Nonlocality of Accelerated Systems

The conceptual basis for the nonlocality of accelerated systems is presented. The nonlocal theory of accelerated observers and its consequences are briefly described. Nonlocal field equations are developed for the case of the electrodynamics of linearly accelerated systems.Comment: LaTeX file, no figures, 9 pages, to appear in: "Black Holes, Gravitational Waves and Cosmology" (World Scientific, Singapore, 2003

On Foundation of the Generalized Nambu Mechanics

We outline the basic principles of canonical formalism for the Nambu mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the Poisson bracket to the multiple operation of higher order $n \geq 3$ on classical observables and is described by Hambu-Hamilton equations of motion given by $n-1$ Hamiltonians. We introduce the fundamental identity for the Nambu bracket which replaces Jacobi identity as a consistency condition for the dynamics. We show that Nambu structure of given order defines a family of subordinated structures of lower order, including the Poisson structure, satisfying certain matching conditions. We introduce analogs of action from and principle of the least action for the Nambu mechanics and show how dynamics of loops ($n-2$-dimensional objects) naturally appears in this formalism. We discuss several approaches to the quantization problem and present explicit representation of Nambu-Heisenberg commutation relation for $n=3$ case. We emphasize the role higher order algebraic operations and mathematical structures related with them play in passing from Hamilton's to Nambu's dynamical picture.Comment: 27 page

Amplitude dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics

The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that the combined effects of migration and noise cannot account for the stabilization. The missing ingredient is the dependence of the oscillations' frequency upon their amplitude; with that, noise-induced differences between patches are amplified due to the frequency gradient. Migration among desynchronized regions then stabilizes a "soft" limit cycle in the vicinity of the homogenous manifold. A simple model of diffusively coupled oscillators allows the derivation of quantitative results, like the functional dependence of the desynchronization upon diffusion strength and frequency differences. The oscillations' amplitude is shown to be (almost) noise independent. The results are compared with a numerical integration of the marginally stable Lotka-Volterra equations. An unstable system is extinction-prone for small noise, but stabilizes at larger noise intensity

Nonlocal Electrodynamics of Rotating Systems

The nonlocal electrodynamics of uniformly rotating systems is presented and its predictions are discussed. In this case, due to paucity of experimental data, the nonlocal theory cannot be directly confronted with observation at present. The approach adopted here is therefore based on the correspondence principle: the nonrelativistic quantum physics of electrons in circular "orbits" is studied. The helicity dependence of the photoeffect from the circular states of atomic hydrogen is explored as well as the resonant absorption of a photon by an electron in a circular "orbit" about a uniform magnetic field. Qualitative agreement of the predictions of the classical nonlocal electrodynamics with quantum-mechanical results is demonstrated in the correspondence regime.Comment: 23 pages, no figures, submitted for publicatio

Oscillatory behaviour in a lattice prey-predator system

Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in lower-dimensional models. Finite-size analysis indicate that amplitude of these oscillations is finite even in the thermodynamic limit. In our opinion, this is the first example of a microscopic model with stochastic dynamics which exhibits oscillatory behaviour without any external driving force. We suggest that oscillations in our model are induced by some kind of stochastic resonance.Comment: 7 pages, 10 figures, Phys.Rev.E (Nov. 1999

Multiscale Analysis of Discrete Nonlinear Evolution Equations

The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon chain, the Takeno system and a discrete version of the Benjamin-Bona-Mahoney equation. Among the resulting limit models we find a discrete nonlinear Schroedinger equation (with reversed space-time), a 3-wave resonant interaction system and a discrete modified Volterra model.Comment: published in J. Phys. A : Math. Gen. 32 (1999) 927-94

The BH4 domain of Bcl-XL rescues astrocyte degeneration in amyotrophic lateral sclerosis by modulating intracellular calcium signals

