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Front Matter |
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Abstract
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,The Prediction of a Protein and Nucleic Acid Structure: Problems and Prospects, |
Minoru Kanehisa,Charles DeLisi |
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Abstract
Recent advances in DNA and protein-sequencing technologies have made an increasing number of primary structures available for theoretical investigations. The prediction of a higher-order protein, and nucleic acid structure in particular, is an area where computational approaches will be able to complement the lack of experimental observations. We review some of the problems related to structure predictions: sequence homology searches, secondary structure prediction in RNAs, and regular structure prediction in proteins. The first two are mathematically well-defined problems, for it is not usually necessary to consider long-range interactions. The solution to a smaller segment is a part of the solution to the entire sequence. Thus, the problem can be solved by dynamic programming algorithms. The prediction of protein structures poses a more complex combinatorial problem, as illustrated in our statistical mechanical treatment. A promising approximation is to calculate locally optimal structures stabilized by relatively short-range interactions, and then to include longer-range effects as interactions between the locally optimal structures.
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,Association Rates of Diffusion-Controlled Reactions in Two Dimensions, |
Alberto Gandolfi,Anna Gerardi,Federico Marchetti |
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Abstract
A detailed analysis of the main results concerning mathematical models of diffusion-controlled reactions in two dimensions is presented. Specific emphasis is placed on methods for evaluating association rates. After a review of planar models, the effects due to the curvature of the ambient space are investigated. Finally, different possible choices of boundary conditions are considered, and suggestions are given on their aptness to model different physicochemical situations.
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,Some Stochastic Models in Immunology, |
Catherine A. Macken,Alan S. Perelson |
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Abstract
Conditional probability arguments and the theory of continuous-time Markov chains are used to develop models for the kinetics of a cell-mediated cytotoxic reaction. While the models are conceptually simple, when fitted to data, they lead to surprising insights into the mechanisms of the immune response. Based on examples and discussion, we demonstrate the potential for creative and relevant application of mathematics within the rapidly developing field of immunology.
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,Stochastic Formulation of Neural Interaction, |
P. I. M. Johannesma,H. F. P. van den Boogaard |
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Abstract
Starting from basic physiological evidence, stochastic equations are formulated for the interaction between neurons. The generator potential is formed by deterministic linear spatio-temporal integration of action potentials, while the action potentials are considered as stochastic all-or-none events generated under the influence of the local instantaneous value of generator potential and generator current. Properties of the trajectories in state space are indicated. A neural partition function is defined and shown to be related to a statistical description of the neural activity pattern. The relevance of the mathematical formulation is indicated for the relation of neural correlation and synaptic connectivity.
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,Qualitative and Numerical Analysis of a Class of Prey-Predator Models, |
Maurizio Falcone,Giorgio Israel |
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Abstract
We consider a problem of the dynamics of prey-predator populations suggested by the content of a letter of the biologist Umberto D’Ancona to Vito Volterra. The main feature of the problem is the special type of competition between predators of the same species as well as of different species. Two classes of cases are investigated: a first class in which the behaviour of the predator is ‘blind’ and the second one in which the behaviour is `intelligent’. A qualitative analysis of the dynamical systems under consideration is followed by a numerical analysis of the most significant cases.
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,Topological Inverse Problem for Oscillating Systems and its Application, |
Yoshihiro Shikata,Satoru Watanabe |
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Abstract
This note is just an introduction to a problem to find a topological type of potentials from given data and a problem to see which data or experiment is necessary to obtain the topological classification of practical use. Here we propose a method of hysteresis on the space of Fourier coefficients, which reduces to the theory of resonance curves in a very special case. The direction of the hysteresis curve is proved to characterize the (first) topological type of potential. In contrast with the usual direction, which is common to the transistor oscillator, the unusual direction is found in EEG experiments (on humans) called photic driving experiments on a rhythm.
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,Book Reviews, |
Johan Grasman,Robert M. May |
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Abstract
This book stems from a course on ‘mathematical models in biology’ that was given in the spring of 1978 at the Weizmann Institute of Science. The purpose of this course (and of the book) was to demonstrate the use of mathematical models to experimental biologists. It can be seen as a survey of the present state of art in mathematical biology for a community of biologists with a restricted knowledge of the theory of differential equations.
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发表于 2025-3-21 17:07:43
