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Let $m$ and $k \geq 2$ be positive integers. We show that polynomial $P = (1+x)^m(1+x^k)$ is strongly unimodal (frequently known as {\it log concave\/}) if and only if $m \geq k^2 -3$; this is also the criterion for $P$ to be merely unimodal (that is, for $P$ of this form, unimodality implies strong unimodality).{ }In section 2, we investigate an analogous question, concerning the property $\EE$ of functions $f$ analytic on a neighbourhood of the unit circle [H2], and show that the corresponding minimal $m$ is rather surprisingly of order $k^4$.
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arxiv:1102.2961
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In the secure network coding for multicasting, there is loss of information rate due to inclusion of random bits at the source node. We show a method to eliminate that loss of information rate by using multiple statistically independent messages to be kept secret from an eavesdropper. The proposed scheme is an adaptation of Yamamoto et al.'s secure multiplex coding to the secure network coding.
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arxiv:1102.3002
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We discuss aspects of the holographic description of crunching AdS cosmologies. We argue that crunching FRW models with hyperbolic spatial sections are dual to semiclassical condensates in deformed de Sitter CFTs. De Sitter-invariant condensates with a sharply defined energy scale are induced by effective negative-definite relevant or marginal operators, which may or may not destabilize the CFT. We find this result by explicitly constructing a `complementarity map' for this model, given by a conformal transformation of the de Sitter CFT into a static time-frame, which reveals the crunch as an infinite potential-energy fall in finite time. We show that, quite generically, the crunch is associated to a finite mass black hole if the de Sitter O(d,1)-invariance is an accidental IR symmetry, broken down to U(1)xO(d) in the UV. Any such regularization cuts off the eternity of de Sitter space-time. Equivalently, the dimension of the Hilbert space propagating into the crunch is finite only when de Sitter is not eternal.
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arxiv:1102.3015
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We show that backflow correlations in the variational wave function for the Hubbard model greatly improve the previous results given by the Slater-Jastrow state, usually considered in this context. We provide evidence that, within this approach, it is possible to have a satisfactory connection with the strong-coupling regime. Moreover, we show that, for the Hubbard model on the lattice, backflow correlations are essentially short range, inducing an effective attraction between empty (holons) and doubly occupied sites (doublons). In presence of frustration, we report the evidence that the metal to Mott-insulator transition is marked by a discontinuity of the double occupancy, together with a similar discontinuity of the kinetic term that does not change the number of holons and doublons, while the other kinetic terms are continuous across the transition. Finally, we show the estimation of the charge gap, obtained by particle-hole excitations {\it \`a la Feynman} over the ground-state wave function.
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arxiv:1102.3017
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The apparently unusual behaviour of the TSI during the most recent minimum of solar activity has been interpreted as evidence against solar surface magnetism as the main driver of the secular change in the TSI. We test claims that the evolution of the solar surface magnetic field does not reproduce the observed TSI in cycle 23. We use sensitive, 60-minute averaged MDI magnetograms and quasi-simultaneous continuum images as an input to our SATIRE-S model and calculate the TSI variation over cycle 23, sampled roughly twice-monthly. The computed TSI is then compared to the PMOD composite of TSI measurements and to the data from two individual instruments, SORCE/TIM and UARS/ACRIM II, that monitored the TSI during the declining phase of cycle 23 and over the previous minimum in 1996, respectively. Excellent agreement is found between the trends shown by the model and almost all sets of measurements. The only exception is the early, i.e. 1996 to 1998, PMOD data. Whereas the agreement between the model and the PMOD composite over the period 1999-2009 is almost perfect, the modelled TSI shows a steeper increase between 1996 and 1999 than implied by the PMOD composite. On the other hand, the steeper trend in the model agrees remarkably well with the ACRIM II data. A closer look at the VIRGO data, that make the basis of the PMOD composite after 1996, reveals that only one of the two VIRGO instruments, the PMO6V, shows the shallower trend present in the composite, whereas the DIARAD measurements indicate a steeper trend. We conclude that (1) the sensitivity changes of the PMO6V radiometers within VIRGO during the first two years have very likely not been correctly evaluated, and that (2) the TSI variations over cycle 23 and the change in the TSI levels between the minima in 1996 and 2008 are consistent with the solar surface magnetism mechanism.
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arxiv:1102.3077
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This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous and anisotropic smoothness classes that contain Besov classes. Highlighting the interest of such a result in statistics, adaptation in the minimax sense to both inhomogeneity and anisotropy of a related multivariate density estimator is proved. Besides, that estimation procedure can be implemented with a computational complexity simply linear in the sample size.
