Mathematical Models of Effective Topology of Computer Networks for Electric Power Supply Control on Railway Transport

The paper is devoted to analysis of modern directions of innovation-investment formation of intelligent computer networks that control the fast-moving technological processes of electricity supply. It is based on the conclusion that the problem of increasing the productivity of information exchange between information resources and consumers is dominant. A method for increasing the efficiency of information exchange is proposed as a search for the rational location of a new node and the organization of such a set of its connections among the whole set of nodes of the computer network, which provides a minimum average topological distance. Mathematical models of effective topological organization of connections in computer network of power consumption control at the level of traction substations, electric power distances and the railway in general are proposed.

Electrohydrodynamic Drying in Agribusiness: Literature Review

In agribusiness, drying is a unitary operation that optimizes the production and preservation of products and raw materials. Drying is performed through different traditional methods, one of the most recently studied is the electrohydrodynamic drying EHD which uses an electric field that allows decreasing the processing time thus increasing the drying speed of raw materials and consuming less energy. In this article, a review was carried out through Scopus using a search equation with the keywords “Electrohydrodynamic drying,” “food” and “AGRI” which resulted in a total of 145 articles; which were analyzed through in-depth reading, analyzing aspects such as year, author, keywords, countries, quartile, journal, relationship with agroindustry, mathematical models used and applications in agro-industrial products, this analysis was complemented with the application of Vantage Point software through co-occurrence matrices and cluster analysis. Recent applications were found in Carrot, Chicken, Sea Cucumber, Goji Berry, Peppermint Leaf, Quince, Potato, Blueberry, Aquatic Products, Banana Slices, Grape Pomace, Blueberry, Apple, Mushroom, Wheat, and Mushroom Slices, mathematical models with application in EHD drying were also found, such as Henderson and Pabis, Page, Logarithmic, Quadratic, Newton/Lewis, Diffusion and exponential.

Mathematical Models for Cholesterol Metabolism and Transport

Cholesterol is an essential component of eukaryotic cellular membranes. It is also an important precursor for making other molecules needed by the body. Cholesterol homeostasis plays an essential role in human health. Having high cholesterol can increase the chances of getting heart disease. As a result of the risks associated with high cholesterol, it is imperative that studies are conducted to determine the best course of action to reduce whole body cholesterol levels. Mathematical models can provide direction on this. By examining existing models, the suitable reactions or processes for drug targeting to lower whole-body cholesterol can be determined. This paper examines existing models in the literature that, in total, cover most of the processes involving cholesterol metabolism and transport, including: the absorption of cholesterol in the intestine; the cholesterol biosynthesis in the liver; the storage and transport of cholesterol between the intestine, the liver, blood vessels, and peripheral cells. The findings presented in these models will be discussed for potential combination to form a comprehensive model of cholesterol within the entire body, which is then taken as an in-silico patient for identifying drug targets, screening drugs, and designing intervention strategies to regulate cholesterol levels in the human body.

Conceptual and Mathematical Models, Methods, and Technologies for the Study of the Digital Transformation of Economic and Social Systems: A Literature Review and Research Agenda (Part II)

The results of the review of the subject field on the research of the digital transformation of economic and social systems is carried out (part II). We reviewed main theoretical, mathematical tools which could allow solving unsolved problems. The review of such main theoretical tools that can become the basis for developing the “activity paradigm” of research is carried out.

Covid-19 disease dynamics with vaccination: The effect of uncertainty

Rate parameters are critical in estimating the covid burden using mathematical models. In the Covid-19 mathematical models, these parameters are assumed to be constant. However, uncertainties in these rate parameters are almost inevitable. In this paper, we study a stochastic epidemic model of the SARS-CoV-2 virus infection in the presence of vaccination in which some parameters fluctuate around its average value. Our analysis shows that if the stochastic basic reproduction number (SBRN) of the system is greater than unity, then there is a stationary distribution, implying the long-time disease persistence. A sufficient condition for disease eradication is also prescribed for which the exposed class goes extinct, followed by the infected class. The disease eradication criterion may not hold if the rate of vaccine-induced immunity loss increases or/and the force of infection increases. Using the Indian Covid-19 data, we estimated the model parameters and showed the future disease progression in the presence of vaccination. The disease extinction time is estimated under various conditions. It is revealed that the mean extinction time is an increasing function of both the force of infection and immunity loss rate and shows the lognormal distribution. We point out that disease eradication might not be possible even at a higher vaccination rate if the vaccine-induced immunity loss rate is high. Our observation thus indicates the endemicity of the disease for the existing vaccine efficacy. The disease eradication is possible only with a higher vaccine efficacy or a reduced infection rate.

