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- We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. Using the (monotone) interpolation by a communication game technique we establish an exponential-size lower bound on refutations in a certain, considerably strong, fragment of resolution over linear equations, as well as a general polynomial upper bound on (non-monotone) interpolants in this fragment. We then apply these results to extend and improve previous results on multilinear proofs (over fields of characteristic 0), as studied in [RazTzameret06]. Specifically, we show the following: 1. Proofs operating with depth-3 multilinear formulas polynomially simulate a certain, considerably strong, fragment of resolution over linear equations. 2. Proofs operating with depth-3 multilinear formulas admit polynomial-size refutations of the pigeonhole principle and Tseitin graph tautologies. The former improve over a previous result that established small multilinear proofs only for the \emphfunctional pigeonhole principle. The latter are different than previous proofs, and apply to multilinear proofs of Tseitin mod p graph tautologies over any field of characteristic 0. We conclude by connecting resolution over linear equations with extensions of the cutting planes proof system.
- We consider the asymptotic behavior as $n\to\infty$ of the spectra of random matrices of the form \[\frac1\sqrtn-1\sum_k=1^n-1Z_nk\rho_n ((k,k+1)),\]where for each $n$ the random variables $Z_{nk}$ are i.i.d. standard Gaussian and the matrices $\rho_n((k,k+1))$ are obtained by applying an irreducible unitary representation $\rho_n$ of the symmetric group on $\{1,2,...,n\}$ to the transposition $(k,k+1)$ that interchanges $k$ and $k+1$ [thus, $\rho_n((k,k+1))$ is both unitary and self-adjoint, with all eigenvalues either +1 or -1]. Irreducible representations of the symmetric group on $\{1,2,...,n\}$ are indexed by partitions $\lambda_n$ of $n$. A consequence of the results we establish is that if $\lambda_{n,1}\ge\lambda_{n,2}\ge...\ge0$ is the partition of $n$ corresponding to $\rho_n$, $\mu_{n,1}\ge\mu_{n,2}\ge >...\ge0$ is the corresponding conjugate partition of $n$ (i.e., the Young diagram of $\mu_n$ is the transpose of the Young diagram of $\lambda_n$), $\lim_{n\to\infty}\frac{\lambda_{n,i}}{n}=p_i$ for each $i\ge1$, and $\lim_{n\to\infty}\frac{\mu_{n,j}}{n}=q_j$ for each $j\ge1$, then the spectral measure of the resulting random matrix converges in distribution to a random probability measure that is Gaussian with random mean $\theta Z$ and variance $1-\theta^2$, where $\theta$ is the constant $\sum_ip_i^2-\sum_jq_j^2$ and $Z$ is a standard Gaussian random variable.
- Aug 14 2007 astro-ph arXiv:0708.1775v1Observations 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.
- We prove Anderson localization at the internal band-edges for periodic magnetic Schrödinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of the integrated density of states for random magnetic Schrödinger operators, thereby providing the initial length-scale estimate, and a Wegner estimate, for such models.
- The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.
- Aug 14 2007 astro-ph arXiv:0708.1771v2As the number of known planetary systems increases, the ability to follow-up and characterize the extent of any system becomes limited. This paper considers the use of specific angular momentum as a metric to prioritize future observations. We analyze 431 planets in 367 known extrasolar planetary systems from Butler et al. (2006) (including updates to their online catalog, current to April, 2011) and estimate each system's orbital angular momentum. The range of partition- ing of specific angular momentum in these systems is found to be large, spanning several orders of magnitude. The analysis shows that multi-planet systems tend to have the highest values of specific angular momentum normalized against the planetary masses. This suggests that in high angular momentum systems, the dominant contributors have already been discovered, and that single-planet sys- tems with low observed angular momentum may be the most likely candidates for additional undiscovered companions compared to their high angular momentum, single-planet counterparts. The multi-planet system, GJ 581, is considered as a historical case study to demonstrate the concept, examining how the specific angular momentum of the know planetary system evolved with each discovery.
- Aug 14 2007 gr-qc arXiv:0708.1769v1We consider the late-time tails of spherical waves propagating on even-dimensional Minkowski spacetime under the influence of a long range radial potential. We show that in six and higher even dimensions there exist exceptional potentials for which the tail has an anomalously small amplitude and fast decay. Along the way we clarify and amend some confounding arguments and statements in the literature of the subject.
- We have obtained the exact asymptotics of the determinant $\det_{1\leq r,s\leq L}[\binom{r+s-2}{r-1}+\exp(i\theta)\delta_{r,s}]$. Inverse symbolic computing methods were used to obtain exact analytical expressions for all terms up to relative order $L^{-14}$ to the leading term. This determinant is known to give weighted enumerations of cyclically symmetric plane partitions, weighted enumerations of certain families of vicious walkers and it has been conjectured to be proportional to the one point function of the O$(1)$ loop model on a cylinder of circumference $L$. We apply our result to the loop model and give exact expressions for the asymptotics of the average of the number of loops surrounding a point and the fluctuation in this number. For the related bond percolation model, we give exact expressions for the asymptotics of the probability that a point is on a cluster that wraps around a cylinder of even circumference and the probability that a point is on a cluster spanning a cylinder of odd circumference.
