A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface

Given a graph $G$ cellularly embedded on a surface $\Sigma$ of genus $g$, a cut graph is a subgraph of $G$ such that cutting $\Sigma$ along $G$ yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any $\varepsilon >0$, we show how to compute a $(1+ \varepsilon)$ approximation of the shortest cut graph in time $f(\varepsilon, g)n^3$. Our techniques first rely on the computation of a spanner for the problem using the technique of brick decompositions, to reduce the problem to the case of bounded tree-width. Then, to solve the bounded tree-width case, we introduce a variant of the surface-cut decomposition of Ru\'e, Sau and Thilikos, which may be of independent interest

The Large N_c Baryon-Meson I_t = J_t Rule Holds for Three Flavors

It has long been known that nonstrange baryon-meson scattering in the 1/N_c expansion of QCD greatly simplifies when expressed in terms of t-channel exchanges: The leading-order amplitudes satisfy the selection rule I_t = J_t. We show that I_t = J_t, as well as Y_t = 0, also hold for the leading amplitudes when the baryon and/or meson contain strange quarks, and also characterize their 1/N_c corrections, thus opening a new front in the phenomenological study of baryon-meson scattering and baryon resonances.Comment: 12 pages, 0 figures, ReVTe

Scars on the CBR?

We ask whether the universe can be a patchwork consisting of distinct regions of matter and antimatter. In previous work we demonstrated that post-recombination matter-antimatter contact near regional boundaries leads to an observable (but unobserved) gamma-ray flux for domain sizes of less than a few thousand Mpc, thereby excluding such domains. In this paper we consider the pre-recombination signal from domains of larger size.Comment: 6 pages, late

Generation of Rabi frequency radiation using exciton-polaritons

We study the use of exciton-polaritons in semiconductor microcavities to generate radiation spanning the infrared to terahertz regions of the spectrum by exploiting transitions between upper and lower polariton branches. The process, which is analogous to difference-frequency generation (DFG), relies on the use of semiconductors with a nonvanishing second-order susceptibility. For an organic microcavity composed of a nonlinear optical polymer, we predict a DFG irradiance enhancement of $2.8\cdot10^2$, as compared to a bare nonlinear polymer film, when triple resonance with the fundamental cavity mode is satisfied. In the case of an inorganic microcavity composed of (111) GaAs, an enhancement of $8.8\cdot10^3$ is found, as compared to a bare GaAs slab. Both structures show high wavelength tunability and relaxed design constraints due to the high modal overlap of polariton modes.Comment: 8 pages, 7 figure

Non-equilibrium Thermodynamics and Fluctuations

In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit expressions for the ratio of the probability to find the system with a certain value of entropy (or heat) production to that of finding the opposite value. A similar theorem for the fluctuations of the work done on a system has recently been demonstrated experimentally for a simple system in a transient state, consisting of a Brownian particle in water, confined by a moving harmonic potential. In this paper we show that because of the interaction between the stochastic motion of the particle in water and its deterministic motion in the potential, very different new heat theorems are found than in the conventional case. One of the consequences of these new heat Fluctuation Theorems is that the ratio of the probability for the Brownian particle to absorb heat from rather than supply heat to the water is much larger than in the Conventional Fluctuation Theorem. This could be of relevance for micro/nano-technology.Comment: 10 pages, 6 figures. Some corrections in the text were made. Submitted to Physica

Algorithmic Aspects of Switch Cographs

This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm and we take advantage of the involution modular decomposition tree to state several algorithmic results. Cographs are the graphs that are totally decomposable w.r.t modular decomposition. In a similar way, we introduce the class of switch cographs, the class of graphs that are totally decomposable w.r.t involution modular decomposition. This class generalizes the class of cographs and is exactly the class of (Bull, Gem, Co-Gem, C_5)-free graphs. We use our new decomposition tool to design three practical algorithms for the maximum cut, vertex cover and vertex separator problems. The complexity of these problems was still unknown for this class of graphs. This paper also improves the complexity of the maximum clique, the maximum independant set, the chromatic number and the maximum clique cover problems by giving efficient algorithms, thanks to the decomposition tree. Eventually, we show that this class of graphs has Clique-Width at most 4 and that a Clique-Width expression can be computed in linear time

