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One of the classical models in mathematical biology is the Lotka-Volterra competition model, describing the dynamics of two populations competing for resources. Two possible regimes in this system are given by their coexistence or extinction of a weaker population. In a distributed system with diffusive spatial coupling, travelling fronts occur, corresponding to transitions between stationary states. In this work we will consider the competition model extended by extra interaction between involved populations which is given by chemotactic coupling, namely, assuming that one species produces a chemical agent which causes the taxis of another species. It is known that in a one-species model (i.e. Keller-Segel model) production of chemoattractor results in formation of stationary periodic (or Turing-type) patterns. In this work, we will investigate conditions for the formation of stationary periodic patterns in a two-species competition model with chemotaxis. We show that in this system periodic patterns can emerge in the course of Turing-type instability (classical way) or from a stable steady state, corresponding to the extinction of one of the species, due to a finite, or over-threshold, amplitude disturbance. We study the characteristics of emerging periodic pattern, such as its amplitude and wavelength, by means of Fourier analysis. We also perform computational simulations to verify our analytical results.

Computational approaches to predicting mental health conditions in social media have been substantially explored in the past years. Multiple surveys have been published on this topic, providing the community with comprehensive accounts of the research in this area. Among all mental health conditions, depression is the most widely studied due to its worldwide prevalence. The COVID-19 global pandemic, starting in early 2020, has had a great impact on mental health worldwide. Harsh measures employed by governments to slow the spread of the virus (e.g., lockdowns) and the subsequent economic downturn experienced in many countries have significantly impacted people's lives and mental health. Studies have shown a substantial increase of above 50% in the rate of depression in the population. In this context, we present a survey on natural language processing (NLP) approaches to modeling depression in social media, providing the reader with a post-COVID-19 outlook. This survey contributes to the understanding of the impacts of the pandemic on modeling depression in social media. We outline how state-of-the-art approaches and new datasets have been used in the context of the COVID-19 pandemic. Finally, we also discuss ethical issues in collecting and processing mental health data, considering fairness, accountability, and ethics.

Mathematics has long been conveyed through natural language, primarily for human understanding. With the rise of mechanized mathematics and proof assistants, there is a growing need to understand informal mathematical text, yet most existing benchmarks focus solely on English, overlooking other languages. This paper introduces RoMath, a Romanian mathematical reasoning benchmark suite comprising three datasets: RoMath-Baccalaureate, RoMath-Competitions and RoMath-Synthetic, which cover a range of mathematical domains and difficulty levels, aiming to improve non-English language models and promote multilingual AI development. By focusing on Romanian, a low-resource language with unique linguistic features, RoMath addresses the limitations of Anglo-centric models and emphasizes the need for dedicated resources beyond simple automatic translation. We benchmark several open-weight language models, highlighting the importance of creating resources for underrepresented languages. We make the code and dataset available., Comment: 4 Figures, 12 Tables

For any $p \in ( 1, +\infty)$, we give a new inequality for the first nontrivial Neumann eigenvalue $\mu _ p (\Omega, \varphi)$ of the $p$-Laplacian on a convex domain $\Omega \subset \mathbb{R}^N$ with a power-concave weight $\varphi$. Our result improves the classical estimate in terms of the diameter, first stated in a seminal paper by Payne and Weinberger: we add in the lower bound an extra term depending on the second largest John semi-axis of $\Omega$ (equivalent to a power of the width in the special case $N = 2$). The power exponent in the extra term is sharp, and the constant in front of it is explicitly tracked, thus enlightening the interplay between space dimension, nonlinearity and power-concavity. Moreover, we attack the stability question: we prove that, if $\mu _ p (\Omega, \varphi)$ is close to the lower bound, then $\Omega$ is close to a thin cylinder, and $\varphi$ is close to a function which is constant along its axis. As intermediate results, we establish a sharp $L^ \infty$ estimate for the associated eigenfunctions, and we determine the asymptotic behaviour of $\mu _ p (\Omega, \varphi)$ for varying weights and domains, including the case of collapsing geometries., Comment: 1 figure

We consider the minimization property of a Gagliardo-Slobodeckij seminorm which can be seen as the fractional counterpart of the classical problem of functions of least gradient and which is related to the minimization of the nonlocal perimeter functional. We discuss continuity properties for this kind of problem. In particular, we show that, under natural structural assumptions, the minimizers are bounded and continuous in the interior of the ambient domain (and, in fact, also continuous up to the boundary under some mild additional hypothesis). We show that these results are also essentially optimal, since in general the minimizer is not necessarily continuous across the boundary., Comment: 15 pages, 1 figure

We aim to learn the functional co-response group: a group of taxa whose co-response effect (the representative characteristic of the group showing the total topological abundance of taxa) co-responds (associates well statistically) to a functional variable. Different from the state-of-the-art method, we model the soil microbial community as an ecological co-occurrence network with the taxa as nodes (weighted by their abundance) and their relationships (a combination from both spatial and functional ecological aspects) as edges (weighted by the strength of the relationships). Then, we design a method called gFlora which notably uses graph convolution over this co-occurrence network to get the co-response effect of the group, such that the network topology is also considered in the discovery process. We evaluate gFlora on two real-world soil microbiome datasets (bacteria and nematodes) and compare it with the state-of-the-art method. gFlora outperforms this on all evaluation metrics, and discovers new functional evidence for taxa which were so far under-studied. We show that the graph convolution step is crucial to taxa with relatively low abundance (thus removing the bias towards taxa with higher abundance), and the discovered bacteria of different genera are distributed in the co-occurrence network but still tightly connected among themselves, demonstrating that topologically they fill different but collaborative functional roles in the ecological community., Comment: BIOKDD accepted. Note: the first version of this paper is not approved by all authors. the second version is the official version for BIOKDD camera-ready

