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Arxiv.org
Jul 22, 2013 Szymon Wasowicz
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We give a slight extension of the Hermite-Hadamard inequality on simplices and we use it to establish error bounds of the operators connected with the approximate integration.
Source: http://arxiv.org/abs/0807.4130v3
Arxiv.org
Jul 22, 2013 Marco G. Mazza; Kevin Stokely; H. Eugene Stanley; Giancarlo Franzese
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We study a coarse-grained model for a water monolayer that cannot crystallize due to the presence of confining interfaces, such as protein powders or inorganic surfaces. Using both Monte Carlo simulations and mean field calculations, we calculate three response functions: the isobaric specific heat $C_P$, the isothermal compressibility $K_T$, and the isobaric thermal expansivity $\alpha_P$. At low temperature $T$, we find two distinct maxima in $C_P$, $K_T$ and $|\alpha_P|$, all converging...
Source: http://arxiv.org/abs/0807.4267v2
Arxiv.org
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A dense form of matter is formed in relativistic heavy ion collisions. The constituent degrees of freedom in this dense matter are currently unknown. Long-range, forward-backward multiplicity correlations (LRC) are expected to arise due to multiple partonic interactions. Model independent and dependent arguments suggest that such correlations are due to multiple partonic interactions. These correlations are predicted in the context of the Dual Parton Model (DPM). The DPM describes soft partonic...
Source: http://arxiv.org/abs/0807.1941v3
Arxiv.org
Jul 22, 2013 Lian-Gang Li
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The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $\beta$ and the periodic solution, and a conclusion that the critical value of $\beta$ is a fixed one in the over damping situation. These results are of practical significance in the study of charge-density waves in physics.
Source: http://arxiv.org/abs/0807.3288v2
Arxiv.org
Jul 22, 2013 Yong Zeng; Walter Hoyer; Jinjie Liu; Stephan W. Koch; Jerome V. Moloney
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Strong second-harmonic generation has recently been experimentally observed from metamaterials consisting of periodic arrays of metal split ring resonators with an effective negative magnetic permeability [Science, 313, 502 (2006)]. To explore the underlying physical mechanism, a classical model derived from microscopic theory is employed here. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an...
Source: http://arxiv.org/abs/0807.3531v2
Arxiv.org
Jul 22, 2013 Henry Wilton; Pavel Zalesskii
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Let $M$ be a closed, orientable, irreducible, geometrizable 3-manifold. We prove that the profinite topology on the fundamental group of $\pi_1(M)$ is efficient with respect to the JSJ decomposition of $M$. We go on to prove that $\pi_1(M)$ is good, in the sense of Serre, if all the pieces of the JSJ decomposition are. We also prove that if $M$ is a graph manifold then $\pi_1(M)$ is conjugacy separable.
Source: http://arxiv.org/abs/0807.3727v3
Arxiv.org
Jul 22, 2013 Till Bargheer; Niklas Beisert; Florian Loebbert
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We present an integrability-preserving recursion relation for the explicit construction of long-range spin chain Hamiltonians. These chains are generalizations of the Haldane-Shastry and Inozemtsev models and they play an important role in recent advances in string/gauge duality. The method is based on arbitrary nearest-neighbour integrable spin chains and it sheds light on the moduli space of deformation parameters. We also derive the closed chain asymptotic Bethe equations.
Source: http://arxiv.org/abs/0807.5081v3
Arxiv.org
Jul 22, 2013 Mario O. Bourgoin
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We introduce a new cohomology-theoretic method for classifying generic immersed curves in closed compact surfaces by using Gauss codes. This subsumes a result of J.S. Carter on classifying immersed curves in oriented compact surfaces, and provides a criterion for when an immersion is two-colorable. We note an application to twisted virtual link theory.
Source: http://arxiv.org/abs/0807.1311v2
Arxiv.org
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The paper contains a fundamental defect in its framework of using the gauge action to study the rigidity problem. As a result, the calculations leading to the main formula is also incorrect.
Source: http://arxiv.org/abs/0807.3152v5
Arxiv.org
Jul 22, 2013 C. Gros
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An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction...
Source: http://arxiv.org/abs/0807.4838v3
Arxiv.org
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The scaling of the time delay near a "bottleneck" of a generic saddle-node bifurcation is well-known to be given by an inverse square-root law. We extend the analysis to several non-generic cases for smooth vector fields. We proceed to investigate $C^0$ vector fields. Our main result is a new phenomenon in two-parameter families having a saddle-node bifurcation upon changing the first parameter. We find distinct scalings for different values of the second parameter ranging from power...
Source: http://arxiv.org/abs/0807.1546v2
Arxiv.org
Jul 22, 2013 Paul Balmer; Baptiste Calmès
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We compute the total Witt groups of (split) Grassmann varieties, over any regular base X. The answer is a free module over the total Witt ring of X. We provide an explicit basis for this free module, which is indexed by a special class of Young diagrams, that we call even Young diagrams.
Source: http://arxiv.org/abs/0807.3296v3
Arxiv.org
Jul 22, 2013 Charanjit S. Aulakh; Sumit K. Garg
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The supersymmetric SO(10) GUT based on the ${\bf{210\oplus 10\oplus 120\oplus 126\oplus {\bar {126}}}}$ Higgs system provides a minimal framework for the emergence of the R-parity exact MSSM at low energies and a viable supersymmetric seesaw explanation for the observed neutrino masses and mixing angles. We present formulae for MSSM decomposition of the superpotential invariants, tree level light charged fermion effective Yukawa couplings, Weinberg neutrino mass generation operator, and the...
