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.     

Scaling Behaviour and Memory in Heart Rate of Healthy Human

We investigate a set of complex heart rate time series from healthy human in different behaviour states with the detrended fluctuation analysis and diffusion entropy （DE） method. It is proposed that the scaling properties are influenced by behaviour states. The memory detected by DE exhibits an approximately same pattern after a detrending procedure. Both of them demonstrate the long-range strong correlations in heart rate. These findings may be helpful to understand the underlying dynamical evolution process in the heart rate control system, as well as to model the cardiac dynamic process.     

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.     

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.     

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.     

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.     

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.     

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.     

Intermittent Chaotic Neural Firing Characterized by Non-Smooth Features

A chaotic firing pattern, characterized by non-smooth features and generated through the routine of intermittency from period 3, is observed in biological experiments on a neural firing pacemaker and reproduced in simulations by using a theoretical neuronal model with multiple time scales. This chaotic activity exhibits a scale law very similar to those of both the type-Ⅰ intermitteney generated in smooth systems and the type-Ⅴ intermittency in non-smooth systems.     

Biospeckle laser spectral analysis under Inertia Moment, Entropy and Cross-Spectrum methods

Biospeckle or dynamic speckle can be used as a method for analysing activity, biologic or not, from materials illuminated with laser beam. The Spatial Temporal Speckle (STS) contains data of time information of dynamic speckle and it is used as input for many techniques allowing the analysis of the activity which is being monitored. One question that rises from the manipulation of the STS is related with the information inside it, in particular, whether it is possible to access different frequency behaviors in the time series presented in the STS pattern. This study presents the Inertia Moment, the Wavelets based Entropy and the Cross-Spectrum analysis as approaches that can be used for evaluating the STS spectral content. In a simulation, STS lines have been created based on many frequencies of the fundamental harmonic. This was done for verifying as each method acts when analysing different frequencies, varying harmonics offset and amplitude. These techniques were applied to real database, to validate their action mechanism in real samples. The results present that all techniques were able to verify the spectral content of different harmonics. Inertia Moment was more efficient on analysing high frequencies, because it is a second order moment, being able to obtain more information from high variations on activity. Entropy and Cross-Spectrum, in turn, were better on differing lower frequencies. This was attributed to the convolution proccess, which is present in both methods, filtering high frequencies. Although, any of them returned informations on both high and low frequencies at the same time, they can be used simultaneously, since Entropy and Cross-Spectrum were complementary to Inertia Moment.     

Study of the human postural control system during quiet standing using detrended fluctuation analysis

The detrended fluctuation analysis is used to study the behavior of different time series obtained from the trajectory of the center of pressure, the output of the activity of the human postural control system. The results suggest that these trajectories present two different regimes in their scaling properties: persistent (for high frequencies, short-range time scale) to antipersistent (for low frequencies, long-range time scale) behaviors. The similitude between the results obtained for the measurements, done with both eyes open and eyes closed, indicate either that the visual system may be disregarded by the postural control system while maintaining the quiet standing, or that the control mechanisms associated with each type of information (visual, vestibular and somatosensory) cannot be disentangled with the type of analysis performed here.     

基于多尺度传递熵的脑肌电信号耦合分析

神经运动控制中脑肌电同步特征可以反映皮层与肌肉之间的功能联系. 为定量研究脑电和肌电信号在不同时间尺度上的同步耦合特征, 提出多尺度传递熵方法实现静态握力输出下的脑肌电耦合分析: 对同步采集的头皮脑电信号(EEG) 和表面肌电信号(EMG)进行多尺度化, 计算不同尺度因子下EEG与EMG间的传递熵值, 获取不同耦合方向(EEG→EMG及EMG→EEG)上的非线性脑肌电耦合特征; 进一步计算功能频段下的显著性面积指标, 定量分析不同尺度下皮层肌肉功能耦合强度的差异. 分析结果显示, 静态握力输出时beta频段(15–35 Hz)皮层肌肉功能耦合特征显著, 且beta2频段(25–35 Hz)在不同尺度上EEG→EMG方向的耦合强度大于EMG→EEG方向, 耦合强度最大值和方向间耦合强度差异显著值均出现于较高时间尺度. 研究结果揭示: 皮层肌肉功能耦合具有双向性, 且耦合强度在不同时间尺度和不同功能频段上有所差异, 可利用多尺度传递熵定量刻画大脑皮层与肌肉之间的非线性同步特征及功能联系.     

Comparison of immunization strategies in geographical networks

The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time, for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy, especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy, which may have potential applications for preventing the real epidemic spread.     

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.     

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 quantum field theory of the liquid-glass transition in multi-component liquids

An established unified theory of the liquid-glass transition in one-component liquids is extended to multi-component liquids. The universal features such as the Kauzmann paradox, the Vogel-Tamman-Fulcher (VTF) law on the relaxation times and the transport coefficients, the jump of the specific heat at the glass transition temperature and the Boson peaks are elucidated. The Kauzmann entropy in a form of a Curie law with a negative sign comes from the mixing between the sound and the intra-band fluctuation entropies, where the critical temperature corresponds to the sound instability temperature at a reciprocal particle distance. The VTF law is constructed from the Einstein relation on entropy and probability so that the Kauzmann entropy is included as a normal form in exponent of the VTF law. The Kauzmann entropy explains the Kauzmann paradox and the jump of the specific heat so that the universal features of the glass transition are elucidated consistently.     

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.     

On entropy, financial markets and minority games

The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B—Condensed Matter and Complex Systems 15/4 (2000) 733-737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey-Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.     

Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

We investigate the quantum entanglement in a non-Hermitian kicking system. In the Hermitian case, the out-of-time ordered correlators (OTOCs) exhibit the unbounded power-law increase with time. Correspondingly, the linear entropy, which is a common measurement of entanglement, rapidly increases from zero to almost unity, indicating the formation of quantum entanglement. For strong enough non-Hermitian driving, both the OTOCs and linear entropy rapidly saturate as time evolves. Interestingly, with the increase of non-Hermitian kicking strength, the long-time averaged value of both OTOCs and linear entropy has the same transition point where they exhibit the sharp decrease from a plateau, demonstrating the disentanglment. We reveal the mechanism of disentanglement with the extension of Floquet theory to non-Hermitian systems.