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Nanonetworks: The graph theory framework for modeling nanoscale systems

Jelena Živkovic, Bosiljka Tadic (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Nanonetwork is defined as a mathematical model of nanosize objects with biological, physical and chemical attributes, which are interconnected within certain dynamical process. To demonstrate the potentials of this modeling approach for quantitative study of complexity at nanoscale, in this survey, we consider three kinds of nanonetworks: Genes of a yeast are connected by weighted links corresponding to their coexpression along the cell cycle; Gold nanoparticles, arranged on a substrate, are linked...

Necessary Optimality Conditions for a Lotka-Volterra Three Species System

N. C. Apreutesei (2010)

Mathematical Modelling of Natural Phenomena

An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval.

Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system

Jimoh Olarewaju Pedro, Olurotimi Akintunde Dahunsi (2011)

International Journal of Applied Mathematics and Computer Science

This paper presents the design of a neural network based feedback linearization (NNFBL) controller for a two degree-offreedom (DOF), quarter-car, servo-hydraulic vehicle suspension system. The main objective of the direct adaptive NNFBL controller is to improve the system's ride comfort and handling quality. A feedforward, multi-layer perceptron (MLP) neural network (NN) model that is well suited for control by discrete input-output linearization (NNIOL) is developed using input-output data sets...

Neural network based identification of hysteresis in human meridian systems

Yonghong Tan, Ruili Dong, Hui Chen, Hong He (2012)

International Journal of Applied Mathematics and Computer Science

Developing a model based digital human meridian system is one of the interesting ways of understanding and improving acupuncture treatment, safety analysis for acupuncture operation, doctor training, or treatment scheme evaluation. In accomplishing this task, how to construct a proper model to describe the behavior of human meridian systems is one of the very important issues. From experiments, it has been found that the hysteresis phenomenon occurs in the relations between stimulation input and...

Neural network segmentation of images from stained cucurbits leaves with colour symptoms of biotic and abiotic stresses

Jarosław Gocławski, Joanna Sekulska-Nalewajko, Elżbieta Kuźniak (2012)

International Journal of Applied Mathematics and Computer Science

The increased production of Reactive Oxygen Species (ROS) in plant leaf tissues is a hallmark of a plant's reaction to various environmental stresses. This paper describes an automatic segmentation method for scanned images of cucurbits leaves stained to visualise ROS accumulation sites featured by specific colour hues and intensities. The leaves placed separately in the scanner view field on a colour background are extracted by thresholding in the RGB colour space, then cleaned from petioles to...

Neuromorphic features of probabilistic neural networks

Jiří Grim (2007)

Kybernetika

We summarize the main results on probabilistic neural networks recently published in a series of papers. Considering the framework of statistical pattern recognition we assume approximation of class-conditional distributions by finite mixtures of product components. The probabilistic neurons correspond to mixture components and can be interpreted in neurophysiological terms. In this way we can find possible theoretical background of the functional properties of neurons. For example, the general...

New Computational Tools for Modeling Chronic Myelogenous Leukemia

M. M. Peet, P. S. Kim, S.-I. Niculescu, D. Levy (2009)

Mathematical Modelling of Natural Phenomena

In this paper, we consider a system of nonlinear delay-differential equations (DDEs) which models the dynamics of the interaction between chronic myelogenous leukemia (CML), imatinib, and the anti-leukemia immune response. Because of the chaotic nature of the dynamics and the sparse nature of experimental data, we look for ways to use computation to analyze the model without employing direct numerical simulation. In particular, we develop several tools using Lyapunov-Krasovskii analysis that allow...

New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke*

Max Duarte, Marc Massot, Stéphane Descombes, Christian Tenaud, Thierry Dumont, Violaine Louvet, Frédérique Laurent (2011)

ESAIM: Proceedings

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts, spatially very localized. A new resolution strategy was recently introduced ? that combines...

New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model

Bingwen Liu (2015)

Annales Polonici Mathematici

This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays, which is defined on the nonnegative function space. Under appropriate conditions, we establish some criteria to ensure that all solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give an example with numerical simulations to illustrate our main results.

New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations

Mimia Benhadri, Tomás Caraballo (2022)

Mathematica Bohemica

This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.

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