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PubMed1978

[Mathematical model of epidemiology of an anthropozoonose: brucellosis (author's transl)].

We are trying to make a model of the epidemiology of Brucellosis by using a two-type branching process. In this text, we are studying the probability of extinction. A complete study on the theory of process with a finite number of types was made by SEVAST'YANOV (1951) [6]. The study of the behaviour of such a process is made with the help of the generating function of the number of infected animals by a single animal. To express this generating function, we start with the same hypothesis as BARTOSZYNSKI [2] (1965) when he makes an interhuman epidemic model by a simple branching process of GALTON-WATSON. However these hypothesis will be modified in order to adapt them to the types of Brucellosis contamination.

Animals↗
PubMedDate not supplied

[Some new perspectives on V. I. Deshcherevskiy's kinetic theory of muscle contraction].

Deshcherevsky's kinetic theory of muscle contraction (Deshcherevsky, 1968, 1971) is considered in the light of the modern experimental data. The data are discussed, which support the validity of some propositions and conclusions of the theory, including the postulate on the negligibly small probability of pulling cross-bridge detachment. It is shown that if this postulate is accepted and the distance between the neighbouring actin sites for the given myosin cross-bridge attachment on the actin filament is taken as an actin filament half-turn (Sydorenko, 1982, 1984), then simple explanations, which don't contradict the cross-bridge hypothesis of force generation, could be given to a number of muscle behaviour features such as the high efficiency, stepwise shortening, repeated tension recovery after repeated forced step-wise shortening of activated muscle with the time-interval less than 10 ms, step-size up to 90nm powered by a single ATP molecule and so on.

Adenosine Triphosphate↗
PubMed1995

Genomic imprinting and cancer.

Imprinting is vital for normal development, and disruption of imprinting mechanisms on syntenic chromosomes gives very similar phenotypes in mouse and humans. In addition, disruption of normal imprinting provides a plausible explanation for preferential LOH in some embryonal tumours. Moreover, there is evidence that in Wilms' tumour, dysregulation of specific imprinted genes may give rise to the cancer phenotype. Many more questions regarding genomic imprinting need to be answered before the associations described in this review can be properly understood. The most basic issues, such as when and how the imprint is established, can still only be speculated upon. Further study of new imprinted genes and the relationship between their domains and differential replication may show us higher control mechanisms than methylation alone. It remains to be seen if these epigenetic modifications are amenable to therapeutic change in the treatment of inherited syndromes and cancer, or if they can be used to assess individuals at risk of disease. Until then it is probably unwise to speculate on a single unifying theory that explains why a subset of the genome shows such a peculiar non-Mendelian form of inheritance.

Alleles↗
PubMed2000

Semiclassical calculation of chemical reaction dynamics via wavepacket correlation functions.

Calculation of chemical reaction dynamics is central to theoretical chemistry. The majority of calculations use either classical mechanics, which is computationally inexpensive but misses quantum effects, such as tunneling and interference, or quantum mechanics, which is computationally expensive and often conceptually opaque. An appealing middle ground is the use of semiclassical mechanics. Indeed, since the early 1970s there has been great interest in using semiclassical methods to calculate reaction probabilities. However, despite the elegance of classical S-matrix theory, numerical results on even the simplest reactive systems remained out of reach. Recently, with advances both in correlation function formulations of reactive scattering as well as in semiclassical methods, it has become possible for the first time to calculate reaction probabilities semiclassically. The correlation function methods are contrasted with recent flux-based methods, which, although providing somewhat more compact expressions for the cumulative reactive probability, are less compatible with semiclassical implementation.

Journal Article↗
PubMed2006

Theory for non-equilibrium statistical mechanics.

This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is not an extremum. The relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life.

Algorithms↗
PubMed2003

A causal-model theory of conceptual representation and categorization.

