Controlling an oscillating Jackson-type network having state-dependent service rates

We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold.     

Detecting and localizing the foci in human epileptic seizures

We consider the electrical signals recorded from a subdural array of electrodes placed on the pial surface of the brain for chronic evaluation of epileptic patients before surgical resection. A simple and computationally fast method to analyze the interictal phase synchrony between such electrodes is introduced and developed with the aim of detecting and localizing the foci of the epileptic seizures. We evaluate the method by comparing the results of surgery to the localization predicted here. We find an indication of good correspondence between the success or failure in the surgery and the agreement between our identification and the regions actually operated on.     

Lubricating bacteria model for branching growth of bacterial colonies

Various bacterial strains (e.g., strains belonging to the genera Bacillus, Paenibacillus, Serratia, and Salmonella) exhibit colonial branching patterns during growth on poor semisolid substrates. These patterns reflect the bacterial cooperative self-organization. A central part of the cooperation is the collective formation of a lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by a nonlinear diffusion coefficient, branching patterns evolve. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.     

Formation of electrically active clusterized neural networks

Ordinarily, in vitro neurons self-organize into homogeneous networks of single neurons linked by dendrites and axons. We show that under special conditions they can also self-organize into neuronal clusters, which are linked by bundles of axons. Multielectrode array measurement reveals that the clusterized networks are also electrically active and exhibit synchronized bursting events similar to those observed in the homogeneous networks. From time-lapse recording, we deduced the features required for the neuronal clusterized versus homogeneous self-organization and developed a simple model for testing their validity.     

Characteristic modes and the transition to chaos of a resonant Josephson circuit

The periodic modes of a voltage-driven resonant small-junction Josephson circuit are studied by accurate numerical methods starting from large dissipation. As dissipation decreases, sections of the average current vs. voltage characteristic become unstable and new branches develop on those sections, corresponding to new modes which are exact subharmonics of the old mode. For low enough dissipation chaotic ranges of voltage occur, i.e., ranges with no stable periodic modes. This circuit is a component of many experimental circuits, e.g., finite junctions, DC and RF squids, etc., and so the behavior found here should occur widely.     

Pattern propagation in nonlinear dissipative systems

We discuss the problem of pattern selection in situations where a stable, nonuniform state of a nonlinear dissipative system propagates into an initially unstable, homogeneous region. Our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known; and we point out that these known properties are consistent with a marginal-stability hypothesis that has been suggested in the theory of dendritic crystal growth. We then describe a more general interpretation of the marginal-stability hypothesis and, finally, present numerical evidence for its validity from three different pattern-forming models.     

Social behavior of bacteria: from physics to complex organization

I describe how bacteria develop complex colonial patterns by utilizing intricate communication capabilities, such as quorum sensing, chemotactic signaling and exchange of genetic information (plasmids) Bacteria do not store genetically all the information required for generating the patterns for all possible environments. Instead, additional information is cooperatively generated as required for the colonial organization to proceed. Each bacterium is, by itself, a biotic autonomous system with its own internal cellular informatics capabilities (storage, processing and assessments of information). These afford the cell certain plasticity to select its response to biochemical messages it receives, including self-alteration and broadcasting messages to initiate alterations in other bacteria. Hence, new features can collectively emerge during self-organization from the intra-cellular level to the whole colony. Collectively bacteria store information, perform decision make decisions (e.g. to sporulate) and even learn from past experience (e.g. exposure to antibiotics)-features we begin to associate with bacterial social behavior and even rudimentary intelligence. I also take Schrdinger’s’ “feeding on negative entropy” criteria further and propose that, in addition organisms have to extract latent information embedded in the environment. By latent information we refer to the non-arbitrary spatio-temporal patterns of regularities and variations that characterize the environmental dynamics. In other words, bacteria must be able to sense the environment and perform internal information processing for thriving on latent information embedded in the complexity of their environment. I then propose that by acting together, bacteria can perform this most elementary cognitive function more efficiently as can be illustrated by their cooperative behavior.