- Aug 14 2007 astro-ph arXiv:0708.1767v1We present a review of the possible sources for r-process nuclei. It is known that there is as yet no self-consistent mechanism to provide abundant neutrons for a robust r-process in the neutrino-driven winds from nascent neutron stars. We consider that the heavy r-nuclei with mass numbers A>130 (Ba and above) cannot be produced in the neutrino-driven winds. Nonetheless, the r-process and the neutrino-driven winds may be directly or indirectly related by some unknown additional mechanism, which, for example, could provide ejecta with very short dynamic timescales of <0.004 s. This undetermined mechanism must supply a neutron source within the same general stellar sites that undergo core collapse to produce the neutron star. Observational data on low-metallicity stars in the Galactic halo show that sites producing the heavy r-nuclei do not produce Fe or any other elements between N and Ge. Insofar as a forming neutron star is key to producing the heavy r-nuclei, then the only possible sources are supernovae resulting from collapse of O-Ne-Mg cores or accretion-induced collapse of white dwarfs, neither of which produce the elements of the Fe group or those of intermediate mass (above C and N). Using a template star with high enrichments of heavy r-nuclei and another with low enrichments we develop a two-component model based on the abundances of Eu (from sources for heavy r-nuclei) and Fe (from Fe core-collapse supernovae). This model gives very good quantitative predictions for the abundances of all the other elements in those metal-poor stars with [Fe/H]<-1.5 for which the Eu and Fe abundances are known. (Abridged)
- Aug 14 2007 astro-ph arXiv:0708.1766v1Luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs) dominate the star formation rate budget of the universe at z > 1, yet no local measurements of their heavy element abundances exist. We measure nuclear or near-nuclear oxygen abundances in a sample of 100 star-forming LIRGs and ULIRGs using new, previously published, and archival spectroscopy of strong emission lines (including [O II] 3727, 3729 A) in galaxies with redshifts <z> ~ 0.1. When compared to local emission-line galaxies of similar luminosity and mass (using the near-infrared luminosity-metallicity and mass-metallicity relations), we find that LIRGs and ULIRGs are under-abundant by a factor of two on average. As a corollary, LIRGs and ULIRGs also have smaller effective yields. We conclude that the observed under-abundance results from the combination of a decrease of abundance with increasing radius in the progenitor galaxies and strong, interaction- or merger-induced gas inflow into the galaxy nucleus. This conclusion demonstrates that local abundance scaling relations are not universal, a fact that must be accounted for when interpreting abundances earlier in the universe's history when merger-induced star formation was the dominant mode. We use our local sample to compare to high-redshift samples and assess abundance evolution in LIRGs and ULIRGs. We find that abundances in these systems increased by ~0.2 dex from z ~ 0.6 to z ~ 0.1. Evolution from z ~ 2 submillimeter galaxies to z ~ 0.1 ULIRGs also appears to be present, though uncertainty due to spectroscopic limitations is large.
- Aug 14 2007 astro-ph arXiv:0708.1764v2The origin of brown dwarfs (BDs) is still an unsolved mystery. While the standard model describes the formation of BDs and stars in a similar way recent data on the multiplicity properties of stars and BDs show them to have different binary distribution functions. Here we show that proper treatment of these uncovers a discontinuity of the multiplicity-corrected mass distribution in the very-low-mass star (VLMS) and BD mass regime. A continuous IMF can be discarded with extremely high confidence. This suggests that VLMSs and BDs on the one hand, and stars on the other, are two correlated but disjoint populations with different dynamical histories. The analysis presented here suggests that about one BD forms per five stars and that the BD-star binary fraction is about 2%-3% among stellar systems.
- Aug 14 2007 cond-mat.str-el arXiv:0708.1765v1We investigate quantum phase transitions in the extended periodic Anderson model, which includes electron correlations within and between itinerant and localized bands. We calculate zero and finite temperature properties of the system using the combination of dynamical mean-field theory and the numerical renormalization group. At half filling, a phase transition between a Mott insulating state and a Kondo insulating state occurs in the strong coupling regime. We furthermore find that a metallic state is stabilized in the weak coupling regime. This state should be adiabatically connected to the orbital selective Mott state with one orbital localized and the other itinerant. The effect of hole doping is also addressed.
- In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as the underlying symmetry algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.
- Aug 14 2007 math.CV arXiv:0708.1726v1We consider a continuous function $f$ on a domain in $\mathbf C^n$ satisfying the inequality that $|\bar \partial f|\leq |f|$ off its zero set. The main conclusion is that the zero set of $f$ is a complex variety. We also obtain removable singularity theorem of Rado type for J-holomorphic maps. Let $\Omega$ be an open subset in $\mathbf C$ and let $E$ be a closed polar subset of $\Omega$. Let $u$ be a continuous map from $\Omega$ into an almost complex manifold $(M,J)$ with $J$ of class $C^1$. We show that if $u$ is J-holomorphic on $\Omega\setminus E$ then it is J-holomorphic on $\Omega$.
