Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment

When people solve real-life SAP they tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the SAP under uncertain environment. He formulates the IFSAP and utilizes the TIFN to deal with uncertainty and hesitation. The SAP has uncertainty and hesitation in cost/time/profit/production is known as FIFSAP. The PSK (P. Senthil Kumar) method for finding an optimal solution for FIFAP is extended to solve the FIFSAP and the optimal objective value of FIFSAP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution/assignment of FIFSAP is obtained without using the Hungarian method and intuitionistic fuzzy reduction method. Moreover, the proposed method is computationally very simple and easy to understand. The numerical example is presented to demonstrate computing procedure. The results affirm efficiency of the proposed method.

SAMPLES DISTINCTION BY PARAMETRIC AND NONPARAMETRIC STATISTICS IN SPSS

Testing samples distinction is necessary in a wide range of practical tasks. Medicine, sociology, psychology, marketing - this is a short list of industries where it is required to conduct tests that establish effectiveness or inefficiency of a certain technology.Diversity of situations and techniques applied to sample distinction create a problem for compliance of testing procedures. The problem rises for tests including large and small samples (dependent or independent) with various distributions. The article proposes a list of problems created by testing differences between two samples. Limits of applicability of parametric and non-parametric tests are established based on selected distribution. Informative examples are included based on simulated data.SPSS software was used for sample distinction tests. It is important to double-check the operation of the machine computing procedure "manually” to understand the nature of tests and in educational purposes. The article provides mathematical illustration for the algorithms used, which can be considered as supplementary information for SPSS help.

Semisupervised Clustering by Iterative Partition and Regression with Neuroscience Applications

Regression clustering is a mixture of unsupervised and supervised statistical learning and data mining method which is found in a wide range of applications including artificial intelligence and neuroscience. It performs unsupervised learning when it clusters the data according to their respective unobserved regression hyperplanes. The method also performs supervised learning when it fits regression hyperplanes to the corresponding data clusters. Applying regression clustering in practice requires means of determining the underlying number of clusters in the data, finding the cluster label of each data point, and estimating the regression coefficients of the model. In this paper, we review the estimation and selection issues in regression clustering with regard to the least squares and robust statistical methods. We also provide a model selection based technique to determine the number of regression clusters underlying the data. We further develop a computing procedure for regression clustering estimation and selection. Finally, simulation studies are presented for assessing the procedure, together with analyzing a real data set on RGB cell marking in neuroscience to illustrate and interpret the method.

A New Method to Model Spherical Roller Bearings due to Self-Aligning Feature

This research presents an analytical model to describe the indeterminate contact status and analyze the loaded condition, then acquire the key design parameters so as to improve the carrying capacity of spherical roller bearings. The model based on the non-Hertzian contact theory is applied to reflect the indeterminate contact status due to the self-aligning feature. The loaded condition, which is including the load distribution, the size of the contact region and the maximum contact pressure, is calculated according to the force analysis of spherical roller bearings. The non-linear equations are solved by using secant method and the proposed model is validated by comparing with the published reference. The importance of the indeterminate contact status is illustrated by comparing with the computing results of the Hertzian contact model. The fitted method based on the least square method is used to obtain the equivalent stiffness and the load-deformation exponent, whereby the computing procedure is simplified. In view of the operating condition and the lubricated effect, properly increasing the osculation number or the number of the rollers will obviously improve the carrying ability of spherical roller bearings.

BALANCE SHEET ANALYSIS OF CREDIT AND DEBT NETWORKS

In this paper, we present a computing procedure to analyze a network of credit and debt among agents (nodes) from a standpoint of balance sheet dependencies. The aim is to develop a method to assess thoroughly the sensitivity of the network to potential individual insolvencies. For this purpose, given a state of the network, the insolvency of an agent is assumed and the cascade of provoked insolvencies is simulated. Exploring the matrix definition of the network, this is made systematically for all agents. Therefore, in only one run of the procedure, all the possible trajectories of insolvencies, each beginning in a different agent, are calculated. This allows spotting at a glance which agents are “systemically riskier”. Determination of adequate capital levels can be made on a case basis by running the procedure repeatedly. This work contributes with two new aspects to the existing literature. First, given a known situation of a credit and debt network, a computing procedure is presented that allows to assess the network sensitivity to the exogenous insolvency of any of its nodes. Second, continued monitoring of a credit and debt network is computationally feasible. This “proof of concept” software can be extended into a tool useful for research and regulation, if the relevant information is made available.