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We propose an imaging method to enhance and reveal structures within samples by using a polarization-based filter. This filter removes the isotropic content while amplifying the anisotropic component of depolarization. Whereas isotropic depolarization leads to a complete loss of polarimetric information, the anisotropic one is connected with intrinsic characteristics of samples. The filter has the capability to diminish the isotropic depolarization of samples, revealing their inherent information. As representative cases, we analyze the effect of the filter in heart and brain sections of animal origin. Results highlight the outstanding performance of the filter. In heart, myocardial and subendocardial structures are better visualized, whereas in the brain, fiber tracts are identified. These proves the significance of this filter in the medical field, paving the way to the early detection of pathologies. The methodologies here presented could be applied in a wide range of applications, providing a significant advance in polarization imaging where high isotropic depolarization response is present, this being a common scenario in nature.

Mixed-integer programming (MIP) is a well-established framework for computer-aided molecular design (CAMD). By precisely encoding the molecular space and score functions, e.g., a graph neural network, the molecular design problem is represented and solved as an optimization problem, the solution of which corresponds to a molecule with optimal score. However, both the extremely large search space and complicated scoring process limit the use of MIP-based CAMD to specific and tiny problems. Moreover, optimal molecule may not be meaningful in practice if scores are imperfect. Instead of pursuing optimality, this paper exploits the ability of MIP in molecular generation and proposes Limeade as an end-to-end tool from real-world needs to feasible molecules. Beyond the basic constraints for structural feasibility, Limeade supports inclusion and exclusion of SMARTS patterns, automating the process of interpreting and formulating chemical requirements to mathematical constraints., Comment: 32 pages, 2 figures

This study builds upon a model proposed by Joanny and collaborators that examines the dynamics of interfaces between two distinct cell populations, particularly during tumor growth in healthy tissues. This framework leads to the investigation of a general model with a non-local and strongly nonlinear advection term representing the biomechanical interaction between both populations. The model captures the evolution of front propagation, reflecting the interaction between cell population dynamics and tissue mechanics. We explore the existence of traveling wave solutions to this problem and establish upper and lower bounds on the propagation speed across various biological parameters. In this way, the model accounts for both biomechanical and biochemical interactions.

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs) using a Rectified Linear Unit (ReLU) activation function. Because our work builds on mixed-integer optimization, it encodes a wide variety of subproblems, for example it admits (i) both adding and removing edges, (ii) both global and local budgets, and (iii) both topological perturbations and feature modifications. Our key technology, topology-based bounds tightening, uses graph structure to tighten bounds. We also experiment with aggressive bounds tightening to dynamically change the optimization constraints by tightening variable bounds. To demonstrate the effectiveness of these strategies, we implement an extension to the open-source branch-and-cut solver SCIP. We test on both node and graph classification problems and consider topological attacks that both add and remove edges.

Computer-aided molecular design (CAMD) studies quantitative structure-property relationships and discovers desired molecules using optimization algorithms. With the emergence of machine learning models, CAMD score functions may be replaced by various surrogates to automatically learn the structure-property relationships. Due to their outstanding performance on graph domains, graph neural networks (GNNs) have recently appeared frequently in CAMD. But using GNNs introduces new optimization challenges. This paper formulates GNNs using mixed-integer programming and then integrates this GNN formulation into the optimization and machine learning toolkit OMLT. To characterize and formulate molecules, we inherit the well-established mixed-integer optimization formulation for CAMD and propose symmetry-breaking constraints to remove symmetric solutions caused by graph isomorphism. In two case studies, we investigate fragment-based odorant molecular design with more practical requirements to test the compatibility and performance of our approaches., Comment: 35 pages, 8 figures, 7 tables

Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves optimization problems constrained by trained graph neural networks (GNNs). To circumvent the symmetry issue caused by graph isomorphism, we propose two types of symmetry-breaking constraints: one indexing a node 0 and one indexing the remaining nodes by lexicographically ordering their neighbor sets. To guarantee that adding these constraints will not remove all symmetric solutions, we construct a graph indexing algorithm and prove that the resulting graph indexing satisfies the proposed symmetry-breaking constraints. For the classical GNN architectures considered in this paper, optimizing over a GNN with a fixed graph is equivalent to optimizing over a dense neural network. Thus, we study the case where the input graph is not fixed, implying that each edge is a decision variable, and develop two mixed-integer optimization formulations. To test our symmetry-breaking strategies and optimization formulations, we consider an application in molecular design., Comment: 10 main pages, 27 with appendix, 10 figures, 7 tables