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arxiv:1102.3108
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The capacity region of the 3-user Gaussian Interference Channel (GIC) with mixed strong-very strong interference was established in \cite{ChS}. The mixed strong-very strong interference conditions considered in \cite{ChS} correspond to the case where, at each receiver, one of the interfering signals is strong and the other is very strong. In this paper, we derive the capacity region of $K$-user $(K\geq 3)$ Discrete Memoryless Interference Channels (DMICs) with a mixed strong-very strong interference. This corresponds to the case where, at each receiver one of the interfering signals is strong and the other $(K-2)$ interfering signals are very strong. This includes, as a special case, the 3-user DMIC with mixed strong-very strong interference. The proof is specialized to the 3-user GIC case and hence an alternative simpler derivation for the capacity region of the 3-user GIC with mixed strong-very strong interference is provided.
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arxiv:1102.3140
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Multi-valued functions are common in computable analysis (built upon the Type 2 Theory of Effectivity), and have made an appearance in complexity theory under the moniker search problems leading to complexity classes such as PPAD and PLS being studied. However, a systematic investigation of the resulting degree structures has only been initiated in the former situation so far (the Weihrauch-degrees). A more general understanding is possible, if the category-theoretic properties of multi-valued functions are taken into account. In the present paper, the category-theoretic framework is established, and it is demonstrated that many-one degrees of multi-valued functions form a distributive lattice under very general conditions, regardless of the actual reducibility notions used (e.g. Cook, Karp, Weihrauch). Beyond this, an abundance of open questions arises. Some classic results for reductions between functions carry over to multi-valued functions, but others do not. The basic theme here again depends on category-theoretic differences between functions and multi-valued functions.
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arxiv:1102.3151
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In this work we study zero vs. epsilon-error capacity in network coding instances. For multicast network coding it is well known that all rates that can be delivered with arbitrarily small error probability can also be delivered with zero error probability; that is, the epsilon-error multicast capacity region and zero-error multicast capacity region are identical. For general network coding instances in which all sources originate at the same source node, Chan and Grant recently showed [ISIT 2010] that, again, epsilon-error communication has no rate advantage over zero-error communication. We start by revisiting the setting of co-located sources, where we present an alternative proof to that given by Chan and Grant. While the new proof is based on similar core ideas, our constructive strategy complements the previous argument.We then extend our results to the setting of index coding, which is a special and representative form of network coding that encapsulates the "source coding with side information" problem. Finally, we consider the "edge removal" problem (recently studied by Jalali, Effros, and Ho in [Allerton 2010] and [ITA 2011]) that aims to quantify the loss in capacity associated with removing a single edge from a given network. Using our proof for co-located sources, we tie the "zero vs. epsilon-error" problem in general network coding instances with the "edge removal" problem. Loosely speaking, we show that the two problem are equivalent.
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arxiv:1102.3162
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We present the first polynomial time approximation algorithm for computing shortest paths in weighted three-dimensional domains. Given a polyhedral domain $\D$, consisting of $n$ tetrahedra with positive weights, and a real number $\eps\in(0,1)$, our algorithm constructs paths in $\D$ from a fixed source vertex to all vertices of $\D$, whose costs are at most $1+\eps$ times the costs of (weighted) shortest paths, in $O(\C(\D)\frac{n}{\eps^{2.5}}\log\frac{n}{\eps}\log^3\frac{1}{\eps})$ time, where $\C(\D)$ is a geometric parameter related to the aspect ratios of tetrahedra. The efficiency of the proposed algorithm is based on an in-depth study of the local behavior of geodesic paths and additive Voronoi diagrams in weighted three-dimensional domains, which are of independent interest. The paper extends the results of Aleksandrov, Maheshwari and Sack [JACM 2005] to three dimensions.
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arxiv:1102.3165
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Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization problem into a noisy channel coding problem. The optimal approximation capacity of this channel controls the appropriate strength of regularization to suppress noise. In simulation experiments, this information theoretic method to determine the optimal rank competes with state-of-the art model selection techniques.
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arxiv:1102.3176
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We investigate the LHC discovery potential of R-parity violating supersymmetric models with a right-handed selectron or smuon as the lightest supersymmetric particle (LSP). These LSPs arise naturally in R-parity violating minimal supergravity models. We classify the hadron collider signatures and perform for the first time within these models a detailed signal over background analysis. We develop an inclusive three-lepton search and give prospects for a discovery at a center-of-mass energy of 7 TeV as well as 14 TeV. There are extensive parameter regions which the LHC can already test with 7 TeV and an integrated luminosity of 1 inverse femtobarn. We also propose a method for the mass reconstruction of the supersymmetric particles within our models at 14 TeV.
