A new dimer model is introduced to describe the behavior of dimeric processive motor proteins in general. A single motor domain is modeled using our previous work on hybrid motors that exhibit elements of both a powerstroke and a Brownian motor mechanism. The different behavior observed in Myosins V and VI can be explained by varying the physical parameters describing the coupling between the two motor domains. The dynamics of the resulting stepping mechanics under loaded and unloaded conditions are examined. The results from this dimer model are compared with experimental data for two-headed processive motors.

Protein-mediated DNA loop formation is an important biological process that regulates key functions such as transcription. We present a mechanical model for these DNA-protein complexes that can take effects of the DNA sequence such induced curvature into account. This model provides the equilibrium shape and elastic energy of the DNA loop, using boundary conditions from the protein crystal structure. We then construct a Hamiltonian for small perturbations of the DNA around the equilibrium shape, which in turn allows us to calculate the eigenmodes and the entropic contributions of the thermal fluctuations to the free energy of the DNA loop. Here we present computations related to the short wild-type lactose repressor loop of Escheria coli (E. coli), and find that the entropic contributions are significant and amount to up to 3.9 k_BT of the free energy. We also show that this entropic contribution from the stiffening of the DNA loop depends strongly on the phase angle between the two operator sites, which adds to the known phasing effect of the elastic energy of the loop.

Three mutations of domain C5 of Myosin Binding Protein C are involved in Familial Hypertrophic Cardiomyopathy. We assess their impact through Molecular Dynamics simulations within the framework of a native-centric coarse-grained model. We characterize the clinical relevance of a mutation by: the extent of temperature shift it induces in the unfolding transition, the increase of the kinetic unfolding rates with respect to the wild type, and by &Fgr;-value analysis. Further analysis of folding stages based on the evolution of native contact probabilities reveals an entropy-driven pathway originating in the protein region close to Res115 and ending up in the area of Res28. The mutation of the former residue thus appears to be responsible for an early interruption of the folding process, leaving the protein largely unstructured and yielding a serious impairment of cardiac function. Mut28, on the contrary, thwarts a late stage of folding when the protein is almost completely native-like, leading to a mild phenotype. A bio-informatic analisys of the long and destabilizing CD loop finally shows an excess of negative charge and a low hydrophobicity indicating a possible classification as a natively unfolded sequence. Accordingly, the folding mechanism is suggested to be coupled with binding with a specific ligand.

We present a model for a molecular pump of neutral particles which is powered by a flashing ratchet mechanism. This device obeys a Langevin equation with multiplicative noise and it is embedded in a cell membrane bounded by two particle reservoirs. Thus, and unlike typical Brownian motors, the boundary conditions are not periodic nor the normalization condition is imposed. Instead, we study the steady state either at zero or finite flux and derive an exact solution for the density profile of particles. The ratio of concentrations created at both ends of the system and the flux are explored as a function of the parameters of the model.

It is shown that for systems with a periodic potential, the flux is very sensitive to the strength of additive and/or multiplicative noise. Multiplicative noise becomes important when its strength is of order the barrier height, and it provides a means of additional control of the flux (voltage-current characteristics for a Josephson junction). In addition to a numerical analysis, the cases of weak and strong additive noise have been considered analytically.

A novel conceptual model is introduced in which ion permeation is coupled to the protein wall vibration and the later in turn modulates exponentially strongly the permeation via radial oscillations of the potential of mean force. In the framework of this model of ion-wall-water interaction we discuss problems of selectivity between alike ions and coupling of ion permeation to gating.

Ionic motion in the bulk solution away from the mouth of a biological ion channel, and inside the channel, is analyzed using Poisson-Nernst-Planck (PNP) equation. The one-dimensional method allows us to connect in a self-consistent way ion dynamics in the bulk solution and inside the channel by taking into account access resistance to the channel. In order to glue the PNP solution in the bulk to that inside the channel, a continuity condition is used for the concentration and the current near the channel mouth at the surface of the hemisphere. The resulting one dimensional (1D) current-voltage characteristics are compared with the Kurnikova¹⁶ results which are in good agreement with experimental measurement on the channel, by using a filling factor as the only fitting parameter. The filling factor compensates the fact that the radial charge distribution is non-uniform in a real channel as compared to the cylindrically symmetrical channel used in the 1D approximation.

