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The RESISTO project represents a pioneering initiative in Europe aimed at enhancing the resilience of the power grid through the integration of advanced technologies. This includes artificial intelligence and thermal surveillance systems to mitigate the impact of extreme meteorological phenomena. RESISTO endeavors to predict, prevent, detect, and recover from weather-related incidents, ultimately enhancing the quality of service provided and ensuring grid stability and efficiency in the face of evolving climate challenges. In this study, we introduce one of the fundamental pillars of the project: a monitoring system for the operating temperature of different regions within power transformers, aiming to detect and alert early on potential thermal anomalies. To achieve this, a distributed system of thermal cameras for real-time temperature monitoring has been deployed in The Do\~nana National Park, alongside servers responsible for the storing, analyzing, and alerting of any potential thermal anomalies. An adaptive prediction model was developed for temperature forecasting, which learns online from the newly available data. In order to test the long-term performance of the proposed solution, we generated a synthetic temperature database for the whole of the year 2022. Overall, the proposed system exhibits promising capabilities in predicting and detecting thermal anomalies in power electric transformers, showcasing potential applications in enhancing grid reliability and preventing equipment failures.

The RESISTO project, a pioneer innovation initiative in Europe, endeavors to enhance the resilience of electrical networks against extreme weather events and associated risks. Emphasizing intelligence and flexibility within distribution networks, RESISTO aims to address climatic and physical incidents comprehensively, fostering resilience across planning, response, recovery, and adaptation phases. Leveraging advanced technologies including AI, IoT sensors, and aerial robots, RESISTO integrates prediction, detection, and mitigation strategies to optimize network operation. This article summarizes the main technical aspects of the proposed solutions to meet the aforementioned objectives, including the development of a climate risk detection platform, an IoT-based monitoring and anomaly detection network, and a fleet of intelligent aerial robots. Each contributing to the project's overarching objectives of enhancing network resilience and operational efficiency.

We prove Sobolev-Poincar\'e and Poincar\'e inequalities in variable Lebesgue spaces $L^{p(\cdot)}(\Omega)$, with $\Omega\subset{\mathbb R}^n$ a bounded John domain, with weaker regularity assumptions on the exponent $p(\cdot)$ that have been used previously. In particular, we require $p(\cdot)$ to satisfy a new \emph{boundary $\log$-H\"older condition} that imposes some logarithmic decay on the oscillation of $p(\cdot)$ towards the boundary of the domain. Some control over the interior oscillation of $p(\cdot)$ is also needed, but it is given by a very general condition that allows $p(\cdot)$ to be discontinuous at every point of $\Omega$. Our results follows from a local-to-global argument based on the continuity of certain Hardy type operators. We provide examples that show that our boundary $\log$-H\"older condition is essentially necessary for our main results. The same examples are adapted to show that this condition is not sufficient for other related inequalities. Finally, we give an application to a Neumann problem for a degenerate $p(\cdot)$-Laplacian.

Let $\A$ be a $\k$-algebra where $\k$ a field of arbitrary characteristic, and let $\mathscr{A}_\k$ be a full subcategory of $\A$-Mod, the abelian category of left $\A$-modules.Following M. Kleiner and I. Reiten, $\mathscr{A}_\k$ is {\it Hom-finite} if the hom-space between any two objects in $\mathscr{A}_\k$ is finite-dimensional over $\k$. We further say that $\mathscr{A}_\k$ is {\it Ext-finite} if $\dim_\k\Ext^i_\A(X,Y)<\infty$ for all objects $X$ and $Y$ in $\mathscr{A}_\k$. Let $V$ be an object in $\mathscr{A}_\k$. In this note we prove that if $\End_\A(V)$ is isomorphic to $\k$, then $V$ has a universal deformation ring $R(\A,V)$, which is a local complete Noetherian commutative $\k$-algebra whose residue field is also isomorphic to $\k$. We use this result to prove that if $\A$ is a local two-point infinite dimensional gentle $\k$-algebra (in the sense of V. Bekkert et al), then $R(\A,V)$ is isomorphic either to $\k$, to $\k[\![t]\!]/(t^2)$ or to $\k[\![t]\!]$.

Variable sharing is a fundamental property in the static analysis of logic programs, since it is instrumental for ensuring correctness and increasing precision while inferring many useful program properties. Such properties include modes, determinacy, non-failure, cost, etc. This has motivated significant work on developing abstract domains to improve the precision and performance of sharing analyses. Much of this work has centered around the family of set-sharing domains, because of the high precision they offer. However, this comes at a price: their scalability to a wide set of realistic programs remains challenging and this hinders their wider adoption. In this work, rather than defining new sharing abstract domains, we focus instead on developing techniques which can be incorporated in the analyzers to address aspects that are known to affect the efficiency of these domains, such as the number of variables, without affecting precision. These techniques are inspired in others used in the context of compiler optimizations, such as expression reassociation and variable trimming. We present several such techniques and provide an extensive experimental evaluation of over 1100 program modules taken from both production code and classical benchmarks. This includes the Spectector cache analyzer, the s(CASP) system, the libraries of the Ciao system, the LPdoc documenter, the PLAI analyzer itself, etc. The experimental results are quite encouraging: we have obtained significant speed-ups, and, more importantly, the number of modules that require a timeout was cut in half. As a result, many more programs can be analyzed precisely in reasonable times., Comment: 61 pages, 10 figures, 7 tables, submitted to ICLP 2024