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arxiv:1102.3189
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We report the observation and characterization of field emission current from individual single- and few-layer graphene flakes laid on a flat SiO2/Si substrate. Measurements were performed in a scanning electron microscope chamber equipped with nanoprobes, used as electrodes to realize local measurements of the field emission current. We achieved field emission currents up to 1 {\mu}A from the flat part of graphene flakes at applied fields of few hundred V/{\mu}m. We found that emission process is stable over a period of several hours and that it is well described by a Fowler-Nordheim model for currents over 5 orders of magnitude.
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arxiv:1102.3273
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We have investigated the formation and growth of nano sized ripple topography on ZnO thin films by 10 keV O1+ bombardment at impact angles of 80{\degree} and 60{\degree}, varying the ion fluence from 5{times}10^16 to 1{\times}10^18 ions/cm2. At 800 the ripples are oriented along the ion beam direction whereas at 600 it is perpendicular to the ion beam direction. The developed ion induced structures are characterized by Atomic Force Microscopy (AFM) and the alignment, variation of rms roughness, wavelength and correlation length of the structures are discussed with the existing model and basic concept of ion surface interaction.
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arxiv:1102.3309
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A dynamical model is presented for chiral change in DNA molecules. The model is an extension of the conventional elastic model which incorporates the structure of base pairs and uses a spinor representation for the DNA configuration together with a gauge principle. Motivated by a recent experiment reporting chiral transitions between right-handed B-DNA and left-handed Z-DNA [M. Lee, et. al., Proc. Natl. Acad. Sci. (USA) 107, 4985 (2010)], we analyze the free energy for the particular case of linear DNA with an externally applied torque. The model shows that there exists, at low temperature, a rapid structural change depending on the torque exerted on the DNA, which causes switching in B and Z domain sizes. This can explain the frequent switches of DNA extension observed in experiments.
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arxiv:1102.3313
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On the manifold $\Met(M)$ of all Riemannian metrics on a compact manifold $M$ one can consider the natural $L^2$-metric as described first by \cite{Ebin70}. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition when Ricci flow is a gradient flow for one of these metrics.
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arxiv:1102.3347
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We study the fine structure of the sets of involutions avoiding either 4312 (I(4321)) or 3412 (I(3412)), connecting the point of view of the decomposition theorems with the one of the associated labelled Motzkin paths. The algebraic generating function of the simple involutions in I(4321) is given, together with other generating functions, while the set I(3412) is shown containing no simple involutions of length n>2. The reverse-complement bijection maintains the fine structures of I(4321) and trivially of I(3412).
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arxiv:1102.3359
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The aim of this paper is to describe the origin, first solutions, further progress, the state of art, and a new ansatz in the treatment of a problem dating back to the 1920's, which still has not found a satisfactory solution and deserves to be better known.
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arxiv:1102.3383
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Linear Programming (LP) decoding is emerging as an attractive alternative to decode Low-Density Parity-Check (LDPC) codes. However, the earliest LP decoders proposed for binary and nonbinary LDPC codes are not suitable for use at moderate and large code lengths. To overcome this problem, Vontobel et al. developed an iterative Low-Complexity LP (LCLP) decoding algorithm for binary LDPC codes. The variable and check node calculations of binary LCLP decoding algorithm are related to those of binary Belief Propagation (BP). The present authors generalized this work to derive an iterative LCLP decoding algorithm for nonbinary linear codes. Contrary to binary LCLP, the variable and check node calculations of this algorithm are in general different from that of nonbinary BP. The overall complexity of nonbinary LCLP decoding is linear in block length; however the complexity of its check node calculations is exponential in the check node degree. In this paper, we propose a modified BCJR algorithm for efficient check node processing in the nonbinary LCLP decoding algorithm. The proposed algorithm has complexity linear in the check node degree. We also introduce an alternative state metric to improve the run time of the proposed algorithm. Simulation results are presented for $(504, 252)$ and $(1008, 504)$ nonbinary LDPC codes over $\mathbb{Z}_4$.
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arxiv:1102.3390
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According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters providing the right sides of the differential equations are analytic in the variables, the time, and the parameters. We describe how these Taylor expansions may be obtained, to any desired order, by integration of what we call the complete variational equations. As illustrated in a Duffing equation stroboscopic map example, these Taylor expansions, truncated at an appropriate order thereby providing polynomial approximations, can well reproduce the behavior (including infinite period doubling cascades and strange attractors) of the solutions of the underlying differential equations.
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arxiv:1102.3394
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We fabricate nanoscale lamps which have a filament consisting of a single multiwalled carbon nanotube. After determining the nanotube geometry with a transmission electron microscope, we use Joule heating to bring the filament to incandescence, with peak temperatures in excess of 2000 K. We image the thermal light in both polarizations simultaneously as a function of wavelength and input electrical power. The observed degree of polarization is typically of the order of 75%, a magnitude predicted by a Mie model of the filament that assigns graphene's optical conductance $\pi e^2/2 h$ to each nanotube wall.
