We study the formation of singularities for the problem {u(t) = [phi(u)](xx) + epsilon[psi(u)](txx) in Omega x (0, T) phi(u) + epsilon[psi(u)](t) = 0 in partial derivative Omega x(0, T) u = u(0) >= 0 in Omega x {0}, where epsilon and Tare positive constants, Omega a bounded interval, u(0) a nonnegative Radon measure on Omega, phi a nonmonotone and nonnegative function with phi(0) = phi(infinity) = 0, and psi an increasing bounded function. We show that if u(0) is a bounded or continuous function, singularities may appear spontaneously.

We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, which is usually the case in the existing literature, we elicit the epsilon-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis.

We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.

We consider a mathematical model describing population dynamics of normal and abnormal cell densities with contact inhibition of cell growth from a theoretical point of view. In the first part of this paper, we discuss the global existence of a solution satisfying the segregation property in one space dimension for general initial data. Here, the term segregation property means that the different types of cells keep spatially segregated when the initial densities are segregated.

Current theories of schizophrenia emphasize the role of altered information integration as the core dysfunction of this illness. While ample neuroimaging evidence for such accounts comes from investigations of spatial connectivity, understanding temporal disruptions is important to fully capture the essence of dysconnectivity in schizophrenia.

GPU version of AMG preconditioner

Derivations of the Jarzynski equality (JE) appear to be quite general, and applicable to any particle system, whether deterministic or stochastic, under equally general perturbations of an initial equilibrium state at given temperatureT. At the same time, the definitions of the quantities appearing in the JE, in particular the work, have been questioned. Answers have been given, but a deeper understanding of the range of phenomena to which the JE applies is necessary, both conceptually and in order to interpret the experiments in which it is used.

In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation.

Recent years have witnessed a massive push towards reproducible research in neuroscience. Unfortunately, this endeavor is often challenged by the large diversity of tools used, project-specific custom code and the difficulty to track all user-defined parameters. NeuroPycon is an open-source multi-modal brain data analysis toolkit which provides Python-based template pipelines for advanced multi-processing of MEG, EEG, functional and anatomical MRI data, with a focus on connectivity and graph theoretical analyses.

Effective treatment of glioma and other central nervous system (CNS) diseases is hindered by the presence of the blood-brain barrier (BBB). A novel nano-delivery vehicle system composed of PLGA-lysoGM1/DOX micelles was developed to cross the BBB for CNS treatment. We have shown that doxorubicin (DOX) as a model drug encapsulated in PLGA-lysoGM1 micelles can achieve up to 3.8% loading efficiency and 61.6% encapsulation efficiency by the orthogonal test design.