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PubMed2002

Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm.

We developed a new image reconstruction algorithm for magnetic resonance electrical impedance tomography (MREIT). MREIT is a new EIT imaging technique integrated into magnetic resonance imaging (MRI) system. Based on the assumption that internal current density distribution is obtained using magnetic resonance imaging (MRI) technique, the new image reconstruction algorithm called J-substitution algorithm produces cross-sectional static images of resistivity (or conductivity) distributions. Computer simulations show that the spatial resolution of resistivity image is comparable to that of MRI. MREIT provides accurate high-resolution cross-sectional resistivity images making resistivity values of various human tissues available for many biomedical applications.

Algorithms↗
PubMed1987

Statistical inference on spontaneous neuronal discharge patterns. I. Single neuron.

A statistical analysis was performed on extracellularly recorded spike trains of spontaneously active mesencephalic reticular neurons of rats. Only stationary records were used for detailed examination. The moments of interspike intervals were computed, hypothesis of renewal process and its specific forms was tested. Implications for statistical methodology are considered on the basis of the results. The main emphasis is laid on the connection between experimental results and stochastic neuronal models.

Animals↗
PubMed1998

Temporal precision of the encoding of motion information by visual interneurons.

BACKGROUND: There is much controversy about the timescale on which neurons process and transmit information. On the one hand, a vast amount of information can be processed by the nervous system if the precise timing of individual spikes on a millisecond timescale is important. On the other hand, neuronal responses to identical stimuli often vary considerably and stochastic response fluctuations can exceed the mean response amplitude. Here, we examined the timescale on which neural responses could be locked to visual motion stimuli. RESULTS: Spikes of motion-sensitive neurons in the visual system of the blowfly are time-locked to visual motion with a precision in the range of several tens of milliseconds. Nevertheless, different motion-sensitive neurons with largely overlapping receptive fields generate a large proportion of spikes almost synchronously. This precision is brought about by stochastic rather than by motion-induced membrane-potential fluctuations elicited by the common peripheral input. The stochastic membrane-potential fluctuations contain more power at frequencies above 30-40 Hz than the motion-induced potential changes. A model of spike generation indicates that such fast membrane-potential changes are a major determinant of the precise timing of spikes. CONCLUSIONS: The timing of spikes in neurons of the motion pathway of the blowfly is controlled on a millisecond timescale by fast membrane-potential fluctuations. Despite this precision, spikes do not lock to motion stimuli on this timescale because visual motion does not induce sufficiently rapid changes in the membrane potential.

Action Potentials↗
PubMed1996

Spatio-temporal firing patterns in the frontal cortex of behaving monkeys.

Recording the activity of several neurons in parallel in the frontal cortex of behaving monkeys reveals that firing times of neurons can maintain +/- 1 ms accuracy even after delays of over 400 ms. The accurate firing structures were associated with behavior. Neural networks that can sustain such accuracy can learn 'learn' to bind with each other and thus may serve as building blocks for cognitive processes.

Action Potentials↗
PubMed2005

Signal-to-noise ratio gain of a noisy neuron that transmits subthreshold periodic spike trains.

The transmission properties of an integrate-and-fire neuron model that transmits coherent subthreshold spike trains in a shot noise environment are investigated by numerical simulation. For very weak coherent couplings, it is shown that the input-output signal-to-noise ratio (SNR) gain is easier to exceed unity; while for stronger coherent couplings it is difficult to observe the SNR gain larger than unity at the optimal noise intensity. These observations are different from those acquired in the case of continuous noise. Our analysis further suggests that the larger SNR gain in the very weak coherent coupling case should be due to the noise-induced resonance. It is also shown that there is more possibility of the SNR gain above unity for slower periodic spike trains transmitted by the model. The results may be useful in understanding the performance of real noisy neurons acting as signal-processing elements.

Action Potentials↗
PubMed2006

Non-neutral vegetation dynamics.

