Towards a noncommutative version of Gravitation

Alain Connes' noncommutative theory led to an interesting model including both Standard Model of particle physics and Euclidean Gravity. Nevertheless, an hyperbolic version of the gravitational part would be necessary to make physical predictions, but it is still under research. We shall present the difficulties to generalize the model from Riemannian to Lorentzian Geometry and discuss key ideas and current attempts.Comment: 7 pages, to appear in the AIP proceedings of the "Invisible Universe International Conference", UNESCO-Paris, June 29-July 3, 200

Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation

The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an information-theoretic description of the process of coding inter- and intra-community transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original Map coding scheme, which is both block-averaged and one-step, neglects the internal structure of the communities and introduces an upper scale, the `field-of-view' limit, in the communities it can detect. As a consequence, Map is well tuned to detect clique-like communities but can lead to undesirable overpartitioning when communities are far from clique-like. We show that a signature of this behavior is a large compression gap: the Map description length is far from its ideal limit. To address this issue, we propose a simple dynamic approach that introduces time explicitly into the Map coding through the analysis of the weighted adjacency matrix of the time-dependent multistep transition matrix of the Markov process. The resulting Markov time sweeping induces a dynamical zooming across scales that can reveal (potentially multiscale) community structure above the field-of-view limit, with the relevant partitions indicated by a small compression gap.Comment: 10 pages, 6 figure

Activity ageing in growing networks

We present a model for growing information networks where the ageing of a node depends on the time at which it entered the network and on the last time it was cited. The model is shown to undergo a transition from a small-world to large-world network. The degree distribution may exhibit very different shapes depending on the model parameters, e.g. delta-peaked, exponential or power-law tailed distributions.Comment: 9 pages, 2 figure

Plausible "faster-than-light" displacements in a two-sheeted spacetime

In this paper, we explore the implications of a two-point discretization of an extra-dimension in a five-dimensional quantum setup. We adopt a pragmatic attitude by considering the dynamics of spin-half particles through the simplest possible extension of the existing Dirac and Pauli equations. It is shown that the benefit of this approach is to predict new physical phenomena while maintaining the number of constitutive hypothesis at minimum. As the most striking feature of the model, we demonstrate the possibility of fermionic matter oscillations between the two four-dimensional sections and hyper-fast displacements in case of asymmetric warping (without conflicting special relativity). This result, similar to previous reported ones in brane-world theories, is completely original as it is derived by using quantum mechanics only without recourse to general relativity and bulk geodesics calculation. The model allows causal contact between normally disconnected regions. If it proves to be physically founded, its practical aspects could have deep implications for the search of extra-dimensions.Comment: 17 pages, 1 figure. Final version. Accepted for publication in Phys. Rev.

Pre-Big Bang Scenario on Self-T-Dual Bouncing Branes

We consider a new class of 5-dimensional dilatonic actions which are invariant under T-duality transformations along three compact coordinates, provided that an appropriate potential is chosen. We show that the invariance remains when we add a boundary term corresponding to a moving 3-brane, and we study the effects of the T-duality symmetry on the brane cosmological equations. We find that T-duality transformations in the bulk induce scale factor duality on the brane, together with a change of sign of the pressure of the brane cosmological matter. However, in a remarkable analogy with the Pre-Big Bang scenario, the cosmological equations are unchanged. Finally, we propose a model where the dual phases are connected through a scattering of the brane induced by an effective potential. We show how this model can realise a smooth, non-singular transition between a pre-Big Bang superinflationary Universe and a post-Big Bang accelerating Universe.Comment: 18 pages, minor typos corrected, Sec. 2 expanded with more details on the self-T-dual background, Sec.4 and 5 revised accordingly. Version to appear on JCA

Opinion Formation in Laggard Societies

We introduce a statistical physics model for opinion dynamics on random networks where agents adopt the opinion held by the majority of their direct neighbors only if the fraction of these neighbors exceeds a certain threshold, p_u. We find a transition from total final consensus to a mixed phase where opinions coexist amongst the agents. The relevant parameters are the relative sizes in the initial opinion distribution within the population and the connectivity of the underlying network. As the order parameter we define the asymptotic state of opinions. In the phase diagram we find regions of total consensus and a mixed phase. As the 'laggard parameter' p_u increases the regions of consensus shrink. In addition we introduce rewiring of the underlying network during the opinion formation process and discuss the resulting consequences in the phase diagram.Comment: 5 pages, eps fig

Reconciling MOND and dark matter?

Observations of galaxies suggest a one-to-one analytic relation between the inferred gravity of dark matter at any radius and the enclosed baryonic mass, a relation summarized by Milgrom's law of modified Newtonian dynamics (MOND). However, present-day covariant versions of MOND usually require some additional fields contributing to the geometry, as well as an additional hot dark matter component to explain cluster dynamics and cosmology. Here, we envisage a slightly more mundane explanation, suggesting that dark matter does exist but is the source of MOND-like phenomenology in galaxies. We assume a canonical action for dark matter, but also add an interaction term between baryonic matter, gravity, and dark matter, such that standard matter effectively obeys the MOND field equation in galaxies. We show that even the simplest realization of the framework leads to a model which reproduces some phenomenological predictions of cold dark matter (CDM) and MOND at those scales where these are most successful. We also devise a more general form of the interaction term, introducing the medium density as a new order parameter. This allows for new physical effects which should be amenable to observational tests in the near future. Hence, this very general framework, which can be furthermore related to a generalized scalar-tensor theory, opens the way to a possible unification of the successes of CDM and MOND at different scales.Comment: 9 page

Synthetic fosmidomycin analogues with altered chelating moieties do not inhibit 1-deoxy-D-xylulose 5-phosphate reductoisomerase or Plasmodium falciparum growth in vitro

Fourteen new fosmidomycin analogues with altered metal chelating groups were prepared and evaluated for inhibition of E. coli Dxr, M. tuberculosis Dxr and the growth of P. falciparum K1 in human erythrocytes. None of the synthesized compounds showed activity against either enzyme or the Plasmodia. This study further underlines the importance of the hydroxamate functionality and illustrates that identifying effective alternative bidentate ligands for this target enzyme is challenging

The Lemaitre-Schwarzschild Problem Revisited

The Lemaitre and Schwarzschild analytical solutions for a relativistic spherical body of constant density are linked together through the use of the Weyl quadratic invariant. The critical radius for gravitational collapse of an incompressible fluid is shown to vary continuously from 9/8 of the Schwarzschild radius to the Schwarzschild radius itself while the internal pressures become locally anisotropic.Comment: Final version as accepted by GR&G (to appear in vol. 34, september 2002

Functional brain networks before the onset of psychosis : a prospective fMRI study with graph theoretical analysis

Individuals with an at-risk mental state (ARMS) have a risk of developing a psychotic disorder significantly greater than the general population. However, it is not currently possible to predict which ARMS individuals will develop psychosis from clinical assessment alone. Comparison of ARMS subjects who do, and do not, develop psychosis can reveal which factors are critical for the onset of illness. In the present study, 37 patients with an ARMS were followed clinically at least 24 months subsequent to initial referral. Functional MRI data were collected at the beginning of the follow-up period during performance of an executive task known to recruit frontal lobe networks and to be impaired in psychosis. Graph theoretical analysis was used to compare the organization of a functional brain network in ARMS patients who developed a psychotic disorder following the scan (ARMS-T) to those who did not become ill during the same follow-up period (ARMS-NT) and aged-matched controls. The global properties of each group's representative network were studied (density, efficiency, global average path length) as well as regionally-specific contributions of network nodes to the organization of the system (degree, farness-centrality, betweenness-centrality). We focused our analysis on the dorsal anterior cingulate cortex (ACC), a region known to support executive function that is structurally and functionally impaired in ARMS patients. In the absence of between-group differences in global network organization, we report a significant reduction in the topological centrality of the ACC in the ARMS-T group relative to both ARMS-NT and controls. These results provide evidence that abnormalities in the functional organization of the brain predate the onset of psychosis, and suggest that loss of ACC topological centrality is a potential biomarker for transition to psychosis