Segmentation of the response of a neuronal network into clusters with similar activity

An important question in the analysis of the electrical activity of a large population of neurons is the detection of families of neurons having a similar pattern of electrical activity, so that the original neuronal network can be decomposed into distinct clusters. This paper describes how it is possible to segment the activity of a neuronal network into clusters of sites with similar patterns of activity. Such a segmentation gives insight on how the network is organized, on how it functions and on its behavior as a dynamical system. Simulation and experiments on real data suggest that the correct approach to solve these problems must use multiresolution analysis. The method has been applied to both synthetic data and real data coming from a network of dissociated cortical neurons from neonatal rat brain.     

Human subconscious as a p-adic dynamical system

We propose a mathematical model of the process of thinking based on dynamical systems over a configuration space of ideas. These dynamical systems are assumed to be located in the human subconscious and are controlled by the human conscious which fixes parameters of the dynamical systems in the subconscious and transmits to the subconscious generating ideas which initiate iterations of the dynamical systems in the subconscious. Thus, we present the mathematical model which is not based on the rule of reason. Mathematically the space of ideas is described by so-called p-adic numbers. In fact, a p-adic metric on the space of ideas corresponds to the following nearness between ideas: two ideas x and y are close if they have sufficiently long common root. Already the simplest p-adic dynamical systems might describe some sides of human psychological and social behaviour.     

The referential dynamics of cognition and action.

Referential behavior theory (RBT), a general dynamical approach to psychological and related systems that operate through a control or referencing process, is introduced. A review of existing evidence shows that this approach can apply to a variety of human and animal systems and tasks, whether the framing language is that of homeostasis, error correction, coupled biological oscillators, motor control, adaptive change, cognitive goal-setting, evaluation and refinement, or neural network learning. Thus, RBT provides a path for reconciliation of dynamical and information-processing accounts of action and cognition. RBT generates a class of mathematical equations, one of which, the discrete control equation (DCE), forms the basis for more detailed investigation. The primary focus here is on the application of the DCE to the temporal structure of regular human movement. Given certain conditions, the equation produces various standard (and new, more general) forms of the circle map class that governs relative phase in motor coordination and, hence, generates well-documented nonlinear "dynamical" motor phenomena such as behavioral attractors, phase transitions, critical slowing, and so on. Under certain other conditions, the DCE produces the linear stochastic timing models… (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Stress and the adaptive self-organization of neuronal connectivity during early childhood

A conceptual framework is proposed for a better understanding of the biological role of the stress-response and the relationship between stress and brain development. According to this concept environmental stimuli (in children mainly psychosocial challenges and demands) exert profound effects on neuronal connectivity through repeated or long-lasting changes in the release of especially such transmitters and hormones which contribute, as trophic, organizing signals, to the stabilization or destabilization of neuronal networks in the developing brain. The increased release of noradrenaline associated with the repeated short-lasting activation of the central stress-responsive systems in the course of the stress-reaction-process to psychosocial challenges which are felt to be controllable acts as a trigger for the stabilization and facilitation of those synaptic and neuronal pathways which are activated in the course of the cognitive, behavioral and emotional response to such stressors. The long-lasting activation of the central stress-responsive systems elicited by uncontrollable psychosocial conflicts in conjunction with the activation of glucocorticoid receptors by the sustained elevation of circulating glucocorticoid levels favors the destabilization of already established synaptic connections and neuronal pathways in associative cortical and limbic brain structures. The facilitation and stabilization of neuronal pathways triggered by the experience of controllable stress is thus opposed, attenuated or even reversed in the course of lon-lasting uncontrollable stress. This destabilization of previously established synaptic connections and neuronal pathways in cortical and limbic brain structures is a prerequisite for the acquisition of novel patterns of appraisal and coping and for the reorganization of the neuronal connectivity in the developing brain. Alternating experiences of repeated controllable stress and of long-lasting uncontrollable stress are therefore needed for the "self-adjustment" of neuronal connectivity and information processing the developing brain to changing environmental (psychosocial) demands during childhood. The brain structures and neuronal circuits involved in the regulation of behavioral responding become thus repeatedly reoptimized and refitted, not the changing conditions of life per se but rather to those conditions which are still able to activate the central stress responsive systems of an individual at a certain developmental stage.     

Stability of Iterative Learning Control with Data Dropouts via Asynchronous Dynamical System

In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control (ILC) system with data dropouts can be modeled as an asynchronous dynamical system with rate constraints on events in the iteration domain. The stability condition is providcd in the form of linear matrix inequalities (LMIS) depending on the stability of asynchronous dynamical systems. The analysis is supported by simulations.     