The neutral theory of biodiversity constitutes a reference null hypothesis for the interpretation of ecosystem dynamics and produces relatively simple analytical descriptions of basic system properties, which can be easily compared to observations. On the contrary, investigations in non-neutral dynamics have in the past been limited by the complexity arising from heterogeneous demographic behaviours and by the relative paucity of detailed observations of the spatial distribution of species diversity (beta-diversity): These circumstances prevented the development and testing of explicit non-neutral mathematical descriptions linking competitive strategies and observable ecosystem properties. Here we introduce an exact non-neutral model of vegetation dynamics, based on cloning and seed dispersal, which yields closed-form characterizations of beta-diversity. The predictions of the non-neutral model are validated using new high-resolution remote-sensing observations of salt-marsh vegetation in the Venice Lagoon (Italy). Model expressions of beta-diversity show a remarkable agreement with observed distributions within the wide observational range of scales explored (5 x 10(-1) m divided by 10(3) m). We also consider a neutral version of the model and find its predictions to be in agreement with the more limited characterization of beta-diversity typical of the neutral theory (based on the likelihood that two sites be conspecific or heterospecific, irrespective of the species). However, such an agreement proves to be misleading as the recruitment rates by propagules and by seed dispersal assumed by the neutral model do not reflect known species characteristics and correspond to averages of those obtained under the more general non-neutral hypothesis. We conclude that non-neutral beta-diversity characterizations are required to describe ecosystem dynamics in the presence of species-dependent properties and to successfully relate the observed patterns to the underlying processes.

Biodiversity↗
PubMed1997

A study of the breast cancer dynamics in North Carolina.

This work is concerned with the study of breast cancer incidence in the State of North Carolina. Methodologically, the current analysis illustrates the importance of spatiotemporal random field modelling and introduces a mode of reasoning that is based on a combination of inductive and deductive processes. The composite space/time analysis utilizes the variability characteristics of incidence and the mathematical features of the random field model to fit it to the data. The analysis is significantly general and can efficiently represent non-homogeneous and non-stationary characteristics of breast cancer variation. Incidence predictions are produced using data at the same time period as well as data from other time periods and disease registries. The random field provides a rigorous and systematic method for generating detailed maps, which offer a quantitative description of the incidence variation from place to place and from time to time, together with a measure of the accuracy of the incidence maps. Spatiotemporal mapping accounts for the geographical locations and the time instants of the incidence observations, which is not usually the case with most empirical Bayes methods. It is also more accurate than purely spatial statistics methods, and can offer valuable information about the breast cancer risk and dynamics in North Carolina. Field studies could be initialized in high-rate areas identified by the maps in an effort to uncover environmental or life-style factors that might be responsible for the high risk rates. Also, the incidence maps can help elucidate causal mechanisms, explain disease occurrences at a certain scale, and offer guidance in health management and administration.

Breast Neoplasms↗
PubMed2005

Toward integration of systems biology formalism: the gene regulatory networks case.

We consider the problem of integrating different systems biology formalisms, namely, the process calculi based formalism, the modeling approach based on systems of differential equations, and the one relying on automata-like descriptions (and model checking). Specifically, we define automatic procedures for translating stochastic pi-calculus descriptions of gene regulatory networks to S-systems differential equations. Tools for extracting and reasoning on (approximate) solutions of S-systems have been recently developed in the literature, and can be exploited to establish a link with automata-based systems biology and model checking techniques.

Animals↗
PubMed2005

An alternative approach to modelling relapse in cancer with an application to adenocarcinoma of the prostate.