- Aug 14 2007 astro-ph arXiv:0708.1761v1We review our attempts to discover lost baryons at low redshift with ``X-ray forest'' of absorption lines from the warm-hot intergalactic medium. We discuss the best evidence to date along the Mrk 421 sightline. We then discuss the missing baryons in the Local Group and the significance of the z=0 absorption systems in X-ray spectra. We argue that the debate over the Galactic vs. extragalactic origin of the z=0 systems is premature as these systems likely contain both components. Observations with next generation X-ray missions such as Constellation-X and XEUS will be crucial to map out the warm-hot intergalactic medium.
- Aug 14 2007 gr-qc arXiv:0708.1747v1Orbits of test particles and light rays are an important tool to study the properties of space-time metrics. Here we systematically study the properties of the gravitational field of a globally regular magnetic monopole in terms of the geodesics of test particles and light. The gravitational field depends on two dimensionless parameters, defined as ratios of the characteristic mass scales present. For critical values of these parameters the resulting metric coefficients develop a singular behavior, which has profound influence on the properties of the resulting space-time and which is clearly reflected in the orbits of the test particles and light rays.
- The Cauchy problem is revisited for the so-called relativistic Vlasov-Poisson system in the attractive case. Global existence and uniqueness of spherical classical solutions is proved under weaker assumptions than previously used. A new class of blowing up solutions is found when these conditions are violated. A new, non-gravitational physical vindication of the model which (unlike the gravitational one) is not restricted to weak fields, is also given.
- Aug 14 2007 physics.data-an cs.IT math.IT math.ST physics.comp-ph physics.pop-ph stat.AP stat.CO stat.ME stat.TH arXiv:0708.1593v2We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and moments is obtained. We discuss the general problem of non-commuting constraints, when they should be processed sequentially and when simultaneously. As an illustration, the multinomial example of die tosses is solved in detail for two superficially similar but actually very different problems.
- Aug 14 2007 physics.ed-ph arXiv:0708.1759v2Even though there has been a tremendous amount of research done in how to help students learn physics, students are still coming away missing a crucial piece of the puzzle: why bother with physics? Students learn fundamental laws and how to calculate, but come out of a general physics course without a deep understanding of how physics has transformed the world around them. In other words, they get the "how" but not the "why". Studies have shown that students leave introductory physics courses almost universally with decreased expectations and with a more negative attitude. This paper will detail an experiment to address this problem: a course weblog or "blog" which discusses real-world applications of physics and engages students in discussion and thinking outside of class. Specifically, students' attitudes towards the value of physics and its applicability to the real-world were probed using a 26-question Likert scale survey over the course of four semesters in an introductory physics course at a comprehensive Jesuit university. We found that students who did not participate in the blog study generally exhibited a deterioration in attitude towards physics as seen previously. However, students who read, commented, and were involved with the blog maintained their initially positive attitudes towards physics. Student response to the blog was overwhelmingly positive, with students claiming that the blog made the things we studied in the classroom come alive for them and seem much more relevant.
- Aug 14 2007 math.RT arXiv:0708.1757v1For each type of classical Lie algebra, we list the dominant highest weights $\zeta$ for which $(\zeta;\mu_i)$ is not a primitive pair and the weight space $V_{\mu_i}$ has dimension one where $\mu_i$ are the highest long and short roots in each case. These dimension one weight spaces lead to examples of nilmanifolds for which we cannot prove or disprove the density of closed geodesics.
- We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.
- An effective theory based on ensembles of either regular gauge instantons or merons is shown to produce confinement in SU(2) Yang-Mills theory. When the scale is set by the string tension, the action density, topological susceptibility and low-lying glueball spectrum are similar to those arising in lattice QCD. The physical mechanism producing confinement is explained, and a number of analytical insights into the effective theory are presented.
- This paper concerns with numerical approximations of solutions of second order fully nonlinear partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for second order fully nonlinear PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called vanishing moment method, hence, they can be readily computed by existing numerical methods such as finite difference, finite element, spectral Galerkin, and discontinuous Galerkin methods with "guaranteed" convergence. The main idea of the proposed vanishing moment method is to approximate a second order fully nonlinear PDE by a higher order, in particular, a fourth order quasilinear PDE. We show by various numerical experiments the viability of the proposed vanishing moment method. All our numerical experiments show the convergence of the vanishing moment method, and they also show that moment solutions coincide with viscosity solutions whenever the latter exist.