We analyze the consequences of interactions between the pore and the translocating molecule within the framework of a continuous diffusion model using the Smoluchowski equation with the radiation boundary conditions. We describe the solute-pore interaction in terms of the potential of mean force. Several of our analytical findings are quite counterintuitive. Three of the examples to be discussed here are: (i) "Sticking" to the channel slows down translocation (a particle spends more time in the channel) but increases the flux; (ii) If the potential well modeling the particle-channel interaction occupies only a part of the channel length, the average translocation time is non-monotonic in the width of the potential well, first increasing and then decreasing; (iii) At a finite potential bias applied to the channel, the mean "up-hill" and "downhill" particle translocation times (and their distributions) are identical.

We argue that when individuals enunciate sounds which are perceived to be the same, the sounds have the commonalty that their spectra can be transformed into a new domain which results in identical spectra except for a speaker dependent translation factor. We call the transformation function the speech scale. The speech scale is experimentally obtained. In this paper we explore the mathematical issues involved and obtain various criteria for when a transformation to a new domain results in a speaker independent transform.

We have investigated how optimal coding for neural systems changes with the time available for decoding. Optimization was in terms of maximizing information transmission. We have estimated the parameters for Poisson neurons that optimize Shannon transinformation with the assumption of rate coding. We observed a hierarchy of phase transitions from binary coding, for small decoding times, toward discrete (M-ary) coding with two, three and more quantization levels for larger decoding times. We postulate that the presence of subpopulations with specific neural characteristics could be a signiture of an optimal population coding scheme and we use the mammalian auditory system as an example.

Liposomes are self-assembled spherical vesicles comprised of a lipid bilayer membrane that segregates an internal aqueous environment from an external aqueous environment. These nanometer-scale structures have demonstrated potential for targeted drug delivery applications. For liposomes to be useful in vivo, the liposome size and dosage of molecules contained within them needs to be controlled. We present here a fluorescence-based technique for characterizing the relative encapsulation efficiency, leakage rate, and shelf life of liposome formulations. We report results from three different liposome solutions over a period of two months that show the liposome brightness remains stable while the background dye concentration increases. These parameters may prove useful for optimizing the liposome formation process.

Kinetic aspects of receptor-mediated endocytosis are identified, particularly as relating to the stochastic formation and released of clathrin coated vesicles at the plasma membrane. We discuss how one might account for the coordinated steps of this process, including receptor activation, association with adaptor proteins, coat formation, and the role of phosphoinosotide metabolism as a regulatory mechanism. In anticipation of building a detailed mathematical theory, we discuss an earlier treatment of the way threshold fluctuations affect the firing probability of nerve axons (H. Lecar, and R. Nossal, Biophys. J. 11, pp. 1048--1067, 1971), in which equations were analyzed by distinguishing different time-scales to identify pertinent kinetic variables

The dynamics of cytosolic Ca²⁺ concentration exhibits oscillations with a wide range of periods. It was suggested in recent years by several modelling studies that these oscillations do not result from an oscillatory local dynamics but that fluctuations drive the formation of spatial and temporal structures in a non-oscillatory dynamic regime. Fluctuations arise from the random opening and closing of release channels on the membrane of the endoplasmic reticulum. Consequently, the interspike interval (ISI) has not a sharp value as with regular oscillations but distributions of ISI arise. We present these distributions and relate them to underlying processes. Oscillations with long average ISI can be comprehended as repetitive wave triggering. The standard deviation of the ISI approximates the inverse of the triggering rate. Oscillations with short average ISI are often complex oscillations consisting of base line oscillations and intermittent oscillations on an elevated cytosolic Ca²⁺ level.

We have modified the standard diploid Penna model of ageing in such a way that instead of threshold of defective loci resulting in genetic death of individuals, the fluctuation of environment and "personal" fluctuations of individuals were introduced. The sum of the both fluctuations describes the health status of the individual. While environmental fluctuations are the same for all individuals in the population, the personal component of fluctuations is composed of fluctuations corresponding to each physiological function (gene, genetic locus). It is rather accepted hypothesis that physiological parameters of any organism fluctuate highly nonlinearly. Transition to the synchronized behaviors could be a very strong diagnostic signal of the life threatening disorder. Thus, in our model, mutations of genes change the chaotic fluctuations representing the function of a wild gene to the synchronized signals generated by mutated genes. Genes are switched on chronologically, like in the standard Penna model. Accumulation of defective genes predicted by Medawar's theory of ageing leads to the replacement of uncorrelated white noise corresponding to the healthy organism by the correlated signals of defective functions. As a result we have got the age distribution of population corresponding to the human demographic data.