This paper proposes an alternative approach to modelling relapse in cancer. In particular, the dynamic model for the tumor or biomarker will be subjected to a lower elastic boundary at which the process either will be absorbed or reflected. The likelihood of reflection then can be interpreted as the probability of relapse. This framework will be exemplified for prostatic cancer by extending the recently proposed stochastic model of Dayananda et al. [P.W.A. Dayananda, J.T. Kemper, M.M. Shvartsman, A stochastic model for prostate-specific antigen levels, Math. Biosci. 190 (2004) 113] that focussed on the dynamics of the prostate-specific antigen (PSA) biomarker. Analytical results for the conditional density function, given a non-negative lower boundary, are obtained for the extreme cases of certain cure and of certain relapse. Simulations illustrate the relevance of the relapse probability and of the normal value of the biomarker for the design of treatment strategies. The paper thus points to two additional (patient-specific) characteristics that might enter treatment design and monitoring of progress in therapy.

Adenocarcinoma↗
PubMed2005

Rate processes with non-Markovian dynamical disorder.

Rate processes with dynamical disorder are investigated within a simple framework provided by unidirectional electron transfer (ET) with fluctuating transfer rate. The rate fluctuations are assumed to be described by a non-Markovian stochastic jump process which reflects conformational dynamics of an electron transferring donor-acceptor molecular complex. A tractable analytical expression is obtained for the relaxation of the donor population (in the Laplace-transformed time domain) averaged over the stationary conformational fluctuations. The corresponding mean transfer time is also obtained in an analytical form. The case of two-state fluctuations is studied in detail for a model incorporating substate diffusion within one of the conformations. It is shown that an increase of the conformational diffusion time results in a gradual transition from the regime of fast modulation characterized by the averaged ET rate to the regime of quasistatic disorder. This transition occurs at the conformational mean residence time intervals fixed much less than the inverse of the corresponding ET rates. An explanation of this paradoxical effect is provided. Moreover, its presence is also manifested for the simplest, exactly solvable non-Markovian model with a biexponential distribution of the residence times in one of the conformations. The nontrivial conditions for this phenomenon to occur are found.

Journal Article↗
PubMed2004

Orientation tuning and synchronization in the hypercolumn model.

The orientation selectivity in the firing rate of neurons is one of the most well-known properties of neurons in the primary visual cortex. To understand the dynamical mechanism of the orientation tuning, we introduce a biologically plausible network for a hypercolumn and investigate dynamical responses of its columnar activities. Numerical simulations show that the spike activities between excitatory cells in the same column exhibit strong synchronization and sharp orientation selectivity. The tuning curves for the synchronized activities also show orientation selectivity similar to those for the firing rate. The comparison between the two tuning curves for the firing rate and the synchronized activities suggests that the orientation selectivity is strongly correlated with the synchronized activities. We find from the analysis of columnar activities that the orientation selectivity depends strongly upon the inhibitory coupling strength and the synchronization upon the excitatory coupling strength. In particular, we find that at appropriate coupling parameters both sharp orientation selectivity and maximal synchronization can be achieved. This suggests the importance of the balance between the excitatory coupling and the inhibitory coupling in the primary visual cortex for visual information processing.

Action Potentials↗
PubMed2006

Variability control: key to regulatory compliance and sustainability goals.

The focus of this paper is on variability concerns in wastewater treatment and approaches to control unacceptable fluctuations in effluent quality. Areas considered include: factors contributing to variability in both waste loads and process technology performance; variability assessment; control of variability employing the process best management practice (BMP); design/operation of biological waste treatment technologies for variability reduction; and modelling to enhance process control.

Bioreactors↗
PubMed1987

Gross electrocortical activity as a linear wave phenomenon with variable temporal damping, regulated by ascending catecholamine neurones.