The fundamental gap conjecture proved by Andrews and Clutterbuck in 2011 provides the sharp lower bound for the difference between the first two Dirichlet Laplacian eigenvalues in terms of the diameter of a convex set in $\mathbb{R}^N$. The question concerning the rigidity of the inequality, raised by Yau in 1990, was left open. Going beyond rigidity, our main result strengthens Andrews-Clutterbuck inequality, by quantifying geometrically the excess of the gap compared to the diameter in terms of flatness. The proof relies on a localized, variational interpretation of the fundamental gap, allowing a dimension reduction via the use of convex partitions \`a la Payne-Weinberger: the result stems by combining a new sharp result for one dimensional Schr\"odinger eigenvalues with measure potentials, with a thorough analysis of the geometry of the partition into convex cells. As a by-product of our approach, we obtain a quantitative form of Payne-Weinberger inequality for the first nontrivial Neumann eigenvalue of a convex set in $\mathbb{R}^N$, thus proving, in a stronger version, a conjecture from 2007 by Hang-Wang., Comment: 5 figures

The main result of the paper shows that the regular $n$-gon is a local minimizer for the first Dirichlet-Laplace eigenvalue among $n$-gons having fixed area for $n \in \{5,6\}$. The eigenvalue is seen as a function of the coordinates of the vertices in $\Bbb R^{2n}$. Relying on fine regularity results of the first eigenfunction in a convex polygon, an explicit a priori estimate is given for the eigenvalues of the Hessian matrix associated to the discrete problem, whose coefficients involve the solutions of some Poisson equations with singular right hand sides. The a priori estimates, in conjunction with certified finite element approximations of these singular PDEs imply the local minimality for $n \in \{5,6\}$. All computations, including the finite element computations, are realized using interval arithmetic.

Biological pattern formation is one of the most intriguing phenomena in nature. Simplest examples of such patterns are represented by travelling waves and stationary periodic patterns which occur during various biological processes including morphogenesis and population dynamics. Formation of these patterns in populations of motile microorganisms such as Dictyostelium discoideum and E. coli have been shown in a number of experimental studies. Conditions for formation of various types of patterns are commonly addressed in mathematical studies of dynamical systems containing diffusive and advection terms. In this work, we do mathematical study of spatio-temporal patterns forming in growing population of chemotactically active bacteria. In particular, we perform linear analysis to find conditions for formation of stationary periodic patterns, and nonlinear (Fourier) analysis to find characteristics, such as amplitude and wavelength, of these patterns. We verify our analytical results by means of numerical simulations.

A generalized two-dimensional cubic Lotka-Volterra model with infinitesimal parameters is studied. Three different cases have been considered, one non-degenerate and two degenerate. The local behavior of the model has been studied in the three cases. Six bifurcation diagrams with thirty different regions have been obtained in the non-degenerate case, respectively, sixteen diagrams with forty regions in the two degenerate cases.

We propose a novel model-selection method for dynamic networks. Our approach involves training a classifier on a large body of synthetic network data. The data is generated by simulating nine state-of-the-art random graph models for dynamic networks, with parameter range chosen to ensure exponential growth of the network size in time. We design a conceptually novel type of dynamic features that count new links received by a group of vertices in a particular time interval. The proposed features are easy to compute, analytically tractable, and interpretable. Our approach achieves a near-perfect classification of synthetic networks, exceeding the state-of-the-art by a large margin. Applying our classification method to real-world citation networks gives credibility to the claims in the literature that models with preferential attachment, fitness and aging fit real-world citation networks best, although sometimes, the predicted model does not involve vertex fitness., Comment: Main text: 13 pages, 4 figures. Supplementary: 12 pages; Textual changes

For an open set $\Om \subset \R^2$ let $\lambda(\Om)$ denote the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Om)$. Let $w_\Om$ be the torsion function for $\Om$, and let $\|.\|_p$ denote the $L^p$ norm. It is shown there exists $\eta>0$ such that $\|w_{\Om}\|_{\infty} \lambda(\Om)\ge 1+\eta$ for any non-empty, open, simply connected set $\Om\subset \R^2$ with $\lb(\Om) >0$. Moreover, if the measure $|\Om|$ of $\Om$ is finite, then $\|w_{\Om}\|_1\lambda(\Om)\le (1-\eta)|\Om|$., Comment: 18 pages, 1 figure

Depression, a prominent contributor to global disability, affects a substantial portion of the population. Efforts to detect depression from social media texts have been prevalent, yet only a few works explored depression detection from user-generated video content. In this work, we address this research gap by proposing a simple and flexible multi-modal temporal model capable of discerning non-verbal depression cues from diverse modalities in noisy, real-world videos. We show that, for in-the-wild videos, using additional high-level non-verbal cues is crucial to achieving good performance, and we extracted and processed audio speech embeddings, face emotion embeddings, face, body and hand landmarks, and gaze and blinking information. Through extensive experiments, we show that our model achieves state-of-the-art results on three key benchmark datasets for depression detection from video by a substantial margin. Our code is publicly available on GitHub., Comment: Accepted at 46th European Conference on Information Retrieval (ECIR 2024)