Physician resource utilization in radiation oncology: a model based on management of carcinoma of the prostate

The lamellar spacing dl of purple membrane (PM) multilayer systems was investigated with neutron diffraction as a function of temperature and of the level of hydration. The observed large T-dependent variations of dl indicate that PM is partially dehydrated when cooled below a "hydration water freezing point". This phenomenon is reversible, but a hysteresis is observed when PM is rehydrated upon reheating. The hydration water remaining bound to the membrane below about 240 K is non-freezing. Its amount was found to be hnf=0.24(+/-0.02) g 2H2O/g BR for all samples equilibrated at room temperature in the presence of 2H2O vapour at >/=84% r.h. It is evident, that the dehydration/rehydration behaviour of PM is strongly correlated with the temperature-dependent behaviour of the dynamical structure factor. Above the well-known "dynamical transition" announcing the onset of localized diffusive molecular motions between 190 K and 230 K, a second dynamical transition is caused by the temperature-induced rehydration of the PM starting near 255 K. This is also correlated with the deviation from a pure Arrhenius law of the rate-limiting process in the photocycle, known to occur upon cooling beyond the ice point into the same temperature region. Our results suggest that the phenomenon of dehydration and rehydration induced by cooling and reheating, respectively, is a general property of biological membranes.     

Comparison of two quantitative methods for the evaluation of neuronal number in the frontal cortex in Alzheimer disease

How to assess the substantial neuronal loss in a neurodegenerative disease such as Alzheimer disease is still being debated. Recently, stereological procedures have been proposed that claim improved accuracy and statistical power, but the results of some of these investigations have been controversial. In this study we compared and correlated the cell density results calculated per unit of volume obtained by a stereological technique, the "selector," with the cell counts per unit area obtained by computer-aided image analysis morphometry, in the same sections of midfrontal cortex in Alzheimer disease and control cases. The "selector" revealed a significant decrease in neuronal density that correlated well with a similar fall in large neuronal counts per unit area, as estimated by image analysis morphometry. These results indicate that stereological techniques and image analysis morphometry are complementary methods in reliably assessing cellular populations in neurodegenerative disorders.     

Evaluation of a dynamical model of speech perception

Previous work (Tuller, Case, Ding, & Kelso, 1994) has revealed signature properties of nonlinear dynamical systems in how people categorize speech sounds. The data were modeled by using a two-well potential function that deformed with stimulus properties and was sensitive to context. Here we evaluate one prediction of the model--namely, that the rate of change of the potential's slope should increase when the category is repeatedly perceived. Judged goodness of category membership was used as an index of the slope of the potential. Stimuli from a "say"-"stay" continuum were presented with gap duration changing sequentially throughout the range from 0 to 76 to 0 msec, or from 76 to 0 to 76 msec. Subjects identified each token as either "say" or "stay" and rated how good an exemplar it was of the identified category. As predicted, the same physical stimulus presented at the end of a sequence was judged a better exemplar of the category than was the identical stimulus presented at the beginning of the sequence. In contrast, stimuli presented twice near the middle of a sequence with few (or no) stimuli between them, as well as stimuli presented with an intervening random set, showed no such differences. These results confirm the hypothesis of a context-sensitive dynamical representation underlying speech.     

钢锭加热的动态优化及待轧策略

依据钢锭热过程数学模型所进行的动态钢温跟踪及烧好预报，进行动态均热炉优化加热控制。在动态的待轧策略中，将待轧按时间长短分为“计划待轧”和“非计划待轧”二种情况分别处理。     

Continuum models in neurobiology and information processing

Continuum models have been used with considerable success for single neurons but have been neglected in the study of neuronal populations. In more popular discrete neuronal network models, the geometric details of the neuronal centers are usually neglected. We here give a continuum nonlinear dynamical model and an approximate model which admits the possibility of ascertaining the roles of the various connectivity patterns from center to center in the central nervous system. Frequency transfer characteristics are used to incorporate the nonlinear dynamics of single neurons. Simple examples are evaluated both analytically and numerically and the results presented graphically.     

Functional genetic tests of DNA mismatch repair protein activity in Saccharomyces cerevisiae

Firing rate histogram is a widely used mathematical method for representing the activity of single neurons and small neural networks. Nevertheless, observation of fine temporal modulation or correlations of spike trains might be troublesome if the mean firing rate is low or rapid local changes occur. The spike density function (SDF) obtained by convolving the spike train with smooth and continuous kernel function proves to be a more appropriate approach in characterization of the firing pattern. The resulting time-function is a continuous and derivable one, thus it can be used as a dynamical variable of the neuronal activity. In the present paper applications of SDF in analysis of the firing patterns of Lymnaea neurons are described and its performance is compared to other quantitative methods.     

