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In this paper, we use the unitary representation theory of $SL_2(\mathbb R)$ to understand the Rankin-Cohen brackets for modular forms. Then we use this interpretation to study the corresponding deformation problems that Paula Cohen, Yuri Manin and Don Zagier initiated. Two uniqueness results are established.
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arxiv:0708.1528
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On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra-Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variables model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed.
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arxiv:0708.1539
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Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4d Riemannian quantum gravity that generalises the well-known Barrett-Crane model and resolves the inherent to it ultra-locality problem. The BF formulation of 4d gravity possesses two sectors: gravitational and topological ones. The model presented here is shown to give a quantization of the gravitational sector, and is dual to the recently proposed spin foam model of Engle et al. which, we show, corresponds to the topological sector. Our methods allow us to introduce the Immirzi parameter into the framework of spin foam quantisation. We generalize some of our considerations to the Lorentzian setting and obtain a new spin foam model in that context as well.
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arxiv:0708.1595
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We study the Casimir effect at finite temperature for a massless scalar field in the parallel plates geometry in N spatial dimensions, under various combinations of Dirichlet and Neumann boundary conditions on the plates. We show that in all these cases the entropy, in the limit where energy equipartitioning applies, is a geometrical factor whose sign determines the sign of the Casimir force.
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arxiv:0708.1615
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In this paper I discuss the magnetic phases of the three-flavor color superconductor. These phases can take place at different field strengths in a highly dense quark system. Given that the best natural candidates for the realization of color superconductivity are the extremely dense cores of neutron stars, which typically have very large magnetic fields, the magnetic phases here discussed could have implications for the physics of these compact objects.
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arxiv:0708.1619
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Given a quasi-compact, quasi-separated scheme X, a bijection between the tensor localizing subcategories of finite type in Qcoh(X) and the set of all subsets $Y\subseteq X$ of the form $Y=\bigcup_{i\in\Omega}Y_i$, with $X\setminus Y_i$ quasi-compact and open for all $i\in\Omega$, is established. As an application, there is constructed an isomorphism of ringed spaces (X,O_X)-->(Spec(Qcoh(X)),O_{Qcoh(X)}), where $(Spec(Qcoh(X)),O_{Qcoh(X)})$ is a ringed space associated to the lattice of tensor localizing subcategories of finite type. Also, a bijective correspondence between the tensor thick subcategories of perfect complexes $\perf(X)$ and the tensor localizing subcategories of finite type in Qcoh(X) is established.
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arxiv:0708.1622
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The computation of n-point planar amplitudes in N=4 SYM at strong coupling is known to be reduced to the search for solutions of the integrable 2d SO(4,2) sigma-model with growing asymptotics on the world-sheet and to the study of their Whitham deformations induced by an epsilon-regularization, which breaks both integrability and SO(4,2) symmetry. A multi-parameter (moduli) family of such solutions is constructed for n=4. They all correspond to the same s and t and some are related by SO(4,2) transformations. Nevertheless, they lead to different regularized areas, whose minimum is the Alday-Maldacena solution. A brief review of results on n-point amplitudes is also provided, with special emphasis on the underlying equivalence of the above regularized minimal area in AdS and a double contour integral along the same boundary, two purely geometric quantities.
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arxiv:0708.1625
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We verify whether the O/H abundances of galaxies can be derived from the equivalent width (EW) R23 instead of the extinction-corrected flux R23, and eventually propose a method of improving the reliability of this empirical method, which is often used for the non-flux calibrated spectra of galaxies. We select 37,173 star-forming galaxies from the SDSS-DR2, which offers a wide range of properties to test the EW method. The EW-R23 method brings with it a significant bias: for the bulk of SDSS galaxies, it may affect the determination of log(O/H) by factors ranging from -0.2 to 0.1 dex and for some galaxies by factors ranging from -0.5 to 0.2 dex. We characterize this discrepancy (or bias) by alpha = (I_[OII]/I_Hbeta)/(EW_[OII]/EW_Hbeta), which is virtually independent of dust extinction, while tightly correlating with Dn(4000), although at a lower significance, with (g-r) colors. The EW-R23 method cannot be used as a proxy for the extinction-corrected flux R23 method. From analytical third-order polynomial fits of alpha versus (g-r) colors, we have been able to correct the EW-R23 method. With this additional and easy correction, the EW-R23 method provides O/H abundance values similar to those derived from the extinction-corrected flux R23 method with an accuracy of ~0.1 dex for >92% of the SDSS galaxies.
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arxiv:0708.1650
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We present preliminary results of a search for $B\to X_d\gamma$ decays with a hadronic mass 1.0 GeV/$c^2<M(X_d)<$1.8 GeV/$c^2$. We consider seven final states with up to four charged pions and one neutral pion or $\eta$, which correspond to about 50% of the total $X_d$ fragmentation in this mass range. Based on a sample of 383 million $B\bar{B}$ events collected by the BaBar experiment at PEP-II, we measure a partial branching fraction $\sum\nolimits^{7}_{X_d=1}{{\ensuremath{\cal B}\xspace}}(B\to X_d\gamma)|_{(1.0{GeV}/c^2 <M(X_d)<1.8 {GeV}/c^2)}= (3.1\pm0.9 ^{+0.6}_{-0.5} \pm0.5)\cdot 10^{-6},$ where the uncertainties are statistical, systematic and model-dependent respectively.
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arxiv:0708.1652
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The interpretations of octonion wave equations in eight dimensional space-time have been discussed. We have made an attempt to discuss the octonion field equation as the equation of motion for particles carrying simultaneously electric and magnetic charges (i.e. dyons) in external and internal spaces respectively. It has been concluded that the component of octonion potential wave equations behaves neither the generalized electromagnetic fields of monopoles nor the dyons. Rather, they have the mixed behaviour of electromagnetic fields associated with the electric and magnetic charges in external and internal spaces. We have also made an attempt to investigate the split octonion wave equation and its interpretation in classical electrodynamics and accordingly the consistent and compact forms of eight-dimensional potential and current equation of dyons are obtained in terms of Zorn's vector matrix realization of split octonions.Visualizing the external four space as the localization space for tachyons, it is shown that the split octonion wave equation reduces to the Maxwell's equation (field equation) for bradyons in R^{4}- space as well as that for tachyons in T^{4}- space in the absence of other.
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arxiv:0708.1664
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On June 12, 2007 the Cassini probe sent the images of a small moon of Saturn called Atlas which is located between the ring A and the small ring R/2004 S 1. These images have shown that the Atlas morphology is very different from other moons of similar dimensions. In the present article we propose a reasonable theory, to that we denominated "flying dune", that explains its morphologic characteristics from its magnitudes like mass, diameters and orbital radius, as well as its orbital position and the interpretation of the images caught by the Cassini probe.
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arxiv:0708.1678
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Observations of outflows associated with pre-main-sequence stars reveal details about morphology, binarity and evolutionary states of young stellar objects. We present molecular line data from the Berkeley-Illinois-Maryland Association array and Five Colleges Radio Astronomical Observatory toward the regions containing the Herbig Ae/Be stars LkHa 198 and LkHa 225S. Single dish observations of 12CO 1-0, 13CO 1-0, N2H+ 1-0 and CS 2-1 were made over a field of 4.3' x 4.3' for each species. 12CO data from FCRAO were combined with high resolution BIMA array data to achieve a naturally-weighted synthesized beam of 6.75'' x 5.5'' toward LkHa 198 and 5.7'' x 3.95'' toward LkHa 225S, representing resolution improvements of factors of approximately 10 and 5 over existing data. By using uniform weighting, we achieved another factor of two improvement. The outflow around LkHa 198 resolves into at least four outflows, none of which are centered on LkHa 198-IR, but even at our resolution, we cannot exclude the possibility of an outflow associated with this source. In the LkHa 225S region, we find evidence for two outflows associated with LkHa 225S itself and a third outflow is likely driven by this source. Identification of the driving sources is still resolution-limited and is also complicated by the presence of three clouds along the line of sight toward the Cygnus molecular cloud. 13CO is present in the environments of both stars along with cold, dense gas as traced by CS and (in LkHa 225S) N2H+. No 2.6 mm continuum is detected in either region in relatively shallow maps compared to existing continuum observations.
