Analysis of an information-theoretic model for communication

We study the cost-minimization problem posed by Ferrer i Cancho and Sol\'e in their model of communication that aimed at explaining the origin of Zipf's law [PNAS 100, 788 (2003)]. Direct analysis shows that the minimum cost is $\min {\lambda, 1-\lambda}$, where $\lambda$ determines the relative weights of speaker's and hearer's costs in the total, as shown in several previous works using different approaches. The nature and multiplicity of the minimizing solution changes discontinuously at $\lambda=1/2$, being qualitatively different for $\lambda 1/2$, and $\lambda=1/2$. Zipf's law is found only in a vanishing fraction of the minimum-cost solutions at $\lambda = 1/2$ and therefore is not explained by this model. Imposing the further condition of equal costs yields distributions substantially closer to Zipf's law, but significant differences persist. We also investigate the solutions reached by the previously used minimization algorithm and find that they correctly recover global minimum states at the transition.Comment: 19 pages, 4 figures. Important references and new results adde

Structure of resonance eigenfunctions for chaotic systems with partial escape

Physical systems are often neither completely closed nor completely open, but instead are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main properties of resonance eigenfunctions of chaotic quantum systems with partial escape. We construct a family of conditionally invariant measures with varying decay rates by interpolating between the natural measures of the forward and backward dynamics. Numerical simulations in a representative system show that our classical measures correctly describe the main features of the quantum eigenfunctions: their multifractal phase-space distribution, their product structure along stable and unstable directions, and their dependence on the decay rate. The (Jensen-Shannon) distance between classical and quantum measures goes to zero in the semiclassical limit for long- and short-lived eigenfunctions, while it remains finite for intermediate cases

D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds

We investigate field theories on the worldvolume of a D3-brane transverse to partial resolutions of a $\Z_3\times\Z_3$ Calabi-Yau threefold quotient singularity. We deduce the field content and lagrangian of such theories and present a systematic method for mapping the moment map levels characterizing the partial resolutions of the singularity to the Fayet-Iliopoulos parameters of the D-brane worldvolume theory. As opposed to the simpler cases studied before, we find a complex web of partial resolutions and associated field-theoretic Fayet-Iliopoulos deformations. The analysis is performed by toric methods, leading to a structure which can be efficiently described in the language of convex geometry. For the worldvolume theory, the analysis of the moduli space has an elegant description in terms of quivers. As a by-product, we present a systematic way of extracting the birational geometry of the classical moduli spaces, thus generalizing previous work on resolution of singularities by D-branes.Comment: 52 pages, 9 figure

Characterizing Weak Chaos using Time Series of Lyapunov Exponents

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase-space associated to them. Applying our methodology to a chain of coupled standard maps we obtain: (i) that it allows for an improved numerical characterization of stickiness in high-dimensional Hamiltonian systems, when compared to the previous analyses based on the distribution of recurrence times; (ii) that the transition probabilities between different regimes are determined by the phase-space volume associated to the corresponding regions; (iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure

XenDB: Full length cDNA prediction and cross species mapping in Xenopus laevis

BACKGROUND: Research using the model system Xenopus laevis has provided critical insights into the mechanisms of early vertebrate development and cell biology. Large scale sequencing efforts have provided an increasingly important resource for researchers. To provide full advantage of the available sequence, we have analyzed 350,468 Xenopus laevis Expressed Sequence Tags (ESTs) both to identify full length protein encoding sequences and to develop a unique database system to support comparative approaches between X. laevis and other model systems. DESCRIPTION: Using a suffix array based clustering approach, we have identified 25,971 clusters and 40,877 singleton sequences. Generation of a consensus sequence for each cluster resulted in 31,353 tentative contig and 4,801 singleton sequences. Using both BLASTX and FASTY comparison to five model organisms and the NR protein database, more than 15,000 sequences are predicted to encode full length proteins and these have been matched to publicly available IMAGE clones when available. Each sequence has been compared to the KOG database and ~67% of the sequences have been assigned a putative functional category. Based on sequence homology to mouse and human, putative GO annotations have been determined. CONCLUSION: The results of the analysis have been stored in a publicly available database XenDB . A unique capability of the database is the ability to batch upload cross species queries to identify potential Xenopus homologues and their associated full length clones. Examples are provided including mapping of microarray results and application of 'in silico' analysis. The ability to quickly translate the results of various species into 'Xenopus-centric' information should greatly enhance comparative embryological approaches. Supplementary material can be found at