In the noisy Penna model of ageing, instead of counting the number of defective loci which eventually kill an individual, the noise describing the health status of individuals is introduced. This white noise is composed of two components: the environmental one and the personal one. If the sum of both trespasses the limit set for the individuals homeodynamics the individual dies. The energy of personal fluctuations depends on the number of defective loci expressed in the individuals genome. Environmental fluctuations, the same for all individuals can include some signals, corresponding to the exposition to pathogens which could be dangerous for a fraction of the organisms. Personal noise and the component of random environmental fluctuations, when superimposed on the signal can be life threatening if they are stronger than the limit set for individuals homeodynamics. Nevertheless, some organisms survive the period of dangerous signal and they may remember the signal in the future, like antigens are remembered by our immune systems. Unfortunately, this memory weakens with time and, even worse, some additional defective genes are switched on during the ageing. If the same pathogens (signals) emerge during the lifespan of the population, a fraction of the population could remember it and could respond by increasing the resistance to it. Again, unfortunately for some individuals, their memory could be too weak and their own health status has worsened due to the accumulated mutations, they have to die. Though, a fraction of individuals can survive the pandemics due to the immune memory, but a fraction of population has no such a memory because they were born after the last pandemic or they didnt notice this pandemic. Our simple model, by implementing the noise instead of deterministic threshold of genetic defects, describes how the impact of pandemics on populations depends on the time which elapsed between the two incidents and how the different age groups of populations can respond for the second pandemic.

We study the noise activated dynamics of a model autapse neuron system that consists of a subcritical Hopf oscillator with a time delayed nonlinear feedback. The coherence of the noise driven pulses of the neuron exhibits a novel double peaked structure as a function of the noise amplitude. The two peaks correspond to separate optimal noise levels for excitation of single spikes and multiple spikes (bursts) respectively. The relative magnitudes of these peaks are found to be a sensitive function of time delay. The physical significance of our results and its practical implications in various real life systems are discussed.

We examine the question of how a population of independently noisy sensory neurons should be configured to optimize the encoding of a random stimulus into sequences of neural action potentials. For the case where firing rates are the same in all neurons, we consider the problem of optimizing the noise distribution for a known stimulus distribution, and the converse problem of optimizing the stimulus for a given noise distribution. This work is related to suprathreshold stochastic resonance (SSR). It is shown that, for a large number of neurons, the SSR model is equivalent to a single rate-coding neuron with multiplicative output noise.

Pooling networks are composed of noisy independent neurons that all noisily process the same information in parallel. The output of each neuron is summed into a single output by a fusion center. In this paper we study such a network in a detection or discrimination task. It is shown that if the network is not properly matched to the symmetries of the detection problem, the internal noise may restore at least partially some kind of optimality. This is shown for both (i) noisy threshold model neurons, as well as (ii) Poisson neuron models. We also study an optimized version of the network, mimicking the notion of excitation/inhibition. We show that, when properly tuned, the network may reach optimality in a very robust way. Furthermore, we find in this optimization that some neurons remain inactive. The pattern of inactivity is organized in a strange branching structure, the meaning of which remains to be elucidated.

We discuss the relationship of endogenous neural noise (ENN) to performance of behavioral tasks and to information processing in the brain. Spontaneous neural activity is closely linked to development and perception, and is correlated with behavior. Some of this activity is probably related to internal processing of task- and goal-relevant information, but some is simply noise. Two previous studies have reported correlations between performance on behavioral tasks and measures of neural noise and have characterized these relationships as intrinsic stochastic resonance (SR). We argue that neither of these studies demonstrated intrinsic SR, and discuss several alternative ways of measuring ENN in humans from EEG or MEG records. Using one of these, random-phase power in the 30-50 Hz range 1 sec before the onset of the signal, we demonstrate a kind of intrinsic SR that optimizes detection of weak visual signals. Minimum response time was obtained when this EEG measure of ENN was in a middle decile. No other measure of ENN was related either to response time or to an unbiased measure of detection accuracy (e.g., d'). A discussion of the implications of these findings for the study of intrinsic SR concludes the paper.

