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In this work we study an inhomogeneous two-phase obstacle-type problem associated to the $s$-fractional $p$-Laplacian. Besides the existence and uniqueness of solutions, we study the convergence of the solutions when $s\to 1$ to the classical problem. We also study the continuous dependence with respect to the level-set function $v$, yielding an existence result for a two-phase obstacle-type problem with an implicit level-set function., Comment: 21 pages

The recent discoveries of Neptune-sized ultra-short period planets (USPs) challenge existing planet formation theories. It is unclear whether these residents of the Hot Neptune Desert have similar origins to smaller, rocky USPs, or if this discrete population is evidence of a different formation pathway altogether. We report the discovery of TOI-3261b, an ultra-hot Neptune with an orbital period $P$ = 0.88 days. The host star is a $V = 13.2$ magnitude, slightly super-solar metallicity ([Fe/H] $\simeq$ 0.15), inactive K1.5 main sequence star at $d = 300$ pc. Using data from the Transiting Exoplanet Survey Satellite and the Las Cumbres Observatory Global Telescope, we find that TOI-3261b has a radius of $3.82_{-0.35}^{+0.42}$ $R_{\oplus}$. Moreover, radial velocities from ESPRESSO and HARPS reveal a mass of $30.3_{-2.4}^{+2.2}$ $M_{\oplus}$, more than twice the median mass of Neptune-sized planets on longer orbits. We investigate multiple mechanisms of mass loss that can reproduce the current-day properties of TOI-3261b, simulating the evolution of the planet via tidal stripping and photoevaporation. Thermal evolution models suggest that TOI-3261b should retain an envelope potentially enriched with volatiles constituting $\sim$5% of its total mass. This is the second highest envelope mass fraction among ultra-hot Neptunes discovered to date, making TOI-3261b an ideal candidate for atmospheric follow-up observations., Comment: 20 pages, 11 figures, accepted to AJ

The conservation of stone-based cultural heritage sites is a critical concern for preserving cultural and historical landmarks. With the advent of Large Multimodal Models, as GPT-4omni (OpenAI), Claude 3 Opus (Anthropic) and Gemini 1.5 Pro (Google), it is becoming increasingly important to define the operational capabilities of these models. In this work, we systematically evaluate the abilities of the main foundational multimodal models to recognise and classify anomalies and deterioration patterns of the stone elements that are useful in the practice of conservation and restoration of world heritage. After defining a taxonomy of the main stone deterioration patterns and anomalies, we asked the foundational models to identify a curated selection of 354 highly representative images of stone-built heritage, offering them a careful selection of labels to choose from. The result, which varies depending on the type of pattern, allowed us to identify the strengths and weaknesses of these models in the field of heritage conservation and restoration., Comment: 10 pages, 5 figures, submitted to Journal of Cultural Heritage

We consider the one and the two obstacles problems for the nonlocal nonlinear anisotropic $g$-Laplacian $\mathcal{L}_g^s$, with $0

We show that the solutions to the nonlocal obstacle problems for the nonlocal $-\Delta_p^s$ operator, when the fractional parameter $s\to\sigma$ for $0<\sigma\leq1$, converge to the solution of the corresponding obstacle problem for $-\Delta_p^\sigma$, being $\sigma=1$ the classical obstacle problem for the local $p$-Laplacian. We discuss the weak stability of the quasi-characteristic functions of coincidence sets of the solution with the obstacle, which is a strong convergence of their characteristic functions when $s\nearrow 1$ under a nondegeneracy condition. This stability can be shown also in terms of the convergence of the free boundaries, as well as of the coincidence sets, in Hausdorff distance when $s\nearrow 1$, under non-degeneracy local assumptions on the external force and a local topological property of the coincidence set of the limit classical obstacle problem for the local $p$-Laplacian, essentially when the limit coincidence set is the closure of its interior.