This article presents a theory of categorization that accounts for the effects of causal knowledge that relates the features of categories. According to causal-model theory, people explicitly represent the probabilistic causal mechanisms that link category features and classify objects by evaluating whether they were likely to have been generated by those mechanisms. In 3 experiments, participants were taught causal knowledge that related the features of a novel category. Causal-model theory provided a good quantitative account of the effect of this knowledge on the importance of both individual features and interfeature correlations to classification. By enabling precise model fits and interpretable parameter estimates, causal-model theory helps place the theory-based approach to conceptual representation on equal footing with the well-known similarity-based approaches.

Causality↗
PubMed1998

Multilayer neural networks and Bayes decision theory.

There are many applications of multilayer neural networks to pattern classification problems in the engineering field. Recently, it has been shown that Bayes a posteriori probability can be estimated by feedforward neural networks through computer simulation. In this paper, Bayes decision theory is combined with the approximation theory on three-layer neural networks, and the two-category n-dimensional Gaussian classification problem is studied. First, we prove theoretically that three-layer neural networks with at least 2n hidden units have the capability of approximating the a posteriori probability in the two-category classification problem with arbitrary accuracy. Second, we prove that the input-output function of neural networks with at least 2n hidden units tends to the a posteriori probability as Back-Propagation learning proceeds ideally. These results provide a theoretical basis for the study of pattern classification by computer simulation.

Journal Article↗
PubMed2001

Probability density function learning by unsupervised neurons.

In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals.

Algorithms↗
PubMed2006

Mesoscopic theory of critical fluctuations in isolated granular gases.

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed only by vorticity fluctuations that also lead to a renormalization of the average total energy. The theory predicts a power-law divergent behavior of the scaled second moment of the fluctuations, and a scaling property of their probability distribution, both in agreement with simulations results. A more quantitative comparison between theory and simulation for the critical amplitudes and the form of the scaling function is also carried out.

Computer Simulation↗
PubMed2005

Electron localization function as information measure.

The conditional two-electron probability function, which defines the electron localization function (ELF) of Becke and Edgecombe in the Kohn-Sham theory, is interpreted as the nonadditive (interorbital) Fisher information contained in the electron distribution. The probability normalization considerations suggest a use of the related information measure defined in terms of the unity-normalized probability distributions (shape factors of the electron densities), as the key ingredient of the modified information-theoretic ELF. This modified Fisher information density is validated by a comparison with the original two-electron probability function. Illustrative applications to typical molecular systems demonstrate the adequacy of the modified information-theoretic ELF in extracting the key features of the electron distributions in molecules. The overall Fisher information itself and the associated information-distance quantities are also proposed as complementary localization functions.

Journal Article↗
PubMed1979

Decision rules and signal detectability in a reinforcement-density discrimination.

Two probabilistic schedules of reinforcement, one richer in reinforcement, the other leaner, were overlapping stimuli to be discriminated in a choice situation. One of two schedules was in effect for 12 seconds. Then, during a 6-second choice period, the first left-key peck was reinforced if the richer schedule had been in effect, and the first right-key peck was reinforced if the leaner schedule had been in effect. The two schedule stimuli may be viewed as two binomial distributions of the number of reinforcement opportunities. Each schedule yielded different frequencies of 16 substimuli. Each substimulus had a particular type of outcome pattern for the 12 seconds during which a schedule was in effect, and consisted of four consecutive light-cued 3-second T-cycles, each having 0 or 1 reinforced center-key pecks. Substimuli therefore contained 0 to 4 reinforcers. On any 3-second cycle, the first center-key peck darkened that key and was reinforced with probability .75 or .25 in the richer or leaner schedules, respectively. In terms of the theory of signal detection, detectability neared the maximum possible d' for all four pigeons. Left-key peck probability increased when number of reinforcers in a substimulus increased, when these occurred closer to choice, or when pellets were larger for correct left-key pecks than for correct right-key pecks. Averaged over different temporal patterns of reinforcement in a substimulus, substimuli with the same number of reinforcers produced choice probabilities that matched relative expected payoff rather than maximized one alternative.

Journal Article↗
PubMed1979

A clinical epidemiologic study of hyperphenylalaninemia.