Source: http://arxiv.org/abs/0807.0917v3
Arxiv.org
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A new family of restricted post-Newtonian-accurate waveforms, termed TaylorEt approximants, was recently proposed for searching gravitational wave (GW) signals from inspiraling non-spinning compact binaries having arbitrary mass-ratios. We perform detailed fitting factor (FF) studies to probe if the TaylorEt (3.5PN) signals for non-spinning comparable mass compact binaries can be effectually and faithfully searched with TaylorT1, TaylorT4, and TaylorF2 (3.5PN) templates in LIGO, Advanced LIGO,...
Source: http://arxiv.org/abs/0807.2400v2
Arxiv.org
Jul 22, 2013 Gopal Prasad; Sai-Kee Yeung
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We show that there are no arithmetic fake compact hermitian symmetric spaces of type other than An for n>4.
Source: http://arxiv.org/abs/0807.2077v4
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Jul 22, 2013 Vinod M. Prabhakaran; Krishnan Eswaran; Kannan Ramchandran
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Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are available -- correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources. We are interested in characterizing the fundamental trade-off between the rates of the secret message...
Source: http://arxiv.org/abs/0807.0942v2
Arxiv.org
Jul 22, 2013 C. Landim; R. D. Portugal; B. F. Svaiter
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Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields model. Fix $n\ge 1$ and $\beta>0$. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate $\beta(n-k)/n$, where $k$ is the distance from the node to the root. Denote by $Z_n(t)$ the number of nodes with no descendants at time $t$...
Source: http://arxiv.org/abs/0807.1750v2
Arxiv.org
Jul 22, 2013 Jacob Sznajdman
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We give a new elementary proof of the Brian\c{c}on-Skoda theorem, which states that for an $m$-generated ideal $\mathfrak{a}$ in the ring of germs of analytic functions at $0\in \C^n$, the $\nu$:th power of its integral closure is contained in $\mathfrak{a}$, where $\nu = \min(m,n)$.
Source: http://arxiv.org/abs/0807.0142v2
Arxiv.org
Jul 22, 2013 Tobias Schmidt
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Let L be a p-adic local field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) is a stably flat completion of its universal enveloping algebra. As a consequence the relative cohomology for the locally convex algebra F(g) coincides with the underlying Lie algebra cohomology. Final version. Some minor items corrected. Appeared in Journal of Algebra (2010).
Source: http://arxiv.org/abs/0807.2847v2
Arxiv.org
Jul 22, 2013 Leonid V. Bogachev; Sakhavat M. Zarbaliev
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Let ${\varPi}_n$ be the set of convex polygonal lines $\varGamma$ with vertices on $\mathbb {Z}_+^2$ and fixed endpoints $0=(0,0)$ and $n=(n_1,n_2)$. We are concerned with the limit shape, as $n\to\infty$, of "typical" $\varGamma\in {\varPi}_n$ with respect to a parametric family of probability measures $\{P_n^r,0
Source: http://arxiv.org/abs/0807.3682v4
Arxiv.org
Jul 22, 2013 Julien Berestycki; Nathanaël Berestycki; Vlada Limic
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Consider a $\Lambda$-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number $N_t$ of blocks at any positive time $t>0$). We exhibit a deterministic function $v:(0,\infty)\to(0,\infty)$ such that $N_t/v(t)\to1$, almost surely, and in $L^p$ for any $p\geq1$, as $t\to0$. Our approach relies on a novel martingale technique.
Source: http://arxiv.org/abs/0807.4278v3
Arxiv.org
Jul 22, 2013 Kangjin Han; Sijong Kwak
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A projective scheme $X$ is called `quadratic' if $X$ is scheme-theoretically cut out by homogeneous equations of degree 2. Furthermore, we say $X$ satisfies `property $\textbf{N}_{2,p}$' if it is quadratic and the quadratic ideal has only linear syzygies up to first $p$-th steps. In the present paper, we compare the linear syzygies of the inner projections with those of $X$ and obtain a theorem on `embedded linear syzygies' as one of our main results. This is the natural projection-analogue of...
Source: http://arxiv.org/abs/0807.4976v4
Arxiv.org
Jul 20, 2013 Daniil Ryabko; Boris Ryabko
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In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. Namely, three problems are considered: goodness-of-fit (or identity) testing, process classification, and the change point problem. For each of the problems a test is constructed that is asymptotically accurate for the case when the data is generated...
Source: http://arxiv.org/abs/0804.0510v4
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Jul 20, 2013 T. K. Samanta; Iqbal H. Jebril
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Following the definition of intuitionistic fuzzy n-norm [ 3 ], we have introduced the definition of intuitionistic fuzzy norm (in short IFN) over a linear space and there after a few results on intuitionistic fuzzy normed linear space and finite dimensional intuitionistic fuzzy normed linear space. Lastly, we have introduced the definitions of intuitionistic fuzzy continuity and sequentially intuitionistic fuzzy continuity and proved that they are equivalen
Source: http://arxiv.org/abs/0804.1645v2
Arxiv.org
Jul 20, 2013 Igor Nikolaev
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The real multiplication conjecture of Yu. I. Manin says that abelian extensions of the real quadratic number fields come from the so-called pseudo-lattices with real multiplication; the conjecture is based on an observation that for the imaginary quadratic fields such extensions are obtained from the lattices with complex multiplication. In this paper we prove Manin's conjecture using theory of the Hecke eigenforms (of weight two) and associated measured foliations on the modular surfaces.
Source: http://arxiv.org/abs/0804.0057v6
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After reviewing known results on sensitiveness and also on robustness of attractors together with observations on their proofs, we show that for attractors of three-dimensional flows, robust chaotic behavior meaning sensitiveness to initial conditions for the past as well for the future for all nearby flows) is equivalent to the existence of certain hyperbolic structures. These structures, in turn, are associated to the existence of physical measures. In short in low dimensions, robust chaotic...
