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A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

M. Pons-Salort, B. van der Sanden, A. Juhem, A. Popov, A. Stéphanou (2012)

Mathematical Modelling of Natural Phenomena

A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....

A family of model predictive control algorithms with artificial neural networks

Maciej Ławryńczuk (2007)

International Journal of Applied Mathematics and Computer Science

This paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used...

A free boundary problem for a predator-prey model with nonlinear prey-taxis

Mohsen Yousefnezhad, Seyyed Abbas Mohammadi, Farid Bozorgnia (2018)

Applications of Mathematics

This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary...

A free boundary problem for some modified predator-prey model in a higher dimensional environment

Hongmei Cheng, Qinhe Fang, Yang Xia (2022)

Applications of Mathematics

We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as t goes to infinity and survives in the new environment, or it fails to establish...

A hyperbolic model of chemotaxis on a network: a numerical study

G. Bretti, R. Natalini, M. Ribot (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the...

A mathematical model for file fragment diffusion and a neural predictor to manage priority queues over BitTorrent

Christian Napoli, Giuseppe Pappalardo, Emiliano Tramontana (2016)

International Journal of Applied Mathematics and Computer Science

BitTorrent splits the files that are shared on a P2P network into fragments and then spreads these by giving the highest priority to the rarest fragment. We propose a mathematical model that takes into account several factors such as the peer distance, communication delays, and file fragment availability in a future period also by using a neural network module designed to model the behaviour of the peers. The ensemble comprising the proposed mathematical model and a neural network provides a solution...

A Modeling Framework For Immune-related Diseases

F. Castiglione, S. Motta, F. Pappalardo, M. Pennisi (2012)

Mathematical Modelling of Natural Phenomena

About twenty five years ago the first discrete mathematical model of the immune system was proposed. It was very simple and stylized. Later, many other computational models have been proposed each one adding a certain level of sophistication and detail to the description of the system. One of these, the Celada-Seiden model published back in 1992, was already mature at its birth, setting apart from the topic-specific nature of the other models. This...

A new application of the homotopy analysis method in solving the fractional Volterra's population system

Mehdi Ghasemi, Mojtaba Fardi, Reza Khoshsiar Ghaziani (2014)

Applications of Mathematics

This paper considers a Volterra's population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.

A nonlinear dynamic inversion-based neurocontroller for unmanned combat aerial vehicles during aerial refuelling

Jimoh Olarewaju Pedro, Aarti Panday, Laurent Dala (2013)

International Journal of Applied Mathematics and Computer Science

The paper presents the development of modelling and control strategies for a six-degree-of-freedom, unmanned combat aerial vehicle with the inclusion of the centre of gravity position travel during the straight-leg part of an in-flight refuelling manoeuvre. The centre of gravity position travel is found to have a parabolic variation with an increasing mass of aircraft. A nonlinear dynamic inversion-based neurocontroller is designed for the process under investigation. Three radial basis function...

A Periodic Lotka-Volterra System

Tsvetkov, D. (1996)

Serdica Mathematical Journal

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters.

A simplex trained neural network-based architecture for sensor fusion and tracking of target maneuvers

Yee Chin Wong, Malur K. Sundareshan (1999)

Kybernetika

One of the major applications for which neural network-based methods are being successfully employed is in the design of intelligent integrated processing architectures that efficiently implement sensor fusion operations. In this paper we shall present a novel scheme for developing fused decisions for surveillance and tracking in typical multi-sensor environments characterized by the disparity in the data streams arriving from various sensors. This scheme employs an integration of a multilayer neural...

A Team Approach to Undergraduate Research in Biomathematics: Balance Control

J. Milton, A. Radunskaya, W. Ou, T. Ohira (2011)

Mathematical Modelling of Natural Phenomena

The question, how does an organism maintain balance? provides a unifying theme to introduce undergraduate students to the use of mathematics and modeling techniques in biological research. The availability of inexpensive high speed motion capture cameras makes it possible to collect the precise and reliable data that facilitates the development of relevant mathematical models. An in–house laboratory component ensures that students have the opportunity...

A topological model of site-specific recombination that predicts the knot and link type of DNA products

Karin Valencia (2014)

Banach Center Publications

This is a short summary of a topological model of site-specific recombination, a cellular reaction that creates knots and links out of circular double stranded DNA molecules. The model is used to predict and characterise the topology of the products of a reaction on double stranded DNA twist knots. It is shown that all such products fall into a small family of Montesinos knots and links, meaning that the knot and link type of possible products is significantly reduced, thus aiding their experimental...

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