We present a scheme for the implementation of fast arbitrary qubit gates in the ground state of the negatively charged nitrogen-vacancy (NV$^-$) defect in diamond. The protocol is especially useful in the low-field regime and for high-frequency sensing applications. It constitutes an extension to the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level thanks to an effective Raman coupling. Here we derive a full theoretical framework of the scheme, identifying the complete unitary associated to the approach, and more specifically the relevant basis change for each of two characteristic pulse durations. Based on this insight, we propose a scheme to perform fast qubit transformations in the double quantum transition. We study its robustness with respect to pulse-timing errors resulting from faulty identification of system parameters or phase-control limitations. We finally demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields., Comment: 26 pages, 6 figures, comments welcome

We study the relative asymptotics of two sequences of multiple orthogonal polynomials corresponding to two Nikishin systems of measures on the real line, the second one of which is obtained from the first one perturbing the generating measures with non-negative integrable functions. Each Nikishin system consists of two measures., Comment: 21 pages

Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such information is typically represented as functions of input data sizes. More generally, recurrence equations have been increasingly used to automatically obtain non-linear numerical invariants. However, state-of-the-art recurrence solvers and cost analysers suffer from serious limitations when dealing with the (complex) features of recurrences arising from cost analyses. We address this challenge by developing a novel order-theoretical framework where recurrences are viewed as operators and their solutions as fixpoints, which allows leveraging powerful pre/postfixpoint search techniques. We prove useful properties and provide principles and insights that enable us to develop techniques and combine them to design new solvers. We have also implemented and experimentally evaluated an optimisation-based instantiation of the proposed approach. The results are quite promising: our prototype outperforms state-of-the-art cost analysers and recurrence solvers, and can infer tight non-linear lower/upper bounds, in a reasonable time, for complex recurrences representing diverse program behaviours., Comment: Preprint of a paper accepted at SAS 2024

Automatic static cost analysis infers information about the resources used by programs without actually running them with concrete data, and presents such information as functions of input data sizes. Most of the analysis tools for logic programs (and many for other languages), as CiaoPP, are based on setting up recurrence relations representing (bounds on) the computational cost of predicates, and solving them to find closed-form functions. Such recurrence solving is a bottleneck in current tools: many of the recurrences that arise during the analysis cannot be solved with state-of-the-art solvers, including Computer Algebra Systems (CASs), so that specific methods for different classes of recurrences need to be developed. We address such a challenge by developing a novel, general approach for solving arbitrary, constrained recurrence relations, that uses machine-learning (sparse-linear and symbolic) regression techniques to guess a candidate closed-form function, and a combination of an SMT-solver and a CAS to check if it is actually a solution of the recurrence. Our prototype implementation and its experimental evaluation within the context of the CiaoPP system show quite promising results. Overall, for the considered benchmarks, our approach outperforms state-of-the-art cost analyzers and recurrence solvers, and solves recurrences that cannot be solved by them. Under consideration in Theory and Practice of Logic Programming (TPLP)., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP). Extended, revised version of our work published in ICLP (Klemen et al. 2023, arXiv:2309.07259). arXiv admin note: text overlap with arXiv:2309.07259

Advances in natural language processing techniques, such as named entity recognition and normalization to widely used standardized terminologies like UMLS or SNOMED-CT, along with the digitalization of electronic health records, have significantly advanced clinical text analysis. This study presents ClinLinker, a novel approach employing a two-phase pipeline for medical entity linking that leverages the potential of in-domain adapted language models for biomedical text mining: initial candidate retrieval using a SapBERT-based bi-encoder and subsequent re-ranking with a cross-encoder, trained by following a contrastive-learning strategy to be tailored to medical concepts in Spanish. This methodology, focused initially on content in Spanish, substantially outperforming multilingual language models designed for the same purpose. This is true even for complex scenarios involving heterogeneous medical terminologies and being trained on a subset of the original data. Our results, evaluated using top-k accuracy at 25 and other top-k metrics, demonstrate our approach's performance on two distinct clinical entity linking Gold Standard corpora, DisTEMIST (diseases) and MedProcNER (clinical procedures), outperforming previous benchmarks by 40 points in DisTEMIST and 43 points in MedProcNER, both normalized to SNOMED-CT codes. These findings highlight our approach's ability to address language-specific nuances and set a new benchmark in entity linking, offering a potent tool for enhancing the utility of digital medical records. The resulting system is of practical value, both for large scale automatic generation of structured data derived from clinical records, as well as for exhaustive extraction and harmonization of predefined clinical variables of interest.

