A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Effect of a supplement rich in alkaline minerals on acid-base balance in humans

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Molecular psychiatry of zebrafish

Due to their well-characterized neural development and high genetic homology to mammals, zebrafish (Danio rerio) have emerged as a powerful model organism in the field of biological psychiatry. Here, we discuss the molecular psychiatry of zebrafish, and its implications for translational neuroscience research and modeling central nervous system (CNS) disorders. In particular, we outline recent genetic and technological developments allowing for in vivo examinations, high-throughput screening and whole-brain analyses in larval and adult zebrafish. We also summarize the application of these molecular techniques to the understanding of neuropsychiatric disease, outlining the potential of zebrafish for modeling complex brain disorders, including attention-deficit/hyperactivity disorder (ADHD), aggression, post-traumatic stress and substance abuse. Critically evaluating the advantages and limitations of larval and adult fish tests, we suggest that zebrafish models become a rapidly emerging new field in modern molecular psychiatry research

Visualization and Curve-Parameter Estimation Strategies for Efficient Exploration of Phenotype Microarray Kinetics

The Phenotype MicroArray (OmniLog® PM) system is able to simultaneously capture a large number of phenotypes by recording an organism's respiration over time on distinct substrates. This technique targets the object of natural selection itself, the phenotype, whereas previously addressed '-omics' techniques merely study components that finally contribute to it. The recording of respiration over time, however, adds a longitudinal dimension to the data. To optimally exploit this information, it must be extracted from the shapes of the recorded curves and displayed in analogy to conventional growth curves.The free software environment R was explored for both visualizing and fitting of PM respiration curves. Approaches using either a model fit (and commonly applied growth models) or a smoothing spline were evaluated. Their reliability in inferring curve parameters and confidence intervals was compared to the native OmniLog® PM analysis software. We consider the post-processing of the estimated parameters, the optimal classification of curve shapes and the detection of significant differences between them, as well as practically relevant questions such as detecting the impact of cultivation times and the minimum required number of experimental repeats.We provide a comprehensive framework for data visualization and parameter estimation according to user choices. A flexible graphical representation strategy for displaying the results is proposed, including 95% confidence intervals for the estimated parameters. The spline approach is less prone to irregular curve shapes than fitting any of the considered models or using the native PM software for calculating both point estimates and confidence intervals. These can serve as a starting point for the automated post-processing of PM data, providing much more information than the strict dichotomization into positive and negative reactions. Our results form the basis for a freely available R package for the analysis of PM data

Elucidating Poor Decision-Making in a Rat Gambling Task

Although poor decision-making is a hallmark of psychiatric conditions such as attention deficit/hyperactivity disorder, pathological gambling or substance abuse, a fraction of healthy individuals exhibit similar poor decision-making performances in everyday life and specific laboratory tasks such as the Iowa Gambling Task. These particular individuals may provide information on risk factors or common endophenotypes of these mental disorders. In a rodent version of the Iowa gambling task – the Rat Gambling Task (RGT), we identified a population of poor decision makers, and assessed how these rats scored for several behavioral traits relevant to executive disorders: risk taking, reward seeking, behavioral inflexibility, and several aspects of impulsivity. First, we found that poor decision-making could not be well predicted by single behavioral and cognitive characteristics when considered separately. By contrast, a combination of independent traits in the same individual, namely risk taking, reward seeking, behavioral inflexibility, as well as motor impulsivity, was highly predictive of poor decision-making. Second, using a reinforcement-learning model of the RGT, we confirmed that only the combination of extreme scores on these traits could induce maladaptive decision-making. Third, the model suggested that a combination of these behavioral traits results in an inaccurate representation of rewards and penalties and inefficient learning of the environment. Poor decision-making appears as a consequence of the over-valuation of high-reward-high-risk options in the task. Such a specific psychological profile could greatly impair clinically healthy individuals in decision-making tasks and may predispose to mental disorders with similar symptoms