Generalized relative entropy in functional magnetic resonance imaging

The generalized Kullback-Leibler distance D_q (q is the Tsallis parameter) is shown to be an useful measure for analysis of functional magnetic resonance imaging (fMRI) data series. This generalized form of entropy is used to evaluate the “distance” between the probability functions p₁ and p₂ of the signal levels related to periods of stimulus and non-stimulus in event-related fMRI experiments. The probability densities of the mean distance (averaged over the N epochs of the entire experiment) are obtained through numerical simulations for different values of signal-to-noise ratio (SNR) and found to be fitted very well by Gamma distributions (χ²<0.0008) for small values of N (N<30). These distributions allow us to determine the sensitivity and specificity of the method by construction of the receiver operating characteristic (ROC) curves. The performance of the method is also investigated in terms of the parameters q and L (number of signal levels) and our results indicate that the optimum choice is q=0.8 and L=3. The entropic index q is found to exert control on both sensitivity and specificity of the method. As q (q>0) is raised, sensitivity increases but specificity decreases. Finally, the method is applied in the analysis of a real event-related fMRI motor stimulus experiment and the resulting maps show activation in primary and secondary motor brain areas.     

Frequency Selectivity Behaviour in the Auditory Midbrain： Implications of Model Study

By numerical simulations on frequency dependence of the spiking threshold, i.e. on the critical amplitude of periodic stimulus, for a neuron to fire, we find that bushy cells in the cochlear nuclear exhibit frequency selec- tivity behaviour. However, the selective frequency band of a bushy cell is far away from that of the preferred spectral range in human and mammal auditory perception. The mechanism underlying this neural activity is also discussed. Further studies show that the ion channel densities have little impact on the selective frequency band of bushy cells. These findings suggest that the neuronal behaviour of frequency selectivity in bushy cells at both the single cell and population levels may be not functionally relevant to frequency discrimination. Our results may reveal a neural hint to the reconsideration on the busily cell functional role in auditory information processing of sound frequency.     

Stochastic resonance of a periodically driven neuron under non-Gaussian noise

We investigate the first-passage-time statistics of the integrate-fire neuron model driven by a sub-threshold harmonic signal superposed with a non-Gaussian noise. Here, we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term. Such a mechanism generates a power-law distributed noise whose characteristic decay exponent can be finely tuned. We performed numerical simulations to analyze the influence of the noise non-Gaussian character on the stochastic resonance condition. We found that when the noise deviates from Gaussian statistics, the resonance condition occurs at weaker noise intensities, achieving a minimum at a finite value of the distribution function decay exponent. We discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons, as the present result indicates that neurons would require a lower noise level to detect a sub-threshold signal when its statistics departs from Gaussian.     

Comparison of the energetic properties and the dynamical stability in a mathematical model of the stretch reflex

The previous studies on finite-time thermodynamic engines have shown that some of the parameters affecting their thermodynamic performance also affect their stability. Moreover, such parameters have to be tuned to reach an optimal trade-off between these two generic properties. In the present work we carry out a similar analysis on a mathematical model of the stretch reflex regulatory pathway, which is a simplified version of a previously published model. We show that the model has a unique stable fixed point in the absence of time delays. However, when the system inherent time delays are considered, they can destabilize the fixed point and engender a stable limit cycle. We further explore the parameter space to analyse the sensitivity of the system stability to variations in the parameter values. Particular attention is paid to the parameter here denoted as α, which has been shown to determine the muscle thermodynamic properties during steady-state contractions: larger values of α mean more powerful and less efficient muscles. Our results indicate that the stretch reflex pathway is less stable in the more powerful and less efficient muscles. We finally compare these observations with those obtained on thermal engines.     

Statistically robust evidence of stochastic resonance in human auditory perceptual system

In human perception, exogenous noise is known to yield a masking effect, i.e. an increase of the perceptual threshold relative to a stimulus acting on the same modality. However, somehow counter-intuitively, the opposite mechanism can occasionally occur: a decrease of the perceptual threshold for a non-vanishing, virtuous amount of noise. This mechanism, called stochastic resonance, is deemed to provide important information about the role of noise in the human brain. In this paper, we investigate stochastic resonance in a detection task in the auditory modality. Normal-hearing participants were asked to judge the presence of acoustic stimuli of different intensity and superimposed to different levels of white noise. The matrix-like outcomes of a behavioural experiment were fitted by a two-dimensional, noise-dependent psychometric function. The fit revealed a statistically significant stochastic resonance in 43% of the experimental runs. We conclude that, in the auditory modality, stochastic resonance is a tiny effect that, under conventional circumstances, is largely overrun by standard masking.     

