Moduli Spaces of Abelian Vortices on Kahler Manifolds

We consider the self-dual vortex equations on a positive line bundle L --> M over a compact Kaehler manifold of arbitrary dimension. When M is simply connected, the moduli space of vortex solutions is a projective space. When M is an abelian variety, the moduli space is the projectivization of the Fourier-Mukai transform of L. We extend this description of the moduli space to the abelian GLSM, i.e. to vortex equations with a torus gauge group acting linearly on a complex vector space. After establishing the Hitchin-Kobayashi correspondence appropriate for the general abelian GLSM, we give explicit descriptions of the vortex moduli space in the case where the manifold M is simply connected or is an abelian variety. In these examples we compute the Kaehler class of the natural L^2-metric on the moduli space. In the simplest cases we compute the volume and total scalar curvature of the muduli space. Finally, we note that for abelian GLSM the vortex moduli space is a compactification of the space of holomorphic maps from M to toric targets, just as in the usual case of M being a Riemann surface. This leads to various natural conjectures, for instance explicit formulae for the volume of the space of maps CP^m --> CP^n.Comment: v2: 48 pages; significant changes; description of the vortex moduli spaces of the GLSM extended to allow general values of the parameters, beyond the generic values of v

Vortex equations in abelian gauged sigma-models

We consider nonlinear gauged sigma-models with Kahler domain and target. For a special choice of potential these models admit Bogomolny (or self-duality) equations -- the so-called vortex equations. We find the moduli space and energy spectrum of the solutions of these equations when the gauge group is a torus T^n, the domain is compact, and the target is C^n or CP^n. We also obtain a large family of solutions when the target is a compact Kahler toric manifold.Comment: v2: 60 pages, more details than in CMP versio

Network Mutual Information and Synchronization under Time Transformations

We investigate the effect of general time transformations on the phase synchronization (PS) phenomenon and the mutual information rate (MIR) between pairs of nodes in dynamical networks. We demonstrate two important results concerning the invariance of both PS and the MIR. Under time transformations PS can neither be introduced nor destroyed and the MIR cannot be raised from zero. On the other hand, for proper time transformations the timing between the cycles of the coupled oscillators can be largely improved. Finally, we discuss the relevance of our findings for communication in dynamical networks.Comment: 15 p

A spiral structure in the disk of EX Draconis on the rise to outburst maximum

We report on the R-band eclipse mapping analysis of high-speed photometry of the dwarf nova EX Dra on the rise to the maximum of the November 1995 outburst. The eclipse map shows a one-armed spiral structure of ~180 degrees in azimuth, extending in radius from R ~0.2 to 0.43 R_{L1} (where R_{L1} is the distance from the disk center to the inner Lagrangian point), that contributes about 22 per cent of the total flux of the eclipse map. The spiral structure is stationary in a reference frame co-rotating with the binary and is stable for a timescale of at least 5 binary orbits. The comparison of the eclipse maps on the rise and in quiescence suggests that the outbursts of EX Dra may be driven by episodes of enhanced mass-transfer from the secondary star. Possible explanations for the nature of the spiral structure are discussed.Comment: To appear in the Astrophysical Journal Letters; 8 pages, 2 figures; coded with AAS latex styl

Optimal network topologies for information transmission in active networks

This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.Comment: 20 pages, 12 figure

Eclipse studies of the dwarf-nova Ex Draconis

We report on high speed photometry of EX Dra in quiescence and in outburst. The analysis of the lightcurves indicates that the outbursts do not start in the outer disc regions. The disc expands during rise to maximum and shrinks during decline and along the quiescent period. At the end of two outbursts the system was seen to go through a phase of lower brightness, characterized by an out-of-eclipse level ~15 per cent lower than the typical quiescent level and by the fairly symmetric eclipse of a compact source at disc centre with little evidence of a bright spot at disc rim. New eclipse timings were measured and a revised ephemeris was derived. The residuals with respect to the linear ephemeris are well described by a sinusoid of amplitude 1.2 minutes and period \~4 years and are possibly related to a solar-like magnetic activity cycle in the secondary star. Eclipse phases of the compact central source and of the bright spot were used to derive the geometry of the binary. By constraining the gas stream trajectory to pass through the observed position of the bright spot we find q=0.72+/-0.06 and i= 85 +3/-2 degrees. The binary parameters were estimated by combining the measured mass ratio with the assumption that the secondary star obeys an empirical main sequence mass-radius relation. We find M_1= 0.75+/-0.15 M_sun and M_2= 0.54+/-0.10 M_sun. The white dwarf at disc centre is surrounded by an extended and variable atmosphere or boundary layer of at least 3 times its radius and a temperature of T ~28000 K. The fluxes at mid-eclipse yield an upper limit to the contribution of the secondary star and lead to a lower limit photometric parallax distance of D= 290+/-80 pc. The fluxes of the secondary star are well matched by those of a M0+/-2 main sequence star.Comment: submitted to MNRAS, 12 pages, 9 figures; coded with MNRAS latex styl

Sensitive Dependence on Parameters of Continuous-time Nonlinear Dynamical Systems

We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1 and 2013/26598-0, CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPostprin