Winner-take-all selection in a neural system with delayed feedback

We consider the effects of temporal delay in a neural feedback system with excitation and inhibition. The topology of our model system reflects the anatomy of the avian isthmic circuitry, a feedback structure found in all classes of vertebrates. We show that the system is capable of performing a 'winner-take-all' selection rule for certain combinations of excitatory and inhibitory feedback. In particular, we show that when the time delays are sufficiently large a system with local inhibition and global excitation can function as a 'winner-take-all' network and exhibit oscillatory dynamics. We demonstrate how the origin of the oscillations can be attributed to the finite delays through a linear stability analysis.     

New stability criterion of neural networks with leakage delays and impulses: a piecewise delay method

This paper analyzes the global asymptotic stability of a class of neural networks with time delay in the leakage term and time-varying delays under impulsive perturbations. Here the time-varying delays are assumed to be piecewise. In this method, the interval of the variation is divided into two subintervals by its central point. By developing a new Lyapunov–Krasovskii functional and checking its variation in between the two subintervals, respectively, and then we present some sufficient conditions to guarantee the global asymptotic stability of the equilibrium point for the considered neural network. The proposed results which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily verified via the linear matrix inequality (LMI) control toolbox in MATLAB. Finally, a numerical example and its simulation are given to show the conditions obtained are new and less conservative than some existing ones in the literature.     

Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

An susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity. However, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations while the basic reproduction number is greater than unity. Finally, some examples for numerical simulations are included to support the theoretical prediction.     

Spontaneously active cells induce state transitions in a model of olfactory cortex

The existence of neurons with intrinsic oscillations does not in itself explain the synchronization of local populations of neurons, but it is likely to pace population rhythms when the neurons are suitably coupled by chemical and/or electrical synapses. In the present study, we have investigated the role of spontaneously active cells as noisy or pacemaker units in setting global oscillations in a three-layered cortical model. The presence of a small number of noisy (spontaneously active) units induce oscillations at the network level in the range of the gamma rhythm. The number of noisy units in the network and their type (excitatory or inhibitory or excitatory and inhibitory together) determines the emergence of regular oscillations or aperiodic (chaotic) behaviour. It also determines the onset of the global behaviour. On replacing a noisy unit by a pacemaker unit, similar gamma oscillations were generated. With both noisy and pacemaker units, we found that certain characteristics of the spontaneous activity determine the delay period for the onset of global activity. Preliminary studies have been carried out with spontaneously active units having a chaotic dynamics but the results are much similar to that with a noisy burst. Different functional roles have been suggested for cortical oscillations, such as determining global functional states and specifying connectivity during development. Oscillations at different frequency bands, in particular in the gamma band (around 40 Hz), have also been associated with memory and attention. The presence of spontaneously active neurons, either with noisy or oscillatory activity, could be responsible for global oscillations in the absence of external stimuli in certain cortical areas in the mature brain.     

Quantifying robustness and dissipation cost of yeast cell cycle network: the funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio (RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.     

Oscillatory viral dynamics in a delayed HIV pathogenesis model

We consider an HIV pathogenesis model incorporating antiretroviral therapy and HIV replication time. We investigate the existence and stability of equilibria, as well as Hopf bifurcations to sustained oscillations when drug efficacy is less than 100%. We derive sufficient conditions for the global asymptotic stability of the uninfected steady state. We show that time delay has no effect on the local asymptotic stability of the uninfected steady state, but can destabilize the infected steady state, leading to a Hopf bifurcation to periodic solutions in the realistic parameter ranges.     

Delay, noise and phase locking in pulse coupled neural networks

This paper studies the effect of several delay times and noise on the stability of the phase-locked state in the lighthouse model and the integrate and fire model of a pulse coupled neural network. The coupling between neurons may be arbitrary. In both models the increase of delay times leads to a weakening of the stability and to the occurrence of relaxation oscillations.     