Within high-performance computing (HPC), solving large sparse linear systems efficiently remains paramount, with iterative methods being the predominant choice. However, the performance of these methods is tightly coupled to the aptness of the chosen preconditioner. The multifaceted nature of sparse matrices makes the universal prescription of preconditioners elusive. Notably, the key attribute of sparsity is not precisely captured by scalar metrics such as bandwidth or matrix dimensions. Advancing prior methodologies, this research introduces matrix sparsity depiction via RGB images. Utilizing a convolutional neural network (CNN), the task of preconditioner selection turns into a multi-class classification problem. Extensive tests on 126 SuiteSparse matrices emphasize the enhanced prowess of the CNN model, noting a 32% boost in accuracy and a 25% reduction in computational slowdown., Comment: 23 pages, 8 figures, 9 tables

We consider weak solutions for the obstacle-type viscoelastic ($\nu>0$) and very weak solutions for the obstacle inviscid ($\nu=0$) Dirichlet problems for the heterogeneous and anisotropic wave equation in a fractional framework based on the Riesz fractional gradient $D^s$ ($0

We report the discovery of two exoplanets orbiting around HD 212729 (TOI\,1052, TIC 317060587), a $T_{\rm eff}=6146$K star with V=9.51 observed by TESS in Sectors 1 and 13. One exoplanet, TOI-1052b, is Neptune-mass and transits the star, and an additional planet TOI-1052c is observed in radial velocities but not seen to transit. We confirm the planetary nature of TOI-1052b using precise radial velocity observations from HARPS and determined its parameters in a joint RV and photometry analysis. TOI-1052b has a radius of $2.87^{+0.29}_{-0.24}$ R$_{\oplus}$, a mass of $16.9\pm 1.7$ M$_{\oplus}$, and an orbital period of 9.14 days. TOI-1052c does not show any transits in the TESS data, and has a minimum mass of $34.3^{+4.1}_{-3.7}$ M$_{\oplus}$ and an orbital period of 35.8 days, placing it just interior to the 4:1 mean motion resonance. Both planets are best fit by relatively high but only marginally significant eccentricities of $0.18^{+0.09}_{-0.07}$ for planet b and $0.24^{+0.09}_{-0.08}$ for planet c. We perform a dynamical analysis and internal structure model of the planets as well as deriving stellar parameters and chemical abundances. The mean density of TOI-1052b is $3.9^{+1.7}_{-1.3}$ g cm$^{-3}$ consistent with an internal structure similar to Neptune. A nearby star is observed in Gaia DR3 with the same distance and proper motion as TOI-1052, at a sky projected separation of ~1500AU, making this a potential wide binary star system., Comment: Accepted to MNRAS. 11 pages

We present the discovery of an exoplanet transiting TOI-908 (TIC-350153977) using data from TESS sectors 1, 12, 13, 27, 28 and 39. TOI-908 is a T = 10.7 mag G-dwarf ($T_{eff}$ = 5626 $\pm$ 61 K) solar-like star with a mass of 0.950 $\pm$ 0.010 $M_{\odot}$ and a radius of 1.028 $\pm$ 0.030 $R_{\odot}$. The planet, TOI-908 b, is a 3.18 $\pm$ 0.16 $R_{\oplus}$ planet in a 3.18 day orbit. Radial velocity measurements from HARPS reveal TOI-908 b has a mass of approximately 16.1 $\pm$ 4.1 $M_{\oplus}$ , resulting in a bulk planetary density of 2.7+0.2-0.4 g cm-3. TOI-908 b lies in a sparsely-populated region of parameter space known as the Neptune desert. The planet likely began its life as a sub-Saturn planet before it experienced significant photoevaporation due to X-rays and extreme ultraviolet radiation from its host star, and is likely to continue evaporating, losing a significant fraction of its residual envelope mass., Comment: 17 pages, 17 figures

We prove the existence of generalised solutions of the Monge-Kantorovich equations with fractional $s$-gradient constraint, $0

Reservoir simulations for petroleum fields and seismic imaging are known as the most demanding workloads for high-performance computing (HPC) in the oil and gas (O&G) industry. The optimization of the simulator numerical parameters plays a vital role as it could save considerable computational efforts. State-of-the-art optimization techniques are based on running numerous simulations, specific for that purpose, to find good parameter candidates. However, using such an approach is highly costly in terms of time and computing resources. This work presents TunaOil, a new methodology to enhance the search for optimal numerical parameters of reservoir flow simulations using a performance model. In the O&G industry, it is common to use ensembles of models in different workflows to reduce the uncertainty associated with forecasting O&G production. We leverage the runs of those ensembles in such workflows to extract information from each simulation and optimize the numerical parameters in their subsequent runs. To validate the methodology, we implemented it in a history matching (HM) process that uses a Kalman filter algorithm to adjust an ensemble of reservoir models to match the observed data from the real field. We mine past execution logs from many simulations with different numerical configurations and build a machine learning model based on extracted features from the data. These features include properties of the reservoir models themselves, such as the number of active cells, to statistics of the simulation's behavior, such as the number of iterations of the linear solver. A sampling technique is used to query the oracle to find the numerical parameters that can reduce the elapsed time without significantly impacting the quality of the results. Our experiments show that the predictions can improve the overall HM workflow runtime on average by 31%., Comment: 21 pages, 9 figures. Preprint submitted to Journal of Computational Science

