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General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis

A. N. Gorban, E. V. Smirnova, T. A. Tyukina (2009)

Mathematical Modelling of Natural Phenomena

We study ensembles of similar systems under load of environmental factors. The phenomenon of adaptation has similar properties for systems of different nature. Typically, when the load increases above some threshold, then the adapting systems become more different (variance increases), but the correlation increases too. If the stress continues to increase then the second threshold appears: the correlation achieves maximal value, and start to decrease, but the variance continue to increase. In many...

Genetic and combinatorial algorithms for optimal sizing and placement of active power filters

Marcin Maciążek, Dariusz Grabowski, Marian Pasko (2015)

International Journal of Applied Mathematics and Computer Science

The paper deals with cost effective compensator placement and sizing. It becomes one of the most important problems in contemporary electrical networks, in which voltage and current waveform distortions increase year-by-year reaching or even exceeding limit values. The suppression of distortions could be carried out by means of three types of compensators, i.e., passive filters, active power filters and hybrid filters. So far, passive filters have been more popular mainly because of economic reasons,...

Global stability analysis and control of leptospirosis

Kazeem Oare Okosun, M. Mukamuri, Daniel Oluwole Makinde (2016)

Open Mathematics

The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction...

High Resolution Tracking of Cell Membrane Dynamics in Moving Cells: an Electrifying Approach

R.A. Tyson, D.B.A. Epstein, K.I. Anderson, T. Bretschneider (2010)

Mathematical Modelling of Natural Phenomena

Cell motility is an integral part of a diverse set of biological processes. The quest for mathematical models of cell motility has prompted the development of automated approaches for gathering quantitative data on cell morphology, and the distribution of molecular players involved in cell motility. Here we review recent approaches for quantifying cell motility, including automated cell segmentation and tracking. Secondly, we present our own novel...

High-performance simulation-based algorithms for an alpine ski racer's trajectory optimization in heterogeneous computer systems

Roman Dębski (2014)

International Journal of Applied Mathematics and Computer Science

Effective, simulation-based trajectory optimization algorithms adapted to heterogeneous computers are studied with reference to the problem taken from alpine ski racing (the presented solution is probably the most general one published so far). The key idea behind these algorithms is to use a grid-based discretization scheme to transform the continuous optimization problem into a search problem over a specially constructed finite graph, and then to apply dynamic programming to find an approximation...

Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling

G. Bocharov, V. Chereshnev, I. Gainova, S. Bazhan, B. Bachmetyev, J. Argilaguet, J. Martinez, A. Meyerhans (2012)

Mathematical Modelling of Natural Phenomena

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally disrupted? (ii)...

Image recall using a large scale generalized Brain-State-in-a-Box neural network

Cheolhwan Oh, Stanisław Żak (2005)

International Journal of Applied Mathematics and Computer Science

An image recall system using a large scale associative memory employing the generalized Brain-State-in-a-Box (gBSB) neural network model is proposed. The gBSB neural network can store binary vectors as stable equilibrium points. This property is used to store images in the gBSB memory. When a noisy image is presented as an input to the gBSB network, the gBSB net processes it to filter out the noise. The overlapping decomposition method is utilized to efficiently process images using their binary...

Immunotherapy with interleukin-2: A study based on mathematical modeling

Sandip Banerjee (2008)

International Journal of Applied Mathematics and Computer Science

The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.

Improving prediction models applied in systems monitoring natural hazards and machinery

Marek Sikora, Beata Sikora (2012)

International Journal of Applied Mathematics and Computer Science

A method of combining three analytic techniques including regression rule induction, the k-nearest neighbors method and time series forecasting by means of the ARIMA methodology is presented. A decrease in the forecasting error while solving problems that concern natural hazards and machinery monitoring in coal mines was the main objective of the combined application of these techniques. The M5 algorithm was applied as a basic method of developing prediction models. In spite of an intensive development...

Integrating Photosynthesis, Respiration, Biomass Partitioning, and Plant Growth: Developing a Microsoft Excel®-based Simulation Model of Wisconsin Fast Plant (Brassica rapa, Brassicaceae) Growth with Undergraduate Students

Y. L. Grossman, A. B. Berdanier, M. L. Custic, L. R. Feeley, S. F. Peake, A. J. Saenz, K. S. Sitton (2011)

Mathematical Modelling of Natural Phenomena

This paper demonstrates the development of a simple model of carbon flow during plant growth. The model was developed by six undergraduate students and their instructor as a project in a plant ecophysiology course. The paper describes the structure of the model including the equations that were used to implement it in Excel®, the plant growth experiments that were conducted to obtain information for parameterizing and testing the model, model performance, student responses to the modeling project,...

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