The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number $q$. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here $q$-Breathers (QB). They are characterized by time periodicity, exponential localization in the $q$-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.Comment: 4 pages, 4 figure

The Fermi-Pasta-Ulam (FPU) problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here q-Breathers (QB). They are characterized by time periodicity, exponential localization in the q-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.

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The Integrated Information is a quantitative measure from information theory how tightly all parts of a system are interconnected in terms of information exchange. In this study we show that astrocyte, playing an important role in regulation of information transmission between neurons, may contribute to a generation of positive Integrated Information in neuronal ensembles. Analytically and numerically we show that the presence of astrocyte may be essential for this information attribute in neuro-astrocytic ensembles. Moreover, the proposed "spiking-bursting" mechanism of generating positive Integrated Information is shown to be generic and not limited to neuroglial networks, and is given a complete analytic description.

We describe a conceptual design of a distributed classifier formed by a population of genetically engineered microbial cells. The central idea is to create a complex classifier from a population of weak or simple classifiers. We create a master population of cells with randomized synthetic biosensor circuits that have a broad range of sensitivities toward chemical signals of interest that form the input vectors subject to classification. The randomized sensitivities are achieved by constructing a library of synthetic gene circuits with randomized control sequences (e.g., ribosome-binding sites) in the front element. The training procedure consists in reshaping of the master population in such a way that it collectively responds to the “positive” patterns of input signals by producing above-threshold output (e.g., fluorescent signal), and below-threshold output in case of the “negative” patterns. The population reshaping is achieved by presenting sequential examples and pruning the population using either graded selection/counterselection or by fluorescence-activated cell sorting (FACS). We demonstrate the feasibility of experimental implementation of such system computationally using a realistic model of the synthetic sensing gene circuits.