Within-Host Viral Dynamics in a Multi-compartmental Environment.

The discrepancy in the turnover of cells and virus in different organs or viral reservoirs necessitates the investigation of multiple compartments within a host. Establishing a multi-compartmental structure that describes the complexity of various organs, where viral infection comprehensively proceeds, provides a modeling framework for exploring the effect of spatial heterogeneity on viral dynamics. To successfully suppress within-host viral replication, it is imperative to determine drug administration during therapy, particularly for a combination of antiretroviral drugs. The proposed model provides quantitative insights into pharmacokinetics and the resulting virus population, which substantially relates to environmental heterogeneity. The main results are the following: (1) A model incorporating drug treatment admits threshold dynamics, driving to either viral extinction or uniform persistence, regardless of non-trivial initial infection, in the entire system. (2) Viral infection may be underestimated if a well-mixed (single-compartmental) model is used. (3) Optimal drug administration depends not only on the drug distribution over various compartments but also on the timing, described by phase shifts, of the administration of different drugs in a combined therapy.

Delayed transiently chaotic neural networks and their application.

In this paper, we propose a novel model, a delayed transiently chaotic neural network (DTCNN), and numerically confirm that the model performs better in finding the global minimum for the traveling salesman problem (TSP) than the traditional transiently chaotic neural network. The asymptotic stability and chaotic behavior of the dynamical system with time delay are fully discussed. We not only theoretically prove the existence of Marotto's chaos for the delayed neural network without the cooling schedule by geometrically constructing a transversal homoclinic orbit, but we also discuss the stability of nonautonomous delayed systems using LaSalle's invariance principle. The result of the application to the TSP by the DTCNN might further explain the importance of systems with time delays in the neural system.

On an age structured population model with density-dependent dispersals between two patches.

Motivated by an age-structured population model over two patches that assumes constant dispersal rates, we derive a modified model that allows density-dependent dispersal, which contains both nonlinear dispersal terms and delayed non-local birth terms resulted from the mobility of the immature individuals between the patches. A biologically meaningful assumption that the dispersal rate during the immature period depends only on the mature population enables us investigate the model theoretically. Well-posedness is confirmed, criteria for existence of a positive equilibrium are obtained, threshold for extinction/persistence is established. Also addressed are a positive invariant set and global convergence of solutions under certain conditions. Although the levels of the density- dependent dispersals play no role in determining extinction/persistence, our numerical results show that they can affect, when the population is persistent, the long term dynamics including the temporal- spatial patterns and the final population sizes.

Impaired frontal synchronization of spontaneous magnetoencephalographic activity in patients with bipolar disorder.

Recent functional imaging studies demonstrated that brain exhibit coherent, synchronized activities during resting state and the dynamics may be impaired in various psychiatric illnesses. In order to investigate the change of neural dynamics in bipolar disorder, we used a new nonlinear measurement "similarity index" to analyze the magnetoencephalography (MEG) recordings and test the hypothesis that there are synchronization changes within different frequency bands in the frontal cortex of patients with bipolar disorder. Ten patients with bipolar I disorder during euthymic phase and ten normal controls underwent 2min eye-closed resting recording with a whole-head 306-channel MEG system. Eleven channels of MEG data from frontal area were selected for analysis. Synchronization level in the delta (2-4Hz), theta (4-8Hz), alpha (8-12Hz) and beta (12-24Hz) bands was calculated for each subject and compared across group. The results showed that significant dynamic changes in bipolar patients can be characterized by increased synchronization of slow frequency oscillations (delta) and decreased synchronization of fast frequency oscillations (beta). Furthermore, the positive correlation between beta synchronization level and preservative errors in Wisconcin card sorting task was found which would implicate the deficit of executive function in bipolar patients. Our findings indicate that analysis of spontaneous MEG recordings at resting state using nonlinear dynamic approaches may disclose the subtle regional changes of neural dynamics in BD.

Detection of synchronization between chaotic signals: An adaptive similarity-based approach.