In this paper, we study the existence of solutions of the equation $(-\Delta)_1^s u=f$ in a bounded open set with Lipschitz boundary $\Omega\subset \Rn$, vanishing on $\Co \Omega$, for some given $s\in (0,1)$, and asymptotics as $p\to 1$ of solutions of $(-\Delta)_p^s u=f$. We obtain existence and convergence by comparing the $L^{\frac{n}{s}}$ norm of $f$ to the sharp fractional Sobolev constant, or, when $f$ is non-negative, the weighted fractional Cheegar constant to $1$ -- in this case, the results are sharp. We further prove that solutions are "flat" on sets of positive Lebesgue measure., Comment: 35 pages

Let A and A' be abelian varieties defined over a number field k such that Hom(A,A') = 0. Under the Generalized Riemann hypothesis for motivic L-functions attached to A and A', we show that there exists a prime p of k of good reduction for A and A' at which the Frobenius traces of A and A' are nonzero and differ by sign, and such that the norm Nm(p) is O(log(2NN')^2), where N and N' respectively denote the absolute conductors of A and A'. Our method extends that of Chen, Park, and Swaminathan who considered the case in which A and A' are elliptic curves., Comment: 9 pages. Includes material formerly appearing in arXiv:2002.08807

This paper presents the methodology and data used for the automatic extraction of the Romanian Academic Word List (Ro-AWL). Academic Word Lists are useful in both L2 and L1 teaching contexts. For the Romanian language, no such resource exists so far. Ro-AWL has been generated by combining methods from corpus and computational linguistics with L2 academic writing approaches. We use two types of data: (a) existing data, such as the Romanian Frequency List based on the ROMBAC corpus, and (b) self-compiled data, such as the expert academic writing corpus EXPRES. For constructing the academic word list, we follow the methodology for building the Academic Vocabulary List for the English language. The distribution of Ro-AWL features (general distribution, POS distribution) into four disciplinary datasets is in line with previous research. Ro-AWL is freely available and can be used for teaching, research and NLP applications.

In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming to get almost concavity results for a relevant class of anisotropic semilinear elliptic problems with spatially dependent source and diffusion., Comment: 16 pages, types corrected, to appear on Asymptotic Analysis

In this work, we present the contribution of the BLUE team in the eRisk Lab task on searching for symptoms of depression. The task consists of retrieving and ranking Reddit social media sentences that convey symptoms of depression from the BDI-II questionnaire. Given that synthetic data provided by LLMs have been proven to be a reliable method for augmenting data and fine-tuning downstream models, we chose to generate synthetic data using ChatGPT for each of the symptoms of the BDI-II questionnaire. We designed a prompt such that the generated data contains more richness and semantic diversity than the BDI-II responses for each question and, at the same time, contains emotional and anecdotal experiences that are specific to the more intimate way of sharing experiences on Reddit. We perform semantic search and rank the sentences' relevance to the BDI-II symptoms by cosine similarity. We used two state-of-the-art transformer-based models (MentalRoBERTa and a variant of MPNet) for embedding the social media posts, the original and generated responses of the BDI-II. Our results show that using sentence embeddings from a model designed for semantic search outperforms the approach using embeddings from a model pre-trained on mental health data. Furthermore, the generated synthetic data were proved too specific for this task, the approach simply relying on the BDI-II responses had the best performance.

We answer the question whether, when forming constellations in the night sky, people in astronomical cultures around the world and through time consistently imagined and assigned the same symbolism to the same (type of) star group. Evidence of semantic parallels has so far been anecdotal. We use two complementary definitions for a star group: (1) a star group in a fixed region of the sky (regardless of its exact star composition), and (2) a star group with a particular shape and brightness (regardless of its location in the sky). Over a dataset of 2003 constellations from 82 astronomical cultures, we find many semantic parallels which are likely naturally induced by the shape and composition of the star pattern. In certain cultural regions, geometric and group symbols are perceived consistently over small and uniformly bright star groups, naturalistic humanoids in large star groups with non-linear minimum spanning tree (MST) and stars inside the convex hull, and reptiles in star groups with low aspect ratio or linear MST. These naturally induced semantics, seemingly endogenous to certain sky patterns, show that there are universal (rather than learnt) patterns behind forming and naming constellations., Comment: Part 2 of arXiv:2110.12329 published in PLOS ONE 17(7): e0272270 (2022). Shares the dataset

