The computation of n-point Gaussian quadrature rules for symmetric weight functions is considered in this paper. It is shown that the nodes and the weights of the Gaussian quadrature rule can be retrieved from the singular value decomposition of a bidiagonal matrix of size n/2. The proposed numerical method allows to compute the nodes with high relative accuracy and a computational complexity of O(n). We also describe an algorithm for computing the weights of a generic Gaussian quadrature rule with high relative accuracy. Numerical examples show the effectiveness of the proposed approach.

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation.

This proof-of-concept (PoC) study presents a pipeline made by two blocks: 1. the identification of the network that generates interictal epileptic activity; and 2. the study of the time course of the electrical activity that it generates, called neurodynamics, and the study of its functional connectivity to the other parts of the brain.

Mass currents in astrophysics generate gravitomagnetic fields of enormous complexity. Gravitomagnetic helicity, in direct analogy with magnetic helicity, is a measure of entwining of the gravitomagnetic field lines. We discuss gravitomagnetic helicity within the gravitoelectromagnetic (GEM) framework of linearized general relativity. Furthermore, we employ the spacetime curvature approach to GEM in order to determine the gravitomagnetic helicity for static observers in Kerr spacetime.

Background: In a systems biology perspective, protein-protein interactions (PPI) are encoded in machine-readable formats to avoid issues encountered in their retrieval for the reconstruction of comprehensive interaction maps and biological pathways. However, the information stored in electronic formats currently used doesn't allow a valid automatic reconstruction of biological pathways.Results: We propose a logical model of PPI that takes into account the "state" of proteins before and after the interaction.

In this paper we devise a microscopic (agent-based) mathematical model for reproducing crowd behavior in a specific scenario: a number of pedestrians, consisting of numerous social groups, flow along a corridor until a gate located at the end of the corridor closes. People are not informed about the closure of the gate and perceive the blockage observing dynamically the local crowd conditions. Once people become aware of the new conditions, they stop and then decide either to stay, waiting for reopening, or to go back and leave the corridor forever.

The neuronal functional connectivity is a complex and non-stationary phenomenon creating dynamic networks synchronization determining the brain states and needed to produce tasks. Here, as a measure that quantifies the synchronization between the neuronal electrical activity of two brain regions, we used the normalized compression distance (NCD), which is the length of the compressed file constituted by the concatenated two signals, normalized by the length of the two compressed files including each single signal.

BACKGROUND: Network science represents a powerful and increasingly promising method for studying complex real-world problems. In the last decade, it has been applied to psychometric data in the attempt to explain psychopathologies as complex systems of causally interconnected symptoms. One category of mental disorders, relevant for their severity, incidence and multifaceted structure, is that of eating disorders (EDs), serious disturbances that negatively affect a person's eating behavior.

Background: The aging phenotype in humans is very heterogeneous and can be described as a complex mosaic resulting from the interaction of a variety of environmental, stochastic and genetic-epigenetic variables. Therefore, each old person must be considered as a singleton, and consequently the definition of 'aging phenotype' is very difficult. Objective: We discuss the phenotype of centenarians, the best example of successful aging, as well as other models exploited to study human aging and longevity, such as families enriched in long-living subjects, twins and cohorts of unrelated subjects.