New Evidence of Active Tuning in Cochlea

The wonderful performance of hearing systems is mainly attributed to the tuning tiltering of basilar membrane （BM）. Although theory of the cochlear mechanism has been greatly developed since the 1970s and the amplification or sensitivity of the cochlea has been concluded due to the out hair cells, the mechanics underlying the sharp-tuning or frequency selectivity of cochlea remains a puzzle. We use the cochlear translation function derived from the data of an experiment of the BM in vivo to calculate basilar responses to tone bursts, and find that there are resonant peaks with the characteristic frequency at the corresponding place in the initial and terminal part of the responses. However, when the translation function is shallower, there will be no resonant peaks in the responses. The result indicates that the sharp tuning is due to existence of the active resonant tuning mechanism.     

Stochastic resonance in the FitzHugh-Nagumo model from a dynamic mutual information point of view

Stochastic resonance(SR) in a FitzHugh-Nagumo neuron model is investigated based on a dynamic mutual information (DMI) between the input and the corresponding output signals. The DMI is expressed in terms of the (cross)power spectra of the input and output time series. Both stochastic-periodic and aperiodic SR are treated based on the DMI and our results are in good accord with the SR measured by the signal to noise ratio(SNR) for the case of the stochastic-periodic input and the power norm for the case of the aperiodic input.     

Nonlinear attractor dynamics in the fundamental and extended prism adaptation paradigm

Adaptation and re-adaptation processes are studied in terms of dynamic attractors that evolve and devolve. In doing so, a theoretical account is given for the fundamental observation that adaptation and re-adaptation processes do not exhibit one-trial learning. Moreover, the emergence of the latent aftereffect in the extended prism paradigm is addressed.     

Comparison of the small-world topology between anatomical and functional connectivity in the human brain

We applied graph analysis to both anatomical and functional connectivity in the human brain. Anatomical connectivity was acquired from diffusion tensor imaging data by probabilistic fiber tracking, and functional connectivity was extracted from resting-state functional magnetic resonance imaging data by calculating correlation maps of time series. For the same subject, anatomical networks seemed to be disassortative, while functional networks were significantly assortative. Anatomical networks showed higher efficiency and smaller diameters than functional networks. It can be proposed that anatomical connectivity, as a major constraint of functional connectivity, has a relatively stable and efficient structure to support functional connectivity that is more changeable and flexible.     

Bifurcation in neuronal networks with hub structure

We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris-Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed.     

Effect of Rolling Massage on Particle Moving Behaviour in Blood Vessels

The rolling massage manipulation is a classic Chinese massage, which is expected to eliminate many diseases. Here the effect of the rolling massage on the particle moving property in the blood vessels under the rolling massage manipulation is studied by the lattice Boltzmann simulation. The simulation results show that the particle moving behaviour depends on the rolling velocity, the distance between particle position and rolling position. The average values, including particle translational velocity and angular velocity, increase as the rolling velocity increases almost linearly. The result is helpful to understand the mechanism of the massage and develop the rolling techniques.     

Lattice Boltzmann Simulations of Particle-Particle Interaction in Steady Poiseuille Flow

The moving behaviour of two- and three-particles in a pressure-driven flow is studied by the lattice Boltzmann simulation in two dimensions. The time-dependent values, including particles＇ radial positions, translational velocities, angular velocities, and the x-directional distance between the particles are analysed extensively. The effect of flow Reynolds number on particle motion is also investigated numerically. The simulation results show that the leading particle equilibrium position is closer to the channel centre while the trailing particle equilibrium position is closer to the channel wall. If Reynolds number Re is less than 85.30, the larger flow Reynolds number results in the smaller x-directional equilibrium distance, otherwise the x-directional distance increases almost linearly with the increase of time and the particles separate finally. The simulation results are helpful to understand the particle-particle interaction in suspensions with swarms of particles.     

The effects of neuron heterogeneity and connection mechanism in cortical networks

The mammalian cortices show an specific architecture close to the optimum, represented by the high clustering, short processing steps and short wiring length. What are the key factors that influence the layout of neural connectivity networks? Here a model to investigate the conditions leading to the small-world cortical networks with minimal global wiring is presented. The essential factors in this model are the introductions of the unequal number distribution of heterogeneous neurons and two connection mechanisms, the preferential attachment to neurons with large spatial coverage (PANLSC) and distance preference. Outcomes show that the specific architecture close to the optimum can only result from the PANLSC when the number distribution of neurons with diverse spatial coverage is highly unequal. This suggests the PANLSC may be an important connection mechanism in cortical systems.     

