Stochastic analysis of environmental fluctuations in a compartmental system

In this paper the general two-compartment system with environmental stochasticity is investigated. The transfer rates and outputs are assumed to be random telegraph processes. The Laplace-transform of the mean-value function of the amount of substance present in the two compartments is evaluated. The Gaussian white noise limit case is also discussed and the stability of the system is examined. It is shown that while the deterministic model is stable, environmental stochasticity may induce in the mean-value function all sorts of behaviour — stable, unstable and oscillatory. This is in contrast to the intrinsic stochasticity in linear models wherefor the mean-value function is the same as the solution of the deterministic counterpart.     

Pink-noise behaviour of biosystems

Pink (1/f) noise is one of the most common behaviours of biosystems. Our present paper is devoted to clarify the origin of this interesting phenomenon. It is shown that the stationary random stochastic processes under self-similar conditions (as we have in living objects) generate pink noise independently of the kind and number of variables.     

Noise Properties in the Ideal Kirchhoff-Law-Johnson-Noise Secure Communication System

In this paper we determine the noise properties needed for unconditional security for the ideal Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system using simple statistical analysis. It has already been shown using physical laws that resistors and Johnson-like noise sources provide unconditional security. However real implementations use artificial noise generators, therefore it is a question if other kind of noise sources and resistor values could be used as well. We answer this question and in the same time we provide a theoretical basis to analyze real systems as well.     

Social class differences in years of potential life lost: size,trends, and principal causes.

British social class differences in mortality are examined in terms of years of potential life lost, a measure that gives more weight to deaths that take place at younger ages. It shows wider class differences during the years of working life than those found when mortality is expressed in terms of standardised mortality ratios. Examination of the change in class differences between 1971 and 1981 for all causes of death combined and for the three categories of death which during these ages make a major contribution to total years of potential life lost shows complex changes. Inequalities in years of potential life lost have increased between 1971 and 1981, during which all the principal causes of death have shown stationary or rising rates among the manual classes. The use of years of potential life lost as a measure of population health trends focuses attention on the major contribution of violent death, which occurs mainly in younger men, to widening class differences in mortality.     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。     

A measuring system for biotechnical processes based on discrete methods of estimation

An adaptive measuring system of the main variables of biotechnical processes based on the theory of estimation is elaborated upon here. All stages of system synthesis are considered. It is shown that for an adaptive measuring system all a priori information on modelling and measurement noise and process mathematical models must be used. The data of direct and indirect measurements are used for estimating the main variables. The performance of the proposed measuring system was checked using imitative modelling.     

Size-Independent Differences between the Mean of Discrete Stochastic Systems and the Corresponding Continuous Deterministic Systems

In this paper, it is shown that for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is a stable stationary state for the discrete stochastic system, and other finite states have zero probability of existence at large times. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.     

BIO-RESPONSE TO WHITE NOISE EXCITATION

Pink (1/f-) noise is one of the most common behaviors of biosystems. This paper is devoted to clarifying the stochastic answer given to white-noise excitation of bio-systems.

It is assumed that a living system in general is a bifurcative self-organizing system, and has cyclic symmetry with infinite degrees of freedom, and stationary random stochastic processes characterize their dynamism.

We show that this bifurcation characterizes all levels of bioactivity, and the white-noise excited biosystem has a filter function, and generates a pink-noise spectrum.

Environmental white-noise electromagnetic excitation (like ‘electrosmog’ in general) is filtered by the biosystem, and it gives a characteristic pink-noise answer-signal to this excitation.     

Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks

The multiobjective problem of minimizing all intermediate concentrations is solved for a model of glycolysis, the pentose monophosphate shunt and the glutathione system in human erythrocytes. It turns out that one solution out of four obtained corresponds qualitatively to the real system. Furthermore, it is shown that for any reaction system, the mentioned optimality principle implies distinct time hierarchy in that some reactions are infinitely fast and subsist in quasi-equilibrium. Finally, the relationships to the standard method of deriving enzymatic rate laws are discussed.     