Thirty-nine cases of hyperphenylalaninemia from four diagnostic-treatment centers in Ohio were investigated in a retrospective cohort analysis. None of the centers is included in the PKU Collaborative Study. Epidemiologic analysis showed that early treatment is effective and that degree of dietary control (within limits) does not affect the probability of retardation or borderline retardation. Regression analysis supported the critical period hypothesis rather than the maximum concentration theory. Exposure to serum phenylalanine of 23--27 mg./dl. corresponds to 50 per cent probability retardation. The clinical epidemiologic approach offers an alternative methodology for designing collaborative studies.

Child, Preschool↗
PubMed1996

Aids, violence and behavioral coding: information theory, risk behavior and dynamic process on core-group sociogeographic networks.

Elsewhere we have presented a traveling-wave analysis of HIV transmission on a tightly self-interactive, geographically-focused core group social network (Wallace R. Soc. Sci. Med. 32, 847, 1991; Soc. Sci. Med. 33, 1155, 1991; Environ. Plan. A. 26, 767, 1994; Wallace R. and Fullilove M. Environ. Plan. A. 23, 1701 1991). Here we reanalyze the problem in probability space and recover a close analog of the Shannon Coding Theorem of information theory. Subsequent direct application of information-theoretic methods provides striking insight regarding the spread of disease along the sociogeographic networks of marginalized subgroups, suggesting that 'risk behaviors' for infection may constitute essential components of a behavioral code for the transmission of information within the noisy channel of a marginalized community's social networks. The code's form, including the incorporation of risk behaviors, arises as a direct consequence of the external oppressive forces which structure marginalization. This viewpoint suggests an explanation of the sometime-observed rapid transmission of both infection and of control strategies for infection along the same network, but suggests further that if risk behaviors are indeed parts of a behavioral code for the transmission of group norms, statements of individual worth or resource sharing, then high rates of relapse are inevitable, given the persistence of the external oppression which gives those behaviors symbolic value. We suggest that violent acts in particular may emerge as key behavioral symbols for 'sending a message' in socially disorganized communities, implying that school-based or other individual-oriented harm reduction strategies for violence prevention, in the absence of a comprehensive, multifactorial reform program, cannot significantly reverse the effects of continuing economic and social constraints or of public policies of planned shrinkage and benign neglect, factors primarily responsible for the disorganization of urban minority communities within the United States.

Acquired Immunodeficiency Syndrome↗
PubMed2006

Visual complexity: a review.

The idea of visual complexity, the history of its measurement, and its implications for behavior are reviewed, starting with structuralism and Gestalt psychology at the beginning of the 20th century and ending with visual complexity theory, perceptual learning theory, and neural circuit theory at the beginning of the 21st. Evidence is drawn from research on single forms, form and texture arrays and visual displays. Form complexity and form probability are shown to be linked through their reciprocal relationship in complexity theory, which is in turn shown to be consistent with recent developments in perceptual learning and neural circuit theory. Directions for further research are suggested.

Humans↗
PubMed1994

Reduction-of-dimensionality kinetics at reaction-limited cell surface receptors.

It has been suggested for several years that reactions between ligands and cell surface receptors can be speeded up by nonspecific adsorption of the ligand to the cell surface followed by two-dimensional surface diffusion to the receptor, a mechanism referred to as "reduction-of-dimensionality" (RD) rate enhancement. Most of the theoretical treatments of this and related problems have assumed that the receptor is an irreversibly absorbing perfect sink. Such receptors induce a depletion zone of ligand probability density around themselves. The reaction rate in this case (called "diffusion-limited") is limited only by the time required for ligands to diffuse through this depletion zone. In some cases, however, the receptor may be far from "perfect" such that a collision with a ligand only rarely leads to binding. Receptors then do not create significant local depletion zones of ligand probability density, and the reaction rate becomes strongly affected by the (small) probability of reaction success per diffusive encounter (the "reaction-limited" case). This article presents a simple theory of RD rate enhancement for reaction-limited receptors that are either reversible or irreversible binders. In contrast to the diffusion-limited theories, the reaction-limited theory presented here: (a) differs quantitatively from diffusion-limited models; (b) is simple and algebraic in closed form; (c) exhibits significant rate enhancement in some realistic cases; (d) depends strongly on the actual Brownian rather than pure diffusive nature of the ligand's motion; (e) depends (for irreversibly binding receptors only) on the kinetic rates (not just equilibria) of reversible adsorption to nontarget regions, in contrast to some previous approximate theories of reduction of dimensionality; and (f) is applicable to actual ligand/receptor systems with binding success probabilities at the opposite extreme from the perfect sink/diffusion-limited models.