Cochlear implants are prosthetic devices used to provide hearing to people who would otherwise be profoundly deaf. The deliberate addition of noise to the electrode signals could increase the amount of information transmitted, but standard cochlear implants do not replicate the noise characteristic of normal hearing because if noise is added in an uncontrolled manner with a limited number of electrodes then it will almost certainly lead to worse performance. Only if partially independent stochastic activity can be achieved in each nerve fibre can mechanisms like suprathreshold stochastic resonance be effective. We are investigating the use of stochastic beamforming to achieve greater independence. The strategy involves presenting each electrode with a linear combination of independent Gaussian noise sources. Because the cochlea is filled with conductive salt solutions, the noise currents from the electrodes interact and the effective stimulus for each nerve fibre will therefore be a different weighted sum of the noise sources. To some extent therefore, the effective stimulus for a nerve fibre will be independent of the effective stimulus of neighbouring fibres. For a particular patient, the electrode position and the amount of current spread are fixed. The objective is therefore to find the linear combination of noise sources that leads to the greatest independence between nerve discharges. In this theoretical study we show that it is possible to get one independent point of excitation (one null) for each electrode and that stochastic beamforming can greatly decrease the correlation between the noise exciting different regions of the cochlea.

The goal of this work is to study the fluctuations the eye is subjected to, from the point of view of noise-enhanced processing. In this paper we consider a basic model of retina: a regular sampler subjected to space and time fluctuations to model the random sampling and the eye-tremor respectively. We also take into account the filtering made by the photoreceptors and we focus on a stochastic model of natural scene. To quantify the effect of the noise, we study the correlation coefficient between the signal acquired by a given photoreceptor, and a given point of the scene the eye is looking at. We then show on academic examples as well as on a more realistic case that the fluctuations which affect the retina can induce noise-enhanced processing effects. Finally, we interpret why this effect is possible. We especially interpret the microsaccadic movement of the retina as a stochastic control.

Inference of direction of coupling, or causality, as we can say when we consider two, possibly coupled systems, is a complex and complicated task. In this paper we discuss some problems encountered in inference of causality from bivariate time series and propose ways to cope with them in order to perform tests with high sensitivity and low rate of false positive results.

We address the problem of interactions between the phase of cardiac and respiration oscillatory components. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical with original one.

We present a model of the cardiovascular system (CVS) based on a system of coupled oscillators. Using this approach we can describe several complex physiological phenomena that can have a range of applications. For instance, heart rate variability (HRV), can have a new deterministic explanation. The intrinsic dynamics of the HRV is controlled by deterministic couplings between the physiological oscillators in our model and without the need to introduce external noise as is commonly done. This new result provides potential applications not only for physiological systems but also for the design of very precise electronic generators where the frequency stability is crucial. Another important phenomenon is that of oscillation death. We show that in our CVS model the mechanism leading to the quenching of the oscillations can be controlled, not only by the coupling parameter, but by a more general scheme. In fact, we propose that a change in the relative current state of the cardiovascular oscillators can lead to a cease of the oscillations without actually changing the strength of the coupling among them. We performed real experiments using electronic oscillators and show them to match the theoretical and numerical predictions. We discuss the relevance of the studied phenomena to real cardiovascular systems regimes, including the explanation of certain pathologies, and the possible applications in medical practice.

Heart rate variability (HRV) measures cycle-to-cycle correlations in the instantaneous oscillation period of the heart. In this paper it is shown that a simple model process, consisting of a sum of uncoupled sinusoidal oscillators with slightly different frequencies, has a HRV spectrum with a 1/f scaling over a range of frequencies. This implies that the appearance of 1/f HRV spectra in experiments should not be considered evidence of oscillator coupling or other more complex dynamics. The origin of the 1/f scaling in the model is examined analytically, and its dependence upon the sampling of low-amplitude fluctuations of the process is highlighted.