On a nonlinear theory of elastic shells

Nonlinear theory of elastic shells with deformation gradient

A subset solution to the sign problem in random matrix simulations

We present a solution to the sign problem in dynamical random matrix simulations of a two-matrix model at nonzero chemical potential. The sign problem, caused by the complex fermion determinants, is solved by gathering the matrices into subsets, whose sums of determinants are real and positive even though their cardinality only grows linearly with the matrix size. A detailed proof of this positivity theorem is given for an arbitrary number of fermion flavors. We performed importance sampling Monte Carlo simulations to compute the chiral condensate and the quark number density for varying chemical potential and volume. The statistical errors on the results only show a mild dependence on the matrix size and chemical potential, which confirms the absence of sign problem in the subset method. This strongly contrasts with the exponential growth of the statistical error in standard reweighting methods, which was also analyzed quantitatively using the subset method. Finally, we show how the method elegantly resolves the Silver Blaze puzzle in the microscopic limit of the matrix model, where it is equivalent to QCD.Comment: 18 pages, 11 figures, as published in Phys. Rev. D; added references; in Sec. VB: added discussion of model satisfying the Silver Blaze for all N (proof in Appendix E

Optical Dielectric Functions of III-V Semiconductors in Wurtzite Phase

Optical properties of semiconductors can exhibit strong polarization dependence due to crystalline anisotropy. A number of recent experiments have shown that the photoluminescence intensity in free standing nanowires is polarization dependent. One contribution to this effect is the anisotropy of the dielectric function due to the fact that most nanowires crystalize in the wurtzite form. While little is known experimentally about the band structures wurtzite phase III-V semiconductors, we have previously predicted the bulk band structure of nine III-V semiconductors in wurtzite phase.Here, we predict the frequency dependent dielectric functions for nine non-Nitride wurtzite phase III-V semiconductors (AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs and InSb). Their complex dielectric functions are calculated in the dipole approximation by evaluating the momentum matrix elements on a dense grid of special k-points using empirical pseudopotential wave functions. Corrections to the momentum matrix elements accounting for the missing core states are made using a scaling factor which is determined by using the optical sum rules on the calculated dielectric functions for the zincblende polytypes. The dielectric function is calculated for polarizations perpendicular and parallel to the c-axis of the crystal

Crinoid phylogeny: a preliminary analysis (Echinodermata: Crinoidea)

We describe the first molecular and morphological analysis of extant crinoid high-level inter-relationships. Nuclear and mitochondrial gene sequences and a cladistically coded matrix of 30 morphological characters are presented, and analysed by phylogenetic methods. The molecular data were compiled from concatenated nuclear-encoded 18S rDNA, internal transcribed spacer 1, 5.8S rDNA, and internal transcribed spacer 2, together with part of mitochondrial 16S rDNA, and comprised 3,593 sites, of which 313 were parsimony-informative. The molecular and morphological analyses include data from the bourgueticrinid Bathycrinus; the antedonid comatulids Dorometra and Florometra; the cyrtocrinids Cyathidium, Gymnocrinus, and Holopus; the isocrinids Endoxocrinus, and two species of Metacrinus; as well as from Guillecrinus and Caledonicrinus, whose ordinal relationships are uncertain, together with morphological data from Proisocrinus. Because the molecular data include indel-rich regions, special attention was given to alignment procedure, and it was found that relatively low, gene-specific, gap penalties gave alignments from which congruent phylogenetic information was obtained from both well-aligned, indel-poor and potentially misaligned, indel-rich regions. The different sequence data partitions also gave essentially congruent results. The overall direction of evolution in the gene trees remains uncertain: an asteroid outgroup places the root on the branch adjacent to the slowly evolving isocrinids (consistent with palaeontological order of first appearances), but maximum likelihood analysis with a molecular clock places it elsewhere. Despite lineage-specific rate differences, the clock model was not excluded by a likelihood ratio test. Morphological analyses were unrooted. All analyses identified three clades, two of them generally well-supported. One well-supported clade (BCG) unites Bathycrinus and Guillecrinus with the representative (chimaeric) comatulid in a derived position, suggesting that comatulids originated from a sessile, stalked ancestor. In this connection it is noted that because the comatulid centrodorsal ossicle originates ontogenetically from the column, it is not strictly correct to describe comatulids as unstalked crinoids. A second, uniformly well-supported clade contains members of the Isocrinida, while the third clade contains Gymnocrinus, a well-established member of the Cyrtocrinida, together with the problematic taxon Caledonicrinus, currently classified as a bourgueticrinid. Another cyrtocrinid, Holopus, joins this clade with only weak molecular, but strong morphological support. In one morphological analysis Proisocrinus is weakly attached to the isocrinid clade. Only an unusual, divergent 18S rDNA sequence was obtained from the morphologically strange cyrtocrinid Cyathidium. Although not analysed in detail, features of this sequence suggested that it may be a PCR artefact, so that the apparently basal position of this taxon requires confirmation. If not an artefact, Cyathidium either diverged from the crinoid stem much earlier than has been recognised hitherto (i.e., it may be a Palaeozoic relic), or it has an atypically high rate of molecular evolution