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arxiv:1102.3484
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Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. Families of genetic (4*4)- and (8*8)-matrices show unexpected connections of the genetic system with Walsh functions and Hadamard matrices, which are known in theory of noise-immunity coding, digital communication and digital holography. Dyadic-shift decompositions of such genetic matrices lead to sets of sparse matrices. Each of these sets is closed in relation to multiplication and defines relevant algebra of hypercomplex numbers. It is shown that genetic Hadamard matrices are identical to matrix representations of Hamilton quaternions and its complexification in the case of unit coordinates. The diversity of known dialects of the genetic code is analyzed from the viewpoint of the genetic algebras. An algebraic analogy with Punnett squares for inherited traits is shown. Our results are used in analyzing genetic phenomena. The statement about existence of the geno-logic code in DNA and epigenetics on the base of the spectral logic of systems of Boolean functions is put forward. Our results show promising ways to develop algebraic-logical biology, in particular, in connection with the logic holography on Walsh functions.
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arxiv:1102.3596
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We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice Zd are asymptotic to 2de as the dimension goes to infinity, and that their critical one-point functions converge to e. Similar results are obtained in dimensions d>8 in the limit of increasingly spread-out models; in this case the result for the growth constant is a special case of previous results of M. Penrose. The proof is elementary, once we apply previous results of T. Hara and G. Slade obtained using the lace expansion.
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arxiv:1102.3682
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We critically examine uncertainties in parton distribution functions (PDFs) at large x arising from nuclear effects in deuterium F2 structure function data. Within a global PDF analysis, we assess the impact on the PDFs from uncertainties in the deuteron wave function at short distances and nucleon off-shell effects, the use of relativistic kinematics, as well as the use of less a restrictive parametrization of the d/u ratio. We find that in particular the d-quark and gluon PDFs vary significantly with the choice of nuclear model. We highlight the impact of these uncertainties on the determination of the neutron structure function, and on W boson production and parton luminosity at the Tevatron and the LHC. Finally, we discuss prospects for new measurements sensitive to the d-quark and gluon distributions but insensitive to nuclear corrections.
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arxiv:1102.3686
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We investigate the evolution of a thin viscous disc surrounding magnetic star, including the spindown of the star by the magnetic torques it exerts on the disc. The transition from an accreting to a non-accreting state, and the change of the magnetic torque across the corotation radius are included in a generic way, the widths of the transition taken in the range suggested by numerical simulations. In addition to the standard accreting state, two more are found. An accreting state can develop into a 'dead' disc state, with inner edge well outside corotation. More often, a 'trapped' state develops, in which the inner disc edge stays close to corotation even at very low accretion rates. The long-term evolution of these two states is different. In the dead state the star spins down incompletely, retaining much of its initial spin. In the trapped state the star asymptotically can spin down to arbitarily low rates, its angular momentum transferred to the disc. We identify these outcomes with respectively the rapidly rotating and the very slowly rotating classes of Ap stars and magnetic white dwarfs.
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arxiv:1102.3697
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We study the spin diffusion in a two-dimensional electron gas at the interface of oxide heterostructure LaAlO$_3$/SrTiO$_3$ grown on multiferroic TbMnO$_3$ at 15 K by means of the kinetic spin Bloch equation approach. The spiral magnetic moments of Mn$^{3+}$ in TbMnO$_3$ interact with the diffusing spins at the LaAlO$_3$/SrTiO$_3$ interface via the Heisenberg exchange interaction. It is demonstrated that the spin diffusion length is always finite, despite the polarization direction of the injected spins. Our study also reveals the important role played by the Coulomb scattering, which can effectively suppress the spin diffusion.
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arxiv:1102.3757
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For N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives, a method for summation of all Feynman diagrams defining the beta-function is presented. Using this method we prove that the beta-function is given by an integral of a total derivative, which can be easily calculated. It is shown that surviving terms give the exact NSVZ beta-function. The results are compared with the explicit three-loop calculation.
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arxiv:1102.3772
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Using highly monochromatic synchrotron X-rays in the energy range from 10.5 keV to 100 keV the temperature dependence of nonproportionality and energy resolution of LaBr3 scintillators doped with 5% Ce3+ were studied at 80K, 295K, and 450K. Improvement of the proportionality and better energy resolution was observed on lowering the temperature. This effect suggests that the already outstanding energy resolution of LaBr3:Ce can be improved even further. It also may provide new clues to better understand the processes that cause nonproportionality of inorganic scintillator response.
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arxiv:1102.3794
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Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process.
