Bulletin of Mathematical Biology

doi: 10.1007/BF02459964pmid: N/A

Segel, Lee

doi: 10.1007/BF02459954pmid: N/A

Tyson, John J.

doi: 10.1007/BF02459956pmid: N/A

Lapidus, I. Richard

doi: 10.1007/BF02459955pmid: N/A

De, S. S.

doi: 10.1007/BF02459957pmid: 3607333

Abstract A stochastic model for the population regulated by logistic growth and spreading in a given region of two-or three-dimensional space has been introduced. For many-species population the interactions among the species have also been icorporated in this model. From the random variables that describe stochastic processes of a Wiener type the space-dependent random population densities have been formed and shown to satisfy the Langevin equations. The Fokker-Planck equation corresponding to these Langevin equations has been approximately solved for the transition probability of the population spreading and it has been found that such approximate expressions of the transition probability depend on the solutions of the deterministic equations of the diffusion model with logistic growth and interactions. Also, the stationary or equilibrium solutions of the Fokker-Planck equation together with the special discussion on the pattern of single-species population spreading have been made.

Ehresmann, A. C.;Vanbremeersch, J. -P.

doi: 10.1007/BF02459958pmid: 3607335

Abstract The notion of an evolutive hierarchical system proposed in this paper is a mathematical model for systems, like organisms, with more or less complex objects. This model, based on category theory, retains the following characteristics of natural systems: they have an internal organization consisting of components with interrelations; they maintain their organization in time though their components are changing; their components are divided into several levels corresponding to the increasing complexity of their own organization, and the system may be studied at any of these levels (e.g. molecular, cellular...). The state of the system at a given instant is modeled by a category whose objects are its components, the state transition by a functor, a complex object by the (direct) limit of a pattern of linked objects (which describes its internal organization). The properties of limits in a category make it possible to ‘measure’ the emergence of properties for a complex object with respect to its components, and to reduce the study of a hierarchical system to that of its components of the lowest degree and their links. Categorical constructions describe the formation of a hierarchical evolutive system stepwise, by means of the operations: absorption of external objects, destruction of some components, formation of new complex objects.

Liang, Z.;Hart, H.

doi: 10.1007/BF02459959pmid: N/A

Abstract A series of Bayesian image processing algorithms which incorporate various classes ofa priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when thea priori information about a source distribution φ j is solely that a non-vanishing probability for each element value φ j exists only in some finite interval,a j ≤φ j ≤φ j . Bayesian image processing equations for thea priori source information that all φ j are finite -∞<φ j <∞ and each φ j distribution has a defined mean φ j and a defined variance σ j are derived. The Bayesian image processing equations are also derived when thea priori source information is that all φ j ≥0 and that each φ j distribution has a defined mean φ j and a defined variance σ j . The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.

Hart, H.;Liang, Z.

doi: 10.1007/BF02459960pmid: N/A

Abstract Bayesian image processing formalisms which incorporatea priori information about valued-uncorrelated and valued-correlated (patterned) source distributions are introduced and the corresponding iterative algorithms are derived using the EM technique. Striking improvement in image processing is demonstrated when applying these algorithms to Poisson and Gaussian randomized data in one-dimensional cases.

Jürgensen, Helmut;Lindenmayer, Aristid

doi: 10.1007/BF02459961pmid: N/A

Abstract An algorithmic formulation is presented for the inference procedure concerning lineage models. The problem is to find lineage rules from observed sequences of tree structures under the assumption that no interactions take place in the course of development and that sufficiently frequent observations are available at equal time intervals. The underlying structural pattern is taken to be a OL system, and the goal is to find propagating and deterministic OL schemes with minimal properties satifsying certain biological reliance criteria. Upper bounds have been found for the complexity of the inference algorithms.

Baishya, M. C.;Chakraborti, C. G.

doi: 10.1007/BF02459962pmid: 3607334

Abstract A statistical theory of non-equilibrium fluctuation in Volterra-Lotka systems has been presented on the basis of the technique of statistical linearization of non-linear coupled stochastic differential equations.