- Aug 14 2007 quant-ph arXiv:0708.1755v3Coquelin et al. studied biperiodic semiconductor superlattices, which consist of alternating cell types, one with wide wells and the other narrow wells, separated by equal strength barriers. If the wells were identical, it would be a simply periodic system of $N = 2n$ half-cells. When asymmetry is introduced, an allowed band splits at the Bragg point into two disjoint allowed bands. The Bragg resonance turns into a transparent state located close to the band edge of the lower(upper) band when the first(second) well is the wider. Analysis of this system gives insight into how band splitting occurs. Further we consider semi-periodic systems having $N= 2n+1$ half-cells. Surprisingly these have very different transmission properties, with an envelope of maximum transmission probability that crosses the envelope of minima at the transparent point.
- Aug 14 2007 physics.chem-ph physics.optics arXiv:0708.1754v1In the currently accepted models of the nonlinear optics, the nonlinear radiation was treated as the result of an infinitesimally thin polarization sheet layer, and a three layer model was generally employed. The direct consequence of this approach is that an apriori dielectric constant, which still does not have a clear definition, has to be assigned to this polarization layer. Because the Second Harmonic Generation (SHG) and the Sum-Frequency Generation vibrational Spectroscopy (SFG-VS) have been proven as the sensitive probes for interfaces with the submonolayer coverage, the treatment based on the more realistic discrete induced dipole model needs to be developed. Here we show that following the molecular optics theory approach the SHG, as well as the SFG-VS, radiation from the monolayer or submonolayer at an interface can be rigorously treated as the radiation from an induced dipole lattice at the interface. In this approach, the introduction of the polarization sheet is no longer necessary. Therefore, the ambiguity of the unaccounted dielectric constant of the polarization layer is no longer an issue. Moreover, the anisotropic two dimensional microscopic local field factors can be explicitly expressed with the linear polarizability tensors of the interfacial molecules. Based on the planewise dipole sum rule in the molecular monolayer, crucial experimental tests of this microscopic treatment with SHG and SFG-VS are discussed. Many puzzles in the literature of surface SHG and SFG spectroscopy studies can also be understood or resolved in this framework. This new treatment may provide a solid basis for the quantitative analysis in the surface SHG and SFG studies.
- Aug 14 2007 hep-ex arXiv:0708.1753v1We present the first measurement of the $B^0\to X_{u}^- \ell^+ {\nu_\ell} $ partial branching fraction in the end-point region of the lepton momentum spectrum, above the threshold for $B\to X_c\ell {\nu_\ell}$ decays. The analysis is based on a sample of 383 million $\Upsilon(4S)$ decays into $B{\bar B}$ pairs collected with the \sc BaBar detector at the PEP-II $e^+e^-$ storage rings. We select $B^0{\bar B}^0$ events by partially reconstructing one $\B$ meson via the ${\bar B}^0\to D^{*+} \ell^- \bar{\nu}_\ell$ decays then select $B^0\to X_{u}^- \ell^+ {\nu_\ell} $ decays identifying a second high momentum lepton. In the momentum interval ranging from 2.3 to 2.6 GeV/c we measure the partial branching fraction $\Delta{\cal B}(B^0\to X_u\ell\nu)=(1.30\pm0.21_{stat}\pm0.07_{syst})\times 10^{-4}$ where the first error is statistical and the second is systematic. By comparing this measurement with the one obtained from untagged B decays we obtain $R^{+/0}=\Delta{\cal B}(B^0\to X_u\ell\nu)/\Delta{\cal B}(B^+\to X_u\ell\nu)= 1.18 \pm 0.35_{stat} \pm 0.17_{syst}$. Using this measurement we extract a limit on the contributions from processes breaking isospin symmetry in charmless semileptonic B decays.
- Context.A new reduction of the astrometric data as produced by the Hipparcos mission has been published, claiming accuracies for nearly all stars brighter than magnitude Hp = 8 to be better, by up to a factor 4, than in the original catalogue. Aims.The new Hipparcos astrometric catalogue is checked for the quality of the data and the consistency of the formal errors as well as the possible presence of error correlations. The differences with the earlier publication are explained. Methods. The internal errors are followed through the reduction process, and the external errors are investigated on the basis of a comparison with radio observations of a small selection of stars, and the distribution of negative parallaxes. Error correlation levels are investigated and the reduction by more than a factor 10 as obtained in the new catalogue is explained. Results.The formal errors on the parallaxes for the new catalogue are confirmed. The presence of a small amount of additional noise, though unlikely, cannot be ruled out. Conclusions. The new reduction of the Hipparcos astrometric data provides an improvement by a factor 2.2 in the total weight compared to the catalogue published in 1997, and provides much improved data for a wide range of studies on stellar luminosities and local galactic kinematics.
- Aug 14 2007 cond-mat.supr-con cond-mat.dis-nn arXiv:0708.1751v1Properties of disordered thin films are discussed based on the viewpoint that superconducting islands are formed in the system. These lead to superconducting correlations confined in space, which are known to form spontaneously in thin films. Application of a perpendicular magnetic field can drive the system from the superconducting state (characterized by phase-rigidity between the sample edges) to an insulating state in which there are no phase-correlations between the edges of the system. On the insulating side the existence of superconducting islands leads to a non-monotonic magnetoresistance. Several other features seen in experiment are explained.
