Modelling imperfect time intervals in a two-dimensional space
Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments
This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the...
Models combination in (max,+) algebra for the implementation of a simulation and analysis software
This paper presents a modeling methodology in (max,+) algebra which has been developed in order to implement a modulary software for the simulation and the analysis of electronic cards production lines. More generally, this approach may be applied to hybrid flowshop type manufacturing systems.
Multiobjective optimal control of HIV dynamics.
Multiphase and Multiscale Trends in Cancer Modelling
While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.
Multiscale modelling of sound propagation through the lung parenchyma
In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium (the parenchyma) with millions of alveoli filled with air. Transmission of sound through the lung above 1 kHz is known to be highly frequency-dependent. We pursue the key idea that the viscoelastic parenchyma structure is highly heterogeneous on the small scale ε and use two-scale homogenization techniques to derive effective...
Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy.
National and ideological influence in the European Parliament
Neuro-rough-fuzzy approach for regression modelling from missing data
Real life data sets often suffer from missing data. The neuro-rough-fuzzy systems proposed hitherto often cannot handle such situations. The paper presents a neuro-fuzzy system for data sets with missing values. The proposed solution is a complete neuro-fuzzy system. The system creates a rough fuzzy model from presented data (both full and with missing values) and is able to elaborate the answer for full and missing data examples. The paper also describes the dedicated clustering algorithm. The...
New challenges in dynamical systems: The networked case
This paper describes new technical challenges that arise from networking dynamical systems. In particular, the paper takes a look at the underlying phenomena and the resulting modeling problems that arise in such systems. Special emphasis is placed on the problem of synchronization, since this problem has not received as much attention in the literature as the phenomena of packet drop, delays, etc. The paper then discusses challenges arising in prominent areas such as congestion control, sensor...
New formula for the failure/repair frequency of multi-state monotone systems and its applications
Noise Shaping in Neural Populations with Global Delayed Feedback
The interplay between intrinsic and network dynamics has been the focus of many investigations. Here we use a combination of theoretical and numerical approaches to study the effects of delayed global feedback on the information transmission properties of neural networks. Specifically, we compare networks of neurons that display intrinsic interspike interval correlations (nonrenewal) to networks that do not (renewal). We find that excitatory and...
Non-exchangeable random variables, Archimax copulas and their fitting to real data
The aim of this paper is to open a new way of modelling non-exchangeable random variables with a class of Archimax copulas. We investigate a connection between powers of generators and dependence functions, and propose some construction methods for dependence functions. Application to different hydrological data is given.
Notes on a hierarchical theory of systems and applications
Numerical modelling and simulation of liquid-impelled loop reactor.
Observers for Canonic Models of Neural Oscillators
We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural membranes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar...
On attaining the prescribed quality of a controlled fourth order system
On mathematical models and the role of the mathematics in knowledge of reality
On network models and the symbolic solution of network equations
This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development of this area. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified so as to obtain an admittance representation for all kinds of multi-ports. N-dimensional networks are...
On the derivation of a state-space model of a periodic process described by recurrent equations