Consider the quasilinear diffusion problem \[\begin{cases}\mathbf{u}'+\Pi(t,x,\mathbf{u},\Sigma \mathbf{u})\mathbb{A}\mathbf{u}=\mathbf{f}(t,x,\mathbf{u},\Sigma \mathbf{u})&\text{ in }]0,T[\times\Omega,\\\mathbf{u}=\mathbf{0}&\text{ in }]0,T[\times\Omega^c,\\\mathbf{u}(0,\cdot)=\mathbf{u}_0(\cdot)&\text{ in }\Omega\end{cases}\] for an open set $\Omega\subset\mathbb{R}^n$, $\mathbf{u}_0\in \mathbf{H}^s_0(\Omega):=[H^s_0(\Omega)]^m$ and any $T\in]0,\infty[$, where $\Sigma \mathbf{u}\in \mathbb{R}^q$ for $0

In this work, we consider the fractional Stefan-type problem in a Lipschitz bounded domain $\Omega\subset\mathbb{R}^d$ with time-dependent Dirichlet boundary condition for the temperature $\vartheta=\vartheta(x,t)$, $\vartheta=g$ on $\Omega^c\times]0,T[$, and initial condition $\eta_0$ for the enthalpy $\eta=\eta(x,t)$, given in $\Omega\times]0,T[$ by \[\frac{\partial \eta}{\partial t} +\mathcal{L}_A^s \vartheta= f\quad\text{ with }\eta\in \beta(\vartheta),\] where $\mathcal{L}_A^s$ is an anisotropic fractional operator defined in the distributional sense by \[\langle\mathcal{L}_A^su,v\rangle=\int_{\mathbb{R}^d}AD^su\cdot D^sv\,dx,\] $\beta$ is a maximal monotone graph, $A(x)$ is a symmetric, strictly elliptic and uniformly bounded matrix, and $D^s$ is the distributional Riesz fractional gradient for $0

The Jordan--Moore--Gibson--Thompson (JMGT) equation is a well-established and recently widely studied model for nonlinear acoustics (NLA). It is a third-order (in time) semilinear Partial Differential Equation (PDE) model with the distinctive feature of predicting the propagation of ultrasound waves at \textit{finite} speed due to heat phenomenon know as \textit{second sound} which leads to the hyperbolic character of heat propagation. In this paper, we consider the problem of stabilizability of the linear (known as) MGT--equation. We consider a special geometry that is suitable for studying the problem of controlling (from the boundary) the acoustic pressure involved in medical treatments like lithotripsy, thermotherapy, sonochemistry, or any other procedures using High Intensity Focused Ultrasound (HIFU).

In this work, we consider the nonlocal obstacle problem with a given obstacle $\psi$ in a bounded Lipschitz domain $\Omega$ in $\mathbb{R}^{d}$, such that $\mathbb{K}_\psi^s=\{v\in H^s_0(\Omega):v\geq\psi \text{ a.e. in }\Omega\}\neq\emptyset$, given by \[u\in\mathbb{K}_\psi^s:\langle\mathcal{L}_au,v-u\rangle\geq\langle F,v-u\rangle\quad\forall v\in\mathbb{K}^s_\psi,\] for $F\in H^{-s}(\Omega)$, the dual space of $H^s_0(\Omega)$, $0

We formulate and study two mathematical models of a thermoforming process involving a membrane and a mould as implicit obstacle problems. In particular, the membrane-mould coupling is determined by the thermal displacement of the mould that depends in turn on the membrane through the contact region. The two models considered are a stationary (or elliptic) model and an evolutionary (or quasistatic) one. For the first model, we prove the existence of weak solutions by solving an elliptic quasi-variational inequality coupled to elliptic equations. By exploring the fine properties of the variation of the contact set under non-degenerate data, we give sufficient conditions for the existence of regular solutions, and under certain contraction conditions, also a uniqueness result. We apply these results to a series of semi-discretised problems that arise as approximations of regular solutions for the evolutionary or quasistatic problem. Here, under certain conditions, we are able to prove existence for the evolutionary problem and for a special case, also the uniqueness of time-dependent solutions., Comment: 34 pages, 2 figures