With a single circulating vector-borne virus, the basic reproduction number incorporates contributions from tick-to-tick (co-feeding), tick-to-host and host-to-tick transmission routes. With two different circulating vector-borne viral strains, resident and invasive, and under the assumption that co-feeding is the only transmission route in a tick population, the invasion reproduction number depends on whether the model system of ordinary differential equations possesses the property of neutrality. We show that a simple model, with two populations of ticks infected with one strain, resident or invasive, and one population of co-infected ticks, does not have Alizon's neutrality property. We present model alternatives that are capable of representing the invasion potential of a novel strain by including populations of ticks dually infected with the same strain. The invasion reproduction number is analysed with the next-generation method and via numerical simulations., Comment: 37 pages and 4 figures

The liberalisation of the European passenger railway markets through the European Directive EU 91/440/EEC states a new scenario where different Railway Undertakings compete with each other in a bidding process for time slots. The infrastructure resources are provided by the Infrastructure Manager, who analyses and assesses the bids received, allocating the resources to each Railway Undertaking. Time slot allocation is a fact that drastically influences the market equilibrium. In this paper, we address the time slot allocation problem within the context of a liberalized passenger railway market as a multi-objective model. The Infrastructure Manager is tasked with selecting a point from the Pareto front as the solution to the time slot allocation problem. We propose two criteria for making this selection: the first one allocates time slots to each company according to a set of priorities, while the second one introduces a criterion of fairness in the treatment of companies to incentive competition. The assessment of the impact of these rules on market equilibrium has been conducted on a liberalized high-speed corridor within the Spanish railway network., Comment: 32 pages and 6 figures

For the Riesz and logarithmic potentials, we consider greedy energy sequences $(a_n)_{n=0}^\infty$ on the unit circle $S^1$, constructed in such a way that for every $n\geq 1$, the discrete potential generated by the first $n$ points $a_0,\ldots,a_{n-1}$ of the sequence attains its minimum value (say $U_n$) at $a_n$. We obtain asymptotic formulae that describe the behavior of $U_n$ as $n\to\infty$, in terms of certain bounded arithmetic functions with a doubling periodicity property. As previously shown in \cite{LopMc2}, after properly translating and scaling $U_n$, one obtains a new sequence $(F_n)$ that is bounded and divergent. We find the exact value of $\liminf F_n$ (the value of $\limsup F_n$ was already given in \cite{LopMc2}), and show that the interval $[\liminf F_n,\limsup F_n]$ comprises all the limit points of the sequence $(F_n)$., Comment: 20 pages. Some minor text modifications and typos were corrected

Automatic static cost analysis infers information about the resources used by programs without actually running them with concrete data, and presents such information as functions of input data sizes. Most of the analysis tools for logic programs (and other languages) are based on setting up recurrence relations representing (bounds on) the computational cost of predicates, and solving them to find closed-form functions that are equivalent to (or a bound on) them. Such recurrence solving is a bottleneck in current tools: many of the recurrences that arise during the analysis cannot be solved with current solvers, such as Computer Algebra Systems (CASs), so that specific methods for different classes of recurrences need to be developed. We address such a challenge by developing a novel, general approach for solving arbitrary, constrained recurrence relations, that uses machine-learning sparse regression techniques to guess a candidate closed-form function, and a combination of an SMT-solver and a CAS to check whether such function is actually a solution of the recurrence. We have implemented a prototype and evaluated it with recurrences generated by a cost analysis system (the one in CiaoPP). The experimental results are quite promising, showing that our approach can find closed-form solutions, in a reasonable time, for classes of recurrences that cannot be solved by such a system, nor by current CASs., Comment: In Proceedings ICLP 2023, arXiv:2308.14898

In this paper we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the left endpoint, where the potential has a singularity. We use some results from the singular Sturm-Liouville theory to show the well-posedness of our system. We obtain a spectral decomposition of a degenerate parabolic operator with Robin conditions at the endpoints, we use Fourier-Dini expansions and the moment method introduced by Fattorini and Russell to prove the null controllability and to obtain an upper estimate of the cost of controllability. We also get a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type., Comment: arXiv admin note: substantial text overlap with arXiv:2304.00178, arXiv:2302.01197

We begin our analysis with the study of two collections of lattice paths in the plane, denoted $\mathcal{D}_{[n,i,j]}$ and $\mathcal{P}_{[n,i,j]}$. These paths consist of sequences of $n$ steps, where each step allows movement in three directions: upward (with a maximum displacement of $q$ units), rightward (exactly one unit), or downward (with a maximum displacement of $p$ units). The paths start from the point $(0,i)$ and end at the point $(n,j)$. In the collection $\mathcal{D}_{[n,i,j]}$, it is a crucial constraint that paths never go below the $x$-axis, while in the collection $\mathcal{P}_{[n,i,j]}$, paths have no such restriction. We assign weights to each path in both collections and introduce weight polynomials and generating series for them. Our main results demonstrate that certain matrices of size $q\times p$ associated with these generating series can be expressed as matrix continued fractions. These results extend the notable contributions previously made by P. Flajolet and G. Viennot in the scalar case $p=q=1$. The generating series can also be interpreted as resolvents of one-sided or two-sided difference operators of finite order. Additionally, we analyze a class of random banded matrices $H$, which have $p+q+1$ diagonals with entries that are independent and bounded random variables. These random variables have identical distributions along diagonals. We investigate the asymptotic behavior of the expected values of eigenvalue moments for the principal $n\times n$ truncation of $H$ as $n$ tends to infinity., Comment: 48 pages, 3 figures

