Regular Series

Vol. 37 (2006), No. 5, pp. 1387 - 1691

Stimulus-Induced Synchronization in Hodgkin–Huxley-type Model Neurons of Cat Retinal Ganglion Cells

Acta Phys. Pol. B 37, 1387 (2006)

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Visual signals converge through the layers of the retinal circuitry from the photoreceptor cells to the retinal ganglion cells such that nearby ganglion cells are driven by essentially the same visual stimulus. We use computational modeling to address the question whether the experimentally observed degree of synchrony in nearby ganglion cells is due to the common visual stimulus or whether active network circuitry is necessary.

Lateral Diffusion Near the Interface of Two Immiscible Liquids

Acta Phys. Pol. B 37, 1397 (2006)

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Diffusion coefficient of a particle diffusing near the interface of two immiscible liquids varies when the particle crosses the interface. We show how the problem of lateral diffusion in such a system can be reduced to that of finding the distribution of the cumulative residence time spent by the particle in one of the layers. The latter problem can be solved with relative ease since the distribution is determined by the one-dimensional motion in the direction normal to the interface. The approach is utilized to find an exact solution for the Fourier–Laplace transform of the lateral propagator, the effective medium approximation for this propagator, and the time-dependent behavior of the lateral diffusion coefficient in several special cases.

How to Evaluate the Electric Noise in a Cell Membrane?

Acta Phys. Pol. B 37, 1409 (2006)

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There has been considerable public anxiety about possible health effects of electromagnetic radiation emitted by high voltage power lines. Power frequencies (60 Hz in the US, 50 Hz in many other countries) are sufficiently slow for the associated electric fields to distribute themselves across the highly resistive cell membranes. To assess the ambient power frequency fields, researchers have compared the voltage that these fields induce across cell membranes to the strength of the electric noise that the membranes generate themselves through Brownian motion. However, there has been disagreement among researchers on how to evaluate this equilibrium membrane electric noise. I will review the different approaches and present an ab initio modeling of membrane electric fields. I will show that different manifestations of Brownian noise lead to an electric noise intensity that is many times larger than what conventional estimates have yielded. Next, the legitimacy of gauging a nonequilibrium external signal against internal equilibrium noise is questioned and a more meaningful criterion is proposed. Finally, an estimate will be derived of the nonequilibrium noise intensity due to the driven ion traffic through randomly opening and closing ion channels.

A Directed Binding Mechanism of Processive Motion for the Kinesin Motor Protein Families

Acta Phys. Pol. B 37, 1425 (2006)

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A novel physical mechanism is discussed for the processive propagation of two-headed motor proteins such as kinesin along protein filaments. Our model uses the fact that the binding of each head must be directionality oriented to the protein filament. The binding sites are realized by a 2D periodic potential due to the filament’s surface. The deviation of the geometry of the kinesin from the relaxed state to the state where both motor domains are simultaneously bound to the filament results in an internal stress of the molecule. Un-binding of one of the motor domains from the filament, which is due to the release of chemical energy from ATP hydrolysis, results in a mechanical movement until the relaxed state is reached again. We develop a simple mathematical and mechanical model in which directed binding of the heads to the filament results in a directed twist away from its relaxed state of the molecule, occurring probably in the neck linker region. Un-binding of the head from the filament relaxes the twist and defines the propagation direction. We show that there must be at least one torsional spring for every head to store elastic energy. It is the internal structure both of the relaxed and tensed-up state that defines the walking direction of kinesin. Calculations based on the model are in good quantitative agreement with experimental observations.

Design of a Mapping for Hyperbolic Diffusion

Acta Phys. Pol. B 37, 1445 (2006)

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In this paper we investigate whether it is possible to obtain a hyperbolic diffusion from a chaotic mapping. We design an appropriate mapping, and explain which features are responsible for the hyperbolicity, together with a quantitative descriptions of the coefficients of the hyperbolic diffusion.

Calibration of the Multi-Factor HJM Model for Energy Market

Acta Phys. Pol. B 37, 1455 (2006)

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The purpose of this paper is to show that using the toolkit of interest rate theory, already well known in financial engineering as the HJM model [D. Heath, R. Jarrow, A. Morton, Econometrica 60, 77 (1992)], it is possible to derive explicite option pricing formula and calibrate the theoretical model to the empirical electricity market. The analysis is illustrated by numerical cases from the European Energy Exchange (EEX) in Leipzig. The multi-factor versus one-factor HJM models are compared.

