In this paper we present the extension of the kinetic logic proposed by René Thomas for analysis of genetic regulatory gene networks. We consider the case with a Gaussian noise added to the regulation function and propose a method of analyzing the resulting model with a discrete time Markov model.
We consider a system of stochastic differential equations which models the dynamics of two populations living in symbiosis. We prove the existence, uniqueness and positivity of solutions. We analyse the long-time behaviour of both trajectories and distributions of solutions. We give a biological interpretation of the model.
A stochastic generalized Born (GB) solver is presented which can give predictions of energies arbitrarily close to those that would be given by exact effective GB radii, and, unlike analytical GB solvers, these errors are Gaussian with estimates that can be easily obtained from the algorithm. This method was tested by computing the electrostatic solvation energies (ΔGsolv) and the electrostatic binding energies (ΔGbind) of a set of DNA-drug complexes, a set of protein-drug complexes, a set of protein-protein...
We present a model of symbiosis given by a system of stochastic differential equations. We consider a situation when the same factor influences both populations or only one population is stochastically perturbed. We analyse the long-time behaviour of the solutions and prove the asymptoptic stability of the system.
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...
In this paper a fuzzy relation-based framework is shown to be suitable to describe not only knowledge-based medical systems, explicitly using fuzzy approaches, but other ways of knowledge representation and processing. A particular example, the practically tested medical expert system Disco, is investigated from this point of view. The system is described in the fuzzy relation-based framework and compared with CADIAG-II-like systems that are a “pattern” for computer-assisted diagnosis systems based...
A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...
A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...
This paper develops and analyzes a time-dependent optimal stopping problem and its application to the decision making process concerning organ transplants. Offers (organs for transplant) appear at jump times of a Poisson process. The values of the offers are i.i.d. random variables with a known distribution function. These values express the degree of histocompatibility between the donor and the recipient. The sequence of offers is independent of the jump times of the Poisson process. The decision...