Pruning-at-Initialization (PaI) algorithms provide Sparse Neural Networks (SNNs) which are computationally more efficient than their dense counterparts, and try to avoid performance degradation. While much emphasis has been directed towards \emph{how} to prune, we still do not know \emph{what topological metrics} of the SNNs characterize \emph{good performance}. From prior work, we have layer-wise topological metrics by which SNN performance can be predicted: the Ramanujan-based metrics. To exploit these metrics, proper ways to represent network layers via Graph Encodings (GEs) are needed, with Bipartite Graph Encodings (BGEs) being the \emph{de-facto} standard at the current stage. Nevertheless, existing BGEs neglect the impact of the inputs, and do not characterize the SNN in an end-to-end manner. Additionally, thanks to a thorough study of the Ramanujan-based metrics, we discover that they are only as good as the \emph{layer-wise density} as performance predictors, when paired with BGEs. To close both gaps, we design a comprehensive topological analysis for SNNs with both linear and convolutional layers, via (i) a new input-aware Multipartite Graph Encoding (MGE) for SNNs and (ii) the design of new end-to-end topological metrics over the MGE. With these novelties, we show the following: (a) The proposed MGE allows to extract topological metrics that are much better predictors of the accuracy drop than metrics computed from current input-agnostic BGEs; (b) Which metrics are important at different sparsity levels and for different architectures; (c) A mixture of our topological metrics can rank PaI algorithms more effectively than Ramanujan-based metrics. The codebase is publicly available at https://github.com/eliacunegatti/mge-snn., Comment: Accepted at Transactions on Machine Learning Research (TMLR)

Let $\Omega\subset\mathbb{R}^n$ be an open set with same volume as the unit ball $B$ and let $\lambda_k(\Omega)$ be the $k$-th eigenvalue of the Laplace operator of $\Omega$ with Dirichlet boundary conditions in $\partial\Omega$. In this work, we answer the following question: if $\lambda_1(\Omega)-\lambda_1(B)$ is small, how large can $|\lambda_k(\Omega)-\lambda_k(B)|$ be ? We establish quantitative bounds of the form $|\lambda_k(\Omega)-\lambda_k(B)|\le C (\lambda_1(\Omega)-\lambda_1(B))^\alpha$ with sharp exponents $\alpha$ depending on the multiplicity of $\lambda_k(B)$. We first show that such an inequality is valid with $\alpha=1/2$ for any $k$, improving previous known results and providing the sharpest possible exponent. Then, through the study of a vectorial free boundary problem, we show that one can achieve the better exponent $\alpha=1$ if $\lambda_{k}(B)$ is simple. We also obtain a similar result for the whole cluster of eigenvalues when $\lambda_{k}(B)$ is multiple, thus providing a complete answer to the question above. As a consequence of these results, we obtain the persistence of the ball as minimizer for a large class of spectral functionals which are small perturbations of the fundamental eigenvalue on the one hand, and a full reverse Kohler-Jobin inequality on the other hand, solving an open problem formulated by M. Van Den Berg, G. Buttazzo and A. Pratelli.

Given a non-increasing and radially symmetric kernel in $L ^ 1 _{\rm loc} (\Bbb{R} ^ 2 ; \Bbb{R}_+)$, we investigate counterparts of the classical Hardy-Littlewood and Riesz inequalities when the class of admissible domains is the family of polygons with given area and $N$ sides. The latter corresponds to study the polygonal isoperimetric problem in nonlocal version. We prove that, for every $N \geq 3$, the regular $N$-gon is optimal for Hardy-Littlewood inequality. Things go differently for Riesz inequality: while for $N = 3$ and $N = 4$ it is known that the regular triangle and the square are optimal, for $N\geq 5$ we prove that symmetry or symmetry breaking may occur (i.e. the regular $N$-gon may be optimal or not), depending on the value of $N$ and on the choice of the kernel.

In this paper we study extremal behaviors of the mean to max ratio of the $p$-torsion function with respect to the geometry of the domain. For $p$ larger than the dimension of the space $N$, we prove that the upper bound is uniformly below $1$, contrary to the case $p \in (1,N]$. For $p=+\infty$, in two dimensions, we prove that the upper bound is asymptotically attained by a disc from which is removed a network of points consisting on the vertices of a tiling of the plane with regular hexagons of vanishing size.

Depression detection from user-generated content on the internet has been a long-lasting topic of interest in the research community, providing valuable screening tools for psychologists. The ubiquitous use of social media platforms lays out the perfect avenue for exploring mental health manifestations in posts and interactions with other users. Current methods for depression detection from social media mainly focus on text processing, and only a few also utilize images posted by users. In this work, we propose a flexible time-enriched multimodal transformer architecture for detecting depression from social media posts, using pretrained models for extracting image and text embeddings. Our model operates directly at the user-level, and we enrich it with the relative time between posts by using time2vec positional embeddings. Moreover, we propose another model variant, which can operate on randomly sampled and unordered sets of posts to be more robust to dataset noise. We show that our method, using EmoBERTa and CLIP embeddings, surpasses other methods on two multimodal datasets, obtaining state-of-the-art results of 0.931 F1 score on a popular multimodal Twitter dataset, and 0.902 F1 score on the only multimodal Reddit dataset., Comment: Accepted at ECIR 2023

In this paper we study obstacles immerged in a Stokes flow with Navier boundary conditions. We prove the existence and regularity of an obstacle with minimal drag, among all shapes of prescribed volume and controlled surface area, taking into account that these shapes may naturally develop geometric features of codimension 1. The existence is carried out in the framework of free discontinuity problems and leads to a relaxed solution in the space of special functions of bounded deformation (SBD). In dimension 2, we prove that the solution is classical.