Dynamics of human postural transitions.

In the present study, the authors examined transitions between postural coordination modes involved in human stance. The analysis was motivated by dynamical theories of pattern formation, in which coordination modes and transitions between modes are emergent, self-organized properties of the dynamics of animal-environment systems. In 2 experiments, standing participants tracked a moving target with the head. Results are consistent with the hypothesis that changes in body coordination follow typical nonequilibrium, phase transitions, exhibiting multistability, bifurcation, critical fluctuations, hysteresis, and critical slowing down. The findings suggest that posture may be organized in terms of dynamical principles and favor the existence of general and common principles governing pattern formation and flexibility in complex systems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Targeting the minor groove of DNA

Congenital nystagmus is an oculomotor disorder in which fixation is disrupted by rhythmical, bilateral involuntary oscillations. Clinically these eye movements have been described with some degree of success in terms of their peak-to-peak amplitude, frequency, mean velocity and waveform shape. However, it has not proved possible to diagnose any underlying pathology from the nystagmus characteristics. Here, we propose a new approach to understanding the nystagmus using dynamical systems theory. Our approach is based on the use of delay embedding techniques, which allow one to relate a time series of scalar observations to the state space dynamics of the underlying dynamical system. Using this approach we quantify the dynamics of the nystagmus in the region of foveation and present evidence to suggest that it is low-dimensional and deterministic. Our results put new constraints on acceptable models of nystagmus and suggest a way to make a closer link between data analysis and model development. This approach raises the hope that techniques originally developed to stabilise chaotic systems, by using small perturbations, may prove useful in the control of nystagmus.     

Work of large information systems

The problem of application of informational ideas to the study of large informational systems, such as brain, is considered. Analysis follows some ideas of Winograd and Kowan's theory of reliable computations in the presence of noise. In the beginning of paper the "material analogy" for intuitive understanding of Shannon's results is proposed. Afterwards there is given the formulation of coding theorem for the case of "informational collective"--a large group of informational sources and receivers. In conclusion it is shown that such properties of neuronal structures as "stochastic" neural connections are reasonable from the point of information theory.     

阵列动力系统广义同步的新理论及计算机模拟

提出了两个定理,据此可构造通过线性变换达到广义同步的阵列动力系统,在定理的基础上,引入了两个达到广义同步的阵列动力系统,数值模拟结果表明,这两个系统分别展示了复杂极限环广义同步和混沌广义同步。     

灰色大系统状态向量及方程解的判定

在现实的大系统分析中,常遇到由若干灰色子系统组成的灰色大系统.文章研究了这类灰色大系统运动方程解的存在性与唯一性,给出了具体的判定方法,且给出了如何选择其状态向量的具体方法.     

Toxicity and neuroendocrine regulation of the immune response: a model analysis

Various models have been proposed for the regulation of the primary immune response. Most of the models focus on the ability of the immune system to control a multiplying pathogen, and take into account the cross-regulations between different immune components. In the present study, we integrate the immune system in the general physiology of the host and consider the interaction between the immune and neuroendocrine systems. In addition to pathogen growth and toxicity, our four-variable model takes into account the toxic consequences for the organism of the immune response itself, as well as a neuro-hormonal retro-control of this immune response. Formally, the dynamics of the model is first explored on the basis of a discrete caricature, with special emphasis on the role of the constitutive feedback loops for determining the essential dynamical behavior of the system. This logical analysis is then completed by a classical continuous approach using differential equations. From a biological point of view, our model accounts for four stable regimes which can be described as "pathogen elimination/organism healthy", "pathogen elimination/ organism death", "pathogen growth/organism death" and "chronic infection". The size of the basins of attraction of these different regimes varies as a function of some crucial parameters. Our model allows moreover to interpret the interplay between pathogen immunogenicity and neuro-hormonal feedback, the effects of stress on immunity and the toxic shock syndrome, in terms of transitions among the steady states.     

Small group research and dynamical systems theory: Conceptual and methodological considerations, a reply to McGrath (1997).

This article responds to J. E. McGrath's (1997) integrative review of the small group literature and subsequent recommendations including the application of dynamical systems theory in group research. Parallels to the patterns and themes found in social psychology research are described from the therapeutic literature. Theoretical and methodological advantages of dynamical systems theory are noted. (PsycINFO Database Record (c) 2010 APA, all rights reserved)