HIGH FREQUENCY OSCILLATIONS IN THE ACTIVITY OF PHOSPHOTYROSINE PHOSPHATASE IN MURINE ERYTHROLEUKAEMIC CELLS: ACTION OF INSULIN AND HEXAMETHYLENE BISACETAMIDE

We have previously reported oscillations in the activities of the phosphoamino acid phosphatases in murine erythroleukaemic cells. In keeping with our predictions we now show that the phosphotyrosine phosphatase activity rhythm has a much shorter period than originally seemed the case, being of the order of 10min and probably less. The periodic changes show evidence of rhythmic modulation of mean, period and amplitude as with all other cellular oscillations studied. Insulin decreases the frequency of the rhythm while the inducer of differentiation, hexamethylene bisacetamide (HMBA) decreases its amplitude. Current ideas on phosphorylation dynamics in relation to metabolism and mitosis may need to be revised in the light of the observations.     

Landscape, flux, correlation, resonance, coherence, stability, and key network wirings of stochastic circadian oscillation

Circadian rhythms with a period of ∼24 h, are natural timing machines. They are broadly distributed in living organisms, such as Neurospora, Drosophila, and mammals. The underlying natures of the rhythmic behavior have been explored by experimental and theoretical approaches. However, the global and physical natures of the oscillation under fluctuations are still not very clear. We developed a landscape and flux framework to explore the global stability and robustness of a circadian oscillation system. The potential landscape of the network is uncovered and has a global Mexican-hat shape. The height of the Mexican-hat provides a quantitative measure to evaluate the robustness and coherence of the oscillation. We found that in nonequilibrium dynamic systems, not only the potential landscape but also the probability flux are important to the dynamics of the system under intrinsic noise. Landscape attracts the systems down to the oscillation ring while flux drives the coherent oscillation on the ring. We also investigated the phase coherence and the entropy production rate of the system at different fluctuations and found that dissipations are less and the coherence is higher for larger number of molecules. We also found that the power spectrum of autocorrelation functions show resonance peak at the frequency of coherent oscillations. The peak is less prominent for smaller number of molecules and less barrier height and therefore can be used as another measure of stability of oscillations. As a consequence of nonzero probability flux, we show that the three-point correlations from the time traces show irreversibility, providing a possible way to explore the flux from the observations. Furthermore, we explored the escape time from the oscillation ring to outside at different molecular number. We found that when barrier height is higher, escape time is longer and phase coherence of oscillation is higher. Finally, we performed the global sensitivity analysis of the underlying parameters to find the key network wirings responsible for the stability of the oscillation system.     

Modeling,analysis and simulation of ant-based network routing protocols

Using the metaphor of swarm intelligence, ant-based routing protocols deploy control packets that behave like ants to discover and optimize routes between pairs of nodes. These ant-based routing protocols provide an elegant, scalable solution to the routing problem for both wired and mobile ad hoc networks. The routing problem is highly nonlinear because the control packets alter the local routing tables as they are routed through the network. We mathematically map the local rules by which the routing tables are altered to the dynamics of the entire networks. Using dynamical systems theory, we map local protocol rules to full network performance, which helps us understand the impact of protocol parameters on network performance. In this paper, we systematically derive and analyze global models for simple ant-based routing protocols using both pheromone deposition and evaporation. In particular, we develop a stochastic model by modeling the probability density of ants over the network. The model is validated by comparing equilibrium pheromone levels produced by the global analysis to results obtained from simulation studies. We use both a Matlab simulation with ideal communications and a QualNet simulation with realistic communication models. Using these analytic and computational methods, we map out a complete phase diagram of network behavior over a small multipath network. We show the existence of both stable and unstable (inaccessible) routing solutions having varying properties of efficiency and redundancy depending upon the routing parameters. Finally, we apply these techniques to a larger 50-node network and show that the design principles acquired from studying the small model network extend to larger networks.     