We present an adaptive similarity-based approach to detect generalized synchronization (GS) with n:m phase synchronization (PS), where n and m are integers and one of them is 1. This approach is based on the similarity index (SI) and Gaussian mixture model with the minimum description length criterion. The clustering method, which is shown to be superior to the closeness and connectivity of a continuous function, is employed in this study to detect the existence of GS with n:m PS. We conducted a computer simulation and a finger-lifting experiment to illustrate the effectiveness of the proposed method. In the simulation of a Rössler-Lorenz system, our method outperformed the conventional SI, and GS with 2:1 PS within the coupled system was found. In the experiment of self-paced finger-lifting movement, cortico-muscular GS with 1:2 and 1:3 PS was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area. The GS with n:m PS ( n or m=1 ) has been simultaneously resolved from both simulation and experiment. The proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science.

Effects of cognitive demands on postmovement motor cortical deactivation.

Postmovement beta-rebounds induced by different intermovement intervals were investigated using magnetoencephalography in 14 healthy participants to test the hypothesis that postmovement motor cortical deactivation over the primary motor cortex depends on movement-related cognitive demands. Shorter latency and lower amplitude in postmovement beta-rebounds over the contralateral primary motor cortex were noted in the short-movement interval movement (repetitive finger lifting). Greater latency span of postmovement beta-rebounds jittering using single-trial analysis in the long-movement interval movement (discrete finger lifting) was observed. The study elucidates that the temporal interval between two adjacent movements reflecting different degrees of cognitive demands can affect postmovement motor cortical deactivation in terms of postmovement beta-rebounds latency and amplitude, and latency span of postmovement beta-rebounds jittering. Postmovement motor cortical deactivation can reflect cognitive demands in addition to motor and somatosensory processing.

Dimensional complexity of neuromagnetic activity reduced during finger movement of greater difficulty.

OBJECTIVE: We investigated the variation in dimensionality (D2) of neuromagnetic activity over the primary sensorimotor cortex (SM1) in healthy adults performing motor tasks of different difficulty. METHODS: Magnetoencephalography (MEG) was used to record neuromagnetic activity during self-paced, brisk unimanual finger extension at a rate of 1 and 2 Hz using the index finger of the dominant and non-dominant hands in 16 healthy subjects. Motor task difficulty was rated by the relative difference in time measurement between 1 and 2 Hz finger movements of both hands. The relative difference in dimensionality of SM1 activity was calculated by subtracting the D2 value in 2 Hz movement from that in 1 Hz one within subjects. RESULTS: Simple regression analyses show a significantly negative relationship between the relative dimensional complexity and the relative motor task difficulty in the contralateral SM1 for the left- (p<0.05), but not the right- (p=0.447) hand movement. CONCLUSIONS: The present data suggest that a motor task of greater difficulty may engender a reduction of simultaneously active quasi-independent neuronal generators in the contralateral SM1 underpinned by stronger neuronal connectivity of a relatively low dimensionality. SIGNIFICANCE: The decrease in dimensional complexity of MEG activity associated with a motor task of greater difficulty gives new insights to motor control strategy.

Transversal homoclinic orbits in a transiently chaotic neural network.

We study the existence of snap-back repellers, hence the existence of transversal homoclinic orbits in a discrete-time neural network. Chaotic behaviors for the network system in the sense of Li and Yorke or Marotto can then be concluded. The result is established by analyzing the structures of the system and allocating suitable parameters in constructing the fixed points and their pre-images for the system. The investigation provides a theoretical confirmation on the scenario of transient chaos for the system. All the parameter conditions for the theory can be examined numerically. The numerical ranges for the parameters which yield chaotic dynamics and convergent dynamics provide significant information in the annealing process in solving combinatorial optimization problems using this transiently chaotic neural network. (c) 2002 American Institute of Physics.

Chaotic simulated annealing by a neural network with a variable delay: design and application.

