scholarly journals New computer technologies to determine postmortem interval by the Henssge method

2021 ◽  
Vol 7 (3) ◽  
pp. 152-158
Author(s):  
German V. Nedugov
Keyword(s):  
Mathematical Models ◽  
Least Squares Method ◽  
Optimization Methods ◽  
Postmortem Interval ◽  
Residual Variance ◽  
Interval Estimate ◽  
Implicit Functions ◽  
External Temperature ◽  
Application Program ◽  
Double Exponential

Background: The Henssge method is still the main thermometric method to determine postmortem interval. However, its existing software implementations are characterized by several disadvantages associated with copying simplified nomographic variants of the original mathematical models without any optimization attempts, as well as procedural imperfection in finding the roots of implicit functions. In this paper, methods are proposed for optimizing solutions to the Henssge mathematical models and determine their errors, as well as software application implementation. Aim: Optimization of the Henssge algorithm and development of a series of applications based on the obtained data, designed to determine postmortem interval. Material and methods: Methods for solving double exponential Henssge models and determining their errors based on computational mathematics and regression modeling using the least-squares method with subsequent implementation in the format of computer programs in C# language optimized. Results: The discrete nature of residual variance changes of the double exponential Henssge models intended to determine the postmortem interval according to rectal and cranioencephalic thermometry data under constant external temperature conditions is eliminated. The interval estimate determination of postmortem interval at any confidence probability is possible. The application program Warm Bodies HR was developed, which implements applied optimization methods. The application program Warm Bodies AHBG, designed to determine postmortem interval by the Henssge method in a single discrete decrease or increase conditions in the constant temperature of the external environment, including a change in the cooling conditions of the corpse, was developed. The search for the roots of implicit functions in programs is carried out using the Newton tangent method, which ensures continuous source data nature and eliminates errors associated with the need to round directly measured physical quantities. Conclusions: The developed programs are recommended for forensic medical expert practice to determine postmortem interval.

scholarly journals Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1604231
Author(s):  
A.N. Pete ◽  
Peter Mathye ◽  
Igor Fedotov ◽  
Michael Shatalov
Keyword(s):  
Experimental Data ◽  
Mathematical Models ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Algebraic Equations ◽  
Systems Of Odes ◽  
Determination Of Parameters ◽  
Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

scholarly journals Ecological Roles of Coleoptera Associated with Carcasses in Caatinga

2013 ◽  
Vol 6 (3) ◽  
pp. 248-250 ◽  
Author(s):  
Wellington Emanuel dos Santos ◽  
Ana Claudia Firmino Alves ◽  
Rodrigo Cesar Azevedo Pereira Farias ◽  
Antonio José Creão-Duarte
Keyword(s):  
Parasite Species ◽  
Postmortem Interval ◽  
Interval Estimate ◽  
Ecological Roles ◽  
Pig Carcasses

The ecological roles of Coleoptera fauna associated with pig carcasses exposed in a Caatinga area were examined. Tray, pitfall and modified Shannon traps were settled together to collect these insects during two seasons (dry and rainy). 4,851 beetles were collected, belonging to 19 families and 88 species. The most abundant ecological category was predator/parasite (72.7%), followed by omnivorous (15.1%), necrophagous (10.9%) and incidental (1.3%). Future researches on the biology of predator/parasite species are required to understand their possible forensic utility for postmortem interval estimate. Papel Ecológico de Coleoptera Associados a Carcaças em Área de Caatinga Resumo. O papel ecológico da coleopterofauna associada a carcaças de porcos em uma área de Caatinga foi examinado. Para captura desses insetos foram utilizadas armadilhas do tipo bandeja, pitfall e Shannon modificada, durante duas estações (seca e chuvosa). 4.851 coleópteros foram coletados, pertencentes a 19 famílias e 88 espécies. A categoria ecológica mais abundante foi predador/parasita (72,7%), seguida por onívoro (15,1%), necrófago (10,9%) e incidental (1,3%). Futuros estudos sobre biologia das espécies predadoras/parasitas são necessários para se determinar sua possível utilidade forense na estimativa do intervalo pós-morte.

scholarly journals APPLICATION OF GLOBAL OPTIMIZATION TO PREDICT STRAINS IN RC COMPRESSED COLUMNS

2021 ◽  
Vol 61 (1) ◽  
pp. 242-252
Author(s):  
Marek Lechman ◽  
Andrzej Stachurski
Keyword(s):  
Least Squares Method ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Trust Region ◽  
Global Solutions ◽  
Optimization Methods ◽  
Box Constraints ◽  
Particle Swarm Method ◽  
Global And Local Optimization ◽  
Global And Local

In this paper, the results of an application of global and local optimization methods to solve a problem of determination of strains in RC compressed structure members are presented. Solutions of appropriate sets of nonlinear equations in the presence of box constraints have to be found. The use of the least squares method leads to finding global solutions of optimization problems with box constraints. Numerical examples illustrate the effects of the loading value and the loading eccentricity on the strains in concrete and reinforcing steel in the a cross-section.Three different minimization methods were applied to compute them: trust region reflective, genetic algorithm tailored to problems with real double variables and particle swarm method. Numerical results on practical data are presented. In some cases, several solutions were found. Their existence has been detected by the local search with multistart, while the genetic and particle swarm methods failed to recognize their presence.

