ЭНТРОПИЯ АБИОТИЧЕСКИХ ГЕОСФЕР И МОДЕЛЬ ДЛЯ ОЦЕНКИ И ПРОГНОЗА ИХ СОСТОЯНИЯ

It has been shown in the present work that the methods used to sum up the coefficients of concentrations (hazards) of different pollutants in the abiotic geospheres are not additive and therefore cannot be universal. Universal is the entropic model developed for the biological structures. However, the classic definition of entropy is not appropriate for the abiotic structures because it comprises both stochastic and deterministic components. In the present work, a novel formula for calculating entropy of abiotic structures based on the environmental risk is proposed and an entropic model for assessing the environmental stability of such structures has been constructed for forecasting their development. The model has been tested by comparing the results of assessing the conditions of a test plot according to the entropic and the classic methodology. The classing one being non-additive yields somewhat overrated rank estimates. The entropic methodology makes it possible to forecast the ecological conditions of the test plot.

THE ANALYTIC HIERARCHY PROCESS IS A PROMISING TOOL WHEN PROCESSING DATA AND MAKING DECISIONS IN PSYCHIATRY

Objectives. Formation of results of processing of rank (clinical, psychometric) information in the scale of relations [1] based on the Analytical Hierarchy Process (AHP, Saaty T. L., 2008). Methods. Clinical, psychometric, statistical and AHP algorithms. Results. When evaluating a patient's state, decisions must be made based on clinical, psychometric, social, and neurobiological characteristics. These characteristics correspond to measurement scales: categorical, rank (dimensional, psychometric), and relationship scales. Only the latter are numerical, so it is not possible [1] to create correct models of states taking into account neurobiological indicators. Rank estimates do not allow calculating even average values. Analysis of the problems of evaluating psychopathological states on the basis of categorical and rank scales shows that these problems can be presented in the form of appropriate hierarchies, the structure of which must be taken into account when processing initial information [1]. Therefore, the use of the AHP tools in these situations is most natural. The implementation of AHP procedures for processing rank information is based on the application of the AHP normative approach. In [1], using the simplest examples of General medical significance, the technique of using the AHP normative approach is demonstrated. In practice, both individual doctor evaluations (personalized patient management method) and average expert evaluations (team method) can be used. Conclusions. The AHP approach is promising when constructing integral models of the corresponding processes and correctly using the resulting estimates in practice and research. References. 1. Mitikhin V.G., Solokhina T.A. S.S. Korsakov Journal of Neurology and Psychiatry, 2019, 119(2): 49-54. doi:10.17116/jnevro201911902149

Assessment of the weight and consistency of the interaction of specialists in the polyprofessional teams

The aim of the work is a systematic analysis of the problem of the effectiveness of interaction between specialists of polyprofessional teams during psychosocial rehabilitation interventions. Formation of procedures and algorithms for processing the results of processing expert information to assess the weight and consistency of decisions based on the method of analysis of hierarchies. The material for this work was a set of Russian and foreign scientific publications devoted to use and processing of the expert data presented in different scales: categorical, rank, scales of relations. Methods of data analysis: rank methods, methods of system data analysis and, in particular, algorithms of the analytic hierarchy process. Results. It is shown that the issues of interdisciplinary interactions of team members, and the procedures for assessing the weight and consistency of decisions made by team members, are naturally represented by the appropriate hierarchies, the analysis of which is carried out by means of the method of hierarchy analysis. Summary. The fundamental difference between the estimates obtained by means of the hierarchy analysis method and the rank estimates is due to the fact that numerical estimates of the weight and consistency of decisions are formed, which depend on the qualification of employees, the patients condition and the characteristics of the environment.

Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs

We investigate the convergence rate of the quantics-TT (QTT) stochas- tic collocation tensor approximations to solutions of multiparametric elliptic PDEs and construct efficient iterative methods for solving arising high-dimensional parameter- dependent algebraic systems of equations. Such PDEs arise, for example, in the para- metric, deterministic reformulation of elliptic PDEs with random field inputs, based, for example, on the M-term truncated Karhunen-Loève expansion. We consider both the case of additive and log-additive dependence on the multivariate parameter. The local-global versions of the QTT-rank estimates for the system matrix in terms of the parameter space dimension is proven. Similar rank bounds are observed in numerics for the solutions of the discrete linear system. We propose QTT-truncated iteration based on the construction of solution-adaptive preconditioner that provides robust conver- gence in both additive and log-additive cases. Various numerical tests indicate that the numerical complexity scales almost linearly in the dimension of parametric space M.

Genetic principal components for live ultrasound scan traits of Angus cattle

Multivariate restricted maximum likelihood analyses were carried out for a large data set comprising records for eye-muscle area, fat depth at the 12/13th rib and the rump P8 site, and percentage intramuscular fat, recorded via live ultrasound scanning of Australian Angus cattle. Records on heifers or steers were treated as separate traits from those on bulls. Reduced rank estimates of the genetic covariance matrix were obtained by restricted maximum likelihood, estimating the leading three, four, five, six, seven and all eight principal components and these were contrasted with estimates from pooled bivariate analyses.Results from analyses fitting five or six genetic principal components agreed closely with estimates from bivariate and eight-variate analyses and literature results. Heritabilities and variances for ‘fatness’ traits measured on heifers or steers were higher than those recorded for bulls, and genetic correlations were less than unity for the same trait measured in different sexes. Eye-muscle area showed little association with the other traits.Reduced rank estimation decreased computational requirements of multivariate analyses dramatically, in essence corresponding to those of an m-variate analysis for m principal components considered. Five or six principal components appeared to be necessary to model genetic covariances adequately. The first three of these components then explained about 97% of the genetic variation among the eight traits.A simulation study showed that errors in reduced rank estimates of the genetic covariance matrix were small, once three or more principal components from analyses fitting five or more components were used in constructing the estimates. Similarly, accuracy of genetic evaluation for the eight traits using the first four components was only slightly less than that using all principal components.Results suggest that reduced rank estimation and prediction is applicable for the eight scan traits considered. The leading three to four principal components sufficed to describe the bulk of genetic variation between animals. However, five or more principal components needed to be considered in estimating covariance matrices and the ‘loadings’ of the original traits to the principal components.

The Black Death in English towns

It seems likely that historians in the past have seriously underestimated the number of English townsmen in the early fourteenth century. In London alone there may have been 80–100,000 around 1300. The population of Norwich in the early fourteenth century was higher than used to be thought, and it was growing: Rutledge proposes 17,000 for 1311 and 25,000 for 1333. Keene's estimate of about 10,000 for Winchester in the early fourteenth century can serve as a basis for estimating the population of other towns in the same period. Those whose taxable value in 1334, and whose contribution to the poll tax of 1377, was at least as great as Winchester's, probably had a population equal to Winchester's or greater around 1300. By this argument about fifteen towns, including London, are likely to have had 10,000 or more people at the beginning of the fourteenth century, and perhaps 5 per cent of England's population lived in towns of this rank. Estimates taking account of smaller towns are much more precarious, but it is possible that all told 10 per cent of England's population lived in towns of over 2,000 inhabitants and that a further 5 per cent lived in small boroughs, some with as few as 300 people. Even this estimate does not take account of many small market towns, not described as boroughs, that had elementary urban characteristics.