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arxiv:1102.3838
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We re-examine the ordering behavior of a one-dimensional fluid of freely rotating hard needles, where the centers of mass of the particles are restricted to a line. Analytical equations are obtained for the equation of state, order parameter and orientational correlation functions using the transfer-matrix method if some simplifying assumptions are applied for either the orientational freedom or the contact distance between two needles. The two-state Zwanzig model accounts for the orientational ordering, but it produces unphysical pressure at high densities and there is no orientational correlation. The four-state Zwanzig model gives reasonable results for orientational correlation function, but the pressure is still poorly represented at high densities. In the continuum limit, apart from the orientational correlation length it is managed to reproduce all relevant bulk properties of the hard needles using an approximate formula for the contact distance. The results show that the orientational correlation length diverges at zero and infinite pressures. The high density behavior of needles is not resolved.
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arxiv:1102.3884
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We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-norm, and present reconstruction guarantees based on existing analysis on the Rademacher complexity of the unit balls of these norms. We show how these are superior in several ways to recently published guarantees based on specialized analysis.
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arxiv:1102.3923
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The risk minimizing problem $\mathbf{E}[l((H-X_T^{x,\pi})^{+})]\overset{\pi}{\longrightarrow}\min$ in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for $l(x)=x$ and $l(x)=x^p$, with $p>1$ for digital, quantos, outperformance and spread options are derived.
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arxiv:1102.3928
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The coefficients determining the dilepton decay angular distribution of vector particles obey certain positivity constraints and a rotation-invariant identity. These relations are a direct consequence of the covariance properties of angular momentum eigenstates and are independent of the production mechanism. The Lam-Tung relation can be derived as a particular case, simply recognizing that the Drell-Yan dilepton is always produced transversely polarized with respect to one or more quantization axes. The dilepton angular distribution continues to be characterized by a frame-independent identity also when the Lam-Tung relation is violated. Moreover, the violation can be easily characterized by measuring a one-dimensional distribution depending on one shape coefficient.
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arxiv:1102.3946
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In the present study we find that nuclei having double width do not emit free nucleons for a long period of time necessary to study heavy-ion collisions. Also, the ground state properties of all the nuclei are also described well. In the low mass region, the obtained nuclei are less bound but stable. Heavy mass nuclei have proper binding energy and are stable
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arxiv:1102.3965
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In this talk we report on selected topics on hadrons in nuclei. The first topic is the renormalization of the width of the $\Lambda(1520)$ in a nuclear medium. This is followed by a short update of the situation of the $\omega$ in the medium. The investigation of the properties of $\bar{K}$ in the nuclear medium from the study of the $(K_{flight},p)$ reaction is also addressed, as well as properties of X,Y,Z charmed and hidden charm resonances in a nuclear medium. Finally we address the novel issue of multimeson states.
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arxiv:1102.3981
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We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space of square integrable functions and the Hilbert space of almost periodic functions. Scalar product for different Hilbert spaces defined at the intersection of these spaces, which contains only one zero element. Therefore, the Fourier integral is not defined in the Hilbert space of square integrable functions with nonzero norm.
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arxiv:1102.3983
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We discuss one important aspect of Waldmeier effect which says that the stronger cycles rise rapidly than weaker cycles. We studied four different data set of solar activity indices, and find strong linear correlation between rise rates and amplitudes of solar activity. We study this effect theoretically by introducing suitable stochastic fluctuations in our regular solar dynamo model.
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arxiv:1102.4052
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In this paper, we investigate some electrically charged magnetic solutions of the SU(2) Yang-Mills-Higgs field theory in the net zero topological charge sector. We only examine the case when the Higgs field vanishes at two points along the z-axis and when the Higgs field vanishes along a ring with the z-axis as its symmetry axis. We study the possible electric charges the dyons can carry in relation to the electric-magnetic charge separations and calculate for the finite total energy and magnet dipole moment of these dyons. These stationary dyon solutions do not satisfy the first order Bogomol'nyi equations and are non BPS solutions. They are axially symmetric saddle point solutions and are characterized by the electric charge parameter, $-1<\eta< 1$, which determines the net electric charges of these dyons. These dyon solutions are solved numerically when the magnetic charges are $n$ = 1, 2, 3, 4, and 5; and when the strength of the Higgs field potential is non vanishing with $\lambda=1$. When $\lambda=1$, we found that the net electric charge approaches a finite critical value as $\eta$ approaches $\pm 1$. Hence the electromagnetic charge separation, total energy, and magnet dipole moment of the dyon also approach finite critical value.
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arxiv:1102.4058
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We generalize the hyperplane inequality in dimensions up to 4 to the setting of arbitrary measures in place of the volume. To prove this generalization we establish stability in the affirmative part of the solution to the Busemann-Petty problem asking whether symmetric convex bodies in R^n with smaller (n-1)-dimensional volume of all central hyperplane sections necessarily have smaller n-dimensional volume.