We extend classical results on variational inequalities with convex sets with gradient constraint to a new class of fractional partial differential equations in a bounded domain with constraint on the distributional Riesz fractional gradient, the $\sigma$-gradient ($0<\sigma<1$). We establish continuous dependence results with respect to the data, including the threshold of the fractional $\sigma$-gradient. Using these properties we give new results on the existence to a class of quasi-variational variational inequalities with fractional gradient constraint via compactness and via contraction arguments. Using the approximation of the solutions with a family of quasilinear penalisation problems we show the existence of generalised Lagrange multipliers for the $\sigma$-gradient constrained problem, extending previous results for the classical gradient case, i.e., with $\sigma=1$., Comment: 18 pages

This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational inequalities. Motivated by models for critical state problems and applications to free boundary problems in Mechanics and in Physics, in this work several known properties are collected and presented and a few novel results and examples are found.

We study the homogenization of obstacle problems in Orlicz-Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the $p(\cdot)$-Laplacian type. Our approach is based on the Lewy-Stampacchia inequalities, which then give access to a compactness argument. We also prove the convergence of the coincidence sets under non-degeneracy conditions., Comment: 13 pages

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type, but are not required to be coercive for the existence of weak solutions, which is obtained by a double penalisation/regularisation for the approximation of the solutions. In the case of time-dependent convex sets that are independent of the solution, we show also the uniqueness and the continuous dependence of the strong solutions of the variational inequalities, extending previous results to a more general framework.

Turbulent radiation flow is commonplace in systems with strong, incoherent, light-matter interactions. In astrophysical contexts, photon bubble turbulence is considered a key mechanism behind enhanced radiation transport, and its importance has been widely asserted for a variety of high energy objects such as accretion disks and massive stars. We demonstrate here that analogous conditions to those of dense astrophysical objects can be obtained in large clouds of cold atoms driven close to a sharp electronic resonance. By accessing the spatially-resolved atom density, we are able to identify a photon bubble instability and the resulting regime of photon bubble turbulence. We also develop a theoretical model describing the coupled dynamics of both photon and atom gases, which accurately describes the statistical properties of the turbulent regime. This study thus opens the possibility of simulating radiation-dominated astrophysical systems in cold atom experiments.

One of the most useful techniques to help visual data analysis systems is interactive filtering (brushing). However, visualization techniques often suffer from overlap of graphical items and multiple attributes complexity, making visual selection inefficient. In these situations, the benefits of data visualization are not fully observable because the graphical items do not pop up as comprehensive patterns. In this work we propose the use of content-based data retrieval technology combined with visual analytics. The idea is to use the similarity query functionalities provided by metric space systems in order to select regions of the data domain according to user-guidance and interests. After that, the data found in such regions feed multiple visualization workspaces so that the user can inspect the correspondent datasets. Our experiments showed that the methodology can break the visual analysis process into smaller problems (views) and that the views hold the expectations of the analyst according to his/her similarity query selection, improving data perception and analytical possibilities. Our contribution introduces a principle that can be used in all sorts of visualization techniques and systems, this principle can be extended with different kinds of integration visualization-metric-space, and with different metrics, expanding the possibilities of visual data analysis in aspects such as semantics and scalability., Comment: Published as Jose Rodrigues, Luciana A. S. Romani, Agma Juci Machado Traina, Caetano Traina Jr (2010), Combining Visual Analytics and Content Based Data Retrieval Technology for Efficient Data Analysis, 14th Int Conf on Inf Visualisation, 61-67

In the last years, Distributed Visualization over Personal Computer (PC) clusters has become important for research and industrial communities. They have made large-scale visualizations practical and more accessible. In this work we survey Distributed Visualization techniques aiming at compiling last decade's literature on the use of PC clusters as suitable alternatives to high-end workstations. We review the topic by defining basic concepts, enumerating system requirements and implementation challenges, and presenting up-to-date methodologies. Our work fulfills the needs of newcomers and seasoned professionals as an introductory compilation at the same time that it can help experienced personnel by organizing ideas.