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arxiv:0708.1775
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The combinatorial basis of entropy, given by Boltzmann, can be written $H = N^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy, $N$ is the number of entities and $\mathbb{W}$ is number of ways in which a given realization of a system can occur (its statistical weight). This can be broadened to give generalized combinatorial (or probabilistic) definitions of entropy and cross-entropy: $H=\kappa (\phi(\mathbb{W}) +C)$ and $D=-\kappa (\phi(\mathbb{P}) +C)$, where $\mathbb{P}$ is the probability of a given realization, $\phi$ is a convenient transformation function, $\kappa$ is a scaling parameter and $C$ an arbitrary constant. If $\mathbb{W}$ or $\mathbb{P}$ satisfy the multinomial weight or distribution, then using $\phi(\cdot)=\ln(\cdot)$ and $\kappa=N^{-1}$, $H$ and $D$ asymptotically converge to the Shannon and Kullback-Leibler functions. In general, however, $\mathbb{W}$ or $\mathbb{P}$ need not be multinomial, nor may they approach an asymptotic limit. In such cases, the entropy or cross-entropy function can be {\it defined} so that its extremization ("MaxEnt'' or "MinXEnt"), subject to the constraints, gives the ``most probable'' (``MaxProb'') realization of the system. This gives a probabilistic basis for MaxEnt and MinXEnt, independent of any information-theoretic justification. This work examines the origins of the governing distribution $\mathbb{P}$.... (truncated)
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arxiv:0708.1861
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We model the electrons/positrons produced by dark matter annihilations in the colliding galaxy cluster system 1E0657-56 (the bullet cluster). These charged particles, confined by the Magnetic field, clearly trace the path of the bullet, which passes through the main cluster with a speed of 3000-5000 km/s. Adding the effect of dark matter substructure (subhalos) in each cluster we find the annihilation rate is enhancedgreatly and the density of positrons in the trail is similar to that within the bullet cluster. This opens the door to unambiguous detection of the annihilation signal through the SZ effect, at significant separation from the thermal electrons.
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arxiv:0708.1891
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This paper studies multiclass loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer classes. The routing of customers follows an overflow scheme, where arriving customers are preferentially directed to the first layer. Stochastic comparison and coupling techniques are developed for studying how the system is affected by packing of customers, altered service rates, and altered server configurations. This analysis leads to easily computable upper and lower bounds for the performance of the system.
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arxiv:0708.1927
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We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then to pick the correct one. In our case the device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible covers (exact or not) of the given set. For selecting the correct solution we assign to each item, from the set to be covered, a special integer number. These numbers will actually represent delays induced to light when it passes through arcs. The solution is represented as a subray arriving at a certain moment in the destination node. This will tell us if an exact cover does exist or not.
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arxiv:0708.1962
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The energy--momentum tensor in general relativity contains only localized contributions to the total energy--momentum. Here, we consider a static, spherically symmetric object consisting of a charged perfect fluid. For this object, the total gravitational mass contains a non--localizable contribution of electric coupling (ordinarily associated with electromagnetic mass). We derive an explicit expression for the total mass which implies that the non--localizable contribution of electric coupling is not bound together by gravity, thus ruling out existence of the objects with pure Lorentz electromagnetic mass in general relativity.
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arxiv:0708.2037
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We show that matrix $Q\times Q$ Self-dual type $S$-integrable Partial Differential Equations (PDEs) possess a family of lower-dimensional reductions represented by the matrix $ Q \times n_0 Q$ quasilinear first order PDEs solved in \cite{SZ1} by the method of characteristics. In turn, these PDEs admit two types of available particular solutions: (a) explicit solutions and (b) solutions described implicitly by a system of non-differential equations. The later solutions, in particular, exhibit the wave profile breaking. Only first type of solutions is available for (1+1)-dimensional nonlinear $S$-integrable PDEs. (1+1)-dimensional $N$-wave equation, (2+1)- and (3+1)-dimensional Pohlmeyer equations are represented as examples. We also represent a new version of the dressing method which supplies both classical solutions and solutions with wave profile breaking to the above $S$-integrable PDEs.
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arxiv:0708.2050
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This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation $u_t+\De\bigl(\eps \De u-\eps^{-1} f(u)\bigr)=0$. It is shown that the {\it a posteriori} error bounds depends on $\eps^{-1}$ only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct an adaptive algorithm for computing the solution of the Cahn-Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.
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arxiv:0708.2116
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An article for the Springer Encyclopedia of Complexity and System Science
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arxiv:0708.2203
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A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a parameter e which characterizes how close a horizon is to extremality and should be calculable in numerical simulations.
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arxiv:0708.2209
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The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order $o(\bar{g})$ in the coupling constant $\bar{g}$. As a first application, based on the Riemann-Liouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non relativistic fractional Schr\"odinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.
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arxiv:0708.2262
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A subset of a group is product-free if it does not contain elements a, b, c such that ab = c. We review progress on the problem of determining the size of the largest product-free subset of an arbitrary finite group, including a lower bound due to the author, and a recent upper bound due to Gowers. The bound of Gowers is more general; it allows three different sets A, B, C such that one cannot solve ab = c with a in A, b in B, c in C. We exhibit a refinement of the lower bound construction which shows that for this broader question, the bound of Gowers is essentially optimal.
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arxiv:0708.2295
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The boron buckyball avoids the high symmetry icosahedral cage structure. The previously reported Ih symmetric structure is not an energy minimum in the potential energy surface and exhibits a spontaneous symmetry breaking to yield a puckered cage with a rare Th symmetry. The HOMO-LUMO gap is twice as large as the reported value and amounts to 1.94 eV at B3LYP/6-31G(d) level. The valence orbital structure of boron buckyball is identical to the one in the carbon analogue.
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arxiv:0708.2331
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Let $S$ be a Riemann surface of type $(p,n)$ with $3p-3+n>0$. Let $\omega$ be a pseudo-Anosov map of $S$ that is obtained from Dehn twists along two families $\{A,B\}$ of simple closed geodesics that fill $S$. Then $\omega$ can be realized as an extremal Teichm\"{u}ller mapping on a surface of type $(p,n)$ which is also denoted by $S$. Let $\phi$ be the corresponding holomorphic quadratic differential on $S$. In this paper, we compare the locations of some distinguished points on $S$ in the $\phi$-flat metric to their locations with respect to the complete hyperbolic metric. More precisely, we show that all possible non-puncture zeros of $\phi$ must stay away from all closures of once punctured disk components of $S\backslash \{A, B\}$, and the closure of each disk component of $S\backslash \{A, B\}$ contains at most one zero of $\phi$. As a consequence of the result, we assert that the number of distinct zeros and poles of $\phi$ is less than or equal to the number of components of $S\backslash \{A, B\}$.
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arxiv:0708.2371
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We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic, Markovian jump process with a specific structure that lends itself naturally to coarse-graining. A perturbative analysis yields a reduced stochastic jump process that approximates the coarse-grained dynamics of the original system. This leads to a non-trivial fluctuation relation that is approximately satisfied by the coarse-grained dynamics. We illustrate our results by computing the large deviations of a particular stochastic jump process. Our results highlight the possibility that observed deviations from fluctuation relations might be due to the presence of unobserved degrees of freedom.
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arxiv:0708.2437
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Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative $\phi^4$-theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed.
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arxiv:0708.2471
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We evaluate the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. We find that the H-Hbar interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ~ 6 a.u. and a barrier rising at r~5 a.u. Additional theoretical and experimental investigations on the nature of these peculiar features will be of great interest.
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arxiv:0708.2477
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The general solution of the one-dimensional stationary Schroedinger equation in the form of a formal power series is considered. Its efficiency for numerical analysis of initial value and boundary value problems is discussed.