Minimal attractors in digraph system models of neuronal networks

We study a class of discrete dynamical systems models of neuronal networks. In these models, each neuron is represented by a finite number of states and there are rules for how a neuron transitions from one state to another. In particular, the rules determine when a neuron fires and how this affects the state of other neurons. In an earlier paper [D. Terman, S. Ahn, X. Wang, W. Just, Reducing neuronal networks to discrete dynamics, Physica D 237 (2008) 324-338], we demonstrate that a general class of excitatory-inhibitory networks can, in fact, be rigorously reduced to the discrete model. In the present paper, we analyze how the connectivity of the network influences the dynamics of the discrete model. For randomly connected networks, we find two major phase transitions. If the connection probability is above the second but below the first phase transition, then starting in a generic initial state, most but not all cells will fire at all times along the trajectory as soon as they reach the end of their refractory period. Above the first phase transition, this will be true for all cells in a typical initial state; thus most states will belong to a minimal attractor of oscillatory behavior (in a sense that is defined precisely in the paper). The exact positions of the phase transitions depend on intrinsic properties of the cells including the lengths of the cells’ refractory periods and the thresholds for firing. Existence of these phase transitions is both rigorously proved for sufficiently large networks and corroborated by numerical experiments on networks of moderate size.     

Excitable scale free networks

When a simple excitable system is continuously stimulated by a Poissonian external source, the response function (mean activity versus stimulus rate) generally shows a linear saturating shape. This is experimentally verified in some classes of sensory neurons, which accordingly present a small dynamic range (defined as the interval of stimulus intensity which can be appropriately coded by the mean activity of the excitable element), usually about one or two decades only. The brain, on the other hand, can handle a significantly broader range of stimulus intensity, and a collective phenomenon involving the interaction among excitable neurons has been suggested to account for the enhancement of the dynamic range. Since the role of the pattern of such interactions is still unclear, here we investigate the performance of a scale-free (SF) network topology in this dynamic range problem. Specifically, we study the transfer function of disordered SF networks of excitable Greenberg-Hastings cellular automata. We observe that the dynamic range is maximum when the coupling among the elements is critical, corroborating a general reasoning recently proposed. Although the maximum dynamic range yielded by general SF networks is slightly worse than that of random networks, for special SF networks which lack loops the enhancement of the dynamic range can be dramatic, reaching nearly five decades. In order to understand the role of loops on the transfer function we propose a simple model in which the density of loops in the network can be gradually increased, and show that this is accompanied by a gradual decrease of dynamic range.     

Duration of transient oscillations in ring networks of unidirectionally coupled neurons

Properties of the duration of long lasting transient oscillations in ring networks of unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling waves in the network. The duration of the transient oscillations occurring from random initial conditions increases exponentially as the number of neurons. The distribution of the duration is approximated by a power-law function when the number of neurons is large. Further, transient oscillations which oscillate about one thousand cycles before ceasing are observed in a network of forty neurons in circuit experiments though the duration decreases owing to random biases.     

Directional Motion of Droplets in a Conical Tube or on a Conical Fibre

Manipulating the directional movement of liquid droplets is of significance for design and fabrication of some microfluidic devices, An energy-based method is adopted to analyse the directional movement of a droplet deposited in a conical tube or on a conical fibre. We perform an experiment to investigate the directional motion of a droplet in an open conical tube. Our theoretical analysis and experimental observations both demonstrate that surface tension can drive the droplet to move in the conical tube. The critical condition of the liquid moving in the conical tube is presented. We also analyse a droplet on a conical hydrophilic fibre, which can move from the thinner to the thicker end.     

A Tsallis’ statistics based neural network model for novel word learning

We invoke the Tsallis entropy formalism, a nonextensive entropy measure, to include some degree of non-locality in a neural network that is used for simulation of novel word learning in adults. A generalization of the gradient descent dynamics, realized via nonextensive cost functions, is used as a learning rule in a simple perceptron. The model is first investigated for general properties, and then tested against the empirical data, gathered from simple memorization experiments involving two populations of linguistically different subjects. Numerical solutions of the model equations corresponded to the measured performance states of human learners. In particular, we found that the memorization tasks were executed with rather small but population-specific amounts of nonextensivity, quantified by the entropic index q. Our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems.     

Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends on the disease parameters, the geometry of the migrations between the patches, and the addition of infected people into a patch. We found that there are significantly longer lived transients and additional “ancillary” epidemics when the reproductive rate R is closer to 1, as would be typical of SARS (Severe Acute Respiratory Syndrome) and bird flu, than when R is closer to 10, as would be typical of measles. In addition we show, both analytical and numerical, how the time delay between the injection of infected people into a patch and the corresponding initial epidemic that it produces depends on R.     

Two mechanisms of spiral-pair-source creation in excitable media

Two new modes of generating spiral pairs in an excitable medium have been found. They depend on a geometrical structure (GS) inside the medium. This may be formed e.g. as a result of scars or fibrosis in the heart tissue, or artificially built in a chemical reaction substrate. Both sources involve a GS composed of a circular “convergent lens” bounded by two opaque “walls”. One mode can be induced by a single wave and behaves as a “flip-flop” type of a limit cycle. The other mode is generated by a train of plane waves impinging on the GS, and is created at the focus of the converging wave-fragments.