- Aug 14 2007 physics.atom-ph arXiv:0708.1750v3We derive the properties of polaritons in single-$\Lambda$ and double-$\Lambda$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\Lambda$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.
- Aug 14 2007 cond-mat.str-el arXiv:0708.1749v3Since the inception of the dynamical mean-field theory, numerous numerical studies have relied on the Hirsch-Fye quantum Monte Carlo (HF-QMC) method for solving the associated impurity problem. Recently developed continuous-time algorithms (CT-QMC) avoid the Trotter discretization error and allow for faster configuration updates, which makes them candidates for replacing HF-QMC. We demonstrate, however, that a state-of-the-art implementation of HF-QMC (with extrapolation of discretization delta_tau -> 0) is competitive with CT-QMC. A quantitative analysis of Trotter errors in HF-QMC estimates and of appropriate delta_tau values is included.
- Aug 14 2007 astro-ph arXiv:0708.1748v1We demonstrate that rapid expansion of the shocked surface layers of an O-Ne-Mg core following its collapse can result in r-process nucleosynthesis. As the supernova shock accelerates through these layers, it makes them expand so rapidly that free nucleons remain in disequilibrium with alpha-particles throughout most of the expansion. This allows heavy r-process isotopes including the actinides to form in spite of the very low initial neutron excess of the matter. We estimate that yields of heavy r-process nuclei from this site may be sufficient to explain the Galactic inventory of these isotopes.
- The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determ ine the social diversity of players engaging in the prisoner's dilemma game. Here the term social diversity is used to address extrinsic factors that determine the mapping of game pay offs to individual fitness. These factors may increase or decrease the fitness of a player depending on its location on the spatial grid. We consider different distributions of extrin sic factors that determine the social diversity of players, and find that the power-law distribution enables the best promotion of cooperation. The facilitation of the cooperative str ategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect. To confirm this, we also study the impact of spatially correlated social diversity and find that coopera tion deteriorates as the spatial correlation length increases. Our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals.
- We construct a universal deformation formula for Connes-Moscovici's Hopf algebra without any projective structure using Fedosov's quantization of symplectic diffeomorphisms.
- Aug 14 2007 cond-mat.mtrl-sci arXiv:0708.1744v2The concept of a CDW induced by Fermi-surface nesting originated from the Peierls idea of electronic instabilities in purely 1D metals and is now often applied to charge ordering in real low-dimensional materials. The idea is that if Fermi surface contours coincide when shifted along the observed CDW wave vector, then the CDW is considered to be nesting-derived. We show that in most cases this procedure has no predictive power, since Fermi surfaces either do not nest at the right wave vector, or nest more strongly at the wrong vector. We argue that only a tiny fraction, if any, of the observed charge ordering phase transitions are true analogues of the Peierls instability because electronic instabilities are easily destroyed by even small deviations from perfect nesting conditions. Using prototypical CDW materials NbSe$_2$, TaSe$_2$, and CeTe$_3$, we show that such conditions are hardly ever fulfilled, and that the CDW phases are actually structural phase transitions, driven by the concerted action of electronic and ionic subsystems, \textiti.e., \textbfq-dependent electron-phonon coupling plays an indispensable part. We also show mathematically that the original Peierls construction is so fragile as to be unlikely to apply to real materials. We argue that no meaningful distinction between a CDW and an incommensurate lattice transition exists.
- Aug 14 2007 astro-ph arXiv:0708.1516v1(abridged) Models of many astrophysical gamma-ray sources assume they contain a homogeneous distribution of electrons that are injected as a power-law in energy and evolve by interacting with radiation fields, magnetic fields and particles in the source and by escaping. This problem is particularly complicated if the radiation fields have higher energy density than the magnetic field and are sufficiently energetic that inverse Compton scattering is not limited to the Thomson regime. We present a simple, time-dependent, semi-analytical solution of the electron kinetic equation that treats both continuous and impulsive injection, cooling via synchrotron and inverse Compton radiation, (taking into account Klein-Nishina effects) and energy dependent particle escape. The kinetic equation for an arbitrary, time-dependent source function is solved by the method of Laplace transformations. Using an approximate expression for the energy loss rate that takes into account synchrotron and inverse Compton losses including Klein-Nishina effects for scattering off an isotropic photon field with either a power-law or black-body distribution, we find explicit expressions for the cooling time and escape probability of individual electrons. This enables the full, time-dependent solution to be reduced to a single quadrature. From the electron distribution, we then construct the time-dependent, multi-wavelength emission spectrum. We compare our solutions with several limiting cases and discuss the general appearance and temporal behaviour of spectral features (i.e., cooling breaks, bumps etc.). As a specific example, we model the broad-band energy spectrum of the open stellar association Westerlund-2 at different times of its evolution, and compare it with observations.