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arxiv:0708.2491
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The Arecibo Legacy Fast ALFA (ALFALFA) survey is an on-going second generation blind extragalactic HI survey exploiting Arecibo's superior sensitivity, angular resolution and digital technology to conduct a census of the local HI universe over a cosmologically significant volume. As of mid-2007, ~4500 good quality extragalactic HI line sources have been extracted in ~15% of the final survey area. ALFALFA is detecting HI masses as low as 10**6 Msun and as high as 10**10.8 Msun with positional accuracies typically better than 20 arcsec, allowing immediate identification of the most probable optical counterparts. Only 3% of all extragalactic HI sources and fewer than 1% of detections with M(HI) > 10**9.5 Msun cannot be identified with a stellar component. First ALFALFA results already suggest, in agreement with previous studies, that there does not appear to be a cosmologically significant population of optically dark but HI rich galaxies. ALFALFA promises a wealthy dataset for the exploration of many issues in near-field cosmology and galaxy evolution studies, setting the stage for their extension to higher redshifts with the Square Kilometer Array (SKA).
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arxiv:0708.2547
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Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of incomplete information and that this value is uniform, i.e. there are epsilon-optimal strategies for both players that are epsilon-optimal in any long enough prefix of the game. We give an example to demonstrate that nonnegativity is essential and expand the results to leavable games.
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arxiv:0708.2556
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The Modular Neutron Array (MoNA) was used in conjunction with a large-gap dipole magnet (Sweeper) to measure neutron-unbound states in oxygen isotopes close to the neutron dripline. While no excited states were observed in 24O, a resonance at 45(2) keV above the neutron separation energy was observed in 23O.
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arxiv:0708.2573
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We analyze the transverse instabilities of spatial bright solitons in nonlocal nonlinear media, both analytically and numerically. We demonstrate that the nonlocal nonlinear response leads to a dramatic suppression of the transverse instability of the soliton stripes, and we derive the asymptotic expressions for the instability growth rate in both short- and long-wave approximations.
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arxiv:0708.2596
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We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found that this model can produce small-world networks with power-law degree distributions. Properties of our model, including the degree distribution, clustering, and the average path length are compared with that of the BA model. Since most real networks are both scale-free and small-world networks, our model may provide a satisfactory description for empirical characteristics of real networks.
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arxiv:0708.2600
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Recent observations have revealed the existence of an enormously energetic > 10^61 erg AGN outburst in the Hydra A cluster of galaxies. This outburst has produced cavities in the intra-cluster medium, apparently supported by pressure from cosmic rays. Here we argue that if these cavities are filled with > GeV particles, these particles are very likely protons and nuclei. For a plausible spatial distribution of the target gas, based on observations and hydrodynamical simulations, we show that the pi^0-decay gamma-rays from these cosmic-rays may be detectable with the H.E.S.S.experiment.
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arxiv:0708.2607
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We construct a family of BCS paired composite fermion wavefunctions that generalize, but remain in the same topological phase as, the Moore-Read Pfaffian state for the half-filled Landau level. It is shown that for a wide range of experimentally relevant inter-electron interactions the groundstate can be very accurately represented in this form.
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arxiv:0708.2680
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The 3+1 GRMHD equations for Schwarzschild spacetime in Rindler coordinates with isothermal state of plasma are formulated. We consider the cases of non-rotating and rotating backgrounds with non-magnetized and magnetized plasmas. For these cases, the perturbed form of these equations are linearized and Fourier analyzed by introducing plane wave type solutions. The determinant of these equations in each case leads to two dispersion relations which give value of the wave number $k$. Using the wave number, we obtain information like phase and group velocities etc. which help to discuss the nature of the waves and their characteristics. These provide interesting information about the black hole magnetosphere near the horizon. There are cases of normal and anomalous dispersion. We find a case of normal dispersion of waves when the plasma admits the properties of Veselago medium. Our results agree with those of Mackay et al. according to which rotation of a black hole is required for negative phase velocity propagation.
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arxiv:0708.2690
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The article presents calculated dissociative recombination (DR) rate coefficients for H+3 . The previous theoretical work on H+3 was performed using the adiabatic hyperspherical approximation to calculate the target ion vibrational states and it considered just a limited number of ionic rotational states. In this study, we use accurate vibrational wave functions and a larger number of possible rotational states of the H3+ ground vibrational level. The DR rate coefficient obtained is found to agree better with the experimental data from storage-ring experiments than the previous theoretical calculation. We present evidence that excited rotational states could be playing an important role in those experiments for collision energies above 10 meV. The DR rate coefficients calculated separately for ortho- and para-H3+ are predicted to differ significantly at low energy, a result consistent with a recent experiment. We also present DR rate coefficients for vibrationally-excited initial states of H3+, which are found to be somewhat larger than the rate coefficient for the ground vibrational level.
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arxiv:0708.2715
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Despite their paucity, massive hot stars are real cosmic engines of fundamental importance in shaping our Universe, from its very early stages up to its current appearance. Understanding the physics of massive stars is then a key issue for many relevant astrophysical phenomena. Probing the massive stellar population of nearby galaxies by means of quantitative spectroscopy allows us to unveil a wealth of information that will aid our current understanding of stellar and galaxy evolution. In addition, blue luminous stars can be used as standard candles for extragalactic distances up to 10 Mpc. In this contribution, we present a brief overview of recent steps we have undertaken in this exciting research field.
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arxiv:0708.2737
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We present an optical cavity QED configuration that is described by a dissipative version of the Lipkin-Meshkov-Glick model of an infinitely coordinated spin system. This open quantum system exhibits both first- and second-order non-equilibrium quantum phase transitions as a single, effective field parameter is varied. Light emitted from the cavity offers measurable signatures of the critical behavior, including that of the spin-spin entanglement.
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arxiv:0708.2753
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The site and mechanism of gamma-ray burst (GRB) prompt emission is still unknown. Although internal shocks have been widely discussed as the emission site of GRBs, evidence supporting other emission sites have been also suggested recently, including the closer-in photosphere where the fireball becomes transparent and further-out radii near the fireball deceleration radius where magnetic dissipation may be important. With the successful operation of the GLAST experiment, prompt high energy emission spectra from many GRBs would be detected in the near future. We suggest that the cut-off energy of the prompt emission spectrum from a GRB depends on both the fireball bulk Lorentz factor and the unknown emission radius from the central engine. If the bulk Lorentz factor could be independently measured (e.g. from early afterglow observations), the observed spectral cutoff energy can be used to diagnose the emission site of gamma-rays. This would provide valuable information to understand the physical origin of the GRB promp emission.
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arxiv:0708.2763
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We report formation of self organized InP nano dots using 3 keV Ar+ ion sputtering, at $15^\circ$ incidence from surface normal, on InP(111) surface. Morphology and optical properties of the sputtered surface, as a function of sputtering time, have been investigated by Scanning Probe Microscopy and Raman Scattering techniques. Uniform patterns of nano dots are observed for different durations of sputtering. The sizes and the heights of these nano dots vary between 10 to 100 nm and 20 to 40 nm, respectively. With increasing of sputtering time, t, the size and height of these nano dots increases up to a certain sputtering time $t_c$. However beyond $t_c$, the dots break down into smaller nanostructures, and as a result, the size and height of these nanostructures decrease. The uniformity and regularity of these structures are also lost for sputtering beyond $t_c$. The crossover behavior is also observed in the rms surface roughness. Raman investigations of InP nano dots reveal optical phonon softening due to phonon confinement in the surface nano dots.
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arxiv:0708.2859
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We report a measurement of the exclusive $B^+$ meson decay to the final state $D_s^- K^+\pi^+$ using $520 \times 10^{6} B\bar{B}$ pairs collected near the $\Upsilon(4S)$ resonance, with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. Using the $D_S^- \to \phi \pi^-$ decay mode to reconstruct $D_s^-$ mesons, we obtain the branching fraction ${\cal B}(B^+\to D_s^-K^+\pi^+)= (1.77^{+0.12}_{-0.12} {\mathrm (stat)} \pm 0.16 {\mathrm (syst)} \pm 0.23 {\cal(B)})\times 10^{-4}$. We also present preliminary results of a study of the two-body $D_sK$, $D_s\pi$ and $K\pi$ subsystems observed in this final state.