Source: http://arxiv.org/abs/0804.3616v2
Arxiv.org
Jul 20, 2013 Hans Raj Tiwary
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We study the complexity of computing the projection of an arbitrary $d$-polytope along $k$ orthogonal vectors for various input and output forms. We show that if $d$ and $k$ are part of the input (i.e. not a constant) and we are interested in output-sensitive algorithms, then in most forms the problem is equivalent to enumerating vertices of polytopes, except in two where it is NP-hard. In two other forms the problem is trivial. We also review the complexity of computing projections when the...
Source: http://arxiv.org/abs/0804.4150v2
Arxiv.org
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A duality transformation in quantum field theory is usually established first through partition functions. It is always important to explore the dual relations between various correlation functions in the transformation. Here, we explore such a dual relation to study quantum phases and phase transitions in an extended boson Hubbard model at 1/3 (2/3) filling on a triangular lattice. We develop systematically a simple and effective way to use the vortex degree of freedoms on dual lattices to...
Source: http://arxiv.org/abs/0804.3429v4
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Jul 20, 2013 Antonio Leon
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This paper examines the consistency of w-order by means of a supertask that functions as a supertrap for the assumed existence of w-ordered collections, which are simultaneously complete (as is required by the Actual infinity) and uncompletable (because no last element completes them).
Source: http://arxiv.org/abs/0804.2939v2
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Jul 20, 2013 K. Sabeeh; M. Tahir; A. MacKinnon
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We present a theoretical study of the electronic structure of magnetically modulated graphene. We consider monolayer graphene in the presence of a perpendicular magnetic field and a unidirectional weak magnetic modulation. The density of states and the bandwidth of the Dirac electrons in this system are determined. We have found magnetic Weiss oscillations in the bandwidth and the density of states. These oscillations are out of phase and larger in amplitude than the ones in the electrically...
Source: http://arxiv.org/abs/0804.4583v2
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Jul 20, 2013 Xinjia Chen
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In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed criterion of absolute and relative errors. By employing the Chernoff-Hoeffding bound and the concept of sampling, the minimization of a probabilistic function is transformed into an optimization problem amenable for gradient descendent algorithms.
Source: http://arxiv.org/abs/0804.1399v3
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Jul 20, 2013 Sunil Srinivasa; Martin Haenggi
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In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying nodal arrangement is almost universally taken to be an infinite Poisson point process. While this assumption is valid in some cases, there are also certain impracticalities to this model. For example, practical networks are non-stationary, and the number of...
Source: http://arxiv.org/abs/0804.4204v3
Arxiv.org
Jul 20, 2013 Eiji Konishi
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We formulate the homotopy associative (A_\infty) category of D-particle field states via gauged S-duality. By invoking the minimal model theorem of this D-particle field category, we investigate the equivalence principle and the A_\infty covariance principle in the theory of gauged S-duality considered as D-particle field theory.
Source: http://arxiv.org/abs/0804.1576v5
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Jul 20, 2013 Dierk Schleicher
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We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. Internal addresses are a convenient and efficient way of describing the combinatorial structure of the Mandelbrot set, and of giving geometric meaning to the ubiquitous kneading sequences in human-readable form (Sections 3 and 4). A simple extension, \emph{angled internal addresses},...
Source: http://arxiv.org/abs/math/9411238v3
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Jul 20, 2013 Pierre-Olivier Amblard; Jean-François Coeurjolly; Frédéric Lavancier; Anne Philippe
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This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and spectral analyses of the increments are investigated. On the other hand we show that (almost) all mfBm's may be reached as the limit of partial sums of (super)linear processes. Finally, an algorithm to perfectly simulate the mfBm is presented and illustrated...
Source: http://arxiv.org/abs/1007.0828v2
Arxiv.org
Jul 20, 2013 Hoeskuldur P. Halldorsson
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We give a classification of all self-similar solutions to the curve shortening flow in the plane.
Source: http://arxiv.org/abs/1007.1617v2
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Jul 20, 2013 Venkat Chandar; Aslan Tchamkerten; David Tse
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The capacity per unit cost, or equivalently minimum cost to transmit one bit, is a well-studied quantity. It has been studied under the assumption of full synchrony between the transmitter and the receiver. In many applications, such as sensor networks, transmissions are very bursty, with small amounts of bits arriving infrequently at random times. In such scenarios, the cost of acquiring synchronization is significant and one is interested in the fundamental limits on communication without...
Source: http://arxiv.org/abs/1007.4872v2
Arxiv.org
Jul 20, 2013 Sebastian Casalaina-Martin; Radu Laza
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A key tool in the study of algebraic surfaces and their moduli is Brieskorn's simultaneous resolution for families of algebraic surfaces with simple (du Val or ADE) singularities. In this paper we show that a similar statement holds for families of curves with at worst simple (ADE) singularities. For a family $\mathscr X\to B$ of ADE curves, we give an explicit and natural resolution of the rational map $B\to \bar M_g$. Moreover, we discuss a lifting of this map to the moduli stack $ \bar...
Source: http://arxiv.org/abs/1007.0265v2
Arxiv.org
Jul 20, 2013 Ery Arias-Castro; Emmanuel J. Candès; Yaniv Plan
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Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have $p$ covariates and that under the alternative, the response only depends upon the order of $p^{1-\alpha}$ of those, $0\le\alpha\le1$....
