Entropic Estimates Research Articles

Accelerated Maximum Entropy Method for Time Series Models Estimation

The work is devoted to the development of a maximum entropy estimation method with soft randomization for restoring the parameters of probabilistic mathematical models from the available observations. Soft randomization refers to the technique of adding regularization to the functional of information entropy in order to simplify the optimization problem and speed up the learning process compared to the classical maximum entropy method. Entropic estimation makes it possible to restore probability distribution functions for model parameters without introducing additional assumptions about the likelihood function; thus, this estimation method can be used in problems with an unspecified type of measurement noise, such as analysis and forecasting of time series.

Spin Seebeck coefficient and spin-thermal diffusion in the two-dimensional Hubbard model

We investigate the spin Seebeck coefficient $S_s$ in the square lattice Hubbard model at high temperatures of relevance to cold-atom measurements. We solve the model with the finite-temperature Lanczos and with the dynamical mean-field theory methods and find they give similar results in the considered regime. $S_s$ exceeds the atomic 'Heikes' estimates and the Kelvin entropic estimates drastically. We analyze the behavior in terms of a mapping onto the problem of a doped attractive model and derive an approximate expression that allows relating the enhancement of $S_s$ to distinct scattering of the spin-majority and the spin-minority excitations. Our analysis reveals the limitations of entropic interpretations of Seebeck coefficient even in the high-temperature regime. Large values of $S_s$ could be observed on optical lattices. We also calculate the full diffusion matrix. We quantify the spin-thermal diffusion, that is, the extent of the mixing between the spin and the thermal diffusion and discuss the results in the context of recent measurements of the spin-diffusion constant in cold atoms.

Entropic estimation of orderliness of transport service of large Russian city in 2020

This article presents approaches to estimate orderliness of transport service of large city by means of city passenger public transport (CPPT). An article considers entropic analysis method as main analytical instrument of orderliness of transportation process. Author presents cause-and-effect chain of formation of results of transportation process by CPPT and process of informational transformation during transportation. An article gives an example of calculation of relative entropy of transportation process by CPPT in Tyumen during March-September 2020. Additional attention was paid to changes of orderliness of transport service during the acute phase of pandemic COVID-19 (April-June 2020). It was established that relative entropy of transportation process decreased during acute phase of pandemic COVID-19 in comparison to periods of sustainable functioning of CPPT system. Respectively orderliness of transportation process increased at the same time. This fact can be explained by structural changes of volume of transported passengers (total volume of traffic – volume of transportation of preferential passengers – volume of transportation of senior citizens). By the results of research author made conclusions and gave recommendations on possible increasing of orderliness of CPPT transportation process.

Enhancing the predictability of crude oil markets with hybrid wavelet approaches

We explore the robustness, efficiency and accuracy of the multi-scale forecasting in crude oil markets. We adopt a novel hybrid wavelet auto-ARMA model to detect the inherent nonlinear dynamics of crude oil returns with an explicitly defined hierarchical structure. Entropic estimation is employed to calculate the optimal level of the decomposition. The wavelet-based forecasting method accounts for the chaotic behavior of oil series, whilst captures drifts, spikes and other non-stationary effects which common frequency-domain methods miss out completely. These results shed new light upon the predictability of crude oil markets in nonstationary settings.

Targeting functional motifs of a protein family.

The structural organization of a protein family is investigated by devising a method based on the random matrix theory (RMT), which uses the physiochemical properties of the amino acid with multiple sequence alignment. A graphical method to represent protein sequences using physiochemical properties is devised that gives a fast, easy, and informative way of comparing the evolutionary distances between protein sequences. A correlation matrix associated with each property is calculated, where the noise reduction and information filtering is done using RMT involving an ensemble of Wishart matrices. The analysis of the eigenvalue statistics of the correlation matrix for the β-lactamase family shows the universal features as observed in the Gaussian orthogonal ensemble (GOE). The property-based approach captures the short- as well as the long-range correlation (approximately following GOE) between the eigenvalues, whereas the previous approach (treating amino acids as characters) gives the usual short-range correlations, while the long-range correlations are the same as that of an uncorrelated series. The distribution of the eigenvector components for the eigenvalues outside the bulk (RMT bound) deviates significantly from RMT observations and contains important information about the system. The information content of each eigenvector of the correlation matrix is quantified by introducing an entropic estimate, which shows that for the β-lactamase family the smallest eigenvectors (low eigenmodes) are highly localized as well as informative. These small eigenvectors when processed gives clusters involving positions that have well-defined biological and structural importance matching with experiments. The approach is crucial for the recognition of structural motifs as shown in β-lactamase (and other families) and selectively identifies the important positions for targets to deactivate (activate) the enzymatic actions.