Given a large-scale graph with millions of nodes and edges, how to reveal macro patterns of interest, like cliques, bi-partite cores, stars, and chains? Furthermore, how to visualize such patterns altogether getting insights from the graph to support wise decision-making? Although there are many algorithmic and visual techniques to analyze graphs, none of the existing approaches is able to present the structural information of graphs at large-scale. Hence, this paper describes StructMatrix, a methodology aimed at high-scalable visual inspection of graph structures with the goal of revealing macro patterns of interest. StructMatrix combines algorithmic structure detection and adjacency matrix visualization to present cardinality, distribution, and relationship features of the structures found in a given graph. We performed experiments in real, large-scale graphs with up to one million nodes and millions of edges. StructMatrix revealed that graphs of high relevance (e.g., Web, Wikipedia and DBLP) have characterizations that reflect the nature of their corresponding domains; our findings have not been seen in the literature so far. We expect that our technique will bring deeper insights into large graph mining, leveraging their use for decision making., Comment: To appear: 8 pages, paper to be published at the Fifth IEEE ICDM Workshop on Data Mining in Networks, 2015 as Hugo Gualdron, Robson Cordeiro, Jose Rodrigues (2015) StructMatrix: Large-scale visualization of graphs by means of structure detection and dense matrices In: The Fifth IEEE ICDM Workshop on Data Mining in Networks 1--8, IEEE

Given a large social or computer network, how can we visualize it, find patterns, outliers, communities? Although several graph visualization tools exist, they cannot handle large graphs with hundred thousand nodes and possibly million edges. Such graphs bring two challenges: interactive visualization demands prohibitive processing power and, even if we could interactively update the visualization, the user would be overwhelmed by the excessive number of graphical items. To cope with this problem, we propose a formal innovation on the use of graph hierarchies that leads to GMine system. GMine promotes scalability using a hierarchy of graph partitions, promotes concomitant presentation for the graph hierarchy and for the original graph, and extends analytical possibilities with the integration of the graph partitions in an interactive environment., Comment: 9 pages, appears in Proceedings of the IEEE International Symposium on Multimedia, 2006 as SuperGraph Visualization In: 8th IEEE International Symposium on Multimedia 227-234 IEEE Press

Several graph visualization tools exist. However, they are not able to handle large graphs, and/or they do not allow interaction. We are interested on large graphs, with hundreds of thousands of nodes. Such graphs bring two challenges: the first one is that any straightforward interactive manipulation will be prohibitively slow. The second one is sensory overload: even if we could plot and replot the graph quickly, the user would be overwhelmed with the vast volume of information because the screen would be too cluttered as nodes and edges overlap each other. GMine system addresses both these issues, by using summarization and multi-resolution. GMine offers multi-resolution graph exploration by partitioning a given graph into a hierarchy of com-munities-within-communities and storing it into a novel R-tree-like structure which we name G-Tree. GMine offers summarization by implementing an innovative subgraph extraction algorithm and then visualizing its output., Comment: 4 pages, Proceedings of the 32nd international conference on Very Large Data Bases, 2006. Specifically: Jose Rodrigues, Hanghang Tong, Agma Traina, Christos Faloutsos, Jure Leskovec (2006), GMine: A System for Scalable, Interactive Graph Visualization and Mining; 32nd International Conference on Very Large Data Bases (VLDB) 1195-1198

Social media could provide valuable information to support decision making in crisis management, such as in accidents, explosions and fires. However, much of the data from social media are images, which are uploaded in a rate that makes it impossible for human beings to analyze them. Despite the many works on image analysis, there are no fire detection studies on social media. To fill this gap, we propose the use and evaluation of a broad set of content-based image retrieval and classification techniques for fire detection. Our main contributions are: (i) the development of the Fast-Fire Detection method (FFDnR), which combines feature extractor and evaluation functions to support instance-based learning, (ii) the construction of an annotated set of images with ground-truth depicting fire occurrences -- the FlickrFire dataset, and (iii) the evaluation of 36 efficient image descriptors for fire detection. Using real data from Flickr, our results showed that FFDnR was able to achieve a precision for fire detection comparable to that of human annotators. Therefore, our work shall provide a solid basis for further developments on monitoring images from social media., Comment: 12 pages, Proceedings of the International Conference on Enterprise Information Systems. Specifically: Marcos Bedo, Gustavo Blanco, Willian Oliveira, Mirela Cazzolato, Alceu Costa, Jose Rodrigues, Agma Traina, Caetano Traina, 2015, Techniques for effective and efficient fire detection from social media images, ICEIS, 34-45

We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a combination of parabolic regularization with a penalization in the nonlinear diffusion coefficient. We also prove the continuous dependence of the solution with respect to the data, as well as, in a coercive case, the asymptotic stabilization as time $t\rightarrow+\infty$ towards the stationary solution. In a particular situation, motivated by the transported sandpile problem, we give sufficient conditions for the equivalence of the first order problem with gradient constraint with a two obstacles problem, the obstacles being the signed distances to the boundary. This equivalence, in special conditions, illustrates also the possible stabilization of the solution in finite time., Comment: 21 pages 1 figure

In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem by a penalization/viscosity method. The mass constraint introduces a nonlocal Lagrange multiplier in the penalized equation, giving rise to a nonlocal parabolic problem. We determine conditions on the initial data and on the obstacle function which ensure global in time existence of solution. These are not smoothness conditions, but relate to the propagation of the support of the initial data.