Source: http://arxiv.org/abs/1007.1434v2
Arxiv.org
Jul 20, 2013 Marco Bardoscia; Roberto Bellotti
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A novel dynamical model for the study of operational risk in banks and suitable for the calculation of the Value at Risk (VaR) is proposed. The equation of motion takes into account the interactions among different bank's processes, the spontaneous generation of losses via a noise term and the efforts made by the bank to avoid their occurrence. Since the model is very general, it can be tailored on the internal organizational structure of a specific bank by estimating some of its parameters...
Source: http://arxiv.org/abs/1007.0026v6
Arxiv.org
Jul 20, 2013 Brian Skinner; B. I. Shklovskii
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In electronic devices where a two-dimensional electron gas (2DEG) comprises one or both sides of a plane capacitor, the resulting capacitance $C$ can be larger than the "geometric capacitance" $C_g$ determined by the physical separation $d$ between electrodes. This larger capacitance is known to result from the Coulomb correlations between individual electrons within the low density 2DEG, which lead to a negative thermodynamic density of states (negative compressibility). Experiments...
Source: http://arxiv.org/abs/1007.5308v3
Arxiv.org
Jul 20, 2013 Xavier Bekaert; Nicolas Boulanger; Per Sundell
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Aiming at non-experts, we explain the key mechanisms of higher-spin extensions of ordinary gravity. We first overview various no-go theorems for low-energy scattering of massless particles in flat spacetime. In doing so we dress a dictionary between the S-matrix and the Lagrangian approaches, exhibiting their relative advantages and weaknesses, after which we high-light potential loop-holes for non-trivial massless dynamics. We then review positive yes-go results for non-abelian cubic...
Source: http://arxiv.org/abs/1007.0435v3
Arxiv.org
Jul 20, 2013 V. Gogokhia; M. Vasúth
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The effective potential approach for composite operators is generalized to non-zero temperature in order to derive the non-perturbative analytical equation of state for pure SU(3) Yang-Mills fields valid in the whole temperature range. Adjusting our parametrization of the gluon plasma pressure to the lattice pressure at high temperature for SU(3) Yang-Mills case, we have reproduced well our analytical curves and numbers not only for the pressure but for all other independent thermodynamic...
Source: http://arxiv.org/abs/1007.1573v2
Arxiv.org
Jul 20, 2013 Lutz Warnke
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The K_4-free process starts with the empty graph on n vertices and at each step adds a new edge chosen uniformly at random from all remaining edges that do not complete a copy of K_4. Let G be the random maximal K_4-free graph obtained at the end of the process. We show that for some positive constant C, with high probability as $n \to \infty$, the maximum degree in G is at most $C n^{3/5}\sqrt[5]{\log n}$. This resolves a conjecture of Bohman and Keevash for the K_4-free process and improves...
Source: http://arxiv.org/abs/1007.3037v3
Arxiv.org
Jul 20, 2013 P. J. Bickel; B. J. K. Kleijn
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In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is shown that, under certain straightforward and interpretable conditions, the assertion of Le Cam's acclaimed, but strictly parametric, Bernstein-von Mises theorem [Univ. California Publ. Statist. 1 (1953) 277-329] holds in the semiparametric situation as well....
Source: http://arxiv.org/abs/1007.0179v3
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Jul 20, 2013 Akaki Tikaradze
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In this paper we discuss an analogue of the Kac-Weisfeiler conjecture for a certain class of almost commutative algebras. In particular, we prove the Kac-Weisfeiler type statement for rational Cherednik algebras.
Source: http://arxiv.org/abs/1007.2387v4
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Jul 20, 2013 Alicia Dickenstein; Federico Nicolás Martínez; Laura Felicia Matusevich
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We study the solutions of irregular A-hypergeometric systems that are constructed from Gr\"obner degenerations with respect to generic positive weight vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1,...,1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of...
Source: http://arxiv.org/abs/1007.4225v2
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Jul 20, 2013 Eviatar B. Procaccia; Eric Shellef
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Let a simple random walk run inside a torus of dimension three or higher for a number of steps which is a constant proportion of the volume. We examine geometric properties of the range, the random subgraph induced by the set of vertices visited by the walk. Distance and mixing bounds for the typical range are proven that are a $k$-iterated log factor from those on the full torus for arbitrary $k$. The proof uses hierarchical renormalization and techniques that can possibly be applied to other...
Source: http://arxiv.org/abs/1007.1401v3
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Jul 20, 2013 Josep Diaz; Alberto Marchetti-Spaccamela; Dieter Mitsche; Paolo Santi; Julinda Stefa
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Several social-aware forwarding strategies have been recently introduced in opportunistic networks, and proved effective in considerably in- creasing routing performance through extensive simulation studies based on real-world data. However, this performance improvement comes at the expense of storing a considerable amount of state information (e.g, history of past encounters) at the nodes. Hence, whether the benefits on routing performance comes directly from the social-aware forwarding...
Source: http://arxiv.org/abs/1007.5240v2
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Jul 20, 2013 Stanislav Volgushev; Holger Dette
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We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quantile curves. Weak uniform consistency and weak convergence is established for both estimates and their finite sample properties are investigated by means of a simulation study. As a by-product, we...