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arxiv:1102.4081
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We prove that special ample line bundles on toric varieties arising from root systems are projectively normal. Here the maximal cones of the fans correspond to the Weyl chambers, and special means that the bundle is torus-equivariant such that the character of the line bundle that corresponds to a maximal Weyl chamber is dominant with respect to that chamber. Moreover, we prove that the associated semigroup rings are quadratic.
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arxiv:1102.4083
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Using special quasirandom structures (SQS's), we perform first-principles calculations studying the metastable bcc NiCu and FeCu alloys which occur in Fe-Cu-Ni alloy steels as precipitated second phase. The mixing enthalpies, density of state, and equilibrium lattice parameters of these alloys are reported. The results show that quasi-chemical approach and vegard rule can well predict the energetic and structural properties of FeCu alloys but fail to yield that of NiCu. The reason rests with the difference of bond energy variation with composition between NiCu and FeCu alloys induced by competition between ferromagnetic and paramagnetic state. Furthermore, the calculated results show that the energetic and structural properties of these alloys can well explain the local composition of the corresponding precipitates in ferrite steels.
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arxiv:1102.4115
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We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z^n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair (sl_{2n}(C), sp_{2n}(C)). This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric Lie algebras. The given actions are inspired by Lusztig's braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP.
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arxiv:1102.4185
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We propose a model of inflation in the framework of brane cosmology driven by background supergravity. Starting from bulk supergravity we construct the inflaton potential on the brane and employ it to investigate for the consequences to inflationary paradigm. To this end, we derive the expressions for the important parameters in brane inflation, which are somewhat different from their counterparts in standard cosmology, using the one loop radiative corrected potential. We further estimate the observable parameters and find them to fit well with recent observational data by confronting with WMAP7 using CAMB. We also analyze the typical energy scale of brane inflation with our model, which resonates well with present estimates from cosmology and standard model of particle physics.
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arxiv:1102.4206
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We report the discovery of a cyclotron resonance scattering feature (CRSF) in the X-ray spectrum of GX 304-1, obtained by RXTE and Suzaku during major outbursts detected by MAXI in 2010. The peak intensity in August reached 600 mCrab in the 2-20 keV band, which is the highest ever observed from this source. The RXTE observations on more than twenty occasions and one Suzaku observation revealed a spectral absorption feature at around 54 keV, which is the first CRSF detection from this source. The estimated strength of surface magnetic field, $4.7 \times 10^{12}$ G, is one of the highest among binary X-ray pulsars from which CRSFs have ever been detected. The RXTE spectra taken during the August outburst also suggest that the CRSF energy changed over 50-54 keV, possibly in a positive correlation with the X-ray flux. The behavior is qualitatively similar to that observed from Her X-1 on long time scales, or from A 0535+26, but different from the negative correlation observed from 4U 0115+63 and X 0331+53.
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arxiv:1102.4232
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We study an ergodic theorem for disjoint C*-dynamical systems, where disjointness here is a noncommutative version of the concept introduced by Furstenberg for classical dynamical systems. This is applied to W*-dynamical systems. We also consider specific examples of disjoint C*-dynamical and W*-dynamical systems, including for actions of other groups than $\mathbb{Z}$. Unique ergodicity and unique ergodicity relative to the fixed point algebra are closely related to disjointness, and are used to give examples of disjoint C*-dynamical systems.
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arxiv:1102.4243
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A family $\mathcal N$ of closed subsets of a topological space $X$ is called a {\em closed $k$-network} if for each open set $U\subset X$ and a compact subset $K\subset U$ there is a finite subfamily $\mathcal F\subset\mathcal N$ with $K\subset\bigcup\F\subset \mathcal N$. A compact space $X$ is called {\em supercompact} if it admits a closed $k$-network $\mathcal N$ which is {\em binary} in the sense that each linked subfamily $\mathcal L\subset\mathcal N$ is centered. A closed $k$-network $\mathcal N$ in a topological group $G$ is {\em invariant} if $xAy\in\mathcal N$ for each $A\in\mathcal N$ and $x,y\in G$. According to a result of Kubi\'s and Turek, each compact (abelian) topological group admits an (invariant) binary closed $k$-network. In this paper we prove that the compact topological groups $S^3$ and $\SO(3)$ admit no invariant binary closed $k$-network.