Spatially-Explicit Bayesian Information Entropy Metrics for Calibrating Landscape Transformation Models

Assessing spatial model performance often presents challenges related to the choice and suitability of traditional statistical methods in capturing the true validity and dynamics of the predicted outcomes. The stochastic nature of many of our contemporary spatial models of land use change necessitate the testing and development of new and innovative methodologies in statistical spatial assessment. In many cases, spatial model performance depends critically on the spatially-explicit prior distributions, characteristics, availability and prevalence of the variables and factors under study. This study explores the statistical spatial characteristics of statistical model assessment of modeling land use change dynamics in a seven-county study area in South-Eastern Wisconsin during the historical period of 1963–1990. The artificial neural network-based Land Transformation Model (LTM) predictions are used to compare simulated with historical land use transformations in urban/suburban landscapes. We introduce a range of Bayesian information entropy statistical spatial metrics for assessing the model performance across multiple simulation testing runs. Bayesian entropic estimates of model performance are compared against information-theoretic stochastic entropy estimates and theoretically-derived accuracy assessments. We argue for the critical role of informational uncertainty across different scales of spatial resolution in informing spatial landscape model assessment. Our analysis reveals how incorporation of spatial and landscape information asymmetry estimates can improve our stochastic assessments of spatial model predictions. Finally our study shows how spatially-explicit entropic classification accuracy estimates can work closely with dynamic modeling methodologies in improving our scientific understanding of landscape change as a complex adaptive system and process.

Relating Structure, Entropy, and Energy of Solvation of Nanoscale Solutes: Application to Gold Nanoparticle Dispersions

Structural estimators for the entropy are combined with an analysis of the different contributions to the energy of solvation to understand the molecular basis of the thermodynamics of solvation of passivated nanoparticles. Molecular dynamics simulations of thiolated gold clusters in ethane are performed over a wide range of densities close to the critical isotherm. The entropic changes associated with solvent reorganization around the passivated nanoparticle are estimated from the nanoparticle-solvent pair correlation function, while the entropy of the ligand shell is estimated from the covariance in the positional fluctuations of the ligand atoms. The ligand-shell entropy (S(L)) is shown to be fairly insensitive to variations in solvent density ranging from vacuum to twice the critical density (ρ(c)). In contrast, the entropy change due to solvent reorganization (ΔS(ns)(ord)) shows a minimum around the critical point where the solvent excess shows a maximum. Combining the entropic estimates with the nanoparticle-solvent interaction energies, the free energy of solvation is shown to decrease with density once the critical point is crossed in a manner qualitatively consistent with available experimental data. The results suggest that such an approach to obtain structural insights into the thermodynamics of solvation of passivated nanoparticles could be useful in understanding the stability of nanoparticle dispersions of widely varying chemistries. This study also demonstrates that the theoretical analysis of solvation and self-assembly developed in the context of biomolecular hydration can be very usefully extended to understand the behavior of inorganic nanoparticle dispersions.

Entropic estimate of cooperative binding of substrate on a single oligomeric enzyme: An index of cooperativity

Here we have systematically studied the cooperative binding of substrate molecules on the active sites of a single oligomeric enzyme in a chemiostatic condition. The average number of bound substrate and the net velocity of the enzyme catalyzed reaction are studied by the formulation of stochastic master equation for the cooperative binding classified here as spatial and temporal. We have estimated the entropy production for the cooperative binding schemes based on single trajectory analysis using a kinetic Monte Carlo technique. It is found that the total as well as the medium entropy production shows the same generic diagnostic signature for detecting the cooperativity, usually characterized in terms of the net velocity of the reaction. This feature is also found to be valid for the total entropy production rate at the non-equilibrium steady state. We have introduced an index of cooperativity, C, defined in terms of the ratio of the surprisals or equivalently, the stochastic system entropy associated with the fully bound state of the cooperative and non-cooperative cases. The criteria of cooperativity in terms of C is compared with that of the Hill coefficient of some relevant experimental result and gives a microscopic insight on the mechanism of cooperative binding of substrate on a single oligomeric enzyme which is usually estimated from the macroscopic reaction rate.

STITCHER: Dynamic assembly of likely amyloid and prion β‐structures from secondary structure predictions

The supersecondary structure of amyloids and prions, proteins of intense clinical and biological interest, are difficult to determine by standard experimental or computational means. In addition, significant conformational heterogeneity is known or suspected to exist in many amyloid fibrils. Previous work has demonstrated that probability-based prediction of discrete β-strand pairs can offer insight into these structures. Here, we devise a system of energetic rules that can be used to dynamically assemble these discrete β-strand pairs into complete amyloid β-structures. The STITCHER algorithm progressively ‘stitches’ strand-pairs into full β-sheets based on a novel free-energy model, incorporating experimentally observed amino-acid side-chain stacking contributions, entropic estimates, and steric restrictions for amyloidal parallel β-sheet construction. A dynamic program computes the top 50 structures and returns both the highest scoring structure and a consensus structure taken by polling this list for common discrete elements. Putative structural heterogeneity can be inferred from sequence regions that compose poorly. Predictions show agreement with experimental models of Alzheimer’s amyloid beta peptide and the Podospora anserina Het-s prion. Predictions of the HET-s homolog HET-S also reflect experimental observations of poor amyloid formation. We put forward predicted structures for the yeast prion Sup35, suggesting N-terminal structural stability enabled by tyrosine ladders, and C-terminal heterogeneity. Predictions for the Rnq1 prion and alpha-synuclein are also given, identifying a similar mix of homogenous and heterogeneous secondary structure elements. STITCHER provides novel insight into the energetic basis of amyloid structure, provides accurate structure predictions, and can help guide future experimental studies.Proteins 2012. © 2011 Wiley Periodicals, Inc.