Source: http://arxiv.org/abs/1007.3376v2
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We study the distribution of eigenvalues for the Green operator occurring in the scattering of electromagnetic waves by an arbitrarily shaped dielectric medium. It is revealed that the totality of eigenvalues (counting multiplicities) can be enumerated as a sequence $ \{\lambda_s\}_{s=1}^N,N\leq\aleph_0$, with only two possible accumulation points $ \{0,-1/2\}$, and the following spectral series converges: $ \sum_{s=1}^N|\lambda_s|^2|1+2\lambda_s|^4
Source: http://arxiv.org/abs/1007.4375v2
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Jul 20, 2013 Jihoon Park; Przemysław Pawełczak; Pål Grønsund; Danijela Čabrić
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We present an analytical model that enables throughput evaluation of Opportunistic Spectrum Orthogonal Frequency Division Multiple Access (OS-OFDMA) networks. The core feature of the model, based on a discrete time Markov chain, is the consideration of different channel and subchannel allocation strategies under different Primary and Secondary user types, traffic and priority levels. The analytical model also assesses the impact of different spectrum sensing strategies on the throughput of...
Source: http://arxiv.org/abs/1007.5080v3
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Jul 20, 2013 Georgi S. Medvedev
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A unified approach to studying convergence and stochastic stability of continuous time consensus protocols (CPs) is presented in this work. Our method applies to networks with directed information flow; both cooperative and noncooperative interactions; networks under weak stochastic forcing; and those whose topology and strength of connections may vary in time. The graph theoretic interpretation of the analytical results is emphasized. We show how the spectral properties, such as algebraic...
Source: http://arxiv.org/abs/1007.1234v3
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Jul 20, 2013 Olivier Bernardi
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Consider a walk in the plane made of $n$ unit steps, with directions chosen independently and uniformly at random at each step. Rayleigh's theorem asserts that the probability for such a walk to end at a distance less than 1 from its starting point is $1/(n+1)$. We give an elementary proof of this result. We also prove the following generalization valid for any probability distribution $\mu$ on the positive real numbers: if two walkers start at the same point and make respectively $m$ and $n$...
Source: http://arxiv.org/abs/1007.4870v3
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Jul 20, 2013 Silvere Bonnabel; Anne Collard; Rodolphe Sepulchre
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The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated...
Source: http://arxiv.org/abs/1007.5494v3
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Jul 20, 2013 Marcin Bienkowski
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In the online packet buffering problem (also known as the unweighted FIFO variant of buffer management), we focus on a single network packet switching device with several input ports and one output port. This device forwards unit-size, unit-value packets from input ports to the output port. Buffers attached to input ports may accumulate incoming packets for later transmission; if they cannot accommodate all incoming packets, their excess is lost. A packet buffering algorithm has to choose from...
Source: http://arxiv.org/abs/1007.1535v3
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Jul 20, 2013 Cuneyt Cevik
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We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
Source: http://arxiv.org/abs/1007.4344v2
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We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related to R. Forman's discrete Morse theory for CW-complexes and generalizes Forman and Chari's results on the face posets of regular CW-complexes. We also introduce a homological variant of the theory that can be used to study the topology of triangulable homology manifolds by means...
Source: http://arxiv.org/abs/1007.1930v2
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Jul 20, 2013 Sergey Rybakov
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Let $A$ be an abelian surface over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ of degree 4. We give a classification of the groups of $k$-rational points on varieties from this class in terms of $f_A$.
Source: http://arxiv.org/abs/1007.0115v2
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Jul 20, 2013 Alberto Enciso; Daniel Peralta-Salas
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Motivated by a question of Rubel, we consider the problem of characterizing which noncompact hypersurfaces in $\RR^n$ can be regular level sets of a harmonic function modulo a $C^\infty$ diffeomorphism, as well as certain generalizations to other PDEs. We prove a versatile sufficient condition that shows, in particular, that any (possibly disconnected) algebraic noncompact hypersurface can be transformed onto a union of components of the zero set of a harmonic function via a diffeomorphism of...
Source: http://arxiv.org/abs/1007.5181v3
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Jul 20, 2013 Marcel Oliver; Claudia Wulff
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We consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. In this setting, we prove the existence of solutions which are temporally smooth in the norm of the lowest rung of the scale for an open set of initial data on the highest rung of the scale. Under the same assumptions, we prove that a class of implicit, $A$-stable Runge--Kutta semidiscretizations in time of...
Source: http://arxiv.org/abs/1007.4703v3
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Jul 20, 2013 Delio Mugnolo; Robin Nittka; Olaf Post
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Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first results in this direction have been obtained only recently, to the best of our knowledge. Here we consider sectorial operators on scales of Hilbert spaces. We define a notion of convergence that generalises convergence of the resolvents in operator norm to the case...
Source: http://arxiv.org/abs/1007.3932v2
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Jul 20, 2013 Constantinos Kardaras
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In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomized stopping time. This perspective has advantages in both the theoretical and practical study of optional processes up to random times. Applications are given to the stochastic behavior of processes up to...
Source: http://arxiv.org/abs/1007.1124v3
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Jul 20, 2013 D. Witthaut; M. D. Lukin; A. S. Sørensen
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We discuss a new method for realizing number-resolving and non-demolition photo detectors by strong coupling of light to individual single photon emitters, which act as strong optical non-linearities. As a specific application we show how these elements can be integrated into an error-proof Bell state analyzer, whose efficiency exceeds the best possible performance with linear optics even for a modest atom-field coupling. The methods are error-proof in the sense that every detection event...
Source: http://arxiv.org/abs/1007.3273v2
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A new analytic treatment of the two-dimensional Hubbard model at finite temperature and chemical potential is presented. A next nearest neighbor hopping term of strength t' is included. This analysis is based upon a formulation of the statistical mechanics of particles in terms of the S-matrix. In the 2-body scattering approximation, the S-matrix allows a systematic expansion in t/U. We show that for U/t large enough, a region of attractive interactions exists near the Fermi surface due to...
