Bechcochran6391

Proteins are characterized by their structures and functions, and these two fundamental aspects of proteins are assumed to be related. To model such a relationship, a single representation to model both protein structure and function would be convenient, yet so far, the most effective models for protein structure or function classification do not rely on the same protein representation. Here we provide a computationally efficient implementation for large datasets to calculate residue cluster classes (RCCs) from protein three-dimensional structures and show that such representations enable a random forest algorithm to effectively learn the structural and functional classifications of proteins, according to the CATH and Gene Ontology criteria, respectively. RCCs are derived from residue contact maps built from different distance criteria, and we show that 7 or 8 Å with or without amino acid side-chain atoms rendered the best classification models. The potential use of a unified representation of proteins is discussed and possible future areas for improvement and exploration are presented.A non-Hermitian operator H defined in a Hilbert space with inner product 〈 · | · 〉 may serve as the Hamiltonian for a unitary quantum system if it is η -pseudo-Hermitian for a metric operator (positive-definite automorphism) η . The latter defines the inner product 〈 · | η · 〉 of the physical Hilbert space H η of the system. For situations where some of the eigenstates of H depend on time, η becomes time-dependent. Therefore, the system has a non-stationary Hilbert space. click here Such quantum systems, which are also encountered in the study of quantum mechanics in cosmological backgrounds, suffer from a conflict between the unitarity of time evolution and the unobservability of the Hamiltonian. Their proper treatment requires a geometric framework which clarifies the notion of the energy observable and leads to a geometric extension of quantum mechanics (GEQM). We provide a general introduction to the subject, review some of the recent developments, offer a straightforward description of the Heisenberg-picture formulation of the dynamics for quantum systems having a time-dependent Hilbert space, and outline the Heisenberg-picture formulation of dynamics in GEQM.In this note, we introduce excess strategic entropy-an entropy-based measure of complexity of the strategy. It measures complexity and predictability of the (mixed) strategy of a player. We show and discuss properties of this measure and its possible applications.New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.Due to the complexity and variability of underwater acoustic channels, ship-radiated noise (SRN) detected using the passive sonar is prone to be distorted. The entropy-based feature extraction method can improve this situation, to some extent. However, it is impractical to directly extract the entropy feature for the detected SRN signals. In addition, the existing conventional methods have a lack of suitable de-noising processing under the presence of marine environmental noise. To this end, this paper proposes a novel feature extraction method based on enhanced variational mode decomposition (EVMD), normalized correlation coefficient (norCC), permutation entropy (PE), and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, EVMD is utilized to obtain a group of intrinsic mode functions (IMFs) from the SRN signals. The noise-dominant IMFs are then eliminated by a de-noising processing prior to PE calculation. Next, the correlation coefficient between each signal-dominant IMF and the raw signal and PE of each signal-dominant IMF are calculated, respectively. After this, the norCC is used to weigh the corresponding PE and the sum of these weighted PE is considered as the final feature parameter. Finally, the feature vectors are fed into the PSO-SVM multi-class classifier to classify the SRN samples. The experimental results demonstrate that the recognition rate of the proposed methodology is up to 100%, which is much higher than the currently existing methods. Hence, the method proposed in this paper is more suitable for the feature extraction of SRN signals.This article provides symbolic analysis tools for specifying spatial econometric models. It firstly considers testing spatial dependence in the presence of potential leading deterministic spatial components (similar to time-series tests for unit roots in the presence of temporal drift and/or time-trend) and secondly considers how to econometrically model spatial economic relations that might contain unobserved spatial structure of unknown form. Hypothesis testing is conducted with a symbolic-entropy based non-parametric statistical procedure, recently proposed by Garcia-Cordoba, Matilla-Garcia, and Ruiz (2019), which does not rely on prior weight matrices assumptions. It is shown that the use of geographically restricted semiparametric spatial models is a promising modeling strategy for cross-sectional datasets that are compatible with some types of spatial dependence. The results state that models that merely incorporate space coordinates might be sufficient to capture space dependence. Hedonic models for Baltimore, Boston, and Toledo housing prices datasets are revisited, studied (with the new proposed procedures), and compared with standard spatial econometric methodologies.When using Bayesian inference, one needs to choose a prior distribution for parameters. The well-known Jeffreys prior is based on the Riemann metric tensor on a statistical manifold. Takeuchi and Amari defined the α -parallel prior, which generalized the Jeffreys prior by exploiting a higher-order geometric object, known as a Chentsov-Amari tensor. In this paper, we propose a new prior based on the Weyl structure on a statistical manifold. It turns out that our prior is a special case of the α -parallel prior with the parameter α equaling - n , where n is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of α -connections. This makes the choice for the parameter α more canonical. We calculated the Weyl prior for univariate Gaussian and multivariate Gaussian distribution. The Weyl prior of the univariate Gaussian turns out to be the uniform prior.