We study the asymptotic count of dihedral quartic extensions over a fixed number field with bounded norm of the relative discriminant. The main term of this count (including a summation formula for the constant) can be found in the literature (see Cohen--Diaz y Diaz--Olivier for the statement without proof and see Kl\"uners for a proof), but a power-saving for the error term has not been explicitly determined except in the case that the base field is $\mathbb{Q}$. In this article, we describe the argument for obtaining both the explicit main term and a power-saving error term for the number of $D_4$-quartic extensions over a general base number field ordered by the norms of their relative discriminants. We also give an extensive overview of the history and development of number field asymptotics.

We prove that the second nontrivial Neumann eigenvalue of the Laplace-Beltrami operator on the unit sphere $\mathbb{S}^n \subseteq \mathbb{R}^{n+1}$ is maximized by the union of two disjoint, equal, geodesic balls among all subsets of $\mathbb{S}^n$ of prescribed volume. In fact, the result holds in a stronger version, involving the harmonic mean of the eigenvalues of order $2$ to $n$, and extends to densities. A (surprising) consequence occurs on the maximality of a geodesic ball for the first nontrivial eigenvalue under the volume constraint: the hemisphere inclusion condition of the Ashbaugh-Benguria result can be relaxed to a weaker one, namely empty intersection with a geodesic ball of the prescribed volume. Although we do not prove that this last inclusion result is sharp, for a mass less than the half of the sphere, we numerically identify a density with higher first eigenvalue than the corresponding geodesic ball and with support equal to the full sphere $\mathbb{S}^2$.

Minimalist game design was introduced a decade ago as a general design principle with a list of key properties for minimalist games: basic controls, simple but aesthetically pleasing visuals, interesting player choices with vast possibility spaces, and sounds that resonate with the design. In this paper, we present an experiment we did to explore minimalism in games using a bottom-up approach. We invited a small group of professional game designers and a larger group of game design students to participate in a seminal experiment on minimalism in game design. We started from the most basic game elements: one pixel and one key which provide the least amount of information we can display and reasonably the most elementary action players can perform. We designed a game that starts with a black pixel and asks players to press a key when the pixel turns white. This minimal game, almost a Skinner box, captures the essential elements of the mechanics of games like "The Impossible Game," which asks players to do nothing more than press a key at the right moment. We presented this game concept to the professional game designers and challenged them to create other games with the least amount of player interaction and displayed information. We did not specify any constraints (as usually done in other contexts) and left them free to express their view of minimalistic game design. We repeated the experiment with 100+ students attending a master-level course on video game design and development at our institution. We then analyzed the creations of the two groups, discussing the idea of minimalistic design that emerges from the submitted game concepts.

This work proposes a transformer architecture for user-level classification of gambling addiction and depression that is trainable end-to-end. As opposed to other methods that operate at the post level, we process a set of social media posts from a particular individual, to make use of the interactions between posts and eliminate label noise at the post level. We exploit the fact that, by not injecting positional encodings, multi-head attention is permutation invariant and we process randomly sampled sets of texts from a user after being encoded with a modern pretrained sentence encoder (RoBERTa / MiniLM). Moreover, our architecture is interpretable with modern feature attribution methods and allows for automatic dataset creation by identifying discriminating posts in a user's text-set. We perform ablation studies on hyper-parameters and evaluate our method for the eRisk 2022 Lab on early detection of signs of pathological gambling and early risk detection of depression. The method proposed by our team BLUE obtained the best ERDE5 score of 0.015, and the second-best ERDE50 score of 0.009 for pathological gambling detection. For the early detection of depression, we obtained the second-best ERDE50 of 0.027.

We analyze strict positivity at the boundary for nonnegative solutions of Robin problems in general (non-smooth) domains, e.g. open sets with rectifiable topological boundaries having finite Hausdorff measure. This question was raised by Bass, Burdzy and Chen in 2008 for harmonic functions, in a probabilistic context. We give geometric conditions such that the solutions of Robin problems associated to general elliptic operators of $p$-Laplacian type, with a positive right hand side, are globally or locally bounded away from zero at the boundary. Our method, of variational type, relies on the analysis of an isoperimetric profile of the set and provides quantitative estimates as well.

We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a uniform Hardy inequality, and (ii) localisation of a sequence of first Dirichlet eigenfunctions for a wide class of elongating horn-shaped domains. We give examples of sequences of simply connected, planar, polygonal domains for which the corresponding sequence of first eigenfunctions with either Dirichlet, or Neumann, boundary conditions $\kappa$-localise in $L^2$., Comment: 23 pages, 5 figures

In this work, we explore the relationship between depression and manifestations of happiness in social media. While the majority of works surrounding depression focus on symptoms, psychological research shows that there is a strong link between seeking happiness and being diagnosed with depression. We make use of Positive-Unlabeled learning paradigm to automatically extract happy moments from social media posts of both controls and users diagnosed with depression, and qualitatively analyze them with linguistic tools such as LIWC and keyness information. We show that the life of depressed individuals is not always bleak, with positive events related to friends and family being more noteworthy to their lives compared to the more mundane happy events reported by control users., Comment: Accepted to LREC 2022

This paper is motivated by the maximization of the $k$-th eigenvalue of the Laplace operator with Neumann boundary conditions among domains of ${\mathbb R}^N$ with prescribed measure. We relax the problem to the class of (possibly degenerate) densities in ${\mathbb R}^N$ with prescribed mass and prove the existence of an optimal density. For $k=1,2$ the two problems are equivalent and the maximizers are known to be one and two equal balls, respectively. For $k \ge 3$ this question remains open, except in one dimension of the space where we prove that the maximal densities correspond to a union of $k$ equal segments. This result provides sharp upper bounds for Sturm-Liouville eigenvalues and proves the validity of the P\'olya conjecture in the class of densities in ${\mathbb R}$. Based on the relaxed formulation, we provide numerical approximations of optimal densities for $k=1, \dots, 8$ in ${\mathbb R}^2$.