Collective evidence indicates that motor neuron degeneration in amyotrophic lateral sclerosis (ALS) is non-cell-autonomous and requires the interaction with the neighboring astrocytes. Recently, we reported that a subpopulation of spinal cord astrocytes degenerates in the microenvironment of motor neurons in the hSOD1G93A mouse model of ALS. Mechanistic studies in vitro identified a role for the excitatory amino acid glutamate in the gliodegenerative process via the activation of its inositol 1,4,5-triphosphate (IP3)-generating metabotropic receptor 5 (mGluR5). Since non-physiological formation of IP3 can prompt IP3 receptor (IP3R)-mediated Ca2+ release from the intracellular stores and trigger various forms of cell death, here we investigated the intracellular Ca2+ signaling that occurs downstream of mGluR5 in hSOD1G93A-expressing astrocytes. Contrary to wild-type cells, stimulation of mGluR5 causes aberrant and persistent elevations of intracellular Ca2+ concentrations ([Ca2+]i) in the absence of spontaneous oscillations. The interaction of IP3Rs with the anti-apoptotic protein Bcl-XL was previously described to prevent cell death by modulating intracellular Ca2+ signals. In mutant SOD1-expressing astrocytes, we found that the sole BH4 domain of Bcl-XL, fused to the protein transduction domain of the HIV-1 TAT protein (TAT-BH4), is sufficient to restore sustained Ca2+ oscillations and cell death resistance. Furthermore, chronic treatment of hSOD1G93A mice with the TAT-BH4 peptide reduces focal degeneration of astrocytes, slightly delays the onset of the disease and improves both motor performance and animal lifespan. Our results point at TAT-BH4 as a novel glioprotective agent with a therapeutic potential for AL

Coexistence and Survival in Conservative Lotka-Volterra Networks

Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time

Synaptic Adhesion Molecules Regulate the Integration of New Granule Neurons in the Postnatal Mouse Hippocampus and their Impact on Spatial Memory.

Postnatal hippocampal neurogenesis induces network remodeling and may participate to mechanisms of learning. In turn, the maturation and survival of newborn neurons is regulated by their activity. Here, we tested the effect of a cell-autonomous overexpression of synaptic adhesion molecules on the maturation and survival of neurons born postnatally and on hippocampal-dependent memory performances. Families of adhesion molecules are known to induce pre- and post-synaptic assembly. Using viral targeting, we overexpressed three different synaptic adhesion molecules, SynCAM1, Neuroligin-1B and Neuroligin-2A in newborn neurons in the dentate gyrus of 7- to 9-week-old mice. We found that SynCAM1 increased the morphological maturation of dendritic spines and mossy fiber terminals while Neuroligin-1B increased spine density. In contrast, Neuroligin-2A increased both spine density and size as well as GABAergic innervation and resulted in a drastic increase of neuronal survival. Surprisingly, despite increased neurogenesis, mice overexpressing Neuroligin-2A in new neurons showed decreased memory performances in a Morris water maze task. These results indicate that the cell-autonomous overexpression of synaptic adhesion molecules can enhance different aspects of synapse formation on new neurons and increase their survival. Furthermore, they suggest that the mechanisms by which new neurons integrate in the postnatal hippocampus conditions their functional implication in learning and memory

Junctions and spiral patterns in Rock-Paper-Scissors type models

We investigate the population dynamics in generalized Rock-Paper-Scissors models with an arbitrary number of species $N$. We show, for the first time, that spiral patterns with $N$-arms may develop both for odd and even $N$, in particular in models where a bidirectional predation interaction of equal strength between all species is modified to include one N-cyclic predator-prey rule. While the former case gives rise to an interface network with Y-type junctions obeying the scaling law $L \propto t^{1/2}$, where $L$ is the characteristic length of the network and $t$ is the time, the later can lead to a population network with $N$-armed spiral patterns, having a roughly constant characteristic length scale. We explicitly demonstrate the connection between interface junctions and spiral patterns in these models and compute the corresponding scaling laws. This work significantly extends the results of previous studies of population dynamics and could have profound implications for the understanding of biological complexity in systems with a large number of species.Comment: 6 pages, 8 figures, published versio