Non-transitive maps in phase synchronization

Concepts from the Ergodic Theory are used to describe the existence of non-transitive maps in attractors of phase synchronous chaotic systems. It is shown that for a class of phase-coherent systems, e.g. the sinusoidally forced Chua's circuit and two coupled R{\"o}ssler oscillators, phase synchronization implies that such maps exist. These ideas are also extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used to real time detection of phase synchronization in experimental systems

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

Toward a Holistic, Intercultural, and Polyphonic Perspective on Health Care: A Brief Prologue to the Paper Titled “Understanding the Personalistic Aspects of Jola Ethnomedicine.”

As a prologue to the paper titled “Understanding the Personalistic Aspects of Jola Ethnomedicine,” the present essay provides a brief anthropologico-philosophical reflection, starting with classic Roman philosopher Seneca and his dictum that “each passing day we die,” and continuing on to the profound existential questions pondered by more contemporary thinkers, including Heidegger and Levinas, about life, death, being, time, totality, and infinity. These agonically deep questions are intimately related to the universal human angst about health, illness, and death and the seeking of a restoration to a functional corporal and mental harmony and well-being through various means and methods, whether based on traditional religious or mythical beliefs and practices or on more modern medical practices. This essay also provides a diachronic philological analysis of the evolution of the word “health” in various languages and its age- old semantic connections to the idea of the “holly” and the “sacred.” These semantic roots lead the author to define health as a “holistic, cosmic, integral, and sacred state of dynamic harmony.

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

HST/FOS Time-resolved spectral mapping of IP Pegasi at the end of an outburst

We report an eclipse mapping analysis of time-resolved ultraviolet spectroscopy covering three eclipses of the dwarf nova IP Pegasi on the late decline of the 1993 May outburst. The eclipse maps of the first run show evidence of one spiral arm, suggesting that spiral structures may still be present in the accretion disc 9 days after the onset of the outburst. In the spatially resolved spectra the most prominent lines appear in emission at any radius, being stronger in the inner disc regions. The spectrum of the gas stream is clearly distinct from the disc spectrum in the intermediate and outer disc regions, suggesting the occurrence of gas stream overflow. The full width half maximum of C IV is approximately constant with radius, in contrast to the expected $v\propto{R^{-1/2}}$ law for a gas in Keplerian orbits. This line probably originates in a vertically extended region (chromosphere + disc wind). The uneclipsed component contributes $\sim{4}$ % of the flux in C IV in the first run, and becomes negligible in the remaining runs. We fit stellar atmosphere models to the spatially resolved spectra. The radial run of the disc color temperature for the three runs is flatter than the expected $T\propto{R^{-3/4}}$ law for steady-state optically thick discs models, with $T\simeq{20000}$ K in the inner regions and $T\simeq{9000}$ K in the outer disc regions. The solid angles that result from the fits are smaller than expected from the parameters of the system. The radial run of the solid angle suggests that the disc is flared in outburst, and decreases in thickness toward the end of the outburst.Comment: 14 pages, 14 figures, in press in Astronomy & Astrophysic

Options and Efficiency in Multiperiod Security Markets

We extend the result of Ross (1976) that European options generate complete markets from the single-period to a multiperiod setting. We find that multiperiod European options on a trading strategy generate dynamic completeness for every arbitrage-free price process, provided that the trading strategy has non-negative terminal dividends and separates states at the terminal date. Furthermore, we show that if the uncertainty and information structure in an economy are such that the number of immediate successors of every non-terminal event is non-decreasing over time, then multiperiod European options on a trading strategy generate dynamic completeness for almost every arbitrage-free price process under a significantly weaker condition on the trading strategy's terminal dividends. This condition requires the trading strategy to have non- negative terminal dividends and to separate states at the terminal date conditional on the information available at the previous date. Finally, we examine the minimum number of options generating dynamic completeness for almost every arbitrage-free price process.

Modeling micro-heterogeneity in mixtures: the role of many body terms

A two-component interaction model is introduced herein, which allows to describe macroscopic miscibility with various modes of tunable micro-segregation, ranging from phase separation to micro-segregation, and in excellent agreement for structural quantities obtained from simulations and the liquid state hypernetted-chain like integral equation theory. The model is based on the conjecture that the many-body correlation bridge function term in the closure relation can be divided into one part representing the segregation effects, which are modeled herein, and the usual part representing random many body fluctuations. Furthermore, the model allows to fully neglect these second contributions, thus increasing the agreement between the simulations and the theory. The analysis of the retained part of the many body correlations gives important clues about how to model the many body bridge functions for more realistic systems exhibiting micro-segregation, such as aqueous mixtures.Comment: 6 figure