Solvated Interaction Energy (SIE) for Scoring Protein–Ligand Binding Affinities. 2. Benchmark in the CSAR-2010 Scoring Exercise

Solvated interaction energy (SIE) is an end-point physics-based scoring function for predicting binding affinities from force-field nonbonded interaction terms, continuum solvation, and configurational entropy linear compensation. We tested the SIE function in the Community Structure-Activity Resource (CSAR) scoring challenge consisting of high-resolution cocrystal structures for 343 protein-ligand complexes with high-quality binding affinity data and high diversity with respect to protein targets. Particular emphasis was placed on the sensitivity of SIE predictions to the assignment of protonation and tautomeric states in the complex and the treatment of metal ions near the protein-ligand interface. These were manually curated from an originally distributed CSAR-HiQ data set version, leading to the currently distributed CSAR-NRC-HiQ version. We found that this manual curation was a critical step for accurately testing the performance of the SIE function. The standard SIE parametrization, previously calibrated on an independent data set, predicted absolute binding affinities with a mean-unsigned-error (MUE) of 2.41 kcal/mol for the CSAR-HiQ version, which improved to 1.98 kcal/mol for the upgraded CSAR-NRC-HiQ version. Half-half retraining-testing of SIE parameters on two predefined subsets of CSAR-NRC-HiQ led to only marginal further improvements to an MUE of 1.83 kcal/mol. Hence, we do not recommend altering the current default parameters of SIE at this time. For a sample of SIE outliers, additional calculations by molecular dynamics-based SIE averaging with or without incorporation of ligand strain, by MM-PB(GB)/SA methods with or without entropic estimates, or even by the linear interaction energy (LIE) formalism with an explicit solvent model, did not further improve predictions.

Asymptotics of Higher Order Entropies

Higher order entropies are kinetic entropy estimators for fluid models. These quantities are quadratic in the velocity v and temperature T derivatives and have temperature dependent coefficients. We investigate asymptotic expansions of higher order entropies for incompressible flows in terms of the Knudsen and Mach numbers. The correspoding entropic inequalities are obtained when is small enough, provided that the temperature dependence of the thermal conductivity λ and the viscosity η is that given by the kinetic theory. As an example of application of higher order entropic estimates we establish an existence theorem for small Mach number flows.

Global weak solutions for elastic equations with damping and different end states

In this paper, we study global weak solutions for elastic equations with damping using the compensated compactness method. When the two end states at ± ∞ are not equal, the selfsimilar solutions for the corresponding parabolic equation are used to get the entropic estimates for both the L∞ and L2 cases.

Uniform convergence for moment problems with Fermi-Dirac type entropies

We consider the best entropic estimation to a unknown density¯x, given some of its algebraic or trigonometric moments. A uniform convergence theorem is established in this paper for such problems using Fermi-Dirac type entropic objectives.

Entropic Profiles of DNA Sequences Through Chaos-game-derived Images

A new method to determine entropic profiles in DNA sequences is presented. It is based on the chaos-game representation (CGR) of gene structure, a technique which produces a fractal-like picture of DNA sequences. First, the CGR image was divided into squares 4 - m in size ( m being the desired resolution), and the point density counted. Second, appropriate intervals were adjusted, and then a histogram of densities was prepared. Third, Shannon's formula was applied to the probability-distribution histogram, thus obtaining a new entropic estimate for DNA sequences, the histogram entropy , a measurement that goes with the level of constraints on the DNA sequence. Lastly, the entropic profile for the sequence was drawn, by considering the entropies at each resolution level, thus providing a way to summarize the complexity of large genomic regions or even entire genomes at different resolution levels. The application of the method to DNA sequences reveals that entropic profiles obtained in this way, as opposed to previously published ones, clearly discriminate between random and natural DNA sequences. Entropic profiles also show a different degree of variability within and between genomes. The results of these analyses are discussed in relation both to the genome compartmentalization in vertebrates and to the differential action of compositional and/or functional constraints on DNA sequences.

Thermodynamics of supercooled liquid simple metals and entropic estimate of their glass transition temperatures

We calculate the thermodynamic properties of supercooled liquid Na, Rb and Mg using the earlier described pseudopotential model and the Weeks-Chandler-Andersen perturbation theory for liquids. The calculated temperature dependences of the specific heat C p ( T) and of the free energy difference Δ G( T) between liquids and crystals are similar to those observed experimentally for the polyvalent metals In, Pb, Sn, Bi which can indicate the existence of a certain “law of corresponding states” for supercooled metals. The lower limit for the glass transition temperature T g is estimated as the Kauzman point at which the excess entropy of the liquid with respect to the crystal vanishes. This gives T g ⪆ 0.4T m where T m is the melting temperature.