- Aug 14 2007 physics.atom-ph arXiv:0708.1743v2Atomic vapor of four different paramagnetic species: gold, silver, lithium, and rubidium, is produced and studied inside several buffer gases: helium, nitrogen, neon, and argon. The paramagnetic atoms are injected into the buffer gas using laser ablation. Wires with diameters 25 $\mu$m, 50 $\mu$m, and 100 $\mu$m are used as ablation targets for gold and silver, bulk targets are used for lithium and rubidium. The buffer gas cools and confines the ablated atoms, slowing down their transport to the cell walls. Buffer gas temperatures between 20 K and 295 K, and densities between $10^{16}$ cm$^{-3}$ and $2\times10^{19}$ cm$^{-3}$ are explored. Peak paramagnetic atom densities of $10^{11}$ cm$^{-3}$ are routinely achieved. The longest observed paramagnetic vapor density decay times are 110 ms for silver at 20 K and 4 ms for lithium at 32 K. The candidates for the principal paramagnetic-atom loss mechanism are impurities in the buffer gas, dimer formation and atom loss on sputtered clusters.
- Aug 14 2007 gr-qc arXiv:0708.1635v1It is known that the biological activity of the brain involves radiation of electric waves. These waves result from ionic currents and charges traveling among the brain's neurons. But it is obvious that these ions and charges are carried by their relevant masses which should give rise, according to the gravitational theory, to extremely weak gravitational waves. We use in the following the stochastic quantization (SQ) theory to calculate the probability to find a large ensemble of brains radiating similar gravitational waves. We also use this SQ theory to derive the equilibrium state related to the known Lamb shift.
- We approximate a Euclidean version of a D+1 dimensional manifold with a bifurcate Killing horizon by a product of a two-dimensional Rindler space and a D-1 dimensional manifold M. We obtain approximate formulas for the Green functions. We study the behaviour of Green functions near the horizon and their dimensional reduction. We show that if M is compact then the massless minimally coupled quantum field contains a zero mode which is a conformal invariant free field on R^2. Then, the Green function near the horizon can be approximated by the Green function of the two-dimensional quantum field theory. The correction term is exponentially small away from the horizon. If the volume of a geodesic ball is growing to infinity with its radius then the Green function cannot be approximated by a two-dimensional one.
- Any group $G$ gives rise to a 2-group of inner automorphisms, $\mathrm{INN}(G)$. It is an old result by Segal that the nerve of this is the universal $G$-bundle. We discuss that, similarly, for every 2-group $G_{(2)}$ there is a 3-group $\mathrm{INN}(G_{(2)})$ and a slightly smaller 3-group $\mathrm{INN}_0(G_{(2)})$ of inner automorphisms. We describe these for $G_{(2)}$ any strict 2-group, discuss how $\mathrm{INN}_0(G_{(2)})$ can be understood as arising from the mapping cone of the identity on $G_{(2)}$ and show that its underlying 2-groupoid structure fits into a short exact sequence $G_{(2)} \to \mathrm{INN}_0(G_{(2)}) \to \Sigma G_{(2)}$. As a consequence, $\mathrm{INN}_0(G_{(2)})$ encodes the properties of the universal $G_{(2)}$ 2-bundle.
- In this work we deform the phi^4 model with distinct deformation functions, to propose a diversity of sine-Gordon-like models. We investigate the proposed models and we obtain all the topological solutions they engender. In particular, we introduce non-polynomial potentials which support some exotic two-kink solutions.
- Aug 14 2007 quant-ph arXiv:0708.1540v2Research in non-orthogonal state discrimination has given rise to two conventional optimal strategies: unambiguous discrimination (UD) and minimum error (ME) discrimination. This paper explores the experimentally relevant range of measurement strategies between the two, where the rate of inconclusive results is minimized for a bounded-error rate. We first provide some constraints on the problem that apply to generalized measurements (POVMs). We then provide the theory for the optimal projective measurement (PVM) in this range. Through analytical and numerical results we investigate this family of projective, bounded-error strategies and compare it to the POVM family as well as to experimental implementation of UD using POVMs. We also discuss a possible application of these bounded-error strategies to quantum key distribution.
- Aug 14 2007 astro-ph arXiv:0708.1599v2We present a simple and efficient empirical algorithm for constructing dark-matter halo merger trees that reproduce the distribution of trees in the Millennium cosmological $N$-body simulation. The generated trees are significantly better than EPS trees. The algorithm is Markovian, and it therefore fails to reproduce the non-Markov features of trees across short time steps, except for an accurate fit to the evolution of the average main progenitor. However, it properly recovers the full main progenitor distribution and the joint distributions of all the progenitors over long-enough time steps, $\Delta \omega \simeq \Delta z>0.5$, where $\omega \simeq 1.69/D(t)$ is the self-similar time variable and $D(t)$ refers to the linear growth of density fluctuations. We find that the main progenitor distribution is log-normal in the variable $\sigma^2(M)$, the variance of linear density fluctuations in a sphere encompassing mass $M$. The secondary progenitors are successfully drawn one by one from the remaining mass using a similar distribution function. These empirical findings may be clues to the underlying physics of merger-tree statistics. As a byproduct, we provide useful, accurate analytic time-invariant approximations for the main progenitor accretion history and for halo merger rates.
