Einstein-Cartan theory as a theory of defects in space-time

The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce the latter as a description of the equilibrium state of a three-dimensional continuum. Despite these important differences, an analogy is built on their common geometrical foundations, and it is shown that a space-time with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects. This formal analogy is useful for illustrating the geometrical concept of torsion by applying it to concrete physical problems. Moreover, the presentation of these theories using a common geometrical basis allows a deeper understanding of their foundations.Comment: 18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal of Physics, revised version with typos correcte

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

A STRAINED SPACE-TIME TO EXPLAIN THE LARGE SCALEPROPERTIES OF THE UNIVERSE

Space-time can be treated as a four-dimensional material continuum. The corresponding generally curved manifold can be thought of as having been obtained, by continuous deformation, from a four-dimensional Euclidean manifold. In a three-dimensional ordinary situation such a deformation process would lead to strain in the manifold. Strain in turn may be read as half the di®erence between the actual metric tensor and the Euclidean metric tensor of the initial unstrained manifold. On the other side we know that an ordinary material would react to the attempt to introduce strain giving rise to internal stresses and one would have correspondingly a deformation energy term. Assuming the conditions of linear elasticity hold, the deformation energy is easily written in terms of the strain tensor. The Einstein-Hilbert action is generalized to include the new deformation energy term. The new action for space-time has been applied to a Friedmann-Lemaitre- Robertson-Walker universe filled with dust and radiation. The accelerated expansion is recovered, then the theory has been put through four cosmological tests: primordial isotopic abundances from Big Bang Nucleosynthesis; Acoustic Scale of the CMB; Large Scale Structure formation; luminosity/redshift relation for type Ia supernovae. The result is satisfying and has allowed to evaluate the parameters of the theor

What do we know about gliotransmitter release from astrocytes?

Astrocytes participate in information processing by actively modulating synaptic properties via gliotransmitter release. Various mechanisms of astrocytic release have been reported, including release from storage organelles via exocytosis and release from the cytosol via plasma membrane ion channels and pumps. It is still not fully clear which mechanisms operate under which conditions, but some of them, being Ca(2+)-regulated, may be physiologically relevant. The properties of Ca(2+)-dependent transmitter release via exocytosis or via ion channels are different and expected to produce different extracellular transmitter concentrations over time and to have distinct functional consequences. The molecular aspects of these two release pathways are still under active investigation. Here, we discuss the existing morphological and functional evidence in support of either of them. Transgenic mouse models, specific antagonists and localization studies have provided insight into regulated exocytosis, albeit not in a systematic fashion. Even more remains to be uncovered about the details of channel-mediated release. Better functional tools and improved ultrastructural approaches are needed in order fully to define specific modalities and effects of astrocytic gliotransmitter release pathways

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

Astrocyte Ca²⁺ signalling: an unexpected complexity.

Astrocyte Ca(2+) signalling has been proposed to link neuronal information in different spatial-temporal dimensions to achieve a higher level of brain integration. However, some discrepancies in the results of recent studies challenge this view and highlight key insufficiencies in our current understanding. In parallel, new experimental approaches that enable the study of astrocyte physiology at higher spatial-temporal resolution in intact brain preparations are beginning to reveal an unexpected level of compartmentalization and sophistication in astrocytic Ca(2+) dynamics. This newly revealed complexity needs to be attentively considered in order to understand how astrocytes may contribute to brain information processing

Astrocytes: Orchestrating synaptic plasticity?

Synaptic plasticity is the capacity of a preexisting connection between two neurons to change in strength as a function of neural activity. Because synaptic plasticity is the major candidate mechanism for learning and memory, the elucidation of its constituting mechanisms is of crucial importance in many aspects of normal and pathological brain function. In particular, a prominent aspect that remains debated is how the plasticity mechanisms, that encompass a broad spectrum of temporal and spatial scales, come to play together in a concerted fashion. Here we review and discuss evidence that pinpoints to a possible non-neuronal, glial candidate for such orchestration: the regulation of synaptic plasticity by astrocytes

Vector field theories in cosmology

Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory (Cosmic Defect theory). We show that the latter fits reasonably well the cosmic observed data with only one, or at most two, adjustable parameters, whilst other vector theories use much more. The Newtonian limits are also compared. Finally we show that the CD theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.Comment: 19 pages, 1 figure, to appear on Phys. Rev.

Spontaneous emergence of spatial patterns ina a predator-prey model

We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the relationship between pattern formation and features of the populations' time series. Our model displays travelling waves solutions, clustering and uniform distributions, all related to the parameters values. We also observed that the regeneration rate, the parameter associated to the primary level of trophic chain, the plants, regulated the presence of predators, as well as the type of spatial configuration.Comment: 17 pages and 15 figure

Four-state rock-paper-scissors games on constrained Newman-Watts networks

We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks with the long-rang connection probability $p$, we depict more realistically the stochastic interactions among species within ecosystems. When we fix mobility and vary the value of $p$ or $R_{max}$, the Monte Carlo simulations show that the spiral waves grow in size, and the system becomes unstable and biodiversity is lost with increasing $p$ or $R_{max}$. These results are similar to recent results of Reichenbach \textit{et al.} [Nature (London) \textbf{448}, 1046 (2007)], in which they increase the mobility only without including long-range interactions. We compared extinctions with or without long-range connections and computed spatial correlation functions and correlation length. We conclude that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.Comment: 6 pages, 7 figure