-based camera. Both technologies are analyzed considering the particular flapping-wing robot specifications and also experimentally analyzing the performance of well-known vision algorithms with data recorded onboard a flapping-wing robot. Our results suggest event cameras as the most suitable sensors for ornithopters. Nevertheless, they also evidence the open challenges for event-based vision on board flapping-wing robots.

Surface tension at cavity walls can play havoc with the mechanical properties of perforated soft solids when the cavities are filled with a fluid. This study is an investigation of the macroscopic elastic properties of elastomers embedding spherical cavities filled with a pressurized liquid in the presence of surface tension, starting with the linearization of the fully nonlinear model and ending with the enhancement properties of the linearized model when many such liquid filled cavities are present.

This paper explores a factorization using bidiagonal matrices of the recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is expressed in terms of ratios involving the generalized hypergeometric function ${}_3F_2$ and is proven using recently discovered contiguous relations. Moreover, employing the multiple Askey scheme, a bidiagonal factorization is derived for the Hahn descendants, including Jacobi-Pi\~neiro, multiple Meixner (kinds I and II), multiple Laguerre (kinds I and II), multiple Kravchuk, and multiple Charlier, all represented in terms of hypergeometric functions. For the cases of multiple Hahn, Jacobi-Pi\~neiro, Meixner of kind II, and Laguerre of kind I, where there exists a region where the recurrence matrix is nonnegative, subregions are identified where the bidiagonal factorization becomes a positive bidiagonal factorization., Comment: 14 pages, 2 figures

This paper investigates stochastic finite matrices and the corresponding finite Markov chains constructed using recurrence matrices for general families of orthogonal polynomials and multiple orthogonal polynomials. The paper explores the spectral theory of transition matrices, utilizing both orthogonal and multiple orthogonal polynomials. Several properties are derived, including classes, periodicity, recurrence, stationary states, ergodicity, expected recurrence times, time-reversed chains, and reversibility. Furthermore, the paper uncovers factorization in terms of pure birth and pure death processes. The case study focuses on hypergeometric orthogonal polynomials, where all the computations can be carried out effectively. Particularly within the Askey scheme, all descendants under Hahn (excluding Bessel), such as Hahn, Jacobi, Meixner, Kravchuk, Laguerre, Charlier, and Hermite, present interesting examples of recurrent reversible birth and death finite Markov chains. Additionally, the paper considers multiple orthogonal polynomials, including multiple Hahn, Jacobi-Pi\~neiro, Laguerre of the first kind, and Meixner of the second kind, along with their hypergeometric representations and derives the corresponding recurrent finite Markov chains and time-reversed chains., Comment: 40 pages, 3 figures

In this work we survey on connections of Markov chains and the theory of multiple orthogonality. Here we mainly concentrate on give a procedure to generate stochastic tetra diagonal Hessenberg matrices, coming from some specific families of multiple orthogonal, such as the ones of Jacobi--Pi\~neiro and Hypergeometric Lima--Loureiro. We show that associated with a positive tetra diagonal nonnegative bounded Hessenberg matrix we can construct two stochastic tetra diagonal ones. These two stochastic tridiagonal nonnegative Hessenberg matrices are shown to be, enlightened by the Poincar\'e theorem, limit transpose of each other.

In this paper we consider optimal control problems where the control variable is a potential and the state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator. The cost functional involves the solution of the state equation and a penalization term for the control variable. While the existence of an optimal solution simply follows by the direct methods of the calculus of variations, the regularity of the optimal potential is a difficult question and under the general assumptions we consider, no better regularity than the $BV$ one can be expected. This happens in particular for the cases in which a bang-bang solution occurs, where optimal potentials are characteristic functions of a domain. We prove the $BV$ regularity of optimal solutions through a regularity result for PDEs. Some numerical simulations show the behavior of optimal potentials in some particular cases., Comment: 29 pages, 4 figures

Explicit expressions for the Hahn multiple polynomials of type I, in terms of Kamp\'e de F\'eriet hypergeometric series, are given. Orthogonal and biorthogonal relations are proven. Then, part of the Askey scheme for multiple orthogonal polynomials type I is completed. In particular, explicit expressions in terms of generalized hypergeometric series and Kamp\'e de F\'eriet hypergeometric series, are given for the multiple orthogonal polynomials of type I for the Jacobi-Pi\~neiro, Meixner I, Meixner II, Kravchuk, Laguerre I, Laguerre II and Charlier families., Comment: 27 pages. Minor typos corrected

This work presents a suite of two optimisation models for the short-term scheduling and redispatch of a virtual power plant (VPP) composed of a wind farm and a Li-ion battery, that participates in the day-ahead energy and secondary regulation reserve markets of the Iberian electricity market. First, a two-stage stochastic mixed-integer linear programming model is used to obtain the VPP's generation and reserve schedule and the opportunity cost of the energy stored in the battery. The model has an hourly resolution and a look-ahead period beyond the markets' scheduling horizon and considers the hourly battery degradation costs as a function of both the depth of discharge and the discharge rate. Different strategies are evaluated to forecast the real-time use of the committed secondary regulation reserves. Second, a deterministic MILP model is used to determine the redispatch of the VPP using as input the generation and reserve schedule and the VPP's storage opportunity cost provided by the former model and is executed on an hourly rolling basis. The results obtained show that the proposed models are effective for the short-term scheduling and redispatch of the VPP used with a low computational time, making them tractable and practical for their daily use., Comment: 13 pages, 8 figures and 2 tables

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results., Comment: 25 pages, 9 figures, 3 tables

This registered report introduces the largest, and for the first time, reproducible experimental survey on biomedical sentence similarity with the following aims: (1) to elucidate the state of the art of the problem; (2) to solve some reproducibility problems preventing the evaluation of most of current methods; (3) to evaluate several unexplored sentence similarity methods; (4) to evaluate an unexplored benchmark, called Corpus-Transcriptional-Regulation; (5) to carry out a study on the impact of the pre-processing stages and Named Entity Recognition (NER) tools on the performance of the sentence similarity methods; and finally, (6) to bridge the lack of reproducibility resources for methods and experiments in this line of research. Our experimental survey is based on a single software platform that is provided with a detailed reproducibility protocol and dataset as supplementary material to allow the exact replication of all our experiments. In addition, we introduce a new aggregated string-based sentence similarity method, called LiBlock, together with eight variants of current ontology-based methods and a new pre-trained word embedding model trained on the full-text articles in the PMC-BioC corpus. Our experiments show that our novel string-based measure sets the new state of the art on the sentence similarity task in the biomedical domain and significantly outperforms all the methods evaluated herein, except one ontology-based method. Likewise, our experiments confirm that the pre-processing stages, and the choice of the NER tool, have a significant impact on the performance of the sentence similarity methods. We also detail some drawbacks and limitations of current methods, and warn on the need of refining the current benchmarks. Finally, a noticeable finding is that our new string-based method significantly outperforms all state-of-the-art Machine Learning models evaluated herein., Comment: 48 pages, 4 figures, 17 tables, three appendices not included in pre-print version