- V. M. Karpan, G. Giovannetti, P. A. Khomyakov, M. Talanana, A. A. Starikov, M. Zwierzycki, J. van den Brink, G. Brocks, P. J. KellyAug 14 2007 cond-mat.mtrl-sci arXiv:0708.1735v1Based upon the observations (i) that their in-plane lattice constants match almost perfectly and (ii) that their electronic structures overlap in reciprocal space for one spin direction only, we predict perfect spin filtering for interfaces between graphite and (111) fcc or (0001) hcp Ni or Co. The spin filtering is quite insensitive to roughness and disorder. The formation of a chemical bond between graphite and the open $d$-shell transition metals that might complicate or even prevent spin injection into a single graphene sheet can be simply prevented by dusting Ni or Co with one or a few monolayers of Cu while still preserving the ideal spin injection property.
- Aug 14 2007 cond-mat.stat-mech arXiv:0708.1641v2The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is proposed in this paper, by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, we obtain $ 0.6627\pm0.0002$, where the exact value is $h_2=0.662798972834$. For three-dimensional lattice with periodic condition, our numerical result is $ 0.7847\pm0.0014$, which agrees with the best known bound $0.7653 \leq h_3 \leq 0.7862$.
- Aug 14 2007 math.PR arXiv:0708.1739v2We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the - suitably centered - empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time of the RWRE and also determine the exact constant in the almost sure upper limit of the maximal local time.
- Aug 14 2007 hep-ex arXiv:0708.1738v1We present a measurement of the branching fractions for anti-B -> D/D*/D(*) pi l^- anti-nu_l decays based on 341.1 fb-1 of data collected at the Upsilon(4S) resonance with the BaBar detector at the pep-II e^+e^- storage rings. Events are tagged by fully reconstructing one of the B mesons in a hadronic decay mode. We obtain BF (B^- -> D^0 l^- anti-nu_l) = (2.33 +/- 0.09(stat.) +/- 0.09(syst.))%, BF (B^- -> D^*0 l^- anti-nu_l) = (5.83 +/- 0.15(stat.) +/- 0.30(syst.))%, BF (B0bar -> D^+ l^- anti-nu_l) = (2.21 +/- 0.11(stat.) +/- 0.12(syst.))%, BF (B0bar -> D^*+ l^- anti-nu_l) = (5.49 +/- 0.16(stat.) +/- 0.25(syst.))%, BF (B^- -> D^+ pi^- l^- anti-nu_l) = (0.42 +/- 0.06(stat.) +/- 0.03(syst.))%, BF (B^- -> D^*+ pi^- l^- anti-nu_l) = (0.59 +/- 0.05(stat.) +/- 0.04(syst.))%, BF (B0bar -> D^0 pi^+ l^- anti-nu_l) = (0.43 +/- 0.08(stat.) +/- 0.03(syst.))% and BF (B0bar -> D^*0 pi^+ l^- anti-nu_l) = (0.48 +/- 0.08(stat.) +/- 0.04(syst.))%.
- Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed by a power n of the Planck mass M_Pl. We show that first and second order terms of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a photon component in cosmic rays above 10^(19) eV that should already have been detected, if corresponding terms for electrons and positrons are significantly smaller. This suggests that Lorentz invariance breakings suppressed up to second order in the Planck scale are unlikely to be phenomenologically viable for photons.
- G. Busso, S. Cassisi, G. Piotto, M. Castellani, M. Romaniello, M. Catelan, S. G. Djorgovski, A. Recio Blanco, A. Renzini, M. R. Rich, A. V. Sweigart, M. ZoccaliAug 14 2007 astro-ph arXiv:0708.1736v1In this paper we present multiband optical and UV Hubble Space Telescope photometry of the two Galactic globular clusters NGC 6388 and NGC 6441. We have obtained the first UV color-magnitude diagrams for NGC 6388 and NGC 6441. These diagrams confirm previous results, obtained in optical bands, about the presence of a sizeable stellar population of extremely hot horizontal branch stars. At least in NGC 6388, we find a clear indication that at the hot end of the horizontal branch the distribution of stars forms a hook-like feature, closely resembling those observed in NGC 2808 and Omega Centauri. We briefly review the theoretical scenarios that have been suggested for interpreting this observational feature. We also investigate the tilted horizontal branch morphology and provide further evidence that supports early suggestions that this feature cannot be interpreted as an effect of differential reddening. We show that a possible solution of the puzzle is to assume that a small fraction - ranging between 10-20% - of the stellar population in the two clusters is strongly helium enriched (Y=0.40 in NGC 6388 and Y=0.35 in NGC 6441). The occurrence of a spread in the He abundance between the canonical value (Y=0.26) and the quoted upper limits can significantly help in explaining the whole morphology of the horizontal branch and the pulsational properties of the variable stars in the target clusters.
- Aug 14 2007 quant-ph arXiv:0708.1734v1We present a new approach to simulate quantum cryptography protocols using event-based processes. The method is validated by simulating the BB84 protocol and the Ekert protocol, both without and with the presence of an eavesdropper.
- In this paper, we address the question of comparison between populations of trees. We study an statistical test based on the distance between empirical mean trees, as an analog of the two sample z statistic for comparing two means. Despite its simplicity, we can report that the test is quite powerful to separate distributions with different means but it does not distinguish between different populations with the same mean, a more complicated test should be applied in that setting. The performance of the test is studied via simulations on Galton-Watson branching processes. We also show an application to a real data problem in genomics.