Signal detection theory,detectability and stochastic resonance effects

 Stochastic resonance is a phenomenon in which the performance of certain non-linear detectors can be enhanced by the addition of appropriate levels of random noise. Signal detection theory offers a powerful tool for analysing this type of system, through an ability to separate detection processes into reception and classification, with the former generally being linear and the latter always non-linear. Through appropriate measures of signal detectability it is possible to decide whether a local improvement in detection via stochastic resonance occurs due to the non-linear effects of the classification process. In this case, improvement of detection through the addition of noise can never improve detection beyond that of a corresponding adaptive system. Signal detection and stochastic resonance is investigated in several integrate-and-fire neuron models. It is demonstrated that the stochastic resonance observed in spiking models is caused by non-linear properties of the spike-generation process itself. The true detectability of the signal, as seen by the receiver part of the spiking neuron (the integrator part), decreases monotonically with input noise level for all signal and noise intensities. Received: 3 April 2001 / Accepted in revised form: 8 March 2002     

Connection of the tangents of the regression slope of the heart rate graph with linear and nonlinear dynamics in stationary short-time series

The connection of the regression slope of heart rate graph (b1) with linear and nonlinear dynamics in stationary short-time series (256 points) was studied. A new index for the estimation of nonlinear dynamics in stationary short-time series was used, which is based on the correlation dimension. The results of the study indicated that the dynamics of heart rate in stationary short-time series can be represented as the sum of linear (periodic) and nonlinear (stochastic) processes. A relation of b1 with both linear and nonlinear dynamics of heart rate was found. The formulas for the calculation of absolute and relative (to the amplitude of periodic fluctuations) noise levels in heart rate dynamics were derived. A comparative analysis of nonlinear dynamics of heart rate in stationary short-time series for different functional states of humans was performed. The increase in the relative noise level in heart rate dynamics with increasing breathing frequency is related not only to a decrease in control breathing amplitude but also to an increase in the noise amplitude. The decrease in the absolute noise level for nervous excitation, fatigue, and mental stress were found. The predominance of nonlinear (stochastic) processes over linear (periodic) processes in the relaxed state was established.     

Effect of noise-induced stress on the quantitative characteristics of rat brain synapses

Rats were exposed to white noise for 1, 2 and 3 weeks. Electron microscopy was used to examine brain sections. The number of synaptic junctions was calculated in the auditory and motor areas of the brain cortex. It has been shown that there was a significantly incremental increase in the number of synaptic junctions in all the layers of the auditory and motor areas of the brain cortex 1, 2 and 3 weeks after exposure to noise.     

Polarized signal classification by complex and quaternionic multi-layer perceptrons

For polarized signals, which arise in many application fields, a statistical framework in terms of quaternionic random processes is proposed. Based on it, the ability of real-, complex- and quaternionic-valued multi-layer perceptrons (MLPs) of performing classification tasks for such signals is evaluated. For the multi-dimensional neural networks the relevance of class label representations is discussed. For signal to noise separation it is shown that the quaternionic MLP yields an optimal solution. Results on the classification of two different polarized signals are also reported.     

A maximum entropy criterion of filtering and coding for stationary autoregressive signals: Its physical interpretations and suggestions for its application to neural information transmission

The operations of encoding and decoding in communication agree with filtering operations of convolution and deconvolution for Gaussian signal processing. In an analogy with power transmission in thermodynamics, an autoregressive model of information transmission is proposed for representing a continuous communication system which requires a pair of an internal noise source and a signal source to encode or decode a message. In this model transinformation (informational entropy) equals the increase in stationary nonequilibrium organization formed through the amplification of white noise by a positive feedback system. The channel capacity is finite due to the existence of inherent noise in the system. The maximum entropy criterion in information dynamics corresponds to the 2^nd law of thermodynamics. If the process is stationary, the communication system is invertible, and has the maximum efficiency of transformation. The total variation in informational entropy is zero in the cycle of the invertible system, while in the noninvertible system the entropy of decoding is less than that of encoding. A noisy autoregressive coding which maximizes transinformation is optimum, but is also ideal.     