In this paper, we have three goals: the first is to delineate the advantages of a variably delayed system, the second is to find a more intuitive Lyapunov function for a delayed neural network, and the third is to design a delayed neural network for a quadratic cost function. For delayed neural networks, most researchers construct a Lyapunov function based on the linear matrix inequality (LMI) approach. However, that approach is not intuitive. We provide a alternative candidate Lyapunov function for a delayed neural network. On the other hand, if we are first given a quadratic cost function, we can construct a delayed neural network by suitably dividing the second-order term into two parts: a self-feedback connection weight and a delayed connection weight. To demonstrate the advantage of a variably delayed neural network, we propose a transiently chaotic neural network with variable delay and show numerically that the model should possess a better searching ability than Chen-Aihara's model, Wang's model, and Zhao's model. We discuss both the chaotic and the convergent phases. During the chaotic phase, we simply present bifurcation diagrams for a single neuron with a constant delay and with a variable delay. We show that the variably delayed model possesses the stochastic property and chaotic wandering. During the convergent phase, we not only provide a novel Lyapunov function for neural networks with a delay (the Lyapunov function is independent of the LMI approach) but also establish a correlation between the Lyapunov function for a delayed neural network and an objective function for the traveling salesman problem.

Mutual-information-based approach for neural connectivity during self-paced finger lifting task.

Frequency-dependent modulation between neuronal assemblies may provide insightful mechanisms of functional organization in the context of neural connectivity. We present a conjoined time-frequency cross mutual information (TFCMI) method to explore the subtle brain neural connectivity by magnetoencephalography (MEG) during a self-paced finger lifting task. Surface electromyogram (sEMG) was obtained from the extensor digitorum communis. Both within-modality (MEG-MEG) and between-modality studies (sEMG-MEG) were conducted. The TFCMI method measures both the linear and nonlinear dependencies of the temporal dynamics of signal power within a pre-specified frequency band. Each single trial of MEG across channels and sEMG signals was transformed into time-frequency domain with use of the Morlet wavelet to obtain better temporal spectral (power) information. As compared to coherence approach (linear dependency only) in broadband analysis, the TFCMI method demonstrated advantages in encompassing detection for the mesial frontocentral cortex and bilateral primary sensorimotor areas, clear demarcation of event- and non-event-related regions, and robustness for sEMG - MEG between-modality study, i.e., corticomuscular communication. We conclude that this novel TFCMI method promises a possibility to better unravel the intricate functional organizations of brain in the context of oscillation-coded communication.

The brain computer interface using flash visual evoked potential and independent component analysis.

In this study flashing stimuli, such as digits or letters, are displayed on a LCD screen to induce flash visual evoked potentials (FVEPs). The aim of the proposed interface is to generate desired strings while one stares at target stimulus one after one. To effectively extract visually-induced neural activities with superior signal-to-noise ratio, independent component analysis (ICA) is employed to decompose the measured EEG and task-related components are subsequently selected for data reconstruction. In addition, all the flickering sequences are designed to be mutually independent in order to remove the contamination induced by surrounding non-target stimuli from the ICA-recovered signals. Since FVEPs are time-locked and phase-locked to flash onsets of gazed stimulus, segmented epochs from ICA-recovered signals based on flash onsets of gazed stimulus will be sharpen after averaging whereas those based on flash onsets of non-gazed stimuli will be suppressed after averaging. The stimulus inducing the largest averaged FVEPs is identified as the gazed target and corresponding digit or letter is sent out. Five subjects were asked to gaze at each stimulus. The mean detection accuracy resulted from averaging 15 epochs was 99.7%. Another experiment was to generate a specified string '0287513694E'. The mean accuracy and information transfer rates were 83% and 23.06 bits/min, respectively.

Orthographic and phonological processing of Chinese characters: an fMRI study.

The present study used functional magnetic resonance imaging (fMRI) to investigate the neural mechanisms underlying the orthographic and phonological processing of Chinese characters. Four tasks were devised, including one homophone judgment and three physical judgments of characters, pseudo-characters, and Korean-like nonsense figures. While the left occipitotemporal region, left dorsal processing stream, and right middle frontal gyrus constitute a network for orthographic processing, the left premotor gyrus, left middle/inferior frontal gyrus, supplementary motor area (SMA), and the left temporoparietal region work in concert for phonological processing. The ventral part of the left inferior frontal cortex responds specifically to the character stimuli, suggesting a general lexical processing role for this region for linguistic material. The stronger activation of the dorsal visual stream by Chinese homophone judgment pinpoints a tight coupling between phonological representation of Chinese characters and corresponding orthographic percepts. The concomitant engagement of sets of regions for different levels of Chinese orthographic and phonological processing is consistent with the notion of distributed parallel processing.