Overdamped Deterministic Ratchets Driven by Multifrequency Forces

Acta Phys. Pol. B 37, 1467 (2006)

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We investigate a dissipative, deterministic ratchet model in the overdamped regime driven by a rectangular force. Extensive numerical calculations are presented in a diagram depicting the drift velocity as a function of a wide range of the driving parameter values. We also present some theoretical considerations which explain some features of the mentioned diagram. In particular, we proof the existence of regions in the driving parameter space with bounded particle motion possessing zero current. Moreover, we present an explicit analytical expression for the drift velocity in the adiabatic limit.

Stochastic Resonance: the Role of \(\alpha \)-Stable Noises

Acta Phys. Pol. B 37, 1479 (2006)

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In order to document and discuss the widespread presence in nature of the stochastic resonance phenomenon (SR), we investigate the generic double-well potential model perturbed by the \(\alpha \)-stable Lévy type noises. Despite possible infinite variance characteristics of the noise term, the SR effect still occurs and can be detected by common quantifiers used in the studies of the phenomenon. The robustness of the SR is examined by use of standard measures within a continuous and a two-state description of the system. Since the \(\alpha \)-stable noises are characterized by a whole set of parameters, our research focuses on the analysis of the influence of noise parameters on a shape of the signal-to-noise ratio and spectral power amplification curves, revealing presence of the SR in the system at hand. Examination of the driving noise asymmetry indicates that the resonant response weakens when the symmetric noises with a decreasing value of the stability index \(\alpha \) are applied.

Analytic Theory of Absolute Negative Mobility in a Microfluidic Device

Acta Phys. Pol. B 37, 1491 (2006)

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We theoretically discuss and analyze the design of a microfluidic device which has recently been demonstrated experimentally to exhibit the phenomenon of absolute negative mobility (i.e. net motion into the direction opposite to a net acting force) for non-interacting Brownian particles. Based on a model for the motion of a colloidal particle in a structured microfluidic system, that includes electroosmotic and electrophoretic effects as well as thermal fluctuations, we derive an analytic approximation for the average particle velocity, comparing very well with data of numerical simulations and experimental measurements.

Entropy Methods in Random Motion

Acta Phys. Pol. B 37, 1503 (2006)

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We analyze a contrasting dynamical behavior of Gibbs–Shannon and conditional Kullback-Leibler entropies, induced by time-evolution of continuous probability distributions. The question of predominantly purpose-dependent entropy definition for non-equilibrium model systems is addressed. The conditional Kullback–Leibler entropy is often believed to properly capture physical features of an asymptotic approach towards equilibrium. We give arguments in favor of the usefulness of the standard Gibbs-type entropy and indicate that its dynamics gives an insight into physically relevant, but generally ignored in the literature, non-equilibrium phenomena. The role of physical units in the Gibbs–Shannon entropy definition is discussed.

The SIS Model for Assessment of Epidemic Control in a Social Network

Acta Phys. Pol. B 37, 1521 (2006)

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The phenomenon of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The SIS model with incubation time and temporal immunity to a disease, is used. In our model location in social structure, effectiveness of different types of interactions and mobility of contemporary communities are taken into account. The influence of control measures on the spreading process is investigated as a function of initial conditions. The cost-effectiveness of mass immunizations campaigns, target vaccinations and the sick leaves is compared. A critical vaccinations coverage, sufficient for suppressing an epidemic as well as the probability that endemic state occurs, are calculated. The results of numerical calculations are similar to the solutions of the master equation for the spreading process.

Quantum Brownian Motion and the Third Law of Thermodynamics

Acta Phys. Pol. B 37, 1537 (2006)

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The quantum thermodynamic behavior of small systems is investigated in presence of finite quantum dissipation. We consider the archetype cases of a damped harmonic oscillator and a free quantum Brownian particle. A main finding is that quantum dissipation helps to ensure the validity of the Third Law. For the quantum oscillator, finite damping replaces the zero-coupling result of an exponential suppression of the specific heat at low temperatures by a power-law behavior. Rather intriguing is the behavior of the free quantum Brownian particle. In this case, quantum dissipation is able to restore the Third Law: Instead of being constant down to zero temperature, the specific heat now vanishes proportional to temperature with an amplitude that is inversely proportional to the ohmic dissipation strength. A distinct subtlety of finite quantum dissipation is the result that the various thermodynamic functions of the sub-system do not only depend on the dissipation strength but depend as well on the prescription employed in their definition.