The paper analyzes the structure and the inner long-term dynamics of the invariant compact sets for the skewproduct flow induced by a family of time-dependent ordinary differential equations of nonhomogeneous linear dissipative type. The main assumptions are made on the dissipative term and on the homogeneous linear term of the equations. The rich casuistic includes the uniform stability of the invariant compact sets, as well as the presence of Li-Yorke chaos and Auslander-Yorke chaos inside the attractor.

Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive class of Fisher-type reaction-diffusion equations with flows in divergence form. We work with regular flows, which may not meet the standard elliptical conditions, but without other types of singularities. We show that the range of speeds at which classic traveling waves move is an interval unbounded to the right. Contrary to classic examples, the infimum may not be reached. When the flow is elliptic or over-elliptic, the minimum speed of propagation is achieved. The classic traveling wave speed threshold is complemented by another value by analyzing an extension of the first order boundary value problem to which the classic case is reduced. This singular minimum speed can be justified as a viscous limit of classic minimal speeds in elliptic or over-elliptic flows. We construct a singular profile for each speed between the minimum singular speed and the speeds at which classic traveling waves move. Under additional assumptions, the constructed profile can be justified as that of a traveling wave of the starting equation in the framework of bounded variation functions. We also show that saturated fronts verifying the Rankine-Hugoniot condition can appear for strictly lower speeds even in the framework of bounded variation functions., Comment: 36 pages, 4 figures

This paper deals with the existence of traveling waves type patterns in the case of the Keller-Segel model with logarithmic sensitivity. The cases in which the diffusion is linear and nonlinear with flux-saturated (of the relativistic heat equation-type) are fully analyzed by comparing the difference between both cases. Moreover, special attention is paid to traveling waves with compact support or with support in the semi-straight line. The existence of these patterns is rigorously proved and the differences between both cases (linear or nonlinear diffusion) are analyzed.

A new type of angular oscillations of the high-frequency conductivity for conductors with a band-contact line has been predicted. The effect is caused by groups of charge carriers near the self-intersection points of the Fermi surface, where the electron energy spectrum is near-linear and can be described by anisotropic Dirac cone model. The amplitude of the resonance peaks satisfies the simple sum rule. The ease in changing the degree of anisotropy of the Dirac cone due to the angle of inclination of the magnetic field makes the considered type of oscillations attractive for experimental observation of relativistic effects, Comment: 7 pages, 3 figures, 28 refs

This paper deals with the analysis of qualitative properties involved in the dynamics of Keller-Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the regularization inside the support of a solution with jump discontinuity at the boundary of the support. We analyze the behavior of the size of the support and blow--up of the solution, and the possible convergence in finite time towards a Dirac mass in terms of the three constants of the system: the mass, the flux--saturated characteristic speed, and the chemoattractant sensitivity constant. These constants of motion also characterize the dynamics of regular and singular traveling waves., Comment: 24 pages

We present both experimentally and theoretically the transformation of radially and azimuthally polarized vector beams when they propagate through a biaxial crystal and are transformed by the conical refraction phenomenon. We show that, at the focal plane, the transverse pattern is formed by a ring-like light structure with an azimuthal node, being this node found at diametrically opposite points of the ring for radial/azimuthal polarizations. We also prove that the state of polarization of the transformed beams is conical refraction-like, i.e. that every two diametrically opposite points of the light ring are linearly orthogonally polarized.

This paper is devoted to the analysis of qualitative properties of flux-saturated type operators in dimension one. Specifically, we study regularity properties and smoothing effects, discontinuous interfaces, the existence of traveling wave profiles, sub- and super-solutions and waiting time features. The aim of the paper is to better understand these kind of phenomena throughout two prototypic operators: The relativistic heat equation and the porous media flux-limited equation. As an important consequence of our results we deduce that solutions to the one-dimensional relativistic heat equation become smooth inside their support on the long time run., Comment: 44 pages, 4 figures. Some misprints were corrected and some remarks were added