Source: http://arxiv.org/abs/1007.1195v2
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Jul 20, 2013 Kamal Jain; Vijay Vazirani
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The problem of arriving at a principled method of pricing goods and services was very satisfactorily solved for conventional goods; however, this solution is not applicable to digital goods. This paper studies pricing of a special class of digital goods, which we call {\em semantically substitutable digital goods}. After taking into consideration idiosyncrasies of goods in this class, we define a market model for it, together with a notion of equilibrium. We prove existence of equilibrium...
Source: http://arxiv.org/abs/1007.4586v4
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Jul 20, 2013 Francesco Mainardi
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The article provides an historical survey of the early contributions on the applications of fractional calculus in linear viscoelasticty. The period under examination covers four decades, since 1930's up to 1970's and authors are from both Western and Eastern countries. References to more recent contributions may be found in the bibliography of the author's book. This paper reproduces, with Publisher's permission, Section 3.5 of the book: F. Mainardi, Fractional Calculus and Waves in Linear...
Source: http://arxiv.org/abs/1007.2959v2
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Jul 20, 2013 Alex Clark; Robbert Fokkink; Olga Lukina
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Blanc showed in his thesis that a compact minimal foliated space with a residual subset of 2-ended leaves can contain only 1 or 2 ended leaves. In this paper we give examples of compact minimal foliated spaces where a topologically generic leaf has 1 end, there is an uncountable set of leaves with 2 ends and a leaf with 2n ends, for a given n>1. The examples we present are weak solenoids, which allows us to represent the graph of the group action on the fibre as the inverse limit of finite...
Source: http://arxiv.org/abs/1007.0746v3
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Jul 20, 2013 Keita Kobayashi; Yoshiya Yamanaka
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We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schr\"odinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the...
Source: http://arxiv.org/abs/1007.3603v2
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Jul 20, 2013 Tomas Brazdil; Stefan Kiefer; Antonin Kucera; Ivana Hutarova Varekova
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We study termination time and recurrence time in programs with unbounded recursion, which are either randomized or operate on some statistically quantified inputs. As the underlying formal model for such programs we use probabilistic pushdown automata (pPDA) which are equivalent to probabilistic recursive state machines. We obtain tail bounds for the distribution of termination time for pPDA. We also study the recurrence time for probabilistic recursive programs that are not supposed to...
Source: http://arxiv.org/abs/1007.1710v2
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Jul 20, 2013 Roman Kompaneets; Alexei V. Ivlev; Sergey V. Vladimirov; Gregor E. Morfill
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The fundamental higher-order Landau plasma modes are known to be generally heavily damped. We show that these modes for the ion component in a weakly ionized plasma can be substantially modified by ion-neutral collisions and a dc electric field driving ion flow so that some of them can become unstable. This instability is expected to naturally occur in presheaths of gas discharges at sufficiently small pressures and thus affect sheaths and discharge structures.
Source: http://arxiv.org/abs/1007.0142v3
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Jul 20, 2013 A. Chamballu; J. G. Bartlett; J. -B. Melin
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Surveys based on the Sunyaev-Zel'dovich (SZ) effect provide a fresh view of the galaxy cluster population, one that is complementary to X-ray surveys. To better understand the relation between these two kinds of survey, we construct an empirical cluster model using scaling relations constrained by current X-ray and SZ data. We apply our model to predict the X-ray properties of the Planck SZ Cluster Catalog (PCC) and compare them to existing X-ray cluster catalogs. We find that Planck should...
Source: http://arxiv.org/abs/1007.3193v2
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Jul 20, 2013 Ivan Donkin; Arthur Hebecker
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We investigate the impact of extra vector-like GUT multiplets on the predicted value of the strong coupling. We find in particular that Yukawa couplings between such extra multiplets and the MSSM Higgs doublets can resolve the familiar two-loop discrepancy between the SUSY GUT prediction and the measured value of alpha_3. Our analysis highlights the advantages of the holomorphic scheme, where the perturbative running of gauge couplings is saturated at one loop and further corrections are...
Source: http://arxiv.org/abs/1007.3990v6
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Jul 20, 2013 Andreas Seeger; James Wright
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We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First, we obtain an $H^1$ to $L^{1,\infty}$ bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an $L^p$ regularity bound for some $p>1$. Secondly, we obtain a necessary and sufficient condition for $L^2$ boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally...
Source: http://arxiv.org/abs/1007.4731v2
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We find locally free resolutions of length one for all semi-stable sheaves supported on curves of multiplicity five in the complex projective plane. In some cases we also find geometric descriptions of these sheaves by means of extensions. We give natural stratifications for their moduli spaces and we describe the strata as certain quotients modulo linear algebraic groups. In most cases we give concrete descriptions of these quotients as fibre bundles.
Source: http://arxiv.org/abs/1007.1815v3
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In this work we apply Bohr-Sommerfeld (Old quantum atomic) theory for analysis of some remarkable electro-dynamical problems, concretely magnetic monopoles, electron electromagnetic mass and fine structure constant. We reproduce exactly some basic elements of the Dirac magnetic monopoles theory, especially Dirac electric/magnetic charge quantization condition. It follows after application of Bohr-Sommerfeld theory at the system, simply called magnetic monopole "atom", consisting of...
Source: http://arxiv.org/abs/1007.0340v5
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We present analytic calculations of angular momentum transport and gas inflow in galaxies, from scales of ~kpc to deep in the potential of a central black hole (BH). We compare these analytic calculations to numerical simulations and use them to develop a sub-grid model of BH growth that can be incorporated into semi-analytic models or cosmological simulations. Both analytic calculations and simulations argue that the strongest torque on gas arises when non-axisymmetric perturbations to the...