Spectral Analysis of Noisy Oscillators Near Hopf Bifurcations

Acta Phys. Pol. B 37, 1551 (2006)

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We compare the dynamics of nonlinear noisy oscillators near the two types of the Hopf bifurcation. Prior to the bifurcation, in the regime of damped oscillations around the stable focus, noise serves as a bifurcation precursor: the power spectrum includes a peak at the frequency of the self-sustained oscillations. Super- and sub-critical Hopf bifurcations differ crucially in the noise dependence of the width of this spectral line. In case of a super-critical bifurcation the width is a monotonically growing function of the noise intensity. In contrast, for a sub-critical bifurcation, growth of the intensity of the weak noise enforces a decrease of the peak width; the width starts to grow only when the noise level exceeds a certain threshold value. Since the inverse spectral width is a measure of coherence, we conclude that true noise-induced coherence can be found only near the sub-critical bifurcation.

Simple Model of Spreading of Two Epidemics: Phase Transition and Pattern Formation

Acta Phys. Pol. B 37, 1561 (2006)

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Spreading of two different diseases in small world network, with restriction that an individual can be ill only with one disease in the same time, is investigated in the frame of SIRS model. It was found that in the special range of control parameters the presence of the second disease can significantly decrease the number of individuals, who passed the first disease. The speed of propagation of the wave-front of the epidemic is calculated analytically and good agreement with numerical calculation is obtained. The influence of additional long range connections on epidemic spreading and phase transition is investigated. It is found that in special conditions spatio-temporal patterns, in particular spiral waves, can emerge in the system. Small number of additional long-range connections increases the probability of emerging of spiral waves.

Time Evolution of the Reaction Front in the System with One Static and One Subdiffusive Reactant

Acta Phys. Pol. B 37, 1571 (2006)

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We study a subdiffusion-reaction system with initially separated reactants in the case where one of the reactants is static. Using the scaling method we show that the reaction front \(x_{\rm f}\) evolves in time according to the power law \(x_{\rm f}\sim t^{\alpha ~/~2}\) where \(\alpha \) is the subdiffusion parameter. Comparing the theoretical formula with the experimental data we find that the transport of acids molecules inside the tooth enamel during the caries progress is of subdiffusive character.

Packet Traffic Dynamics Near Onset of Congestion in Data Communication Network Model

Acta Phys. Pol. B 37, 1579 (2006)

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The dominant technology of data communication networks is the Packet Switching Network (PSN). It is a complex technology organized as various hierarchical layers according to the International Standard Organization (ISO) Open Systems Interconnect (OSI) Reference Model. The Network Layer of the ISO OSI Reference Model is responsible for delivering packets from their sources to their destinations and for dealing with congestion if it arises in a network. Thus, we focus on this layer and present an abstraction of the Network Layer of the ISO OSI Reference Model. Using this abstraction we investigate how onset of traffic congestion is affected for various routing algorithms by changes in network connection topology. We study how aggregate measures of network performance depend on network connection topology and routing. We explore packets traffic spatio-temporal dynamics near the phase transition point from free flow to congestion for various network connection topologies and routing algorithms. We consider static and adaptive routings. We present selected simulation results.

Stochastic Resonance and Resonant Enhancement of Magnetic Flux in Periodically Driven Mesoscopic Cylinders

Acta Phys. Pol. B 37, 1605 (2006)

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Magnetic fluxes in mesoscopic cylinders, driven by an external, time-periodic magnetic field and thermal fluctuations, are investigated. The resonant enhancement of the response of the system is studied and compared with the celebrated phenomenon of Stochastic Resonance phenomenon.

Anomalous Diffusion Schemes Underlying the Stretched Exponential Relaxation. The Role of Subordinators

Acta Phys. Pol. B 37, 1617 (2006)

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The random-variable formalism of anomalous diffusion processes is presented. We elucidate the role of the subordinate stochastic processes as the main mathematical tool that allows us to modify the dynamics of the classical, exponential relaxation process. In particular, we discuss the anomalous diffusion schemes underlying the stretched exponential decay of modes.