Finding the most influential nodes in a network is a computationally hard problem with several possible applications in various kinds of network-based problems. While several methods have been proposed for tackling the influence maximisation (IM) problem, their runtime typically scales poorly when the network size increases. Here, we propose an original method, based on network downscaling, that allows a multi-objective evolutionary algorithm (MOEA) to solve the IM problem on a reduced scale network, while preserving the relevant properties of the original network. The downscaled solution is then upscaled to the original network, using a mechanism based on centrality metrics such as PageRank. Our results on eight large networks (including two with $\sim$50k nodes) demonstrate the effectiveness of the proposed method with a more than 10-fold runtime gain compared to the time needed on the original network, and an up to $82\%$ time reduction compared to CELF.

It has been conjectured by P\'{o}lya and Szeg\"{o} seventy years ago that the planar set which minimizes the first eigenvalue of the Dirichlet-Laplace operator among polygons with $n$ sides and fixed area is the regular polygon. Despite its apparent simplicity, this result has only been proved for triangles and quadrilaterals. In this paper we prove that for each $n \ge 5$ the proof of the conjecture can be reduced to a finite number of certified numerical computations. Moreover, the local minimality of the regular polygon can be reduced to a single numerical computation. For $n=5, 6,7, 8$ we perform this computation and certify the numerical approximation by finite elements, up to machine errors.

Many industrial sectors have been collecting big sensor data. With recent technologies for processing big data, companies can exploit this for automatic failure detection and prevention. We propose the first completely automated method for failure analysis, machine-learning fault trees from raw observational data with continuous variables. Our method scales well and is tested on a real-world, five-year dataset of domestic heater operations in The Netherlands, with 31 million unique heater-day readings, each containing 27 sensor and 11 failure variables. Our method builds on two previous procedures: the C4.5 decision-tree learning algorithm, and the LIFT fault tree learning algorithm from Boolean data. C4.5 pre-processes each continuous variable: it learns an optimal numerical threshold which distinguishes between faulty and normal operation of the top-level system. These thresholds discretise the variables, thus allowing LIFT to learn fault trees which model the root failure mechanisms of the system and are explainable. We obtain fault trees for the 11 failure variables, and evaluate them in two ways: quantitatively, with a significance score, and qualitatively, with domain specialists. Some of the fault trees learnt have almost maximum significance (above 0.95), while others have medium-to-low significance (around 0.30), reflecting the difficulty of learning from big, noisy, real-world sensor data. The domain specialists confirm that the fault trees model meaningful relationships among the variables.

With the rapidly increasing amount of scientific literature,it is getting continuously more difficult for researchers in different disciplines to be updated with the recent findings in their field of study.Processing scientific articles in an automated fashion has been proposed as a solution to this problem,but the accuracy of such processing remains very poor for extraction tasks beyond the basic ones.Few approaches have tried to change how we publish scientific results in the first place,by making articles machine-interpretable by expressing them with formal semantics from the start.In the work presented here,we set out to demonstrate that we can formally publish high-level scientific claims in formal logic,and publish the results in a special issue of an existing journal.We use the concept and technology of nanopublications for this endeavor,and represent not just the submissions and final papers in this RDF-based format,but also the whole process in between,including reviews,responses,and decisions.We do this by performing a field study with what we call formalization papers,which contribute a novel formalization of a previously published claim.We received 15 submissions from 18 authors,who then went through the whole publication process leading to the publication of their contributions in the special issue.Our evaluation shows the technical and practical feasibility of our approach.The participating authors mostly showed high levels of interest and confidence,and mostly experienced the process as not very difficult,despite the technical nature of the current user interfaces.We believe that these results indicate that it is possible to publish scientific results from different fields with machine-interpretable semantics from the start,which in turn opens countless possibilities to radically improve in the future the effectiveness and efficiency of the scientific endeavor as a whole.

We measure the color shifts present in colorized images from the ADE20K dataset, when colorized by the automatic GAN-based DeOldify model. We introduce fine-grained local and regional bias measurements between the original and the colorized images, and observe many colorization effects. We confirm a general desaturation effect, and also provide novel observations: a shift towards the training average, a pervasive blue shift, different color shifts among image categories, and a manual categorization of colorization errors in three classes., Comment: 5 pages, 8 figures

Memes are prevalent on the internet and continue to grow and evolve alongside our culture. An automatic understanding of memes propagating on the internet can shed light on the general sentiment and cultural attitudes of people. In this work, we present team BLUE's solution for the second edition of the MEMOTION shared task. We showcase two approaches for meme classification (i.e. sentiment, humour, offensive, sarcasm and motivation levels) using a text-only method using BERT, and a Multi-Modal-Multi-Task transformer network that operates on both the meme image and its caption to output the final scores. In both approaches, we leverage state-of-the-art pretrained models for text (BERT, Sentence Transformer) and image processing (EfficientNetV4, CLIP). Through our efforts, we obtain first place in task A, second place in task B and third place in task C. In addition, our team obtained the highest average score for all three tasks., Comment: De-Factify: Workshop on Multimodal Fact Checking and Hate Speech Detection, co-located with AAAI 2022