scholarly journals Promising blood-derived biomarkers for estimation of the postmortem interval

2015 ◽  
Vol 4 (6) ◽  
pp. 1443-1452 ◽  
Author(s):  
Isabel Costa ◽  
Félix Carvalho ◽  
Teresa Magalhães ◽  
Paula Guedes de Pinho ◽  
Ricardo Silvestre ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Linear Correlation ◽  
Predictive Value ◽  
Biochemical Parameter ◽  
Postmortem Interval

A linear correlation between blood putrefaction time and biochemical parameter concentrations was obtained. Two mathematical models that may have predictive value for estimation of thepostmorteminterval were developed. The obtained results might be complementary procedures for the methodologies already used.

New Mathematical Models for Effective Drug Diffusivity Estimation in 2D

2007 ◽  
Vol 561-565 ◽  
pp. 1557-1560 ◽  
Author(s):  
Song Wang ◽  
Xia Lou
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mathematical Models ◽  
Analytical Solutions ◽  
Least Squares Method ◽  
Effective Diffusivity ◽  
Data Set ◽  
Initial Burst ◽  
Effective Boundary ◽  
Effective Diffusivities

In this paper we propose several new mathematical models for estimating effective diffusivities of a drug released from a cylinder device to an external finite volume. These models can handle problems with ‘initial burst’ and boundary layers. Analytical solutions to the models are derived. To determine the unknown effective diffusivity, time of a initial burst and width of the effective boundary layer, a least-squares method can be used for a given experimental data set. The models were tested using experimental data and the numerical results show the usefulness and accuracy of these models.

scholarly journals Mathematical Models and Data Analysis of Residential Land Leasing Behavior of District Governments of Beijing in China

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2314
Author(s):  
Jing Cheng
Keyword(s):  
Mathematical Models ◽  
Least Squares Method ◽  
Large City ◽  
Ordinary Least Squares ◽  
Numerical Results ◽  
Policy Implications ◽  
Residential Land ◽  
District Government ◽  
Beijing China ◽  
Land Leasing

To analyze the leasing behavior of residential land in Beijing, the mathematical models of the price and the total area of the leased residential land are presented. The variables of the mathematical models are proposed by analyzing the factors influencing the district government’s leasing behavior for residential land based on the leasing right for residential land in Beijing, China. The regression formulae of the mathematical models are obtained with the ordinary least squares method. By introducing the data of the districts in Beijing from 2004 to 2015 into the mathematical models, the numerical results of the coefficients in the mathematical models are obtained by solving the equations of the regression formulae. After discussing the numerical results of the influencing factors, the district government behavior for leasing residential land in Beijing, China, is investigated. The numerical results show the factors concerning the government and how these factors influence the leased price and the total leased area of residential land for this large city in China. Finally, policy implications for the district government regarding residential land leasing in Beijing are proposed.

scholarly journals The method for identification of mathematical models in two-factor pharmaceutical research

2021 ◽  
Vol 7 (3) ◽  
pp. 3-11
Author(s):  
O.V. Kutova ◽  
R. V. Sahaidak-Nikitiuk ◽  
I. V. Kovalevska
Keyword(s):  
Mathematical Models ◽  
Microcrystalline Cellulose ◽  
Least Squares Method ◽  
Optimal Algorithm ◽  
Potato Starch ◽  
A Priori ◽  
Quantitative Composition ◽  
Cellulose Solution ◽  
Regression Equations ◽  
Quantitative Factor

The methodical approach to solving problems of identification of mathematical models of pharmaceutical objects with two dependent quantitative factors has been considered; the total value of them is determined by the quantitative composition of the mixture and is fixed at a definite level.Aim. To determine the optimal algorithm for processing experimental data using the minimum number of experiments according to the plan 22to establish an adequate mathematical description of research at the technological stage.Materials and methods. Such materials as potato starch (quantitative factor x1) and the microcrystalline cellulose solution (quantitative factor x2) were used. The content of excipients should be 54 % of the total mass. Based on a priori data the content of potato starch x1 should be in the range from 45 to 50 % of the total amount (45 ≤ x1 ≥ 50), and x2 characterizes an aqueous solution of microcrystalline cellulose with a concentration in the range from 2 to 5 % (2 ≤ x2 ≥ 5). The least squares method was applied to determine the coefficients of the regression equations. During our research the Mathcad computer environment (MathSoft Ins., USA) was used.Results. To reduce the number of solutions and make the right decision it is necessary to have a reliable source of information and impose the appropriate restrictions based on a priori data and practical experience of the researcher. Conclusions. The studies have shown that to identify mathematical models the analysis of the main (final) effects of the interaction of factors is effective, it is also expedient to interpret this interaction based on the interpretation of the dependences of objective functions on each factor provided that the variable is fixed at the minimum and maximum levels of variation.

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