Building reaction kinetic models for amiloid fibril growth

In this work we discuss some methodological aspects of the creation and formulation of mathematical models describing the growth of species from the point of view of reaction kinetics. Our discussion is based on familiar examples of growth models such as logistic growth and enzyme kinetics. We propose several reaction network models for the amiloid fibrillation processes in the citoplasm. The solutions of the models are sigmoidal functions graphically visualized using the computer algebra system Mathematica.

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Kinematic support modeling in Sage

Discrete and Continuous Models and Applied Computational Science ◽

10.22363/2658-4670-2020-28-2-141-153 ◽

2020 ◽

Vol 28 (2) ◽

pp. 141-153

Author(s):

Oleg K. Kroytor ◽

Mikhail D. Malykh ◽

Sergei P. Karnilovich

Keyword(s):

Rigid Body ◽

Computer Algebra ◽

Computer Algebra System ◽

Seismic Isolation ◽

Equations Of Motion ◽

Classical Mechanics ◽

Vertical Plane ◽

Base Plate ◽

Euler Method ◽

Point Of View

The article discusses the kinematic support, which allows reducing the horizontal dynamic effects on the building during earthquakes. The model of a seismic isolation support is considered from the point of view of classical mechanics, that is, we assume that the support is absolutely solid, oscillating in a vertical plane above a fixed horizontal solid plate. This approach allows a more adequate description of the interaction of the support with the soil and the base plate of the building. The paper describes the procedure for reducing the complete system of equations of motion of a massive rigid body on a fixed horizontal perfectly smooth plane to a form suitable for applying the finite difference method and its implementation in the Sage computer algebra system. The numerical calculations by the Euler method for grids with different number of elements are carried out and a mathematical model of the support as a perfectly rigid body in the Sage computer algebra system is implemented. The article presents the intermediate results of numerical experiments performed in Sage and gives a brief analysis (description) of the results.

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Reaction networks reveal new links between Gompertz and Verhulst growth functions

BIOMATH ◽

10.11145/j.biomath.2019.04.167 ◽

2019 ◽

Vol 8 (1) ◽

pp. 1904167 ◽

Cited By ~ 1

Author(s):

Svetoslav Marinov Markov

Keyword(s):

Growth Models ◽

Logistic Models ◽

Reaction Network ◽

Measured Data ◽

Reaction Networks ◽

Logistic Growth ◽

Additional Species ◽

One Dimensional ◽

Growth Functions ◽

Intrinsic Mechanism

New reaction network realizations of the Gompertz and logistic growth models are proposed. The proposed reaction networks involve an additional species interpreted as environmental resource. Some natural generalizations and modifications of the Gompertz and the logistic models, induced by the proposed networks, are formulated and discussed. In particular, it is shown that the induced dynamical systems can be reduced to one dimensional differential equations for the growth (resp. decay) species. The reaction network formulation of the proposed models suggest hints for the intrinsic mechanism of the modeled growth process and can be used for analyzing evolutionary measured data when testing various appropriate models, especially when studying growth processes in life sciences.

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Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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Methods of Network Planning and Management when Implementing Territory Planning Projects

Promyshlennoe i Grazhdanskoe Stroitel stvo ◽

10.33622/0869-7019.2019.08.49-54 ◽

2019 ◽

pp. 49-54

Keyword(s):

Large Scale ◽

Housing Stock ◽

Network Planning ◽

Network Models ◽

Point Of View ◽

Residential Areas ◽

Basic Principles ◽

Planning And Management ◽

Planning Project ◽

Complex Process

The success of the Program of housing stock renovation in Moscow depends on the efficiency of resource management. One of the main urban planning documents that determine the nature of the reorganization of residential areas included in the Program of renovation is the territory planning project. The implementation of the planning project is a complex process that has a time point of its beginning and end, and also includes a set of interdependent parallel-sequential activities. From an organizational point of view, it is convenient to use network planning and management methods for project implementation. These methods are based on the construction of network models, including its varieties – a Gantt chart. A special application has been developed to simulate the implementation of planning projects. The article describes the basic principles and elements of modeling. The list of the main implementation parameters of the Program of renovation obtained with the help of the developed software for modeling is presented. The variants of using the results obtained for a comprehensive analysis of the implementation of large-scale urban projects are proposed.

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THEORETICAL AND METHODOLOGICAL ASPECTS OF UNDERSTANDING OF THE SYSTEM OBJECT IN DESIGN

Technical Aesthetics and Design Research ◽

10.34031/2687-0878-2019-1-4-5-10 ◽

2020 ◽

Vol 1 (4) ◽

pp. 5-10

Author(s):

V. Barysheva ◽

O. Druzhinina

Keyword(s):

Scientific Research Institute ◽

Point Of View ◽

Design Stage ◽

Comprehensive Understanding ◽

Design Culture ◽

Design Program ◽

Methodological Aspects ◽

Cultural Experts ◽

Union Scientific Research Institute ◽

Separate Product

The article is devoted to the analysis of the system object from the point of view of design from design, sociocultural and philosophical positions. The authors systematize the definitions of a system object of design proposed in the 1960–1980s by theorists and practitioners, art historians, cultural experts and philosophers from different countries, including Russia, which allows a comprehensive understanding of the phenomenon of design culture. This article is devoted to the characteristic properties of the system object in design. They were considered and analyzed on the example of the «Absheron» design-program when designing of agricultural village). This concept was developed at the All-Union Scientific Research Institute of Technical Aesthetics (VNIITE) in 1983. Using the same example, the features of the approach to designing a system object in design was observed not only as a separate product, but as a sociocultural situation that constantly changes at each design stage.

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