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Spatial Dynamics of Contact-Activated Fibrin Clot Formation in vitro and in silico in Haemophilia B: Effects of Severity and Ahemphil B Treatment

A. A. Tokarev, Yu. V. Krasotkina, M. V. Ovanesov, M. A. Panteleev, M. A. Azhigirova, V. A. Volpert, F. I. Ataullakhanov, A. A. Butilin (2010)

Mathematical Modelling of Natural Phenomena

Spatial dynamics of fibrin clot formation in non-stirred system activated by glass surface was studied as a function of FIX activity. Haemophilia B plasma was obtained from untreated patients with different levels of FIX deficiency and from severe haemophilia B patient treated with FIX concentrate (Ahemphil B) during its clearance with half-life t1/2=12 hours. As reported previously (Ataullakhanov et al. Biochim Biophys Acta 1998; 1425: 453-468), clot growth in space showed two distinct phases:...

Spatiotemporal Dynamics in a Spatial Plankton System

R. K. Upadhyay, W. Wang, N. K. Thakur (2010)

Mathematical Modelling of Natural Phenomena

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially...

Spatio-Temporal Modelling of the p53–mdm2 Oscillatory System

K. E. Gordon, I. M.M. van Leeuwen, S. Laín, M. A.J. Chaplain (2009)

Mathematical Modelling of Natural Phenomena

In this paper we investigate the role of spatial effects in determining the dynamics of a subclass of signalling pathways characterised by their ability to demonstrate oscillatory behaviour. To this end, we formulate a simple spatial model of the p53 network that accounts for both a negative feedback and a transcriptional delay. We show that the formation of protein density patterns can depend on the shape of the cell, position of the nucleus, and the protein diffusion rates. The temporal...

Stability Analysis of Cell Dynamics in Leukemia

H. Özbay, C. Bonnet, H. Benjelloun, J. Clairambault (2012)

Mathematical Modelling of Natural Phenomena

In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized...

Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes

Yanling Tian (2014)

Applications of Mathematics

A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant steady state is studied by analyzing the eigenvalues. Some simple and easily verifiable sufficient conditions for global stability are obtained by virtue of the stability of the related FDE and some monotonous iterative sequences. Numerical simulations and reasonable biological explanations are carried out to illustrate the main results and the justification...

Stability of unique pseudo almost periodic solutions with measure

Boulbaba Ghanmi, Mohsen Miraoui (2020)

Applications of Mathematics

By means of the fixed-point methods and the properties of the μ -pseudo almost periodic functions, we prove the existence, uniqueness, and exponential stability of the μ -pseudo almost periodic solutions for some models of recurrent neural networks with mixed delays and time-varying coefficients, where μ is a positive measure. A numerical example is given to illustrate our main results.

Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems

Sachiko Ishida, Tomomi Yokota (2023)

Archivum Mathematicum

This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.

Stationary solutions of aerotaxis equations

Piotr Knosalla, Tadeusz Nadzieja (2015)

Applicationes Mathematicae

We study the existence and uniqueness of the steady state in a model describing the evolution of density of bacteria and oxygen dissolved in water filling a capillary. The steady state is a stationary solution of a nonlinear and nonlocal problem which depends on the energy function and contains two parameters: the total mass of the colony of bacteria and the concentration (or flux) of oxygen at the end of the capillary. The existence and uniqueness of solutions depend on relations between these...

Statistical analysis of diabetes mellitus

Hilmar Drygas (2009)

Discussiones Mathematicae Probability and Statistics

This paper deals with an application of regression analysis to the regulation of the blood-sugar under diabetes mellitus. Section 2 gives a description of Gram-Schmidt orthogonalization, while Section 3 discusses the difference between Gauss-Markov estimation and Least Squares Estimation. Section 4 is devoted to the statistical analysis of the blood-sugar during the night. The response change of blood-sugar is explained by three variables: time, food and physical activity ("Bewegung"). At the beginning...

Statistical models to study subtoxic concentrations for some standard mutagens in three colon cancer cell lines.

Xavier Bardina, Laura Fernández, Elisabet Piñeiro, Jordi Surrallés, Antonia Velázquez (2006)

SORT

The aim of this work is to propose models to study the toxic effect of different concentrations of some standard mutagens in different colon cancer cell lines. We find estimates and, by means of an inverse regression problem, confidence intervals for the subtoxic concentration, that is the concentration that reduces by thirty percent the number of colonies obtained in the absence of mutagen.

Statistical tools for discovering pseudo-periodicities in biological sequences

Bernard Prum, Élisabeth de Turckheim, Martin Vingron (2010)

ESAIM: Probability and Statistics


Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics...

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