A variational algorithm for the detection of line segments

In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations outside some approximate edge set, which we represent as the union of a finite number of thin strips, the width of which is an order of magnitude smaller than their length. In order to find a near optimal placement of these strips, we compute an asymptotic expansion of the functional with respect to the strip size. This expansion is then employed for defining a (topological) gradient descent like minimization method. As opposed to a recently proposed method by some of the authors, which uses coverings with balls, the usage of strips includes some directional information into the method, which can be used for obtaining finer edges and can also result in a reduction of computation times

Controlling Complex Langevin simulations of lattice models by boundary term analysis

One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, in a previous paper we have studied the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. Here we continue this type of analysis for more physically interesting models, focusing on the boundaries at infinity. We start with abelian and non-abelian one-plaquette models, then we proceed to a Polyakov chain model and finally to high density QCD (HDQCD) and the 3D XY model. We show that the direct estimation of the systematic error of the CL method using boundary terms is in principle possible.Comment: 17 pages, 11 figure

Self-Perception of Health: A Proposed Explanatory Model and a Test of its Clinical Significance

A multivariate model of health self-perceptions was postulated based upon a comprehensive set of health related variables suggested by previous bivariate research. Components of the model included measures of health attitudes, health practices, health locus of control, a measure of stress/ coping, and a physical health measure. A stratified random sampling technique was used to select 10 8 subjects based upon the external measure of physical health which included categories ranging from disability-severe to symptom free-high energy level. All subjects completed a health questionnaire comprised of measures of the model components, two measures of health self-perceptions, and the Health Resource Task, an author designed instrument measuring a subject's ability to generate flexible health alternatives/resources. Bivariate correlational analysis revealed that the physical health, stress/coping, health practices, and locus of control measures and certain of the health attitude subscales were significantly correlated to general health self-ratings. A multivariate model including these variables accounted for almost 50 percent of the variance in one of the general health self-ratings measures and approximately 38 percent of the variance in the Health Resource Task. Suggestions for refining the proposed model were made

Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space

Necessary conditions for variational regularization schemes

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: How could necessary conditions for a variational method to provide a regularization method look like? To this end, we formalize the notion of a variational scheme and start with comparison of three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions. The results are applied to discrepancy functionals given by Bregman distances and especially to the Kullback-Leibler divergence.Comment: To appear in Inverse Problem

Calcium sensor kinase activates potassium uptake systems in gland cells of Venus flytraps

The Darwin plant Dionaea muscipula is able to grow on mineral-poor soil, because it gains essential nutrients from captured animal prey. Given that no nutrients remain in the trap when it opens after the consumption of an animal meal, we here asked the question of how Dionaea sequesters prey-derived potassium. We show that prey capture triggers expression of a K+ uptake system in the Venus flytrap. In search of K+ transporters endowed with adequate properties for this role, we screened a Dionaea expressed sequence tag (EST) database and identified DmKT1 and DmHAK5 as candidates. On insect and touch hormone stimulation, the number of transcripts of these transporters increased in flytraps. After cRNA injection of K+-transporter genes into Xenopus oocytes, however, both putative K+ transporters remained silent. Assuming that calcium sensor kinases are regulating Arabidopsis K+ transporter 1 (AKT1), we coexpressed the putative K+ transporters with a large set of kinases and identified the CBL9-CIPK23 pair as the major activating complex for both transporters in Dionaea K+ uptake. DmKT1 was found to be a K+-selective channel of voltage-dependent high capacity and low affinity, whereas DmHAK5 was identified as the first, to our knowledge, proton-driven, high-affinity potassium transporter with weak selectivity. When the Venus flytrap is processing its prey, the gland cell membrane potential is maintained around -120 mV, and the apoplast is acidified to pH 3. These conditions in the green stomach formed by the closed flytrap allow DmKT1 and DmHAK5 to acquire prey-derived K+, reducing its concentration from millimolar levels down to trace levels

Sparse Regularization with lql^q Penalty Term

We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the standard range condition, we derive the usual convergence rate $O(\sqrt{\delta})$ of the regularized solutions in dependence of the noise level $\delta$. Particular emphasis lies on the case, where the true solution is known to have a sparse representation in a given basis. In this case, if the differential of the operator satisfies a certain injectivity condition, we can show that the actual convergence rate improves up to $O(\delta)$.Comment: 15 page

Parkinson's disease biomarkers: perspective from the NINDS Parkinson's Disease Biomarkers Program

Biomarkers for Parkinson's disease (PD) diagnosis, prognostication and clinical trial cohort selection are an urgent need. While many promising markers have been discovered through the National Institute of Neurological Disorders and Stroke Parkinson's Disease Biomarker Program (PDBP) and other mechanisms, no single PD marker or set of markers are ready for clinical use. Here we discuss the current state of biomarker discovery for platforms relevant to PDBP. We discuss the role of the PDBP in PD biomarker identification and present guidelines to facilitate their development. These guidelines include: harmonizing procedures for biofluid acquisition and clinical assessments, replication of the most promising biomarkers, support and encouragement of publications that report negative findings, longitudinal follow-up of current cohorts including the PDBP, testing of wearable technologies to capture readouts between study visits and development of recently diagnosed (de novo) cohorts to foster identification of the earliest markers of disease onset