Ordinary differential equation (ODE) models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital this is an extremely restrictive assumption as typically a hospital ward has a few dozen, or even fewer, patients. This work reframes a well-known model used in the study of the spread of antibiotic-resistant bacteria in hospitals, to consider the pathogen transmission dynamics in small populations. In this vein, this paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. We determine the probability law of the \emph{exact} reproduction number ${\cal R}_{exact,0}$, which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number ${\cal R}_{exact,0}$ into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods. This guarantees the compatibility of the new, finite-population model, with large population models present in the literature and takes full advantage, in its mathematical analysis, of the intrinsic stochasticity., Comment: 30 pages, 9 figures

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a spectral decomposition of a suitable operator, defined in a weighted Sobolev space, and the moment method by Fattorini and Russell to obtain an upper estimate of the cost of controllability. We also obtain a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type., Comment: 19 pages. arXiv admin note: substantial text overlap with arXiv:2302.01197

We prove the null controllability of a one dimensional degenerate parabolic equation with drift and a singular potential. We study the case the potential arises at the left end point and the weighted Dirichlet boundary control is located at this point. We get a spectral decomposition of a suitable operator, defined in a weighted Sobolev space, involving Bessel functions and their zeros, then we use the moment method by Fattorini and Russell to obtain an upper estimate of the cost of controllability. We also obtain a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type., Comment: 17 pages

We consider several non-standard discrete and continuous Green energy problems in the complex plane and study the asymptotic relations between their solutions. In the discrete setting, we consider two problems; one with variable particle positions (within a given compact set) and variable particle masses, the other one with variable masses but prescribed positions. The mass of a particle is allowed to take any value in the range $0\leq m\leq R$, where $R>0$ is a fixed parameter in the problem. The corresponding continuous energy problems are defined on the space of positive measures $\mu$ with mass $\|\mu\|\leq R$ and supported on the given compact set, with an additional upper constraint that appears as a consequence of the prescribed positions condition. It is proved that the equilibrium constant and equilibrium measure vary continuously as functions of the parameter $R$ (the latter in the weak-star topology). In the unconstrained energy problem we present a greedy algorithm that converges to the equilibrium constant and equilibrium measure. In the discrete energy problems, it is shown that under certain conditions, the optimal values of the particle masses are uniquely determined by the optimal positions or prescribed positions of the particles, depending on the type of problem considered., Comment: This is a revised and improved version of the paper. Accepted for publication in Analysis and Mathematical Physics. 29 pages

Audio fingerprinting is a technique used to identify and match audio recordings based on their unique characteristics. It involves creating a condensed representation of an audio signal that can be used to quickly compare and match against other audio recordings. The fingerprinting process involves analyzing the audio signal to extract certain features, such as spectral content, tempo, and rhythm, among other things. In this paper, we present SpectroMap, an open-source GitHub repository for audio fingerprinting written in Python programming language. It is composed of a peak search algorithm that extracts topological prominences from a spectrogram via time-frequency bands. In this paper, we introduce the algorithm functioning with two experimental applications in a high-quality urban sound dataset and environmental audio recordings to describe how it works and how effective it is in handling the input data. Finally, we have posed two Python scripts that would reproduce the proposed case studies in order to ease the reproducibility of our audio fingerprinting system., Comment: 12 pages, 5 figures

We study certain inequalities and a related result on weighted Sobolev spaces on bounded John domains in $\mathbb{R}^n$. Namely, we prove the existence of a right inverse for the divergence operator, along with the corresponding a priori estimate, the improved and the fractional Poincar\'e inequalities, the Korn inequality and the local Fefferman-Stein inequality. All these results are obtained on weighted Sobolev spaces, where the weight is a power of the distance to the boundary. In all cases the exponent of the weight $d(\cdot,\partial\Omega)^{\beta p}$ is only required to satisfy the restriction: $\beta p>-(n-\dim_A(\partial\Omega))$, where $p$ is the exponent of the Sobolev space and $\dim_A(\partial\Omega)$ is the Assouad dimension of the boundary of the domain. According to our best knowledge, this condition is less restrictive than the ones in the literature., Comment: 21 pages, 2 figures

Light-harvesting complexes in natural photosynthetic systems, such as those in purple bacteria, consist of photo-reactive chromophores embedded in densely packed "antenna" systems organized in well-defined nanostructures. In the case of purple bacteria, the chromophore antennas are composed of natural J-aggregates such as bacteriochlorophylls and carotenoids. Inspired by the molecular composition of such biological systems, we create a library of organic materials composed of densely packed J-aggregates in a polymeric matrix, in which the matrix mimics a protein scaffold. This library of organic materials shows polaritonic properties which can be tuned from the visible to the infrared by choice of the model molecule. Inspired by the molecular architecture of the light-harvesting complexes of \textit{Rhodospirillum molischianum} bacteria, we study the light-matter interactions of J-aggregate-based nanorings with similar dimensions to the analogous natural nanoscale architectures. Electromagnetic simulations show that these nanorings of J-aggregates can act as resonators, with subwavelength confinement of light while concentrating the electric field in specific regions. These results open the door to bio-inspired building blocks for all-organic metamaterials while offering a new perspective on light-matter interactions at the nanoscale in densely packed organic matter in biological organisms including photosynthetic organelles., Comment: Including supplementary information