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arxiv:0708.2885
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We provide a complete proof of the diagrammatic bounds on the lace-expansion coefficients for oriented percolation, which are used in [arXiv:math/0703455] to investigate critical behavior for long-range oriented percolation above 2\min{\alpha,2} spatial dimensions.
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arxiv:0708.2897
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In this talk we argue that the breakdown of global symmetries in no--scale supergravity (SUGRA), which ensures the vanishing of the vacuum energy density near the physical vacuum, leads to a natural realisation of the multiple point principle (MPP). In the MPP inspired SUGRA models the cosmological constant is naturally tiny.
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arxiv:0708.2907
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We present a model for the radio emission from radio-quiet quasar nuclei. We show that a thermal origin for the high brightness temperature, flat spectrum point sources (known as radio ``cores'') is possible provided the emitting region is hot and optically-thin. We hence demonstrate that optically-thin bremsstrahlung from a slow, dense disk wind can make a significant contribution to the observed levels of radio core emission. This is a much more satisfactory explanation, particularly for sources where there is no evidence of a jet, than a sequence of self-absorbed synchrotron components which collectively conspire to give a flat spectrum. Furthermore, such core phenomena are already observed directly via milli-arcsecond radio imaging of the Galactic microquasar SS433 and the active galaxy NGC1068. We contend that radio-emitting disk winds must be operating at some level in radio-loud quasars and radio galaxies as well (although in these cases, observations of the radio cores are frequently contaminated/dominated by synchrotron emission from jet knots). This interpretation of radio core emission mandates mass accretion rates that are substantially higher than Eddington. Moreover, acknowledgment of this mass-loss mechanism as an AGN feedback process has important implications for the input of energy and hot gas into the inter-galactic medium (IGM) since it is considerably less directional than that from jets.
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arxiv:0708.2929
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Tetracyclines are an old class of molecules that constitute a broad-spectrum antibiotics. Since the first member of tetracycline family were isolated, the clinical importance of these compounds as therapeutic and prophylactic agents against a wide range of infections has stimulated efforts to define their mode of action as inhibitors of bacterial reproduction. We used three SAR methodologies for the analysis of biological activity of a set of 104 tetracycline compounds. Our calculation were carried out using the semi-empirical Austin Method One (AM1) and Parametric Method 3 (PM3). Electronic Indices Methodology (EIM), Principal Component Analysis (PCA) and Artificial Neural Networks (ANN) were applied to the classification of 14 old and 90 new proposed derivatives of tetracyclines. Our results make evident the importance of EIM descriptors in pattern recognition and also show that the EIM can be effectively used to predict the biological activity of Tetracyclines.
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arxiv:0708.2931
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We will study the Hitchin's hamiltonian system for a modular stack of principal SL_2(C) bundle on a smooth projective curve which has a parabolic reduction at certain points. As an application we will obtain a generalization of the Beilinson-Drinfeld isomorphism, which is a quantization of the Hitchin's hamiltonian system.
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arxiv:0708.2957
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The second Born corrections to the electrical and thermal conductivities are calculated for the dense matter in the liquid metal phase for various elemental compositions of astrophysical importance. Inclusion up to the second Born corrections is sufficiently accurate for the Coulomb scattering of the electrons by the atomic nuclei with Z < 26. Our approach is semi-analytical, and is in contrast to that of the previous authors who have used fully numerical values of the cross section for the Coulomb scattering of the electron by the atomic nucleus. The merit of the present semi-analytical approach is that this approach affords us to obtain the results with reliable Z-dependence and \rho-dependence. The previous fully numerical approach has made use of the numerical values of the cross section for the scattering of the electron off the atomic nucleus for a limited number of Z-values, Z=6, 13, 29, 50, 82, and 92, and for a limited number of electron energies, 0.05MeV, 0.1MeV, 0.2MeV, 0.4MeV, 0.7MeV, 1MeV, 2MeV, 4MeV, and 10MeV. Our study, however, has confirmed that the previous results are sufficiently accurate. They are recovered, if the terms higher than the second Born terms are taken into account. We make a detailed comparison of the present results with those of the previous authors. The numerical results are parameterized in a form of analytic formulae that would facilitate practical uses of the results. We also extend our calculations to the case of mixtures of nuclear species. The corresponding subroutine can be retrieved from http://www.ph.sophia.ac.jp/~itoh-ken/subroutine/subroutine.htm
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arxiv:0708.2967
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The resistivity of gated graphene is studied taking into account electron and hole scattering by short- and long-range structural imperfections the characteristics of disorder were taken from the scanning tunneling microscopy data and by acoustic phonons. The calculations are based on the quasiclassical kinetic equation with the normalization condition fixed by surface charge. The gate-voltage and temperature effects on the resistance peak, which is centered at the point of intrinsic conductivity, are found to be in agreement with the transport measurements.
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arxiv:0708.2976
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In this paper we consider the problem of estimating a parameter of a probability distribution when we have some prior information on a nuisance parameter. We start by the very simple case where we know perfectly the value of the nuisance parameter. The complete likelihood is the classical tool in this case. Then, progressively, we consider the case where we are given a prior probability distribution on this nuisance parameter. The marginal likelihood is then the classical tool in this case. Then, we consider the case where we only have a fixed number of its moments. Here, we may use the maximum entropy (ME) principle to assign a prior law and thus go back to the previous case. Finally, we consider the case where we know only its median. In our knowledge, there is not any classical tool for this case. We propose then a new tool for this case based on a recently proposed alternative distribution to the marginal probability distribution. This new criterion is obtained by first remarking that the marginal distribution can be considered as the mean value of the original distribution over the prior probability law of the nuisance parameter, and then, by using the median in place of the mean. In this paper, we first summarize the classical tools used for the three first cases, then we give the precise definition of this new criterion and its properties and, finally, present a few examples to show the differences of these cases. Key Words: Nuisance parameter, Bayesian inference, Maximum Entropy, Marginalization, Incomplete knowledge, Mean and Median of the Likelihood over the prior distribution
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arxiv:0708.2999
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We present an example of a highly connected closed network of servers, where the time correlations do not go to zero in the infinite volume limit. This phenomenon is similar to the continuous symmetry breaking at low temperatures in statistical mechanics. The role of the inverse temperature is played by the average load.
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arxiv:0708.3073
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In the course of the NIR/MIR AGN search combining the 6.7 mu ISOCAM Parallel Survey and 2MASS we have discovered 24 type-1 quasars about a third of which are too red to be discriminated by optical/UV search techniques. Here we report on a detailed case study of the reddest type-1 quasar of our sample (J2341) at redshift z=0.236 with M_K=-25.8 and J-K=1.95. We performed spectroscopy in the optical with VLT/FORS1 and in the MIR with Spitzer as well as NIR imaging with ISPI at CTIO. The optical and NIR observations reveal a star forming emission-line galaxy at the same redshift as the quasar with a projected linear separation of 1.8 arcsec (6.7 kpc). The quasar and its companion are embedded in diffuse extended continuum emission. Compared with its companion the quasar exhibits redder optical-NIR colours, which we attribute to hot nuclear dust. The MIR spectrum shows only few emission lines superimposed on a power-law spectral energy distribution. However, the lack of strong FIR emission suggests that our potentially interacting object contains much less gas and dust and is in a stage different from dust reddened ULIRG-AGN like Mrk 231. The optical spectrum shows signatures for reddening in the emission-lines and no post-starburst stellar population is detected in the host galaxy of the quasar. The optical continuum emission of the active nucleus appears absorbed and diluted. Even the combination of absorption and host dilution is not able to match J2341 with standard quasar templates. While the BLR shows only a rather moderate absorption of E_(B-V)=0.3, the continuum shorter than 4500 AA requires strong obscuration with E_(B-V)=0.7, exceeding the constraints from the low upper limit on the 9.7 mu silicate absorption. This leads us to conclude that the continuum of J2341 is intrinsically redder than that of typical quasars.