Flicker-Noise Spectroscopy (FNS), a general approach to the extraction and parameterization of resonant and stochastic components contained in medical time series, is presented. The basic idea of FNS is to treat the correlation links present in sequences of different irregularities, such as spikes, "jumps", and discontinuities in derivatives of different orders, on all levels of the spatiotemporal hierarchy of the system under study as main information carriers. The tools to extract and analyze the information are power spectra and difference moments (structural functions), which complement the information of each other. The structural function stochastic component is formed exclusively by "jumps" of the dynamic variable while the power spectrum stochastic component is formed by both spikes and "jumps" on every level of the hierarchy. The information "passport" characteristics that are determined by fitting the derived expressions to the experimental variations for the stochastic components of power spectra and structural functions are interpreted as the correlation times and parameters that describe the rate of "memory loss" on these correlation time intervals for different irregularities. The number of the extracted parameters is determined by the requirements of the problem under study. Application of this approach to the analysis of tremor velocity signals for a Parkinsonian patient is discussed.

The coexistence of different dynamical regimes of cardiac cell-model at a fixed set of stimulation parameters, i.e. multistability, revealed by noise is presented in this paper. Numerical simulations are performed using Luo-Rudy (LR1) action potential model. Numerical experiments with LR1 model conducted via noisy periodical stimulation showed the coexistence of several periodic rhythms. Weak noise in period of stimulation causes a hopping process between all the (meta-) stable rhythms of cell-model. This process is reflected in several parallel branches of the bifurcation diagram: noise unveils new, invisible before, stable rhythms which could appear in this model at different initial conditions. The phenomenon of multistability is directly evidenced by other numerical experiments: we have established the multistability property of a cell consisting in the fact that different initial conditions of stimulation (different extrasystole application times) lead to different stable periodic rhythms. We have obtained the shaping of attraction basins on the action potential curves. Such basins of attraction contain a set of initial conditions which determinate a stable periodic rhythm. We have found a close association between the attraction basins of the complex rhythms on the curves of action potential and the cardiac vulnerable windows on ECG record, during which extra stimuli can induce life threatening arrhythmias. Obtained results allow us to make a conclusion that multistability is very important for the electrical conduction system of the heart from the cell level to the integrated function of the heart.

The influence of time-delayed feedback on the dynamics of a net of oscillatory FitzHugh-Nagumo elements is investigated. We show that the global oscillation of the net can be suppressed (amplitude death) and excitable network dynamics can be restored via time-delayed feedback for a properly chosen delay time. We investigate the influence of local and global feedback and the dependence of the amplitude death regime on the parameters of the feedback signal. Furthermore the influence of the coupling strength on the transition from the global oscillation to excitable network dynamics is studied. Starting with a net, whose global oscillation is suppressed, weak additive noise can induce excitation waves (noise-induced pattern formation), a fingerprint of excitable network dynamics.

A scientific problem described within a given code is mapped by a corresponding computational problem, We call complexity (algorithmic) the bit length of the shortest instruction which solves the problem. Deterministic chaos in general affects a dynamical systems making the corresponding problem experimentally and computationally heavy, since one must reset the initial conditions at a rate higher than that of information loss (Kolmogorov entropy). One can control chaos by adding to the system new degrees of freedom (information swapping: information lost by chaos is replaced by that arising from the new degrees of freedom). This implies a change of code, or a new augmented model. Within a single code, changing hypotheses is equivalent to fixing different sets of control parameters, each with a different a-priori probability, to be then confirmed and transformed to an a-posteriori probability via Bayes theorem. Sequential application of Bayes rule is nothing else than the Darwinian strategy in evolutionary biology. The sequence is a steepest ascent algorithm, which stops once maximum probability has been reached. At this point the hypothesis exploration stops. By changing code (and hence the set of relevant variables) one can start again to formulate new classes of hypotheses . We call semantic complexity the number of accessible scientific codes, or models, that describe a situation. It is however a fuzzy concept, in so far as this number changes due to interaction of the operator with the system under investigation. These considerations are illustrated with reference to a cognitive task, starting from synchronization of neuron arrays in a perceptual area and tracing the putative path toward a model building.

