MA representation of 2D systems
Matematický model jaterní chromoexkreční funkce
Mathematical and Computational Models in Tumor Immunology
The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies:...
Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices
Electro-muscular disruption (EMD) devices such as TASER M26 and X26 have been used as a less-than-lethal weapon. Such EMD devices shoot a pair of darts toward an intended target to generate an incapacitating electrical shock. In the use of the EMD device, there have been controversial questions about its safety and effectiveness. To address these questions, we need to investigate the distribution of the current density J inside the target produced by the EMD device. One approach is to develop a computational...
Mathematical modelling of molecule evolution in protocells
In this article, we analyse the process of the emergence of RNA polynucleotides located in an enclosed environment, at an early stage of the RNA world. Therefore we prepared a mathematical model, composed of a set of differential equations, which simulates the behaviour of an early biological system bounded by a protocell membrane. There is evidence that enclosed environments were available on the primordial Earth. There are also experimental proofs that RNA strands can develop in these formations....
Mathematical Modelling of Tumour Dormancy
Many tumours undergo periods in which they apparently do not grow but remain at a roughly constant size for extended periods. This is termed tumour dormancy. The mechanisms responsible for dormancy include failure to develop an internal blood supply, individual tumour cells exiting the cell cycle and a balance between the tumour and the immune response to it. Tumour dormancy is of considerable importance in the natural history of cancer. In many cancers, and in particular in breast cancer, recurrence...
Mathematical models of the complete course of HIV infection and AIDS.
Mathematical problems in modeling artificial heart.
Mathematical theory of improvability of production systems.
Media/psychological impact on multiple outbreaks of emerging infectious diseases.
Methods for estimating vehicle queues at a marine terminal: a computational comparison
Minimizing energy use for a road expansion in a transportation system using optimal control theory.
Mining online auction social networks for reputation and recommendation
Mobile sensor routing for parameter estimation of distributed systems using the parallel tunneling method
The paper deals with the problem of optimal path planning for a sensor network with mutliple mobile nodes, whose measurements are supposed to be primarily used to estimate unknown parameters of a system modelled by a partial differential equation. The adopted framework permits to consider two- or three-dimensional spatial domains and correlated observations. Since the aim is to maximize the accuracy of the estimates, a general functional defined on the relevant Fisher information matrix is used...
Model based analysis of signaling pathways
The paper is concerned with application of mathematical modeling to the analysis of signaling pathways. Two issues, deterministic modeling of gene transcription and model-driven discovery of regulatory elements, are dealt with. First, the biological background is given and the importance of the stochastic nature of biological processes is addressed. The assumptions underlying deterministic modeling are presented. Special emphasis is put on describing gene transcription. A framework for including...
Model of shell metal mould heating in the automotive industry
This article focuses on heat radiation intensity optimization on the surface of a shell metal mould. Such moulds are used in the automotive industry in the artificial leather production (the artificial leather is used, e.g., on car dashboards). The mould is heated by infrared heaters. After the required temperature is attained, the inner mould surface is sprinkled with special PVC powder. The powder melts and after cooling down it forms the artificial leather. A homogeneous temperature field of...
Model reduction methods for chaotic systems
Modeling acquaintance networks based on balance theory
An acquaintance network is a social structure made up of a set of actors and the ties between them. These ties change dynamically as a consequence of incessant interactions between the actors. In this paper we introduce a social network model called the Interaction-Based (IB) model that involves well-known sociological principles. The connections between the actors and the strength of the connections are influenced by the continuous positive and negative interactions between the actors and, vice...
Modeling and simulation of a blood pump for the development of a left ventricular assist system controller
A mathematical model describing the pressure-volume relationship of the Novacor left ventricular assist system (LVAS) was developed. The model consisted of lumped resistance, capacitance, and inductance elements with one time-varying capacitor to simulate the cyclical pressure generation of the system. The ejection and filling portions of the pump cycle were modeled with two separate functions. The corresponding model parameters were estimated by least squares fit to experimental data obtained in...
Modeling biomarker dynamics with implications for the treatment of prostate cancer.