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arxiv:0708.3109
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Given a Banach space X, denote by SP_{w}(X) the set of equivalence classes of spreading models of X generated by normalized weakly null sequences in X. It is known that SP_{w}(X) is a semilattice, i.e., it is a partially ordered set in which every pair of elements has a least upper bound. We show that every countable semilattice that does not contain an infinite increasing sequence is order isomorphic to SP_{w}(X) for some separable Banach space X.
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arxiv:0708.3126
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In this paper we study $k$-noncrossing RNA structures with arc-length $\ge 3$, i.e. RNA molecules in which for any $i$, the nucleotides labeled $i$ and $i+j$ ($j=1,2$) cannot form a bond and in which there are at most $k-1$ mutually crossing arcs. Let ${\sf S}_{k,3}(n)$ denote their number. Based on a novel functional equation for the generating function $\sum_{n\ge 0}{\sf S}_{k,3}(n)z^n$, we derive for arbitrary $k\ge 3$ exponential growth factors and for $k=3$ the subexponential factor. Our main result is the derivation of the formula ${\sf S}_{3,3}(n) \sim \frac{6.11170\cdot 4!}{n(n-1)...(n-4)} 4.54920^n$.
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arxiv:0708.3134
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The behavior of a charged scalar field in the RN black hole space time is studied using WKB approximation. In the present work it is assumed that matter waves can get reflected from the event horizon. Using this effect, the Hawking temperature and the absorption cross section for RN black hole placed in a charged scalar field are calculated. The absorption cross section $\sigma _{abs}$ is found to be inversely proportional to square of the Hawking temperature of the black hole.
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arxiv:0708.3146
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We perform a linear dynamical stability analysis of a general hydrodynamic model of chemotactic aggregation [Chavanis & Sire, Physica A, in press (2007)]. Specifically, we study the stability of an infinite and homogeneous distribution of cells against "chemotactic collapse". We discuss the analogy between the chemotactic collapse of biological populations and the gravitational collapse (Jeans instability) of self-gravitating systems. Our hydrodynamic model involves a pressure force which can take into account several effects like anomalous diffusion or the fact that the organisms cannot interpenetrate. We also take into account the degradation of the chemical which leads to a shielding of the interaction like for a Yukawa potential. Finally, our hydrodynamic model involves a friction force which quantifies the importance of inertial effects. In the strong friction limit, we obtain a generalized Keller-Segel model similar to the generalized Smoluchowski-Poisson system describing self-gravitating Langevin particles. For small frictions, we obtain a hydrodynamic model of chemotaxis similar to the Euler-Poisson system describing a self-gravitating barotropic gas. We show that an infinite and homogeneous distribution of cells is unstable against chemotactic collapse when the "velocity of sound" in the medium is smaller than a critical value. We study in detail the linear development of the instability and determine the range of unstable wavelengths, the growth rate of the unstable modes and the damping rate, or the pulsation frequency, of the stable modes as a function of the friction parameter and shielding length. For specific equations of state, we express the stability criterion in terms of the density of cells.
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arxiv:0708.3163
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Let $n$ be a positive integer, and let $k$ be a field (of arbitrary characteristic) accessible to symbolic computation. We describe an algorithmic test for determining whether or not a finitely presented $k$-algebra $R$ has infinitely many equivalence classes of semisimple representations $R \to M_n(k')$, where $k'$ is the algebraic closure of $k$. The test reduces the problem to computational commutative algebra over $k$, via famous results of Artin, Procesi, and Shirshov. The test is illustrated by explicit examples, with $n = 3$.
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arxiv:0708.3190
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The trade size $\omega$ has direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization $C$ is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change $r$ and trade size $\omega$ for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impact. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior $r\sim \omega^\alpha$ with $\alpha\approx2/3$. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation $\alpha=\alpha_\omega/\alpha_r$ is verified, where $\alpha_\omega$ and $\alpha_r$ are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between $r$ and $\omega$ for small-size trades. We anticipate that these regularities may hold in other order-driven markets.
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arxiv:0708.3198
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In this work, we have studied theoretically the effects of gold adsorption on the Al(001) surface, using {\it ab initio} pseudo-potential method in the framework of the density functional theory. Having found the hollow sites at the Al(001) surface as the most preferred adsorption sites, we have investigated the effects of the Au adsorption with different coverages ($\Theta$=0.11, 0.25, 0.50, 0.75, 1.00 ML) on the geometry, adsorption energy, surface dipole moment, and the work-function of the Al(001) surface. The results show that, even though the work-function of the Al substrate increases with the Au coverage, the surface dipole moment decreases with the changes in coverage from $\Theta=0.11$ ML to $\Theta=0.25$ ML. We have explained this behavior by analyzing the electronic and ionic charge distributions. Furthermore, by studying the diffusion of Au atoms in to the substrate, we have shown that at room temperature the diffusion rate of Au atoms in to the substrate is negligible but, increasing the temperature to about 200$^\circ$ C the Au atoms significantly diffuse in to the substrate, in agreement with the experiment.
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arxiv:0708.3200
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Laser-driven acceleration holds great promise for significantly improving accelerating gradient. However, scaling the conventional process of structure-based acceleration in vacuum down to optical wavelengths requires a substantially different kind of structure. We require an optical waveguide that (1) is constructed out of dielectric materials, (2) has transverse size on the order of a wavelength, and (3) supports a mode with speed-of-light phase velocity in vacuum. Photonic crystals--structures whose electromagnetic properties are spatially periodic--can meet these requirements. We discuss simulated photonic crystal accelerator structures and describe their properties. We begin with a class of two-dimensional structures which serves to illustrate the design considerations and trade-offs involved. We then present a three-dimensional structure, and describe its performance in terms of accelerating gradient and efficiency. We discuss particle beam dynamics in this structure, demonstrating a method for keeping a beam confined to the waveguide. We also discuss material and fabrication considerations. Since accelerating gradient is limited by optical damage to the structure, the damage threshold of the dielectric is a critical parameter. We experimentally measure the damage threshold of silicon for picosecond pulses in the infrared, and determine that our structure is capable of sustaining an accelerating gradient of 300 MV/m at 1550 nm. Finally, we discuss possibilities for manufacturing these structures using common microfabrication techniques.
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arxiv:0708.3206
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We explore the possibilities of enforcing and preventing consensus in continuous opinion dynamics that result from modifications in the communication rules. We refer to the model of Weisbuch and Deffuant, where $n$ agents adjust their continuous opinions as a result of random pairwise encounters whenever their opinions differ not more than a given bound of confidence $\eps$. A high $\eps$ leads to consensus, while a lower $\eps$ leads to a fragmentation into several opinion clusters. We drop the random encounter assumption and ask: How small may $\eps$ be such that consensus is still possible with a certain communication plan for the entire group? Mathematical analysis shows that $\eps$ may be significantly smaller than in the random pairwise case. On the other hand we ask: How large may $\eps$ be such that preventing consensus is still possible? In answering this question we prove Fortunato's simulation result that consensus cannot be prevented for $\eps>0.5$ for large groups. % Next we consider opinion dynamics under different individual strategies and examine their power to increase the chances of consensus. One result is that balancing agents increase chances of consensus, especially if the agents are cautious in adapting their opinions. However, curious agents increase chances of consensus only if those agents are not cautious in adapting their opinions.
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arxiv:0708.3244
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During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured $p$-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.
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arxiv:0708.3307
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To make predictions for the existence of ``dark galaxies'', it is necessary to understand what determines whether a gas cloud will form stars. Star formation thresholds are generally explained in terms of the Toomre criterion for gravitational instability. I contrast this theory with the thermo-gravitational instability hypothesis of Schaye (2004), in which star formation is triggered by the formation of a cold gas phase and which predicts a nearly constant surface density threshold. I argue that although the Toomre analysis is useful for the global stability of disc galaxies, it relies on assumptions that break down in the outer regions, where star formation thresholds are observed. The thermo-gravitational instability hypothesis can account for a number of observed phenomena, some of which were thought to be unrelated to star formation thresholds.