AUTOMATION OF CONSTRUCTION OF A SCHEME FOR SOLVING COMPUTE- INTENSIVE PROBLEMS OF MATHEMATICAL PHYSICS ON SUPERCOMPUTERS

В статье представлен подход к разработке информационно-аналитической системы, помогающей исследователю решать вычислительно сложные задачи математической физики на суперкомпьютерах. Система автоматически строит схему решения задачи по спецификации пользователя, введенной им в режиме диалога. Схема включает наиболее подходящие математические модели для решения задачи, численные методы, алгоритмы и параллельные архитектуры, ссылки на доступные фрагменты параллельного кода, которые пользователь может использовать при разработке собственного кода. Построение схемы осуществляется на основе онтологии проблемной области «Решение вычислительно сложных задач математической физики», онтологии заданной предметной области и экспертных правил, построенных с использованием технологии Semantic Web. The paper presents an approach to the development of an information-analytical system that helps a researcher to solve compute-intensive problems of mathematical physics on supercomputers. The system automatically builds a scheme for solving the problem according to the user's specification entered by him in the dialogue mode. The scheme includes the most suitable mathematical models for solving the problem, numerical methods, algorithms and parallel architectures, links to available fragments of parallel code that the user can use when developing their own code. The construction of the scheme is carried out on the basis of the ontology of the problem area "Solving compute-intensive problems of mathematical physics", the ontology of a given subject area and expert rules built using the Semantic Web technology.

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with β-cells and the other with no β-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no β-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with β-cells required more parameters to match the data and we fitted the β-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from 2.10 to 4.05. Our results suggest that the model without β-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

Application of Mathematical Models to Determine the Feasibility of Amorphous Drug Layering in Pan Coaters

Oral solid dosage forms that contain APIs in the amorphous state have become commonplace because of many drug substances exhibiting poor water solubility, which negatively impacts their absorption in the human GI tract. While micronization, solvent spray-drying, and hot-melt extrusion can address solubility issues, spray coating of the APIs onto beads and tablets offers another option for producing amorphous drug products. High-level comparisons between bead and tablet coating technologies have the potential for simpler equipment and operation that can reduce the cost of development and manufacturing. However, spray coating directly onto tablets is not without challenges, especially with respect to meeting uniformity acceptance value (AV) criteria, comprising accuracy (mean) and precision (variance) objectives. The feasibility of meeting AV criteria is examined, based on mathematical models for accuracy and precision. The results indicate that the main difficulty in manufacturing satisfactory drug-layered tablets by spray coating is caused by the practical limitations of achieving the necessary coating precision. Despite this limitation, it is shown that AV criteria can be consistently met by appropriate materials monitoring and control as well as processing equipment setup, operation, and maintenance.

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Reassessment of Thin-Layer Drying Models for Foods: A Critical Short Communication

Modeling the thin-layer drying of foods is based on describing the moisture ratio versus time data by using a suitable mathematical model or models. Several models were proposed for this purpose and almost all studies were related to the application of these models to the data, a comparison and selecting the best-fitted model. A careful inspection of the existing drying data in literature revealed that there are only a limited number of curves and, therefore, the use of some models, especially the complex ones and the ones that require a transformation of the data, should be avoided. These were listed based on evidence with the use of both synthetic and published drying data. Moreover, the use of some models were encouraged, again based on evidence. Eventually, some suggestions were given to the researchers who plan to use mathematical models for their drying studies. These will help to reduce the time of the analyses and will also avoid the arbitrary usage of the models.