Simulation of non-Pauli Channels

Kenneth Goodenough Jun 21 2017 12:48 UTCStefano Pirandola Jun 20 2017 13:26 UTC

...(continued)Hi Kenneth, more precisely that plot is for a particular "Pauli-damping" channel, i.e., a qubit channel that is decomposable into a Pauli channel (1) and an amplitude damping channel (2). This "Pauli-damping" channel can be simulated by performing noisy teleportation over a resource state that corre

Kenneth Goodenough Jun 20 2017 12:47 UTC

Interesting work! I was wondering, how do the new upper bounds for the amplitude-damping channel in Fig. 2 compare to previous bounds?

Barbara Terhal Jun 20 2017 07:25 UTC

It would be good if this conflict on assigning priority and credit is peacefully resolved by the parties involved (i have no opinions on the matter).

Stefano Pirandola Jun 15 2017 05:32 UTC

...(continued)The secret-key capacity of the pure-loss channel -log(1-t) was proven in [9], not in the follow-up work [13] (which appeared 4 months later). Ref. [13] found that this capacity is also a strong converse bound, which is Eq. (1) here. Same story for Eq. (4) that was proven in [9], not in [13]. Again t

Chris Ferrie Jun 09 2017 10:06 UTC

I have posted an open review of this paper here: https://github.com/csferrie/openreviews/blob/master/arxiv.1703.09835/arxiv.1703.09835.md

Eddie Smolansky May 26 2017 05:23 UTC

...(continued)Updated summary [here](https://github.com/eddiesmo/papers).

# How they made the dataset

- collect youtube videos

- automated filtering with yolo and landmark detection projects

- crowd source final filtering (AMT - give 50 face images to turks and ask which don't belong)

- quality control through s

Felix Leditzky May 24 2017 20:43 UTC

...(continued)Yes, that's right, thanks!

For (5), you use the Cauchy-Schwarz inequality $\left| \operatorname{tr}(X^\dagger Y) \right| \leq \sqrt{\operatorname{tr}(X^\dagger X)} \sqrt{\operatorname{tr}(Y^\dagger Y)}$ for the Hilbert-Schmidt inner product $\langle X,Y\rangle := \operatorname{tr}(X^\dagger Y)$ wi

Michael Tolan May 24 2017 20:27 UTC

Just reading over Eq (5) on P5 concerning the diamond norm.

Should the last $\sigma_1$ on the 4th line be replaced with a $\sigma_2$? I think I can see how the proof is working but not entirely certain.

Noon van der Silk May 23 2017 11:15 UTC

...(continued)I think this thread has reached it's end.

I've locked further comments, and I hope that the quantum computing community can thoughtfully find an approach to language that is inclusive to all and recognises the diverse background of all researchers, current and future.

I direct your attention t