Neural circuit architecture is a fundamental characteristic of the brain, and how architecture is bound to biological functions is still an open question. Some neuronal geometries seen in the retina or the cochlea are intriguing: information is processed in parallel by several entities like in "pooling" networks which have recently drawn the attention of signal processing scientists. These systems indeed exhibit the noise-enhanced processing effect, which is also actively discussed in the neuroscience community at the neuron scale. The aim of our project is to use in-vitro ordered neuron networks as living paradigms to test ideas coming from the computational science. The different technological bolts that have to be solved are enumerated and the first results are presented. A neuron is a polarised cell, with an excitatory axon and a receiving dendritic tree. We present how soma confinement and axon differentiation can be induced by surface functionalization techniques. The recording of large neuron networks, ordered or not, is also detailed and biological signals shown. The main difficulty to access neural noise in the case of weakly connected networks grown on micro electrode arrays is explained. This open the door to a new detection technology suitable for sub-cellular analysis and stimulation, whose development will constitute the next step of this project.

Theory of frequency modulation of electroencephalogram (EEG) in human brain with/without photo-stimulation is presented. Firstly, physical/physiological significance of frequency modulation is discussed based on EEG data in the state of closed eyes at rest. Secondly, possible phenomenological theoretical models under photo-stimulation (PS) are examined to explain the features of intrinsic/induced frequency modulation and the frequency responses induced by PS. Properties of a generalized Kubo oscillator with a parametric periodic driving force are demonstrated to give the qualitative understandings of the observed age-dependent and light-induced natures of EEGs.

A Bayesian framework for parameter inference in non-stationary, nonlinear, stochastic, dynamical systems is introduced. It is applied to decode time variation of control parameters from time-series data modelling physiological signals. In this context a system of FitzHugh-Nagumo (FHN) oscillators is considered, for which synthetically generated signals are mixed via a measurement matrix. For each oscillator only one of the dynamical variables is assumed to be measured, while another variable remains hidden (unobservable). The control parameter for each FHN oscillator is varying in time. It is shown that the proposed approach allows one: (i) to reconstruct both unmeasured (hidden) variables of the FHN oscillators and the model parameters, (ii) to detect stepwise changes of control parameters for each oscillator, and (iii) to follow a continuous evolution of the control parameters in the quasi-adiabatic limit.

In this contribution we tackle the problem of simulating the time behavior of self-assembling fatty acid vesicles in different experimental conditions. These systems have been (and are being) explored by various labs as possible precursor models of cellular compartments. By means of our recently developed stochastic simulation platform ('ENVIRONMENT') we are able to reproduce quite satisfactorily experimental data that have been reported on the different growth behavior of this type of proto-cellular systems, depending on the level of osmotic pressure they are under. The work here presented is part of a more general attempt to gain insight into the problem of how self-assembling vesicles (closed bilayer structures) could progressively turn into minimal self-producing and self-reproducing cells: i.e., into interesting candidates for (proto-)biological systems. This involves crossing the traditional gap between in silico and in vitro approaches, as we try to do here, convinced that major adavances in the field require the correct integration of both theoretical and experimental endeavors.

Spike trains recorded in cortical neurons in vivo can be approximated by renewal processes, but are generally not Poisson. Besides, the spiking activity of neighboring neurons display small yet not negligible correlations. The Artificial Neuronal Network theory has traditionally neglected such observations, assuming that neurons could simply be described by their mean firing rate. Here we present a theoretical framework in which the dynamics of a system of neurons is specified in terms of higher-order moments of their spiking activity beyond the mean firing rate.

Starting with a subexcitable net of FitzHugh-Nagumo elements additive parameter-variability (diversity, heterogeneity) is able to induce pattern formation. The patterns are most coherent for an intermediate variability strength. Multiplicative variability is able to induce a transition to an excitable net dynamics. In the present paper the interplay of additive and multiplicative variability in subexcitable nets of FitzHugh-Nagumo elements is examined. It is shown that the diversity in the net leads to a coherent dynamics. The net can generate excitation waves, which spread through the whole net. Furthermore the response of the net with variability to a stochastic forcing (additive noise) is studied. Increasing the strength of the additive noise the net without variability shows spatiotemporal stochastic resonance. The noise strength for which the pattern formation sets in and the shape of the resonance curve strongly depend on the strength of the additive variability. For large values the effect of spatiotemporal stochastic resonance is destroyed. The coherence of the patterns in presence of additive noise and additive variability can be maximized by applying additionally multiplicative variability.