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arxiv:1102.4328
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Based on the ultraviolet to far-infrared photometry already compiled and presented in a companion paper (Barro et al. 2011a, Paper I), we present a detailed SED analysis of nearly 80,000 IRAC 3.6+4.5 micron selected galaxies in the Extended Groth Strip. We estimate photometric redshifts, stellar masses, and star formation rates separately for each galaxy in this large sample. The catalog includes 76,936 sources with [3.6] < 23.75 (85% completeness level of the IRAC survey) over 0.48 square degrees. The typical photometric redshift accuracy is Delta z/(1+z)=0.034, with a catastrophic outlier fraction of just 2%. We quantify the systematics introduced by the use of different stellar population synthesis libraries and IMFs in the calculation of stellar masses. We find systematic offsets ranging from 0.1 to 0.4 dex, with a typical scatter of 0.3 dex. We also provide UV- and IR-based SFRs for all sample galaxies, based on several sets of dust emission templates and SFR indicators. We evaluate the systematic differences and goodness of the different SFR estimations using the deep FIDEL 70 micron data available in the EGS. Typical random uncertainties of the IR-bases SFRs are a factor of two, with non-negligible systematic effects at z$\gtrsim$1.5 observed when only MIPS 24 micron data is available. All data products (SEDs, postage stamps from imaging data, and different estimations of the photometric redshifts, stellar masses, and SFRs of each galaxy) described in this and the companion paper are publicly available, and they can be accessed through our the web-interface utility Rainbow-navigator
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arxiv:1102.4335
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It has recently been proposed that the strong coupling behaviour of quantum field theories on a non-dynamical black hole background can be described, in the context of the AdS/CFT correspondence, by a competition between two gravity duals: a black funnel and a black droplet. We present here thermal equilibrium solutions which represent such spacetimes, providing the first example where the thermal competition between the gravity duals can be studied. The solutions correspond to a special family of charged AdS C-metrics. We compute the corresponding Euclidean actions and find that the black funnel always dominates the canonical ensemble in our example, meaning that the field theory does not undergo a phase transition.
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arxiv:1102.4337
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Consider a group word w in n letters. For a compact group G, w induces a map G^n \rightarrow G$ and thus a pushforward measure {\mu}_w on G from the Haar measure on G^n. We associate to each word w a 2-dimensional cell complex X(w) and prove in Theorem 2.5 that {\mu}_w is determined by the topology of X(w). The proof makes use of non-abelian cohomology and Nielsen's classification of automorphisms of free groups [Nie24]. Focusing on the case when X(w) is a surface, we rediscover representation-theoretic formulas for {\mu}_w that were derived by Witten in the context of quantum gauge theory [Wit91]. These formulas generalize a result of Erd\H{o}s and Tur\'an on the probability that two random elements of a finite group commute [ET68]. As another corollary, we give an elementary proof that the dimension of an irreducible complex representation of a finite group divides the order of the group; the only ingredients are Schur's lemma, basic counting, and a divisibility argument.
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arxiv:1102.4353
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We examine the topology of the subset of controls taking a given initial state to a given final state in quantum control, where "state" may mean a pure state |\psi>, an ensemble density matrix \rho, or a unitary propagator U(0,T). The analysis consists in showing that the endpoint map acting on control space is a Hurewicz fibration for a large class of affine control systems with vector controls. Exploiting the resulting fibration sequence and the long exact sequence of basepoint-preserving homotopy classes of maps, we show that the indicated subset of controls is homotopy equivalent to the loopspace of the state manifold. This not only allows us to understand the connectedness of "dynamical sets" realized as preimages of subsets of the state space through this endpoint map, but also provides a wealth of additional topological information about such subsets of control space.
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arxiv:1102.4360
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We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical process based on (unobserved) errors. Also, we study a residual empirical process with estimated parameters. Its asymptotic distribution can be used to construct Kolmogorov-Smirnov, Cram\'{e}r-Smirnov-von Mises, or other goodness-of-fit tests. Theoretical results are justified by simulation studies.
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arxiv:1102.4368
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We describe powder and single-crystal inelastic neutron scattering experiments on a spinel-type antiferromagnet GeCo$_2$O$_4$, represented by an effective total angular momentum J_eff = 1/2. Several types of non-dispersive short-range magnetic excitations were discovered. The scattering intensity maps in $\vec{Q}$ space are well reproduced by dynamical structure factor analyses using molecular model Hamiltonians. The results of analyses strongly suggest that the molecular excitations below T_N arise from a hidden molecular-singlet ground state, in which ferromagnetic subunits are antiferromagnetically coupled. The quasielastic excitations above T_N are interpreted as its precursor. A combination of frustration and J_eff = 1/2 might induce these quantum phenomena.