Source: http://arxiv.org/abs/1007.2647v2
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Jul 20, 2013 Ion I. Cotaescu; Cosmin Crucean
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We construct the de Sitter QED in Coulomb gauge assuming that the quantum modes are prepared by a global apparatus which is able to determine a stable and invariant vacuum state, independent on the local coordinates. Then we proceed in traditional manner postulating the appropriate equal-time commutators and anti-commutators of the interacting fields and deriving the perturbation expansion of the scattering operator. In this approach the $in -out$ transitions amplitudes, measured by the same...
Source: http://arxiv.org/abs/1007.4647v4
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Jul 20, 2013 Jaroslaw Byrka; MohammadReza Ghodsi; Aravind Srinivasan
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We study LP-rounding approximation algorithms for metric uncapacitated facility-location problems. We first give a new analysis for the algorithm of Chudak and Shmoys, which differs from the analysis of Byrka and Aardal in that now we do not need any bound based on the solution to the dual LP program. Besides obtaining the optimal bifactor approximation as do Byrka and Aardal, we can now also show that the algorithm with scaling parameter equaling 1.58 is, in fact, an 1.58-approximation...
Source: http://arxiv.org/abs/1007.3611v2
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Jul 20, 2013 Robert Thijs Kozma; Jenő Szirmai
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The goal of this paper to determine the optimal horoball packing arrangements and their densities for all four fully asymptotic Coxeter tilings (Coxeter honeycombs) in hyperbolic 3-space $\mathbb{H}^3$. Centers of horoballs are required to lie at vertices of the regular polyhedral cells constituting the tiling. We allow horoballs of different types at the various vertices. Our results are derived through a generalization of the projective methodology for hyperbolic spaces. The main result...
Source: http://arxiv.org/abs/1007.0722v2
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Jul 20, 2013 Aleksey Kostenko; Alexander Sakhnovich; Gerald Teschl
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We develop Weyl-Titchmarsh theory for Schroedinger operators with strongly singular potentials such as perturbed spherical Schroedinger operators (also known as Bessel operators). It is known that in such situations one can still define a corresponding singular Weyl m-function and it was recently shown that there is also an associated spectral transformation. Here we will give a general criterion when the singular Weyl function can be analytically extended to the upper half plane. We will...
Source: http://arxiv.org/abs/1007.0136v3
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Consider the mapping class group $\Mod_{g,p}$ of a surface $\Sigma_{g,p}$ of genus $g$ with $p$ punctures, and a finite collection $\{f_1,...,f_k\}$ of mapping classes, each of which is either a Dehn twist about a simple closed curve or a pseudo-Anosov homeomorphism supported on a connected subsurface. In this paper we prove that for all sufficiently large $N$, the mapping classes $\{f_1^N,...,f_k^N\}$ generate a right-angled Artin group. The right-angled Artin group which they generate can be...
Source: http://arxiv.org/abs/1007.1118v4
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Jul 20, 2013 Holger Dette; Jan Nagel
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In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vectors...
Source: http://arxiv.org/abs/1007.3369v2
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Jul 20, 2013 Pranav Dandekar; Ashish Goel; Ramesh Govindan; Ian Post
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Credit networks represent a way of modeling trust between entities in a network. Nodes in the network print their own currency and trust each other for a certain amount of each other's currency. This allows the network to serve as a decentralized payment infrastructure---arbitrary payments can be routed through the network by passing IOUs between trusting nodes in their respective currencies---and obviates the need for a common currency. Nodes can repeatedly transact with each other and pay for...
Source: http://arxiv.org/abs/1007.0515v3
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Jul 20, 2013 E. D. Mun; S. Jia; S. L. Bud'ko; P. C. Canfield
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The thermoelectric power, $S(T)$, of the heavy fermions YbT$_{2}$Zn$_{20}$ ($T$ = Fe, Ru, Os, Ir, Rh, and Co) has been measured to characterize their strong electronic correlations. A large, negative, local minimum in $S(T)$ with approximately -70 $\mu$V/K is found for all compounds. From the observed local minimum, the energy scales associated with both the Kondo temperature and the crystalline electric field splitting are deduced and compared to previous specific heat measurements. At low...
Source: http://arxiv.org/abs/1007.4244v2
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Jul 20, 2013 Linda M. Carpenter
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In an attempt to maximize General Gauge Mediated parameter space, I propose simple models in which gauginos and scalars are generated from disconnected mechanisms. In my models Dirac gauginos are generated through the supersoft mechanism, while independent R-symmetric scalar masses are generated through operators involving non-zero messenger supertrace. I propose several new methods for generating negative messenger supertraces which result in viable positive mass squareds for MSSM scalars. The...
Source: http://arxiv.org/abs/1007.0017v2
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Jul 20, 2013 D. Dikranjan; Gábor Lukács
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In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of compact connected abelian groups C and subgroups A such that A \cong q(G) and C \cong q(\widetilde G). As a consequence, we show that for every positive integer n or n=\omega, there exist plenty of abelian pseudocompact perfectly minimal n-dimensional groups...
Source: http://arxiv.org/abs/1007.4285v3
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Jul 20, 2013 Leonel Robert
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A classification result is obtained for the C*-algebras that are (stably isomorphic to) inductive limits of 1-dimensional noncommutative CW complexes with trivial $K_1$-group. The classifying functor Cu is defined in terms of the Cuntz semigroup of the unitization of the algebra. For the simple C*-algebras covered by the classification, Cu reduces to the ordered $K_0$-group, the cone of traces, and the pairing between them. As an application of the classification, it is shown that the crossed...