Frouros is an open-source Python library capable of detecting drift in machine learning systems. It provides a combination of classical and more recent algorithms for drift detection: both concept and data drift. We have designed it with the objective of making it compatible with any machine learning framework and easily adaptable to real-world use cases. The library is developed following a set of best development and continuous integration practices to ensure ease of maintenance and extensibility. The source code is available at https://github.com/IFCA/frouros., Comment: 11 pages, 1 table

Optical Tamm States (OTS) are confined optical modes that can occur at the interface between two highly reflective structures. However, due to the strong reflectance required, their implemen-tation with highly processable and metal-free flexible materials has proven challenging. Herein, we develop the first structure supporting OTS based only on organic polymeric materials, demon-strating a photonic platform based on non-critical, widely available, and easily processable mate-rials. The structures fabricated present large areas and consist of a narrowband multi-layered polymeric Distributed Bragg Reflector (DBR) followed by a thin film of J-aggregate molecular exci-tonic material that can act as a highly reflective surface within a narrowband range. We take ad-vantage of the narrowband spectral response of the DBR and of the reflective molecular layer to tune the OTS band by varying the periodicity of the multilayer, opening the door for the fabrica-tion of OTS structures based on lightweight integrable excitonic devices with cost-effective proce-dures., Comment: 15 pages, 8 (3+5) figures, supplementary information included

Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters. However, for $n\approx p$ or $p > n$ such models are poorly determined. Kalaitzis et al. (2013) introduced the Bigraphical Lasso, an estimator for sparse precision matrices based on the Cartesian product of graphs. Unfortunately, the original Bigraphical Lasso algorithm is not applicable in case of large p and n due to memory requirements. We exploit eigenvalue decomposition of the Cartesian product graph to present a more efficient version of the algorithm which reduces memory requirements from $O(n^2p^2)$ to $O(n^2 + p^2)$. Many datasets in different application fields, such as biology, medicine and social science, come with count data, for which Gaussian based models are not applicable. Our multi-way network inference approach can be used for discrete data. Our methodology accounts for the dependencies across both instances and features, reduces the computational complexity for high dimensional data and enables to deal with both discrete and continuous data. Numerical studies on both synthetic and real datasets are presented to showcase the performance of our method.

We give a combinatorial interpretation of vector continued fractions obtained by applying the Jacobi-Perron algorithm to a vector of $p\geq 1$ resolvent functions of a banded Hessenberg operator of order $p+1$. The interpretation consists in the identification of the coefficients in the power series expansion of the resolvent functions as weight polynomials associated with Lukasiewicz lattice paths in the upper half-plane. In the scalar case $p=1$ this reduces to the relation established by P. Flajolet and G. Viennot between Jacobi-Stieltjes continued fractions, their power series expansion, and Motzkin paths. We consider three classes of lattice paths, namely the Lukasiewicz paths in the upper half-plane, their symmetric images in the lower half-plane, and a third class of unrestricted lattice paths which are allowed to cross the $x$-axis. We establish a relation between the three families of paths by means of a relation between the associated generating power series. We also discuss the subcollection of Lukasiewicz paths formed by the partial $p$-Dyck paths, whose weight polynomials are known in the literature as genetic sums or generalized Stieltjes-Rogers polynomials, and express certain moments of bi-diagonal Hessenberg operators., Comment: The presentation of the paper has been improved in this version, no changes in the results. 30 pages

Fake news are affecting a large proportion of the population even becoming a danger to the society. Mostly, this disinformation flow take place through Internet. Being aware of that problem, in this work we propose a synthetic indicator that measures the user reputation in Twitter in order to analyze the credibility of the content in this social network. In order to show the indicator utility, we have analyzed data from some political topics in Spain from 2019 to 2020 and we have checked that bots plays a decisive role into the spread of news and, as might be expected, the link among popularity and reputation reports about the event credibility., Comment: 7 pages, 4 figures, 4 tables,9 references

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, each can be imagined as sampling from a probability density of times to division. The most convenient choice of density in mathematical and computational work, the exponential density, overestimates the probability of short division times. We consider a multi-stage model that produces an Erlang distribution of times to division, and an exponential distribution of times to die. The resulting dynamics of competing fates is a type of cyton model. Using Approximate Bayesian Computation, we compare our model to published cell counts, obtained after CFSE-labelled OT-I and F5 T cells were transferred to lymphopenic mice. The death rate is assumed to scale linearly with the generation (number of divisions) and the number of stages of undivided cells (generation $0$) is allowed to differ from that of cells that have divided at least once (generation greater than zero). Multiple stages are preferred in posterior distributions, and the mean time to first division is longer than the mean time to subsequent divisions., Comment: 26 pages, 11 figures

Natural photosynthetic photonic nanostructures can show sophisticated light matter-interactions including enhanced light absorption by slow light even for highly pigmented systems. Beyond fundamental biology aspects these natural nanostructures are very attractive as blueprints for advanced photonic devices. But the soft-matter biomimetic implementations of such nanostructures is challenging due to the low refractive index contrast of most organic photonic structures. Excitonic organic material with near zero index (NZI) optical properties allow overcoming these bottlenecks. Here we demonstrate that the combination of NZI thin films into photonic multilayers like the ones found in nature enables broadband tuneable strong reflectance as well as slow light absorption enhancement and tailored photoluminescence properties in the full VIS spectrum. Moreover, it is shown that this complex optical response is tuneable, paving the way towards the development of active devices based on all polymer and near zero index materials photonic structures.

Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by cellular division and cellular differentiation, events which lead to a population of cells with unique characteristics. In this paper, we model the dynamics of cells over time across a sequence of compartments. Cells within a compartment may represent being at the same spatial location or sharing the same phenotype. In this sequence of compartments, cells can either die, divide or enter an adjacent compartment. We analyse a set of ordinary differential equations to describe the evolution of the average number of cells in each compartment over time. We also focus on the progeny of a founder cell in terms of a stochastic process and analyse several summary statistics to bring insights into the lifespan of a single cell, the number of divisions during its lifespan, and the probability to die in each compartment. Numerical results inspired by cellular immune processes allow us to illustrate the applicability of our techniques., Comment: 22 pages, 8 figures

Van der Waals heterostructures (vdWHs) combine different layered materials with properties of interest,1 such as two-dimensional (2D) semimetals, semiconductors, magnets or superconductors. These heterostructures provide the possibility of engineering new materials with emergent functionalities that are not accessible in another way. Beyond inorganic 2D materials, layered molecular materials remain still rather unexplored, with only few examples regarding their isolation as atomically thin-layers. By a proper chemical design, the physical properties of these systems can be tuned, as illustrated by the so-called spin-crossover (SCO) compounds, in which a spin transition can be induced by applying external stimuli like light, temperature, pressure or an electric field. Here, we report on vdWHs formed by SCO layers and few-layers graphene, being its properties modified by the strain concomitant to the spin transition. These molecular/inorganic vdWHs represent the deterministic incorporation of bistable molecular layers with other 2D materials of interest in the emergent field of straintronics., Comment: 18 pages, 5 figures

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such as cost, on successive loop iterations. Recurrence solvers are capable of computing closed forms for some recurrences, thus deriving precise relationships capturing the complete loop execution. However, many recurrences extracted from loops cannot be solved, due to their having multiple recursive cases or multiple arguments. In the literature, several techniques for approximating the solution of unsolvable recurrences have been proposed. The approach presented in this paper is to define transformations based on regular path expressions and loop counters that (i) transform multi-path loops to single-path loops, giving rise to recurrences with a single recursive case, and (ii) transform multi-argument recurrences to single-argument recurrences, thus enabling the use of recurrence solvers on the transformed recurrences. Using this approach, precise solutions can sometimes be obtained that are not obtained by approximation methods., Comment: In Proceedings HCVS 2021, arXiv:2109.03988

In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on H\"older-$\alpha$ domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation's solvability, and the improved Poincar\'e, the fractional Poincar\'e, and the Korn inequalities. The proofs are based on a local-to-global argument that involves a kind of atomic decomposition of functions and the validity of a weighted discrete Hardy-type inequality on trees. The novelty of our approach lies in the use of this weighted discrete Hardy inequality and a sufficient condition that allows us to study the weights of our interest. As a consequence, the assumptions on the weight exponents that appear in our results are weaker than those in the literature., Comment: 34 pages, and 3 figures

Diatoms are microscopic algae found in all of Earths water courses. They produce frustules, porous silica exoskeletons, grown by precipitation of silicic acid from water. Frustule components, known as girdles, from some diatom species also feature highly periodic pore arrays with properties on the same scale and quality of ordering as manufactured photonic crystals. Here, the girdles of two diatom species with various lattice constants are used as bio-silica scaffolds for plasmonic crystals, combined with metals chosen for spectral agreement between permittivity and photonic crystal properties. The use of frustules as scaffolds for plasmonic application has been tested earlier, as nano-porous features can enhance scattering and local hotspots, useful for sensing application or SERS. However, both the use of girdles and of continuous metal films are new approaches offering previously unseen plasmonic effects. Angularly resolved dispersions from reflection Fourier spectroscopy are provided for Coscinodiscus granii girdles, forming well-ordered square lattices, and Coscinodiscus wailesii, forming ordered hexagonal lattices, covered with a 40 nm film of silver or with 40 nm of gold, respectively. These were confirmed with optical modelling of the 3D systems, including both metal surface layers and internal frustule structures, allowing for the calculation of dispersions and electric fields. Measurements are further compared with structures produced via Focused Ion Beam microscopy, demonstrating the advantages of girdles as photonic crystal scaffolds and as an alternative to conventional plasmonic crystal fabrication. The results demonstrate that high-quality plasmonic crystal scaffolds from diatoms are available in nature, and their natural diversity can be applied in a controlled way to obtain plasmonic crystals with a wide range of behaviours and spectral responses., Comment: 22 pages, 8 figures