We report critical tests for a theory of electrocortical wave processes, in which telencephalic dendritic potentials reflect the mass action of coupled oscillatory circuits exhibiting complicated and unspecified non-linearities, the whole system being driven by active cell firing. Specific assumptions were: stochastic independence for instantaneous coupling parameters in the system, an individual central tendency to the cycle time for each circuit, and the maintenance of steady state conditions. Application of the central limit theorem to the state transition matrix shows that the gross electrocortical waves should be linear waves, exhibiting a multitude of invariant resonant modes, with the natural frequencies of all the modes being clustered about a smaller number of center values. Ascending brain-stem neurones of at least the dopaminergic and noradrenergic classes should regulate both the power of noise-like signals driving the telencephalic resonant patterns, and the temporal damping of each resonance. We devised tests which involved between hemisphere comparisons of electrocortical spectra, before and after unilateral lesion of transhypothalamic ascending fibres, thus obtaining ratio power changes attributable to post lesion asymmetry of damping and driving, in modes of equivalent left-right center-frequencies. These ratio spectra were curve-fitted to an approximate theoretical expression, and the parameters obtained enabled tests of several specific predictions. Estimates of the center values for resonant mode frequencies, comparison of the relative changes in left/right phase with that expected from the ratio changes in power, and estimates of the surface-to-signal transformation of left and right signals made by a back-calculation, all conform to expectation from the theory, and are consistent across lesion of different types of ascending neurone.

Animals↗
PubMed1989

[A novel method for determining an integrated character in quantitative genetics].

This paper describes a novel method using maximum entropy principle introduced by Shannon to construct a unique integrated character and gives a comparison between this method and multivariate statistics in quantitative genetics. In multivariate genetic analysis multivariate statistics is usually used for a polygenic system of multiple quantitative traits to form several complex character. Genetic analysis can be implemented through treating these correlated elementary traits by using the technique of principal component analysis or canonical correlation. Differing from the multivariate statistics, this paper presents a new method using maximum-entropy principle to obtain a unique integrated character from a set of correlated quantitative traits. This method has the advantages of simple mathematical structure and process, simple and clear results.

Animals↗
PubMed2002

The evolution of alternative cryptic female choice strategies in age-structured populations.

Cryptic female choice is a potentially important aspect of the sexual selection process. According to the theory of sexual dialectics, postcopulation manipulation of relative male fertilization success can provide an avenue by which females can circumvent attempts by males to control female reproduction. Here I use stochastic models to investigate the evolution of cryptic female choice in populations with and without age structure. In populations without age structure, cryptic female choice will evolve only when (1) precopulatory mate choice by females is inefficient, (2) variation in male fitness is correlated with a trait upon which a female can base her choice of mates, and (3) the cost of multiple mating is not too high. In populations with age structure, similar conditions apply. However, selection sometimes favors females that employ alternative strategies of female choice at different ages. These results help to define the types of biological systems in which we should expect to see the evolution of cryptic female choice. They also illustrate that the evolution of choice strategies in females may be complex and may mirror in some important respects the evolution of alternative mating tactics in males.

Age Factors↗
PubMed1987

On visual orientation of dot patterns.

Two-dimensional normally distributed random dot patterns were used in two experiments on visual orientation estimation. In the first experiment the patterns differed in their sample correlation and in dot number. In the second one the number of dots was maintained constant but the patterns were generated as a superposition of two normally distributed orthogonal sets composed of different number of dots. In both experiments the estimated orientation depended on stimuli correlation - with increasing correlation the estimated orientation gets closer to the orientation of the least square distance axis of the pattern. Even at very low unsignificant correlations there still remained a hint about stimulus orientation which was not estimated at random. Equalizing consecutively the number of dots in the two orthogonal dot patterns during the second experiment did not result in chance performance either. The bimodal angular distributions of the obtained responses permitted to approach the problem of orientation ambiguity. The results are discussed in terms of optimization processes taking place in the visual system.

Cybernetics↗
PubMed1979

The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time.

Mean and variance of the first passage time through a constant boundary for the Ornstein-Uhlenbeck process are determined by a straight-forward differentiation of the Laplace transform of the first passage time probability density function. The results of some numerical computations are discussed to shed some light on the input-output behavior of a formal neuron whose dynamics is modeled by a diffusion process of Ornstein-Uhlenbeck type.

Dendrites↗