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arxiv:0708.3366
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We report on a new measurement of $^{14}$N(p,$\gamma$)$^{15}$O for the ground state capture transition at $E_p$ = 360, 380 and 400 keV, using the 400 kV LUNA accelerator. The true coincidence summing effect --the major source of error in the ground state capture determination-- has been significantly reduced by using a Clover--type gamma detector.
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arxiv:0708.3376
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We calculate the structure and neutron content of neutrino-heated MHD winds driven from the surface of newly-formed magnetars (``proto-magnetars'') and from the midplane of hyper-accreting disks, two of the possible central engines for gamma-ray bursts (GRBs) and hyper-energetic supernovae (SNe). Both the surface of proto-magnetars and the midplane of neutrino-cooled accretion flows (NDAFs) are electron degenerate and neutron-rich (neutron-to-proton ratio n/p >> 1). If this substantial free neutron excess is preserved to large radii in ultra-relativistic outflows, several important observational consequences may result. Weak interaction processes, however, can drive n/p to ~1 in the nondegenerate regions that obtain just above the surfaces of NDAFs and proto-magnetars. Our calculations show that mildly relativistic neutron-rich outflows from NDAFs are possible in the presence of a strong poloidal magnetic field. However, we find that neutron-rich winds possess a minimum mass-loss rate that likely precludes simultaneously neutron-rich and ultra-relativistic (Lorentz factor > 100) NDAF winds accompanying a substantial accretion power. In contrast, proto-magnetars are capable of producing neutron-rich long-duration GRB outflows ~10-30 seconds following core bounce for sub-millisecond rotation periods; such outflows would, however, accompany only extremely energetic events, in which the GRB + SN energy budget exceeds ~ 4e52 ergs. Neutron-rich highly relativistic outflows may also be produced during some short-duration GRBs by geometrically thick accretion disks formed from compact object mergers. The implications for r-process nucleosynthesis, optical transients due to non-relativistic neutron-rich winds, and Nickel production in proto-magnetar and NDAF winds are also briefly discussed.
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arxiv:0708.3395
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In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions. It is found also that the algebraic multiplicity of 0 as a root of the secular determinant of H is the sum of the nullities of A and A*.
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arxiv:0708.3456
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The formation of multipartite quantum entanglement by repeated operation of one and two qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a non-local geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the non-local geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and non-local interactions between the qubits.
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arxiv:0708.3481
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A macroscopic phase separation, in which ferromagnetic clusters are observed in an insulating matrix, is sometimes observed, and believed to be essential to the colossal magnetoresistive (CMR) properties of manganese oxides. The application of a magnetic field may indeed trigger large magnetoresistance effects due to the percolation between clusters allowing the movement of the charge carriers. However, this macroscopic phase separation is mainly related to extrinsic defects or impurities, which hinder the long-ranged charge-orbital order of the system. We show in the present article that rather than the macroscopic phase separation, an homogeneous short-ranged charge-orbital order accompanied by a spin glass state occurs, as an intrinsic result of the uniformity of the random potential perturbation induced by the solid solution of the cations on the $A$-sites of the structure of these materials. Hence the phase separation does occur, but in a more subtle and interesting nanoscopic form, here referred as ``homogeneous''. Remarkably, this ``nanoscale phase separation'' alone is able to bring forth the colossal magnetoresistance in the perovskite manganites, and is potentially relevant to a wide variety of other magnetic and/or electrical properties of manganites, as well as many other transition metal oxides, in bulk or thin film form as we exemplify throughout the article.
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arxiv:0708.3524
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Contact algorithm between different bodies plays an important role in solving collision problems. Usually it is not easy to be treated very well. Several ones for material point method were proposed by Bardenhangen, Brackbill, and Sulsky\cite{Bardenhagen2000,Bardenhagen2001}, Hu and Chen\cite{Hu_Chen2003}. An improved one for three-dimensional material point method is presented in this paper. The improved algorithm emphasizes the energy conservation of the system and faithfully recovers opposite acting forces between contacting bodies. Contrasted to the one by Bardenhagen, both the normal and tangential contacting forces are more appropriately applied to the contacting bodies via the contacting nodes of the background mesh; Contrasted to the one by Hu and Chen, not only the tangential velocities but also the normal ones are handled separately in respective individual mesh. This treatment ensures not only the contact/sliding/separation procedure but also the friction between contacting bodies are recovered. The presented contact algorithm is validated via numerical experiments including rolling simulation, impact of elastic spheres, impact of a Taylor bar and impact of plastic spheres. The numerical results show that the multi-mesh material point method with the improved contact algorithm is more suitable for solving collision problems.
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arxiv:0708.3532
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In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The theory permits a treatment of general margin losses, convex or nonconvex, in presence or absence of a dominating class. Three main results are established. First, for any fixed margin loss, there may be a trade-off between the ideal and actual generalization performances with respect to the choice of the class of candidate decision functions, which is governed by the trade-off between the approximation and estimation errors. In fact, different margin losses lead to different ideal or actual performances in specific cases. Second, we demonstrate, in a problem of linear learning, that the convergence rate can be arbitrarily fast in the sample size $n$ depending on the joint distribution of the input/output pair. This goes beyond the anticipated rate $O(n^{-1})$. Third, we establish rates of convergence of several margin classifiers in feature selection with the number of candidate variables $p$ allowed to greatly exceed the sample size $n$ but no faster than $\exp(n)$.
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arxiv:0708.3556
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Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.
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arxiv:0708.3557
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In this paper we offer a definition of monogenicity for functions defined on $\rr^{n+1}$ with values in the Clifford algebra $\rr_n$ following an idea inspired by the recent papers \cite{gs}, \cite{advances}. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra $\rr_n$. We will prove a Cauchy integral formula as well as some of its consequences. Finally, we deal with the zeroes of some polynomials and power series.
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arxiv:0708.3595
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We have linked the structural and dynamic properties in aqueous solution of amphiphilic charged diblock copolymers poly(butyl acrylate)-b-poly(acrylic acid), PBA-b-PAA, synthesized by controlled radical polymerization, with the physico-chemical characteristics of the samples. Despite product imperfections, the samples self-assemble in melt and aqueous solutions as predicted by monodisperse microphase separation theory. However, the PBA core are abnormally large; the swelling of PBA cores is not due to AA (the Flory parameter chiPBA/PAA, determined at 0.25, means strong segregation), but to h-PBA homopolymers (content determined by Liquid Chromatography at the Point of Exclusion and Adsorption Transition LC-PEAT). Beside the dominant population of micelles detected by scattering experiments, capillary electrophoresis CE analysis permitted detection of two other populations, one of h-PAA, and the other of free PBA-b-PAA chains, that have very short PBA blocks and never self-assemble. Despite the presence of these free unimers, the self-assembly in solution was found out of equilibrium: the aggregation state is history dependant and no unimer exchange between micelles occurs over months (time-evolution SANS). The high PBA/water interfacial tension, measured at 20 mN/m, prohibits unimer exchange between micelles. PBA-b-PAA solution systems are neither at thermal equilibrium nor completely frozen systems: internal fractionation of individual aggregates can occur.
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arxiv:0708.3596
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Emissions of free neutrons and protons from the central collisions of 124Sn+124Sn and 112Sn+112Sn reactions are simulated using the Improved Quantum Molecular Dynamics model with two different density dependence of the symmetry energy in the nuclear equation of state. The constructed double ratios of the neutron to proton ratios of the two reaction systems are found to be sensitive to the symmetry terms in the EOS. The effect of cluster formation is examined and found to affect the double ratios mainly in the low energy region. In order to extract better information on symmetry energy with transport models, it is therefore important to have accurate data in the high energy region which also is affected minimally by sequential decays.
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arxiv:0708.3684
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I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one factor. They give a mathematical characterisation of the different possible worlds arising in an evolving closed quantum system, in which each possible world corresponds to a (generally mixed) evolving quantum state. In a realistic model, the states corresponding to different worlds should be expected to tend towards orthogonality as different possible quasiclassical structures emerge or as measurement-like interactions produce different classical outcomes. However, as the worlds have a precise mathematical definition, real world interpretations need no definition of quasiclassicality, measurement, or other concepts whose imprecision is problematic in other interpretational approaches. It is natural to postulate that precisely one world is chosen randomly, using the natural probability distribution, as the world realised in Nature, and that this world's mathematical characterisation is a complete description of reality.