The use of multiple and semantically correlated sources can provide complementary information to each other that may not be evident when working with individual modalities on their own. In this context, multi-modal models can help producing more accurate and robust predictions in machine learning tasks where audio-visual data is available. This paper presents a multi-modal model for automatic scene classification that exploits simultaneously auditory and visual information. The proposed approach makes use of two separate networks which are respectively trained in isolation on audio and visual data, so that each network specializes in a given modality. The visual subnetwork is a pre-trained VGG16 model followed by a bidiretional recurrent layer, while the residual audio subnetwork is based on stacked squeeze-excitation convolutional blocks trained from scratch. After training each subnetwork, the fusion of information from the audio and visual streams is performed at two different stages. The early fusion stage combines features resulting from the last convolutional block of the respective subnetworks at different time steps to feed a bidirectional recurrent structure. The late fusion stage combines the output of the early fusion stage with the independent predictions provided by the two subnetworks, resulting in the final prediction. We evaluate the method using the recently published TAU Audio-Visual Urban Scenes 2021, which contains synchronized audio and video recordings from 12 European cities in 10 different scene classes. The proposed model has been shown to provide an excellent trade-off between prediction performance (86.5%) and system complexity (15M parameters) in the evaluation results of the DCASE 2021 Challenge.

Assertion checking is an invaluable programmer's tool for finding many classes of errors or verifying their absence in dynamic languages such as Prolog. For Prolog programmers this means being able to have relevant properties such as modes, types, determinacy, non-failure, sharing, constraints, cost, etc., checked and errors flagged without having to actually run the program. Such global static analysis tools are arguably most useful the earlier they are used in the software development cycle, and fast response times are essential for interactive use. Triggering a full and precise semantic analysis of a software project every time a change is made can be prohibitively expensive. In our static analysis and verification framework this challenge is addressed through a combination of modular and incremental (context- and path-sensitive) analysis that is responsive to program edits, at different levels of granularity. We describe how the combination of this framework within an integrated development environment (IDE) takes advantage of such incrementality to achieve a high level of reactivity when reflecting analysis and verification results back as colorings and tooltips directly on the program text -- the tool's VeriFly mode. The concrete implementation that we describe is Emacs-based and reuses in part off-the-shelf "on-the-fly" syntax checking facilities (flycheck). We believe that similar extensions are also reproducible with low effort in other mature development environments. Our initial experience with the tool shows quite promising results, with low latency times that provide early, continuous, and precise assertion checking and other semantic feedback to programmers during the development process. The tool supports Prolog natively, as well as other languages by semantic transformation into Horn clauses. This paper is under consideration for acceptance in TPLP., Comment: Paper presented at the 37th International Conference on Logic Programming (ICLP 2021), 16 pages

Sequential methods for synthetic realisation of random processes have a number of advantages compared with spectral methods. In this article, the determination of optimal autoregressive (AR) models for reproducing a predefined target autocovariance function of a random process is addressed. To this end, a novel formulation of the problem is developed. This formulation is linear and generalises the well-known Yule-Walker (Y-W) equations and a recent approach based on restricted AR models (Krenk-Moller approach, K-M). Two main features characterise the introduced formulation: (i) flexibility in the choice for the autocovariance equations employed in the model determination, and (ii) flexibility in the definition of the AR model scheme. Both features were exploited by a genetic algorithm to obtain optimal AR models for the particular case of synthetic generation of homogeneous stationary isotropic turbulence time series. The obtained models improved those obtained with the Y-W and K-M approaches for the same model parsimony in terms of the global fitting of the target autocovariance function. Implications for the reproduced spectra are also discussed. The formulation for the multivariate case is also presented, highlighting the causes behind some computational bottlenecks., Comment: 31 pages, 20 figures, 3 tables, 2 appendices

In this work we investigate greedy energy sequences on the unit circle for the logarithmic and Riesz potentials. By definition, if $(a_n)_{n=0}^{\infty}$ is a greedy $s$-energy sequence on the unit circle, the Riesz potential $U_{N,s}(x):=\sum_{k=0}^{N-1}|a_k-x|^{-s}$, $s>0$, generated by the first $N$ points of the sequence attains its minimum value at the point $a_{N}$, for every $N\geq 1$. In the case $s=0$ we minimize instead the logarithmic potential $U_{N,0}(x):=-\sum_{k=0}^{N-1}\log |a_{k}-x|$. We analyze the asymptotic properties of these extremal values $U_{N,s}(a_N)$, studying separately the cases $s=0$, $01$. We obtain second-order asymptotic formulas for $U_{N,s}(a_N)$ in the cases $s=0$, $01$ is proved, and it is shown that the normalized sequence $U_{N,s}(a_N)/N^s$ is bounded and divergent in this case. We also consider, briefly, greedy energy sequences in which the minimization condition is required starting from the point $a_{p+1}$ (instead of the point $a_{1}$ as previously stated), for some $p\geq 1$. For this more general class of greedy sequences, we prove a first-order asymptotic result for $0\leq s<1$., Comment: 37 pages, several figures. In this version we have added a new result (Theorem 1.8) and some open problems (Problems 1.9 and 1.10). The title is slightly modified, and some new bibliographic references have been added

We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions may be different for entries belonging to different diagonals. For a sequence of $n\times n$ matrices in the class considered, we investigate the asymptotic behavior of their empirical spectral distribution as $n$ tends to infinity., Comment: Minor changes in this version, including some added references, 20 pages