Scale Invariant Properties in Heart Rate Signals

Acta Phys. Pol. B 37, 1627 (2006)

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The rate of heart beat is controlled by autonomic nervous system: accelerated by the sympathetic system and slowed by the parasympathetic system. Scaling properties in heart rate are usually related to the intrinsic dynamics of this physiological regulatory system. The two packages calculating local exponent spectra: Wavelet Transform Modulus Maxima and Multifractal Detrended Fluctuation Analysis (accessible from Physionet home page are tested, and then used to investigate the spectrum of singularity exponents in series of heart rates obtained from patients suffering from reduced left ventricle systolic function. It occurs that this state of a heart could be connected to some perturbation in the regulatory system, because the heart rate appears to be less controlled than in a healthy human heart. The multifractality in the heart rate signal is weakened: the spectrum is narrower and moved to higher values what indicate the higher activity of the sympatethic nervous system.

27-Day Variations of the Galactic Cosmic Ray Intensity and Anisotropy

Acta Phys. Pol. B 37, 1641 (2006)

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We study the relationships of the 27-day variations of the galactic cosmic ray (GCR) intensity and anisotropy with the 27-day variations of the solar wind (SW) velocity, Wolf number (Rz) and interplanetary magnetic field (IMF) strength for different positive \((A\gt 0)\) and negative \((A\lt 0)\) polarity periods of the solar magnetic cycles based on the experimental data. We found that the long-lived active region of the longitudes (with life time more than 22 years) exists on the Sun. This phenomenon is clearly manifested for the \(A\gt 0\) period of the solar magnetic cycle. The stable long-lived active region of the longitudes on the Sun is the source of the 27-day variation of the SW velocity. The maximum of the phase distribution of the 27-day variation of the SW velocity versus the heliolongitudes is preceded by \(170^{\circ }\)–\(180^{\circ }\) the maxima of the phases distributions of the 27-day variations of the GCR intensity and anisotropy for the \(A\gt 0\) polarity period. When comparing the theoretical calculations (obtained by the numerical solutions of the Parker’s transport equation) with the experimental data we conclude that the 27-day variation of the solar wind velocity is the general source of the 27-day variations of the GCR intensity and anisotropy. The average amplitudes of the 27-day variations of the galactic cosmic ray anisotropy and intensity for the minima epochs of solar activity are larger in the \(A\gt 0\) period than in the \(A\lt 0\) period at the Earth orbit.

Coexistence of Resonant Activation and Noise Enhanced Stability in a Model of Tumor–Host Interaction: Statistics of Extinction Times

Acta Phys. Pol. B 37, 1651 (2006)

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We study a Langevin equation derived from the Michaelis–Menten (MM) phenomenological scheme for catalysis accompanying a spontaneous replication of molecules, which may serve as a simple model of cell-mediated immune surveillance against cancer. We examine how two different and statistically independent sources of noise — dichotomous multiplicative noise and additive Gaussian white noise — influence the population’s extinction time. This quantity is identified as the mean first passage time of the system across the zero population state. We observe the effects of resonant activation (RA) and noise-enhanced stability (NES) and we report the evidence for competitive co-occurrence of both phenomena in a given regime of noise parameters. We discuss the statistics of first passage times in this regime and the role of different pseudo-potential profiles on the RA and NES phenomena. The RA/NES coexistence region brings an interesting interpretation for the growth kinetics of cancer cells population, as the NES effect enhancing the stability of the tumoral state becomes strongly reduced by the RA phenomenon.

Features of the Rigidity Spectrum of Galactic Cosmic Ray Intensity During the Recurrent Forbush Effect

Acta Phys. Pol. B 37, 1667 (2006)

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Temporal changes of the rigidity spectrum of the recurrent Forbush effect (16–30 June, 2003) have been studied using the data of the worldwide network of neutron monitors. The rigidity spectrum is soft at the beginning and at the end phases of the recurrent Forbush effect, and it is hard in the minimum phase. The steady-state model based on the Parker’s transport equation is able to explain the changes of the rigidity spectrum of the recurrent Forbush effect of the galactic cosmic ray intensity. An increase of the power spectral density in the lower frequency area of the energy range of the interplanetary magnetic field turbulence (\(\sim 10^{-6}\)– \(10^{-5}\) Hz) causes the hardening of the rigidity spectrum of the recurrent Forbush effect of the GCR intensity.

Two Cross-Correlated Dichotomic Noises: Barrier Crossing Problem

Acta Phys. Pol. B 37, 1677 (2006)

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Escape of an overdamped particle driven by two correlated dichotomic noises (DN) from a triangle potential well is studied. A general description of statistical properties of the noises is developed in terms of master equation and correlation functions. Using the kinetics of these noises, an equation for the mean first-passage times can be deduced, which enables us to investigate the impact of non-zero covariance on the barrier crossing rate. In various cases, both the acceleration and the slowing down of the escape process can be observed.


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