We introduce Sense{\mu} (pronounced "sense me"), a mobile application that aims at supporting awareness in parent- child relationships through the sensing capabilities of mobile devices. We discuss the relevance of three types of awareness information: physical activity inferred from accelerometers, verbal activity during class hours inferred from microphones, and social activity inferred from Bluetooth pair-wise proximity sensing. We describe how we attempt to contextualize these sensing data with the goal of supporting parents' awareness of the educational performance and social wellbeing of their children, as well as motivating and sustaining a two-way communication between parents and teachers over the long term.

The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \partial_t u-\Delta u=a u-b(x) u^p \text{in} \Omega\times \R^+, u(0)=u_0, u(t)|_{\partial \Omega}=0 $$ as $p\to +\infty$, where $\Omega$ is a bounded domain and $b(x)$ is a nonnegative function. We deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards we fully describe its long time behavior., Comment: 15 pages

We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable {\em a priori} estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results.

In image analysis, many tasks require representing two-dimensional (2D) shape, often specified by a set of 2D points, for comparison purposes. The challenge of the representation is that it must not only capture the characteristics of the shape but also be invariant to relevant transformations. Invariance to geometric transformations, such as translation, rotation, and scale, has received attention in the past, usually under the assumption that the points are previously labeled, i.e., that the shape is characterized by an ordered set of landmarks. However, in many practical scenarios, the points describing the shape are obtained from automatic processes, e.g., edge or corner detection, thus without labels or natural ordering. Obviously, the combinatorial problem of computing the correspondences between the points of two shapes in the presence of the aforementioned geometrical distortions becomes a quagmire when the number of points is large. We circumvent this problem by representing shapes in a way that is invariant to the permutation of the landmarks, i.e., we represent bags of unlabeled 2D points. Within our framework, a shape is mapped to an analytic function on the complex plane, leading to what we call its analytic signature (ANSIG). To store an ANSIG, it suffices to sample it along a closed contour in the complex plane. We show that the ANSIG is a maximal invariant with respect to the permutation group, i.e., that different shapes have different ANSIGs and shapes that differ by a permutation (or re-labeling) of the landmarks have the same ANSIG. We further show how easy it is to factor out geometric transformations when comparing shapes using the ANSIG representation. Finally, we illustrate these capabilities with shape-based image classification experiments.

We prove existence of solution of a $p$-curl type evolutionary system arising in electromagnetism with a power nonlinearity of order $p$, $1

We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic external potential. Particles are inserted at the leftmost site at rate $\alpha$, hop to the right at unit rate, and are removed at the rightmost site at rate $\beta$. Our study is motivated by recent experiments on colloidal particles in optical tweezer arrays. The external potential is of the form generated by such an array. Particles spend most of the time near potential minima, approximating the situation in the lattice gas; a short-range repulsive interaction prevents two particles from occupying the same potential well. A constant driving force, representing Stokes drag on particles suspended in a moving fluid, leads to biased motion. Our results for the density profile and current, obtained via numerical integration of the Langevin equation and dynamic Monte Carlo simulations, indicate that the continuous-space model exhibits phase transitions analogous to those observed in the lattice model. The correspondence is not exact, however, due to the lack of particle-hole symmetry in our model., Comment: 26 pages, 12 figures

The parabolic N-membranes problem for the p-Laplacian and the complete order constraint on the components of the solution is studied in what concerns the approximation, the regularity and the stability of the variational solutions. We extend to the evolutionary case the characterization of the Lagrange multipliers associated with the ordering constraint in terms of the characteristic functions of the coincidence sets. We give continuous dependence results, and study the asymptotic behavior as $t \to \infty$ of the solution and the coincidence sets, showing that they converge to their stationary counterparts., Comment: 16 pages

The aim of this paper is twofold: to prove, for L^1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy--Stampacchia inequalities to the general framework of L^1.