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

Scaling in a continuous time model for biological aging

In this paper we consider a generalization to the asexual version of the Penna model for biological aging, where we take a continuous time limit. The genotype associated to each individual is an interval of real numbers over which Dirac $\delta$--functions are defined, representing genetically programmed diseases to be switched on at defined ages of the individual life. We discuss two different continuous limits for the evolution equation and two different mutation protocols, to be implemented during reproduction. Exact stationary solutions are obtained and scaling properties are discussed.Comment: 10 pages, 6 figure

Studying Axon-Astrocyte Functional Interactions by 3D Two-Photon Ca²⁺ Imaging: A Practical Guide to Experiments and "Big Data" Analysis.

Recent advances in fast volumetric imaging have enabled rapid generation of large amounts of multi-dimensional functional data. While many computer frameworks exist for data storage and analysis of the multi-gigabyte Ca <sup>2+</sup> imaging experiments in neurons, they are less useful for analyzing Ca <sup>2+</sup> dynamics in astrocytes, where transients do not follow a predictable spatio-temporal distribution pattern. In this manuscript, we provide a detailed protocol and commentary for recording and analyzing three-dimensional (3D) Ca <sup>2+</sup> transients through time in GCaMP6f-expressing astrocytes of adult brain slices in response to axonal stimulation, using our recently developed tools to perform interactive exploration, filtering, and time-correlation analysis of the transients. In addition to the protocol, we release our in-house software tools and discuss parameters pertinent to conducting axonal stimulation/response experiments across various brain regions and conditions. Our software tools are available from the Volterra Lab webpage at https://wwwfbm.unil.ch/dnf/group/glia-an-active-synaptic-partner/member/volterra-andrea-volterra in the form of software plugins for Image J (NIH)-a de facto standard in scientific image analysis. Three programs are available: <i>MultiROI_TZ_profiler</i> for interactive graphing of several movable ROIs simultaneously, <i>Gaussian_Filter5D</i> for Gaussian filtering in several dimensions, and <i>Correlation_Calculator</i> for computing various cross-correlation parameters on voxel collections through time

Emergence of diversity in a model ecosystem

The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)]. The competition is controlled by an interaction network with fixed links chosen by a Bernoulli process. New species are introduced in the system at a predefined rate. In the limit of small introduction rates, the system becomes bistable and can undergo a phase transition from a state of low diversity to high diversity. We suggest that patches of isolated meta-populations formed by the collapse of cyclic relations are essential for the transition to the state of high diversity.Comment: 7 pages, 6 figures. Accepted for publication in PRE. Typos corrected, Fig.3A and Fig.6 update

Self-organized patterns of coexistence out of a predator-prey cellular automaton

We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one individual of each species or can be empty. The system evolves in time according to a probabilistic cellular automaton composed by a set of local rules which describe interactions between species individuals and mimic the process of birth, death and predation. By performing computational simulations, we found that, depending on the values of the parameters of the model, the following states can be reached: a prey absorbing state and active states of two types. In one of them both species coexist in a stationary regime with population densities constant in time. The other kind of active state is characterized by local coupled time oscillations of prey and predator populations. We focus on the self-organized structures arising from spatio-temporal dynamics of the coexistence. We identify distinct spatial patterns of prey and predators and verify that they are intimally connected to the time coexistence behavior of the species. The occurrence of a prey percolating cluster on the spatial patterns of the active states is also examined.Comment: 19 pages, 11 figure

Lie conformal algebra cohomology and the variational complex

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a g-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.Comment: 56 page

Extinction in Lotka-Volterra model

Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.Comment: 11 pages, 17 figure

Gliotransmitters travel in time and space.

The identification of the presence of active signaling between astrocytes and neurons in a process termed gliotransmission has caused a paradigm shift in our thinking about brain function. However, we are still in the early days of the conceptualization of how astrocytes influence synapses, neurons, networks, and ultimately behavior. In this Perspective, our goal is to identify emerging principles governing gliotransmission and consider the specific properties of this process that endow the astrocyte with unique functions in brain signal integration. We develop and present hypotheses aimed at reconciling confounding reports and define open questions to provide a conceptual framework for future studies. We propose that astrocytes mainly signal through high-affinity slowly desensitizing receptors to modulate neurons and perform integration in spatiotemporal domains complementary to those of neurons

Three-dimensional Ca2+ imaging advances understanding of astrocyte biology.

Astrocyte communication is typically studied by two-dimensional calcium ion (Ca2+) imaging, but this method has not yielded conclusive data on the role of astrocytes in synaptic and vascular function. We developed a three-dimensional two-photon imaging approach and studied Ca2+ dynamics in entire astrocyte volumes, including during axon-astrocyte interactions. In both awake mice and brain slices, we found that Ca2+ activity in an individual astrocyte is scattered throughout the cell, largely compartmented between regions, preponderantly local within regions, and heterogeneously distributed regionally and locally. Processes and endfeet displayed frequent fast activity, whereas the soma was infrequently active. In awake mice, activity was higher than in brain slices, particularly in endfeet and processes, and displayed occasional multifocal cellwide events. Astrocytes responded locally to minimal axonal firing with time-correlated Ca2+ spots

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