For a general radially symmetric, non-increasing, non-negative kernel $h\in L ^ 1 _{loc} ( R ^ d)$, we study the rigidity of measurable sets in $R ^ d$ with constant nonlocal $h$-mean curvature. Under a suitable "improved integrability" assumption on $h$, we prove that these sets are finite unions of equal balls, as soon as they satisfy a natural nondegeneracy condition. Both the radius of the balls and their mutual distance can be controlled from below in terms of suitable parameters depending explicitly on the measure of the level sets of $h$. In the simplest, common case, in which $h$ is positive, bounded and decreasing, our result implies that any bounded open set or any bounded measurable set with finite perimeter which has constant nonlocal $h$-mean curvature has to be a ball., Comment: arXiv admin note: text overlap with arXiv:2102.12389

We consider the $N$-Laplacian Schr\"odinger equation strongly coupled with higher order fractional Poisson's equations. When the order of the Riesz potential $\alpha$ is equal to the Euclidean dimension $N$, and thus it is a logarithm, the system turns out to be equivalent to a nonlocal Choquard type equation. On the one hand, the natural function space setting in which the Schr\"odinger energy is well defined is the Sobolev limiting space $W^{1,N}(\mathbb{R}^N)$, where the maximal nonlinear growth is of exponential type. On the other hand, in order to have the nonlocal energy well defined and prove the existence of finite energy solutions, we introduce a suitable $log$-weighted variant of the Pohozaev-Trudinger inequality which provides a proper functional framework where we use variational methods.

We study a shape optimization problem involving a solid $K\subset\mathbb{R}^n$ that is maintained at constant temperature and is enveloped by a layer of insulating material $\Omega$ which obeys a generalized boundary heat transfer law. We minimize the energy of such configurations among all $(K,\Omega)$ with prescribed measure for $K$ and $\Omega$, and no topological or geometrical constraints. In the convection case (corresponding to Robin boundary conditions on $\partial\Omega$) we obtain a full description of minimizers, while for general heat transfer conditions, we prove the existence and regularity of solutions and give a partial description of minimizers.

Small and medium enterprises rely on detailed Web analytics to be informed about their market and competition. Focused crawlers meet this demand by crawling and indexing specific parts of the Web. Critically, a focused crawler must quickly find new pages that have not yet been indexed. Since a new page can be discovered only by following a new outlink, predicting new outlinks is very relevant in practice. In the literature, many feature designs have been proposed for predicting changes in the Web. In this work we provide a structured analysis of this problem, using new outlinks as our running prediction target. Specifically, we unify earlier feature designs in a taxonomic arrangement of features along two dimensions: static versus dynamic features, and features of a page versus features of the network around it. Within this taxonomy, complemented by our new (mainly, dynamic network) features, we identify best predictors for new outlinks. Our main conclusion is that most informative features are the recent history of new outlinks on a page itself, and of its content-related pages. Hence, we propose a new 'look back, look around' (LBLA) model, that uses only these features. With the obtained predictions, we design a number of scoring functions to guide a focused crawler to pages with most new outlinks, and compare their performance. The LBLA approach proved extremely effective, outperforming other models including those that use a most complete set of features. One of the learners we use, is the recent NGBoost method that assumes a Poisson distribution for the number of new outlinks on a page, and learns its parameters. This connects the two so far unrelated avenues in the literature: predictions based on features of a page, and those based on probabilistic modelling. All experiments were carried out on an original dataset, made available by a commercial focused crawler., Comment: 23 pages, 15 figures, 4 tables, uses arxiv.sty, added new title, heuristic features and their results added, figures 7, 14, and 15 updated, accepted version

In traditional astronomies across the world, groups of stars in the night sky were linked into constellations -- symbolic representations rich in meaning and with practical roles. In some sky cultures, constellations are represented as line (or connect-the-dot) figures, which are spatial networks drawn over the fixed background of stars. We analyse 1802 line figures from 56 sky cultures spanning all continents, in terms of their network, spatial, and brightness features, and ask what associations exist between these visual features and culture type or sky region. First, an embedded map of constellations is learnt, to show clusters of line figures. We then form the network of constellations (as linked by their similarity), to study how similar cultures are by computing their assortativity (or homophily) over the network. Finally, we measure the diversity (or entropy) index for the set of constellations drawn per sky region. Our results show distinct types of line figures, and that many folk astronomies with oral traditions have widespread similarities in constellation design, which do not align with cultural ancestry. In a minority of sky regions, certain line designs appear universal, but this is not the norm: in the majority of sky regions, the line geometries are diverse., Comment: Data repository: https://github.com/doinab/constellation-lines (in progress)