Extinction risk and the 1/f family of noise models

In order to predict extinction risk in the presence of reddened, or correlated, environmental variability, fluctuating parameters may be represented by the family of 1/f noises, a series of stochastic models with different levels of variation acting on different timescales. We compare the process of parameter estimation for three 1/f models (white, pink and brown noise) with each other, and with autoregressive noise models (which are not 1/f noises), using data from a model time-series (length, T) of population. We then calculate the expected increase in variance and the expected extinction risk for each model, and we use these to explore the implication of assuming an incorrect noise model. When parameterising these models, it is necessary to do so in terms of the measured ("sample") parameters rather than fundamental ("population") parameters. This is because these models are non-stationary: their parameters need not stabilize on measurement over long periods of time and are uniquely defined only over a specified "window" of timescales defined by a measurement process. We find that extinction forecasts can differ greatly between models, depending on the length, T, and the coefficient of variability, CV, of the time series used to parameterise the models, and on the length of time into the future which is to be projected. For the simplest possible models, ones with population itself the 1/f noise process, it is possible to predict the extinction risk based on CV of the observed time series. Our predictions, based on explicit formulae and on simulations, indicate that (a) for very short projection times relative to T, brown and pink noise models are usually optimistic relative to equivalent white noise model; (b) for projection timescales equal to and substantially greater than T, an equivalent brown or pink noise model usually predicts a greater extinction risk, unless CV is very large; and (c) except for very small values of CV, for timescales very much greater than T, the brown and pink models present a more optimistic picture than the white noise model. In most cases, a pink noise is intermediate between white and brown models. Thus, while reddening of environmental noise may increase the long-term extinction probability for stationary processes, this is not generally true for non-stationary processes, such as pink or brown noises.     

Estimation of ion channel kinetics from fluctuations of macroscopic currents

For single channel recordings, the maximum likelihood estimation (MLE) of kinetic rates and conductance is well established. A direct extrapolation of this method to macroscopic currents is computationally prohibitive: it scales as a power of the number of channels. An approximated MLE that ignored the local time correlation of the data has been shown to provide estimates of the kinetic parameters. In this article, an improved approximated MLE that takes into account the local time correlation is proposed. This method estimates the channel kinetics using both the time course and the random fluctuations of the macroscopic current generated by a homogeneous population of ion channels under white noise. It allows arbitrary kinetic models and stimulation protocols. The application of the proposed algorithm to simulated data from a simple three-state model on nonstationary conditions showed reliable estimates of all the kinetic constants, the conductance and the number of channels, and reliable values for the standard error of those estimates. Compared to the previous approximated MLE, it reduces by a factor of 10 the amount of data needed to secure a given accuracy and it can even determine the kinetic rates in macroscopic stationary conditions.     

Harvesting in a random environment: Itô or Stratonovich calculus?

We extend to harvesting stochastic differential equation (SDE) models in a random environment our previous work on models without harvesting concerning the resolution of the It?-Stratonovich controversy. The resolution is obtained for the very general class of models dN/dt=N (r(N)-h(N)+sigmaepsilon(t)), where N=N(t) is the population size at time t, r(N) is the (density-dependent) "mean" per capita growth rate, h(N) is the (density-dependent) harvesting effort, epsilon(t) is a standard white noise (representing environmental random fluctuations), and sigma is a noise intensity parameter. It? and Stratonovich calculus in the resolution of SDEs apparently give different qualitative and quantitative results, leading to controversy on which calculus is more appropriate and creating an obstacle on the use of this modeling approach. We show that the apparent difference between the two calculi is due to a semantic confusion based on the fallacious assumption that we are working with the same type of mean rates. After clearing the confusion, the two calculi yield exactly the same results and we obtain important common conditions for extinction and for existence of a stationary density. The resolution of the controversy is intertwined with and sheds light on the estimation issues.