The occurrence of the extensively used herbicide diuron in the environment poses a severe threat to the ecosystem and human health. Four different ligninolytic fungi were studied as biodegradation candidates for the removal of diuron. Among them, T. versicolor was the most effective species, degrading rapidly not only diuron (83%) but also the major metabolite 3,4-dichloroaniline (100%), after 7-day incubation. During diuron degradation, five transformation products (TPs) were found to be formed and the structures for three of them are tentatively proposed. According to the identified TPs, a hydroxylated intermediate 3-(3,4-dichlorophenyl)-1-hydroxymethyl-1-methylurea (DCPHMU) was further metabolized into the N-dealkylated compounds 3-(3,4-dichlorophenyl)-1-methylurea (DCPMU) and 3,4-dichlorophenylurea (DCPU). The discovery of DCPHMU suggests a relevant role of hydroxylation for subsequent N-demethylation, helping to better understand the main reaction mechanisms of diuron detoxification. Experiments also evidenced that degradation reactions may occur intracellularly and be catalyzed by the cytochrome P450 system. A response surface method, established by central composite design, assisted in evaluating the effect of operational variables in a trickle-bed bioreactor immobilized with T. versicolor on diuron removal. The best performance was obtained at low recycling ratios and influent flow rates. Furthermore, results indicate that the contact time between the contaminant and immobilized fungi plays a crucial role in diuron removal. This study represents a pioneering step forward amid techniques for bioremediation of pesticides-contaminated waters using fungal reactors at a real scale., Comment: Published in Science of the Total Environment

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic., Comment: 16 pages, 3 figures, to be published in PLOS Computational Biology

Krein condition have been used as a qualitative result to show the M-indeterminacy of some kind of densities. In this work we use results from the theory of the Hilbert transform to construct families of densities having all the same finite moment sequence as a density $f$ with finite logarithmic integral. Actually, our approach explicitly gives Stieltjes classes with center at $f$ and perturbations involving the Hilbert transform of $\ln f.$ We consider densities supported on the whole real line or the positive half line., Comment: 7 pages

For a parameter $\lambda>0$, we investigate greedy $\lambda$-energy sequences $(a_{n})_{n=0}^{\infty}$ on the unit sphere $S^{d}\subset\mathbb{R}^{d+1}$, $d\geq 1$, satisfying the defining property that each $a_{n}$, $n\geq 1$, is a point where the potential $\sum_{k=0}^{n-1}|x-a_{k}|^{\lambda}$ attains its maximum value on $S^{d}$. We show that these sequences satisfy the symmetry property $a_{2k+1}=-a_{2k}$ for every $k\geq 0$. The asymptotic distribution of the sequence undergoes a sharp transition at the value $\lambda=2$, from uniform distribution ($\lambda<2$) to concentration on two antipodal points ($\lambda>2$). We investigate first-order and second-order asymptotics of the $\lambda$-energy of the first $N$ points of the sequence, as well as the asymptotic behavior of the extremal values $\sum_{k=0}^{n-1}|a_{n}-a_{k}|^{\lambda}$. The second-order asymptotics is analyzed on the unit circle. It is shown that this asymptotic behavior differs significantly from that of $N$ equally spaced points on the unit circle, and a transition in the behavior takes place at $\lambda=1$., Comment: 35 pages, 6 figures, this is the published version

In this paper we propose C2G-Net, a pipeline for image classification that exploits the morphological properties of images containing a large number of similar objects like biological cells. C2G-Net consists of two components: (1) Cell2Grid, an image compression algorithm that identifies objects using segmentation and arranges them on a grid, and (2) DeepLNiNo, a CNN architecture with less than 10,000 trainable parameters aimed at facilitating model interpretability. To test the performance of C2G-Net we used multiplex immunohistochemistry images for predicting relapse risk in colon cancer. Compared to conventional CNN architectures trained on raw images, C2G-Net achieved similar prediction accuracy while training time was reduced by 85% and its model was is easier to interpret., Comment: 10 pages, 5 figures (Figure 3 with 4 sub-figures), Appendix A and Appendix B after the references. Originally submitted to ICML2020 but rejected

In this work we solve a degenerate parabolic equation for the half line with Dirichlet boundary data, and use some results from the theory of Reproducing Kernel Hilbert Spaces to show that the null reachable space of this degenerate parabolic equation is a RKHS of analytic functions on a sector, whose reproducing kernel can be written in terms of the weighted Bergman kernel on the half plane C+., Comment: 13 pages

In a note published in 1925, G. H. Hardy stated the inequality \begin{equation*} \sum_{n=1}^\infty \left(\frac{1}{n}\sum_{k=1}^n a_k \right)^p \leq \left(\frac{p}{p-1}\right)^p \sum_{n=1}^\infty a_n^p, \end{equation*} for any non-negative sequence $\{a_n\}_{n \geq 1}$, and $p>1$. This inequality is known in the literature as the classical discrete Hardy inequality. It has been widely studied and several applications and new versions have been shown. In this work, we use a characterization of a weighted version of this inequality to exhibit a sufficient condition for the existence of solutions of the differential equation ${\rm div}\,{\bf u}=f$ in weighted Sobolev spaces over a certain plane irregular domain. The solvability of this equation is fundamental for the analysis of the Stokes equations. The proof follows from a local-to-global argument based on a certain decomposition of functions which is also of interest for its applications to other inequalities or related results in Sobolev spaces, such as the Korn inequality., Comment: 16 pages, 2 figures