Current benchmark tasks for natural language processing contain text that is qualitatively different from the text used in informal day to day digital communication. This discrepancy has led to severe performance degradation of state-of-the-art NLP models when fine-tuned on real-world data. One way to resolve this issue is through lexical normalization, which is the process of transforming non-standard text, usually from social media, into a more standardized form. In this work, we propose a sentence-level sequence-to-sequence model based on mBART, which frames the problem as a machine translation problem. As the noisy text is a pervasive problem across languages, not just English, we leverage the multi-lingual pre-training of mBART to fine-tune it to our data. While current approaches mainly operate at the word or subword level, we argue that this approach is straightforward from a technical standpoint and builds upon existing pre-trained transformer networks. Our results show that while word-level, intrinsic, performance evaluation is behind other methods, our model improves performance on extrinsic, downstream tasks through normalization compared to models operating on raw, unprocessed, social media text., Comment: In Proceedings of the 7th Workshop on Noisy User-generated Text (WNUT 2021), EMNLP 2021

The use of semantic technologies is gaining significant traction in science communication with a wide array of applications in disciplines including the Life Sciences, Computer Science, and the Social Sciences. Languages like RDF, OWL, and other formalisms based on formal logic are applied to make scientific knowledge accessible not only to human readers but also to automated systems. These approaches have mostly focused on the structure of scientific publications themselves, on the used scientific methods and equipment, or on the structure of the used datasets. The core claims or hypotheses of scientific work have only been covered in a shallow manner, such as by linking mentioned entities to established identifiers. In this research, we therefore want to find out whether we can use existing semantic formalisms to fully express the content of high-level scientific claims using formal semantics in a systematic way. Analyzing the main claims from a sample of scientific articles from all disciplines, we find that their semantics are more complex than what a straight-forward application of formalisms like RDF or OWL account for, but we managed to elicit a clear semantic pattern which we call the 'super-pattern'. We show here how the instantiation of the five slots of this super-pattern leads to a strictly defined statement in higher-order logic. We successfully applied this super-pattern to an enlarged sample of scientific claims. We show that knowledge representation experts, when instructed to independently instantiate the super-pattern with given scientific claims, show a high degree of consistency and convergence given the complexity of the task and the subject. These results therefore open the door for expressing high-level scientific findings in a manner they can be automatically interpreted, which on the longer run can allow us to do automated consistency checking, and much more., Comment: 8 pages

We formulate a general problem: given projective schemes $\mathbb{Y}$ and $\mathbb{X}$ over a global field $K$ and a $K$-morphism $\eta$ from $\mathbb{Y}$ to $\mathbb{X}$ of finite degree, how many points in $\mathbb{X}(K)$ of height at most $B$ have a pre-image under $\eta$ in $\mathbb{Y}(K)$? This problem is inspired by a well-known conjecture of Serre on quantitative upper bounds for the number of points of bounded height on an irreducible projective variety defined over a number field. We give a non-trivial answer to the general problem when $K=\mathbb{F}_q(T)$ and $\mathbb{Y}$ is a prime degree cyclic cover of $\mathbb{X}=\mathbb{P}_{K}^n$. Our tool is a new geometric sieve, which generalizes the polynomial sieve to a geometric setting over global function fields., Comment: Appendix by Joseph Rabinoff, 40 pages

In this work, we provide an extensive part-of-speech analysis of the discourse of social media users with depression. Research in psychology revealed that depressed users tend to be self-focused, more preoccupied with themselves and ruminate more about their lives and emotions. Our work aims to make use of large-scale datasets and computational methods for a quantitative exploration of discourse. We use the publicly available depression dataset from the Early Risk Prediction on the Internet Workshop (eRisk) 2018 and extract part-of-speech features and several indices based on them. Our results reveal statistically significant differences between the depressed and non-depressed individuals confirming findings from the existing psychology literature. Our work provides insights regarding the way in which depressed individuals are expressing themselves on social media platforms, allowing for better-informed computational models to help monitor and prevent mental illnesses., Comment: Accepted to RANLP 2021

Mobile malware are malicious programs that target mobile devices. They are an increasing problem, as seen in the rise of detected mobile malware samples per year. The number of active smartphone users is expected to grow, stressing the importance of research on the detection of mobile malware. Detection methods for mobile malware exist but are still limited. In this paper, we provide an overview of the performance of machine learning (ML) techniques to detect malware on Android, without using privileged access. The ML-classifiers use device information such as the CPU usage, battery usage, and memory usage for the detection of 10 subtypes of Mobile Trojans on the Android Operating System (OS). We use a real-life dataset containing device and malware data from 47 users for a year (2016). We examine which features, i.e. aspects, of a device, are most important to monitor to detect (subtypes of) Mobile Trojans. The focus of this paper is on dynamic hardware features. Using these dynamic features we apply state-of-the-art machine learning classifiers: Random Forest, K-Nearest Neighbour, and AdaBoost. We show classification results on different feature sets, making a distinction between global device features, and specific app features. None of the measured feature sets require privileged access. Our results show that the Random Forest classifier performs best as a general malware classifier: across 10 subtypes of Mobile Trojans, it achieves an F1 score of 0.73 with a False Positive Rate (FPR) of 0.009 and a False Negative Rate (FNR) of 0.380. The Random Forest, K-Nearest Neighbours, and AdaBoost classifiers achieve F1 scores above 0.72, an FPR below 0.02 and, an FNR below 0.33, when trained separately to detect each subtype of Mobile Trojans., Comment: 14 pages content, 22 pages total, to be published in ACM DTRAP (currently in last revision phase)