A model for modulation of neuronal synchronization by D4 dopamine receptor-mediated phospholipid methylation

We describe a new molecular mechanism of dopamine-induced membrane protein modulation that can tune neuronal oscillation frequency to attention-related gamma rhythm. This mechanism is based on the unique ability of D4 dopamine receptors (D4R) to carry out phospholipid methylation (PLM) that may affect the kinetics of ion channels. We show that by deceasing the inertia of the delayed rectifier potassium channel, a transition to 40 Hz oscillations can be achieved. Decreased potassium channel inertia shortens spike duration and decreases the interspike interval via its influence on the calcium-dependent potassium current. This mechanism leads to a transition to attention-related gamma oscillations in a pyramidal cell-interneuron network. The higher frequency and better synchronization is observed with PLM affecting pyramidal neurons only, and recurrent excitation between pyramidal neurons is important for synchronization. Thus dopamine-stimulated methylation of membrane phospholipids may be an important mechanism for modulating firing activity, while impaired methylation can contribute to disorders of attention. Action Editor: Upinder Bhalla     

Membrane and network theta-rhythm generation in hippocampal slices

The hippocampal rhythms observed in vivo are the result of a complex interplay between cellular and synaptic properties within the hippocampus, and extra-hippocampal tonic as well as periodic inputs. For the stable rhythm to occur, the hippocampal circuitry should have the potential to oscillate at the specific frequencies. The in vitro studies revealed multiple mechanisms supporting the generation of the theta rhythm, which is the main operational mode of the hippocampus. In the hippocampus and related structures cellular membranes can oscillate at theta rhythm when they are depolarized to near-threshold membrane potentials; membranes are also adjusted to resonate with the external signal applied at theta frequency. Synaptically connected hippocampal network alone can generate theta rhythm when a necessary tonic excitation is provided. Finally, rhythmic inputs in theta range from the septum and entorhinal cortex have a propensity to synchronize oscillations in the whole hippocampal formation and associated structures to operate in a unified mode of activity. Based on the results obtained in slices and slice cultures, the present review shows this multilevel hierarchy, which serves to guarantee easy occurrence and reliable maintenance of the theta rhythm in the hippocampus.     

Interactions between neural networks: a mechanism for tuning chaos and oscillations

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability. URL: http:// www.ntu.edu.sg/home/elpwang     

Time delays in metabolic control systems

In this work we use mathematical models with discrete and distributed time delays to analyse the stability of metabolic pathways controlled by end product. We assume the kinetics of the intermediates of the path to be unknown, and we cover the lack of information by using a time delay. We find that above a definite substrate value, there is a critical delay Tc in which a transition from stability to instability occurs. For discrete delays, we find that even if the interaction of the end product with the first (allosteric) enzyme is not cooperative, the pathway can potentially become unstable and oscillate. We then show that the existence of cooperative inhibition extends the parametric domain of instability. The introduction of distributed delays shows, when the kernels are not monotonically decreasing, that the dispersion increases the critical delay Tc. Finally, we comment on the possibility that metabolic oscillations are physiological signals useful for triggering adaptive strategies in cell behavior.     

Synchronous versus asynchronous oscillations for antigenically varying Plasmodium falciparum with host immune response

We consider a deterministic intra-host model for Plasmodium falciparum (Pf) malaria infection, which accounts for antigenic variation between n clonal variants of PfEMP1 and the corresponding host immune response (IR). Specifically, the model separates the IR into two components, specific and cross-reactive, respectively, in order to demonstrate that the latter can be a mechanism for the sequential appearance of variants observed in actual Pf infections. We show that a strong variant-specific IR relative to the cross-reactive IR favours the asynchronous oscillations (sequential dominance) over the synchronous oscillations in a number of ways. The decay rate of asynchronous oscillations is smaller than that for the synchronous oscillations, allowing for the parasite to survive longer. With the introduction of a delay in the stimulation of the IR, we show that only a small delay is necessary to cause persistent asynchronous oscillations and that a strong variant-specific IR increases the amplitude of the asynchronous oscillations.