Adsorption↗
PubMed1992

Extending the stochastic two-stage model of carcinogenesis to include self-regulation of the nonmalignant cell population.

One of the challenges of introducing greater biological realism into stochastic models of cancer induction is to find a way to represent the homeostatic control of the normal cell population over its own size without complicating the analysis too much to obtain useful results. Current two-stage models of carcinogenesis typically ignore homeostatic control. Instead, a deterministic growth path is specified for the population of "normal" cells, while the population of "initiated" cells is assumed to grow randomly according to a birth-death process with random immigrations from the normal population. This paper introduces a simple model of homeostatically controlled cell division for mature tissues, in which the size of the nonmalignant population remains essentially constant over time. Growth of the nonmalignant cell population (normal and initiated cells) is restricted by allowing cells to divide only to fill the "openings" left by cells that die or differentiate, thus maintaining the constant size of the nonmalignant cell population. The fundamental technical insight from this model is that random walks, rather than birth-and-death processes, are the appropriate stochastic processes for describing the kinetics of the initiated cell population. Qualitative and analytic results are presented, drawn from the mathematical theories of random walks and diffusion processes, that describe the probability of spontaneous extinction and the size distribution of surviving initiated populations when the death/differentiation rates of normal and initiated cells are known. The constraint that the nonmalignant population size must remain approximately constant leads to much simpler analytic formulas and approximations, flowing directly from random walk theory, than in previous birth-death models.(ABSTRACT TRUNCATED AT 250 WORDS)

Cell Death↗
PubMed2003

Hypothesis testing and theory evaluation at the boundaries: surprising insights from Bayes's theorem.

Because the probability of obtaining an experimental finding given that the null hypothesis is true [p(F\H0)] is not the same as the probability that the null hypothesis is true given a finding [p(H0\F)], calculating the former probability does not justify conclusions about the latter one. As the standard null-hypothesis significance-testing procedure does just that, it is logically invalid (J. Cohen, 1994). Theoretically, Bayes's theorem yields p(H0\F), but in practice, researchers rarely know the correct values for 2 of the variables in the theorem. Nevertheless, by considering a wide range of possible values for the unknown variables, it is possible to calculate a range of theoretical values for p(H0\F) and to draw conclusions about both hypothesis testing and theory evaluation.

Bayes Theorem↗
PubMed2003

Folding-unfolding of FN-III domains in tenascin: an elastically coupled two-state system.

In a single-molecule atomic force microscopy (AFM) experiment, the tenascin molecule is stretched by an external force causing an elongation which is due to the unfolding of the FN-III modules. The features of the force-extension curves depend on the pulling speed and show a saw-tooth pattern (lower speeds) or a smooth pattern (higher speeds). In any case, the unfolded domains are elastically coupled to the unfolded modules, acting as transmitters of the external force. In this communication, the folding-unfolding process of the FN-III domains in tenascin is studied using reaction rate theory and a simple two-state model. The main hypothesis of the study is that, at microscopic level, the force needed to unfold a domain and the unfolding rate (unfolding velocity) can mimic the macroscopic process of measurement by AFM. As the external force is applied, the probability of unfolding increases as dictated by the reaction rate theory. Within this context, a relationship between the unfolding force and the unfolding velocity is obtained. The latter relation will describe microscopically the process in a phenomenological fashion. Moreover, while relating the results of this study with other experimental (AFM measurements) and theoretical (Monte Carlo simulations) data, we found that the graph of unfolding force-unfolding velocity is similar to that of external force-pulling velocity. The refolding process can also be studied within this model and the results show similar trends. The latter suggests a generic and universal behavior of such kind of molecular domains at least in the light of the proposed model.

Computer Simulation↗