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arxiv:0708.3710
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We observed with Suzaku the symbiotic star SS73 17, motivated by the discovery by the INTEGRAL satellite and the Swift BAT survey that it emits hard X-rays. Our observations showed a highly-absorbed X-ray spectrum with NH > 10^23 cm-2, equivalent to A_V > 26, although the source has B magnitude 11.3 and is also bright in UV. The source also shows strong, narrow iron lines including fluorescent Fe K as well as Fe xxv and Fe xxvi. The X-ray spectrum can be fit with a thermal model including an absorption component that partially covers the source. Most of the equivalent width of the iron fluorescent line in this model can be explained as a combination of reprocessing in a dense absorber plus reflection off a white dwarf surface, but it is likely that the continuum is partially seen in reflection as well. Unlike other symbiotic systems that show hard X-ray emission (CH Cyg, RT Cru, T CrB, GX1+4), SS73 17 is not known to have shown nova-like optical variability, X-ray flashes, or pulsations, and has always shown faint soft X-ray emission. As a result, although it is likely a white dwarf, the nature of the compact object in SS73 17 is still uncertain. SS73 17 is probably an extreme example of the recently discovered and relatively small class of hard X-ray emitting symbiotic systems.
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arxiv:0708.3833
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In this article we report on the experimental realization of dimensional crossover phenomena in the chain compound PrBa$_2$Cu$_4$O$_8$ using temperature, high magnetic fields and disorder as independent tuning parameters. In purer crystals of PrBa$_2$Cu$_4$O$_8$, a highly anisotropic three-dimensional Fermi-liquid state develops at low temperatures. This metallic state is extremely susceptible to disorder however and localization rapidly sets in. We show, through quantitative comparison of the relevant energy scales, that this metal/insulator crossover occurs precisely when the scattering rate within the chain exceeds the interchain hopping rate(s), i.e. once carriers become confined to a single conducting element.
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arxiv:0708.3860
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We present recent measurements of the unitarity triangle angle phi2(alpha) using B -> pi pi, B -> rho rho, and B -> rho pi decays. The measurements are based on data samples collected with the Belle and BaBar detectors at the KEKB and PEP-II e+e- colliders, respectively. We also report on a new measurement of a CP-violating asymmetry in B -> a_1+ pi- decay which will allow to constrain further the angle phi2.
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arxiv:0708.3892
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Quantum correlations do not allow signalling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signalling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. We find that the natural figure of merit to consider is the confidence in identifying a state, which is optimised by the maximum confidence strategy. We show that this strategy may be derived from the no-signalling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.
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arxiv:0708.3909
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The charged lepton mass formula can be explained when the masses are propotinal to the squared vacuum expectation values (VEVs) of scalar fields. We introduce U(3) flavor symmetry and its nonet scalar field $\Phi$, whose VEV structure plays an essential role for generating the fermion mass spectrum. We can naturally obtain bilinear form of the Yukawa coupling $Y_{ij} \propto \sum_k <\Phi_{ik}> <\Phi_{kj}>$ without the non-renormalizable interactions, when the flavor symmetry is broken only through the Yukawa coupling and tadpole terms. We also speculate the possible VEV structure of $<\Phi>$.
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arxiv:0708.3913
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We observed an X-ray afterglow of GRB 060904A with the Swift and Suzaku satellites. We found rapid spectral softening during both the prompt tail phase and the decline phase of an X-ray flare in the BAT and XRT data. The observed spectra were fit by power-law photon indices which rapidly changed from $\Gamma = 1.51^{+0.04}_{-0.03}$ to $\Gamma = 5.30^{+0.69}_{-0.59}$ within a few hundred seconds in the prompt tail. This is one of the steepest X-ray spectra ever observed, making it quite difficult to explain by simple electron acceleration and synchrotron radiation. Then, we applied an alternative spectral fitting using a broken power-law with exponential cutoff (BPEC) model. It is valid to consider the situation that the cutoff energy is equivalent to the synchrotron frequency of the maximum energy electrons in their energy distribution. Since the spectral cutoff appears in the soft X-ray band, we conclude the electron acceleration has been inefficient in the internal shocks of GRB 060904A. These cutoff spectra suddenly disappeared at the transition time from the prompt tail phase to the shallow decay one. After that, typical afterglow spectra with the photon indices of 2.0 are continuously and preciously monitored by both XRT and Suzaku/XIS up to 1 day since the burst trigger time. We could successfully trace the temporal history of two characteristic break energies (peak energy and cutoff energy) and they show the time dependence of $\propto t^{-3} \sim t^{-4}$ while the following afterglow spectra are quite stable. This fact indicates that the emitting material of prompt tail is due to completely different dynamics from the shallow decay component. Therefore we conclude the emission sites of two distinct phenomena obviously differ from each other.
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arxiv:0708.3968
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Time-resolved x-ray absorption spectroscopy monitors the transient species generated by one-photon detachment of an electron from aqueous bromide. Hydrated bromine atoms with a lifetime of ca. 17 ns were observed, nearly half of which react with excess Br- to form Br2-. The K-edge spectra of the Br atom and Br2- anion exhibit distinctive resonant transitions that are absent for the Br- precursor. The absorption spectra indicate that the solvent shell around a Br0 atom is defined primarily by hydrophobic interactions, in agreement with a Monte Carlo simulation of the solvent structure.
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arxiv:0708.3985
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Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing ground fields of arithmetic hyperbolic reflection groups are defined, and good bounds of their degrees (over Q) are obtained. For example, degree of the ground field of any arithmetic hyperbolic reflection group in dimension at least 6 is bounded by 56. These results could be important for further classification. We also formulate a mirror symmetric conjecture to finiteness of the number of arithmetic hyperbolic reflection groups which was established in full generality recently.
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arxiv:0708.3991
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Isomorphisms are constructed between generalized Schur algebras in different degrees. The construction covers both the classical case (of general linear groups over infinite fields of arbitrary characteristic) and the quantized case (in type $A$, for any non-zero value of the quantum parameter $q$). The construction does not depend on the characteristic of the underlying field or the choice of $q \neq 0$. The proof combines a combinatorial construction with comodule structures and Ringel duality. Applications range from equivalences of categories to results on the structure and cohomology of Schur algebras to identities of decomposition numbers and also of $p$-Kostka numbers, in both cases reproving and generalizing row and column removal rules.
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arxiv:0708.4019
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The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple abstract form. It is shown that their properties can be obtained from only on a very small set of algebraic assumptions. The presentation is purely algebraic and it does not use any particular definition of method components, such as substructures and coarse degrees of freedom. It is then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC preconditioned operators are of the same algebraic form, and the standard condition number bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is explained on a standard substructuring example.
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arxiv:0708.4031
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The analysis of stochastic loss networks has long been of interest in computer and communications networks and is becoming important in the areas of service and information systems. In traditional settings, computing the well known Erlang formula for blocking probability in these systems becomes intractable for larger resource capacities. Using compound point processes to capture stochastic variability in the request process, we generalize existing models in this framework and derive simple asymptotic expressions for blocking probabilities. In addition, we extend our model to incorporate reserving resources in advance. Although asymptotic, our experiments show an excellent match between derived formulas and simulation results even for relatively small resource capacities and relatively large values of blocking probabilities.
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arxiv:0708.4059
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A phenomenological model of self-organization explaining the emergence of a complexity with features that apparently satisfy the specific criteria usually required for recognizing the appearance of life in laboratory is presented. The described phenomenology, justified by laboratory experiments, is essentially based on local self-enhancement and long-range inhibition. The complexity represents a primitive organism self-assembled in a gaseous medium revealing, immediately after its "birth", many of the prerequisite features that attribute them the quality to evolve, under suitable conditions, into a living cell.
