Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science volume "Pattern Recognition Applications and Methods 2013", part of series on Advances in Intelligent and Soft Computin

Large deviations for the macroscopic motion of an interface

We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac interaction evolving in time according to Glauber (non-conservative) dynamics. Such interfaces separate two stable phases of a ferromagnetic system and in the macroscopic scale are represented by sharp transitions. We derive quantitative estimates for the upper and the lower bound of the cost functional that penalizes all possible deviations and obtain explicit error terms which are valid also in the macroscopic scale. Furthermore, using the result of a companion paper about the minimizers of this cost functional for the macroscopic motion of the interface in a fixed time, we prove that the probability of such events can concentrate on nucleations should the transition happen fast enough

Korn's second inequality and geometric rigidity with mixed growth conditions

Geometric rigidity states that a gradient field which is $L^p$-close to the set of proper rotations is necessarily $L^p$-close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in the theory of plasticity, energy densities with mixed growth appear. We show here that geometric rigidity holds also in $L^p+L^q$ and in $L^{p,q}$ interpolation spaces. As a first step we prove the corresponding linear inequality, which generalizes Korn's inequality to these spaces

Halfvortices in flat nanomagnets

We discuss a new type of topological defect in XY systems where the O(2) symmetry is broken in the presence of a boundary. Of particular interest is the appearance of such defects in nanomagnets with a planar geometry. They are manifested as kinks of magnetization along the edge and can be viewed as halfvortices with winding numbers \pm 1/2. We argue that halfvortices play a role equally important to that of ordinary vortices in the statics and dynamics of flat nanomagnets. Domain walls found in experiments and numerical simulations are composite objects containing two or more of these elementary defects. We also discuss a closely related system: the two-dimensional smectic liquid crystal films with planar boundary condition.Comment: 7 pages, 8 figures, To appear as a chapter in Les Houches summer school on Quantum Magnetis

Regional differences in psychiatric disorders in Chile

BACKGROUND: Psychiatric epidemiological surveys in developing countries are rare and are frequently conducted in regions that are not necessarily representative of the entire country. In addition, in large countries with dispersed populations national rates may have low value for estimating the need for mental health services and programs. METHODS: The Chile Psychiatric Prevalence Study using the Composite International Diagnostic Interview was conducted in four distinct regions of the country on a stratified random sample of 2,978 people. Lifetime and 12-month prevalence and service utilization rates were estimated. RESULTS: Significant differences in the rates of major depressive disorder, substance abuse disorders, non-affective psychosis, and service utilization were found across the regions. The differential prevalence rates could not be accounted by socio-demographic differences between sites. CONCLUSIONS: Regional differences across countries may exist that have both implications for prevalence rates and service utilization. Planning mental health services for population centers that span wide geographical areas based on studies conducted in a single region may be misleading, and may result in areas with high need being underserved

Weakly Consistent Regularisation Methods for Ill-Posed Problems

This Chapter takes its origin in the lecture notes for a 9 h course at the Institut Henri Poincaré in September 2016. The course was divided in three parts. In the first part, which is not included herein, the aim was to first recall some basic aspects of stabilised finite element methods for convection-diffusion problems. We focus entirely on the second and third parts which were dedicated to ill-posed problems and their approximation using stabilised finite element methods. First we introduce the concept of conditional stability. Then we consider the elliptic Cauchy-problem and a data assimilation problem in a unified setting and show how stabilised finite element methods may be used to derive error estimates that are consistent with the stability properties of the problem and the approximation properties of the finite element space. Finally, we extend the result to a data assimilation problem subject to the heat equation

Endothelial Stomatal and Fenestral Diaphragms in Normal Vessels and Angiogenesis

Vascular endothelium lines the entire cardiovascular system where performs a series of vital functions including the control of microvascular permeability, coagulation inflammation, vascular tone as well as the formation of new vessels via vasculogenesis and angiogenesis in normal and disease states. Normal endothelium consists of heterogeneous populations of cells differentiated according to the vascular bed and segment of the vascular tree where they occur. One of the cardinal features is the expression of specific subcellular structures such as plasmalemmal vesicles or caveolae, transendothelial channels, vesiculo-vacuolar organelles, endothelial pockets and fenestrae, whose presence define several endothelial morphological types. A less explored observation is the differential expression of such structures in diverse settings of angiogenesis. This review will focus on the latest developments on the components, structure and function of these specific endothelial structures in normal endothelium as well as in diverse settings of angiogenesis

Induction of Glucose Metabolism in Stimulated T Lymphocytes Is Regulated by Mitogen-Activated Protein Kinase Signaling

T lymphocytes play a critical role in cell-mediated immune responses. During activation, extracellular and intracellular signals alter T cell metabolism in order to meet the energetic and biosynthetic needs of a proliferating, active cell, but control of these phenomena is not well defined. Previous studies have demonstrated that signaling from the costimulatory receptor CD28 enhances glucose utilization via the phosphatidylinositol-3-kinase (PI3K) pathway. However, since CD28 ligation alone does not induce glucose metabolism in resting T cells, contributions from T cell receptor-initiated signaling pathways must also be important. We therefore investigated the role of mitogen-activated protein kinase (MAPK) signaling in the regulation of mouse T cell glucose metabolism. T cell stimulation strongly induces glucose uptake and glycolysis, both of which are severely impaired by inhibition of extracellular signal-regulated kinase (ERK), whereas p38 inhibition had a much smaller effect. Activation also induced hexokinase activity and expression in T cells, and both were similarly dependent on ERK signaling. Thus, the ERK signaling pathway cooperates with PI3K to induce glucose utilization in activated T cells, with hexokinase serving as a potential point for coordinated regulation

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

We consider the numerical solution, by finite differences, of second-order-in-time stochastic partial differential equations (SPDEs) in one space dimension. New timestepping methods are introduced by generalising recently-introduced methods for second-order-in-time stochastic differential equations to multidimensional systems. These stochastic methods, based on leapfrog and Runge–Kutta methods, are designed to give good approximations to the stationary variances and the correlations in the position and velocity variables. In particular, we introduce the reverse leapfrog method and stochastic Runge–Kutta Leapfrog methods, analyse their performance applied to linear SPDEs and perform numerical experiments to examine their accuracy applied to a type of nonlinear SPDE