Source: http://arxiv.org/abs/1007.1964v3
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Jul 20, 2013 Shimon Garti
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Let V be a finite set of points in the plane, not contained in a line. Assume |V| = n is an odd number, and |L \cap V| \leq 3 for every line L which is spanned by V. We prove that every simple line L_{a,b} in V creates a simple wedge (i.e., a triple {a, b, c} \subseteq V such that L_{a,b} and L_{a,c} are simple lines). We also show that both restrictions on V (namely |V| is odd and |L \cap V| \leq 3) are needed. We conjecture, further, that if |V | = n is an odd number then V contains a simple...
Source: http://arxiv.org/abs/1007.1375v2
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We study a random sampling technique to approximate integrals $\int_{[0,1]^s}f(\mathbf{x})\,\mathrm{d}\mathbf{x}$ by averaging the function at some sampling points. We focus on cases where the integrand is smooth, which is a problem which occurs in statistics. The convergence rate of the approximation error depends on the smoothness of the function $f$ and the sampling technique. For instance, Monte Carlo (MC) sampling yields a convergence of the root mean square error (RMSE) of order...
Source: http://arxiv.org/abs/1007.0842v4
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Jul 20, 2013 Alexander Kirillov Jr; Jaimal Thind
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Let \Gamma be a Dynkin diagram of type A,D,E and let R denote the corresponding root system. In this paper we give a categorical construction of R from \Gamma. Instead of choosing an orientation of \Gamma and studying representations of the associated quiver, we study representations of a canonical quiver \Gammahat associated to \Gamma . This construction is very closely related to the preprojective algebra of \Gamma . In particular, the construction gives a certain periodicity result about the...
Source: http://arxiv.org/abs/1007.2623v3
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Jul 20, 2013 Lorenzo Di Biagio; Elisa Postinghel
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A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.
Source: http://arxiv.org/abs/1007.4891v2
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Jul 20, 2013 Alessandra Faggionato; Fabio Martinelli; Cyril Roberto; Cristina Toninelli
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Motivated by several models introduced in the physics literature to study the nonequilibrium coarsening dynamics of one-dimensional systems, we consider a large class of "hierarchical coalescence processes" (HCP). An HCP consists of an infinite sequence of coalescence processes ${\xi^{(n)}(\cdot)}_{n\ge1}$: each process occurs in a different "epoch" (indexed by $n$) and evolves for an infinite time, while the evolution in subsequent epochs are linked in such a way that the...
Source: http://arxiv.org/abs/1007.0109v2
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Jul 20, 2013 Sophie Laruelle; Gilles Pagès
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The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation when the "innovations" satisfy some "light" averaging properties in the presence of a pathwise Lyapunov function. These averaging assumptions allow us to unify apparently remote frameworks where the innovations are simulated (possibly deterministic like in Quasi-Monte Carlo simulation) or exogenous (like market data) with ergodic properties. We propose several fields of...
Source: http://arxiv.org/abs/1007.3578v4
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Jul 20, 2013 A. J. Cuesta; T. E. Jeltema; F. Zandanel; S. Profumo; F. Prada; G. Yepes; A. Klypin; Y. Hoffman; S. Gottloeber; J. Primack; M. A. Sanchez-Conde; C. Pfrommer
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We present all-sky simulated Fermi maps of gamma-rays from dark matter decay and annihilation in the Local Universe. The dark matter distribution is obtained from a constrained cosmological simulation of the neighboring large-scale structure provided by the CLUES project. The dark matter fields of density and density squared are then taken as an input for the Fermi observation simulation tool to predict the gamma-ray photon counts that Fermi would detect in 5 years of all-sky survey for given...
Source: http://arxiv.org/abs/1007.3469v3
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Jul 20, 2013 Sahazada Aziz; Buddhadeb Ghosh
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We study electroweak baryogenesis within the framework of the littlest Higgs model with T parity. This model has shown characteristics of a strong first-order electroweak phase transition, which is conducive to baryogenesis in the early Universe. In the T parity symmetric theory, there are two gauge sectors, viz., the T-even and the T-odd ones. We observe that the effect of the T-parity symmetric interactions between the T-odd and the T-even gauge bosons on gauge-higgs energy functional is...
Source: http://arxiv.org/abs/1007.0485v4
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Jul 20, 2013 Ioannis Souldatos
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This is part I of a study on cardinals that are characterizable by Scott sentences. Building on [3], [6] and [1] we study which cardinals are characterizable by a Scott sentence $\phi$, in the sense that $\phi$ characterizes $\kappa$, if $\phi$ has a model of size $\kappa$, but no models of size $\kappa^+$. We show that the set of cardinals that are characterized by a Scott sentence is closed under successors, countable unions and countable products (cf. theorems 2.3, 3.4, and corollary 3.6)....
Source: http://arxiv.org/abs/1007.2426v3
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Jul 20, 2013 Serge Cantat; Stéphane Lamy
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Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and algebraic geometry to produce elements in the Cremona group that generate non trivial normal subgroups.
Source: http://arxiv.org/abs/1007.0895v2
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Jul 20, 2013 Jean-Pierre Fouque; Sebastian Jaimungal; Matthew Lorig
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Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European options, up-and-out options, double-barrier knock-out options, and options which pay a rebate upon hitting a boundary. For European options, our method is shown to produce option...
Source: http://arxiv.org/abs/1007.4361v2
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Jul 20, 2013 Yossi Azar; Iftah Gamzu
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We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone submodular set function $f: 2^{[n]} \rightarrow \bbR_+$. The objective is to find a set $S$ that maximizes $f(S)$ subject to $A x_{S} \leq b$, where $x_S$ stands for the characteristic vector of the set $S$. A well-studied special case of this problem is when $f$ is...
Source: http://arxiv.org/abs/1007.3604v2