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arxiv:0708.4067
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Extrasolar planets are expected to emit detectable low frequency radio emission. In this paper we present results from new low frequency observations of two extrasolar planetary systems (Epsilon Eridani and HD 128311) taken at 150 MHz with the Giant Metrewave Radio Telescope (GMRT). These two systems have been chosen because the stars are young (with ages < 1 Gyr) and are likely to have strong stellar winds, which will increase the expected radio flux. The planets are massive (presumably) gas giant planets in longer period orbits, and hence will not be tidally locked to their host star (as is likely to be the case for short period planets) and we would expect them to have a strong planetary dynamo and magnetic field. We do not detect either system, but are able to place tight upper limits on their low frequency radio emission, at levels comparable to the theoretical predictions for these systems. From these observations we have a 2.5sigma limit of 7.8 mJy for Epsilon Eri and 15.5 mJy for HD 128311. In addition, these upper limits also provide limits on the low frequency radio emission from the stars themselves. These results are discussed and also the prospects for the future detection of radio emission from extrasolar planets.
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arxiv:0708.4079
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The observation that novice users seldom consult online help was made over twenty years ago. This observation still holds nowadays, although online help to the use of software for the general public has greatly improved in usability during this period. The paper first demonstrates the necessity of online help to the use of new software whatever the transparency of the user interface, as whether online help systems are meant to compensate for interface design weaknesses or actually do provide necessary assistance to the discovery of a new software package functionalities is still an unsolved issue. The discussion relies on results of empirical and experimental studies and theoretical arguments. In the second part, we analyse the specific difficulties raised by the design of effective online help systems for current software intended for the general public so as to try and understand the reluctance of novice users to use online help. In the last part, we present and discuss the possible contributions of various approaches to solving this issue. Recent interaction paradigms and techniques are considered, such as, static and dynamic personalisation, contextual online help and new forms of multimodality.
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arxiv:0708.4082
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We present a simple mechanism by which supersymmetry can be dynamically broken in intersecting brane models, naturally generating an exponentially small scale. Rather than utilize either non-Abelian gauge dynamics or D-instantons, our mechanism uses worldsheet instantons to generate the small scale in a hidden sector.
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arxiv:0708.4116
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Aims. We study the optical spectroscopic properties of Type Ia Supernova (SN Ia) 2004dt, focusing our attention on the early epochs. Methods. Observation triggered soon after the SN 2004dt discovery allowed us to obtain a spectrophotometric coverage from day -10 to almost one year (~353 days) after the B band maximum. Observations carried out on an almost daily basis allowed us a good sampling of the fast spectroscopic evolution of SN 2004dt in the early stages. To obtain this result, low-resolution, long-slit spectroscopy was obtained using a number of facilities. Results. This supernova, which in some absorption lines of its early spectra showed the highest degree of polarization ever measured in any SN Ia, has a complex velocity structure in the outer layers of its ejecta. Unburnt oxygen is present, moving at velocities as high as ~16,700 km/s, with some intermediate-mass elements (Mg, Si, Ca) moving equally fast. Modeling of the spectra based on standard density profiles of the ejecta fails to reproduce the observed features, whereas enhancing the density of outer layers significantly improves the fit. Our analysis indicates the presence of clumps of high-velocity, intermediate-mass elements in the outermost layers, which is also suggested by the spectropolarimetric data.
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arxiv:0708.4119
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Recently, observations of compact stars have provided new data of high accuracy which put strong constraints on the high-density behaviour of the equation of state of strongly interacting matter otherwise not accessible in terrestrial laboratories. The evidence for neutron stars with high mass (M =2.1 +/- 0.2 M_sun for PSR J0751+1807) and large radii (R > 12 km for RX J1856-3754) rules out soft equations of state and has provoked a debate whether the occurence of quark matter in compact stars can be excluded as well. In this contribution it is shown that modern quantum field theoretical approaches to quark matter including color superconductivity and a vector meanfield allow a microscopic description of hybrid stars which fulfill the new, strong constraints. The deconfinement transition in the resulting stiff hybrid equation of state is weakly first order so that signals of it have to be expected due to specific changes in transport properties governing the rotational and cooling evolution caused by the color superconductivity of quark matter. A similar conclusion holds for the investigation of quark deconfinement in future generations of nucleus-nucleus collision experiments at low temperatures and high baryon densities such as CBM @ FAIR.
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arxiv:0708.4216
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The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Lambda=0 conflicts with observation. The possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.
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arxiv:0708.4231
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Let G be the group A_4 or Z_2xZ_2. We compute the integral of \lambda_g on the Hurwitz locus H_G\subset M_g of curves admitting a degree 4 cover of P^1 having monodromy group G. We compute the generating functions for these integrals and write them as a trigonometric expression summed over the positive roots of the E_6 and D_4 root systems respectively. As an application, we prove the Crepant Resolution Conjecture for the orbifolds [C^3/A_4] and [C^3/(Z_2xZ_2)].
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arxiv:0708.4244
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Using Poincare duality, we formulate a formula of Lefschetz type which computes the Lefschetz number of an endomorphism of a separable, nuclear C*-algebra satisfying Poincare duality and the Kunneth theorem. (The Lefschetz number of an endomorphism is the graded trace of the induced map on K-theory tensored with the complex numbers, as in the classical case.) We then consider endomorphisms of Cuntz-Krieger algebras O_A. An endomorphism has an invariant, which is a permutation of an infinite set, and the contracting and expanding behavior of this permutation describes the Lefschetz number of the endomorphism. Using this description we derive a closed polynomial formula for the Lefschetz number depending on the matrix A and the presentation of the endomorphism.
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arxiv:0708.4278
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We propose a BEC stirring device which can be regarded as the incorporation of a quantum pump into a closed circuit: it produces a DC circulating current in response to a cyclic adiabatic change of two control parameters of an optical trap. We demonstrate the feasibility of this concept and point out that such device can be utilized in order to probe the interatomic interactions.
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arxiv:0708.4304
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Phase stabilities of Hf-Si-O and Zr-Si-O have been studied with first-principles and thermodynamic modeling. From the obtained thermodynamic descriptions, phase diagrams pertinent to thin film processing were calculated. We found that the relative stability of the metal silicates with respect to their binary oxides plays a critical role in silicide formation. It was observed that both the HfO$_2$/Si and ZrO$_2$/Si interfaces are stable in a wide temperature range and silicide may form at low temperatures, partially at the HfO$_2$/Si interface.
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arxiv:0708.4356
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In this work we present measurements of vegetation cover over parabolic dunes with different degree of activation along the north-eastern Brazilian coast. We are able to extend the local values of the vegetation cover density to the whole dune by correlating measurements with the gray-scale levels of a high resolution satellite image of the dune field. The empirical vegetation distribution is finally used to validate the results of a recent continuous model of dune motion coupling sand erosion and vegetation growth.
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arxiv:0708.4368
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Dissipative processes in non-equilibrium many-body systems are fundamentally different than their equilibrium counterparts. Such processes are of great importance for the understanding of relaxation in single molecule devices. As a detailed case study, we investigate here a generic spin-fermion model, where a two-level system couples to two metallic leads with different chemical potentials. We present results for the spin relaxation rate in the nonadiabatic limit for an arbitrary coupling to the leads, using both analytical and exact numerical methods. The non-equilibrium dynamics is reflected by an exponential relaxation at long times and via complex phase shifts, leading in some cases to an "anti-orthogonality" effect. In the limit of strong system-lead coupling at zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with {\it voltage difference} activation. This is analogous to the equilibrium spin-boson model, where at strong coupling and high temperatures the spin excitation rate manifests temperature activated Gaussian behavior. We find that there is no simple linear relationship between the role of the temperature in the bosonic system and a voltage drop in a non-equilibrium electronic case. The two models also differ by the orthogonality-catastrophe factor existing in a fermionic system, which modifies the resulting lineshapes. Implications for current characteristics are discussed. We demonstrate the violation of pair-wise Coulomb gas behavior for strong coupling to the leads. The results presented in this paper form the basis of an exact, non-perturbative description of steady-state quantum dissipative systems.
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arxiv:0708.4372
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