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arxiv:1102.4395
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Three schemes, whose expressions are not too complex, are selected for the numerical integration of a system of stochastic differential equations in the Stratonovich interpretation: the integration methods of Heun, Milstein, and derivative-free Milstein. The strong (path-wise) convergence is studied for each method by comparing the final points after integrating with $2^n$ and $2^{n-1}$ time steps. We also compare the time that the computer takes to carry out the integration with each scheme. Putting both things together, we conclude that, at least for our system, the Heun method is by far the best performing one.
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arxiv:1102.4401
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We consider the integrate-and-fire model of the cardiac pacemaker with delayed pulsatile coupling. Sufficient conditions of synchronization are obtained for identical and non-identical oscillators.
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arxiv:1102.4462
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In this paper, we study the power of Gaussian curvature flow of a compact convex hypersurface and establish its Harnack inequality when the power is negative. In the Harnack inequality, we require that the absolute value of the power is strictly positive and strictly less than the inverse of the dimension of the hypersurface.
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arxiv:1102.4507
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We show the triviality of representations of the mapping class group of a genus $g$ surface in $GL(n,C), Diff(S^2)$ and $Homeo(T^2)$ when appropriate restrictions on the genus $g$ and the size of $n$ hold. For example, if $S_g$ is a surface of finite type and $\phi : MCG(S_g) \to GL(n,C)$ is a homomorphism, then $\phi$ is trivial provided the genus $g \ge 3$ and $n < 2g$. We also show that if $S_g$ is a closed surface with genus $g \ge 7$, then every homomorphism $\phi: MCG(S_g) \to Diff(S^2)$ is trivial and that if $g \ge 3$, then every homomorphism $\phi: MCG(S_g) \to Homeo(T^2)$ is trivial.
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arxiv:1102.4584
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We discuss $p$-variation regularity of real-valued functions defined on $[0,T]^2$, based on rectangular increments. When $p>1$, there are two slightly different notions of $p$-variation; both of which are useful in the context of Gaussian rough paths. Unfortunately, these concepts were blurred in previous works; the purpose of this note is to show that the aforementioned notions of $p$-variations are "$\epsilon$-close". In particular, all arguments relevant for Gaussian rough paths go through with minor notational changes.
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arxiv:1102.4587
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The aim of illocutionary logic is to explain how context can affect the meaning of certain special kinds of performative utterances. Recall that performative utterances are understood as follows: a speaker performs the illocutionary act (e.g. act of assertion, of conjecture, of promise) with the illocutionary force (resp. assertion, conjecture, promise) named by an appropriate performative verb in the way of representing himself as performing that act. In the paper I proposed many-valued interpretation of illocutionary forces understood as modal operators. As a result, I built up a non-Archimedean valued logic for formalizing illocutionary acts. A formal many-valued approach to illocutionary logic was offered for the first time.
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arxiv:1102.4636
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An accelerated particle sees the Minkowski vacuum as thermally excited, which is called the Unruh effect. Due to an interaction with the thermal bath, the particle moves stochastically like the Brownian motion in a heat bath. It has been discussed that the accelerated charged particle may emit extra radiation (the Unruh radiation) besides the Larmor radiation, and experiments are under planning to detect such radiation by using ultrahigh intensity lasers. There are, however, counterarguments that the radiation is canceled by an interference effect between the vacuum fluctuation and the radiation from the fluctuating motion. In this reports, we review our recent analysis on the issue of the Unruh radiation. In this report, we particularly consider the thermalization of an accelerated particle in the scalar QED, and derive the relaxation time of the thermalization.
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arxiv:1102.4671
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We propose a type of elastic metamaterial comprising fluid-solid composite inclusions which can possess negative shear modulus and negative mass density over a large frequency region. Such a solid metamaterial has a unique elastic property that only transverse waves can propagate with a negative dispersion while longitudinal waves are forbidden. This leads to many interesting phenomena such as negative refraction, which is demonstrated by using a wedge sample, and a significant amount of mode conversion from transverse waves to longitudinal waves that cannot occur on the interface of two natural solids.
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arxiv:1102.4679
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Prior to the invention of holography or lasers, Bragg's X-ray microscope opened the door to optical computation in short-wavelength studies using spatially coherent visible light, including phase retrieval methods. This optical approach lost ground to semiconductor detection and digital computing in the 1960s. Since then, visible optics including spatial light modulators (SLMs), array detectors and femtosecond lasers have become widely available, routinely allowing versatile and computer-interfaced imposition of optical phase, molecular coherent control, and detection. Today, high brilliance X-ray sources begin to offer opportunities for atomic resolution and ultrafast pump-probe studies. Correspondingly, this work considers an overlooked aspect of Bragg's X-ray microscope - the incoherent ionizing radiation to coherent visible (IICV) conversion that is a necessary prerequisite for coherent optical computations. Technologies are suggested that can accomplish this conversion. Approaches to holographic data storage of short wavelength scattered radiation data, and phase retrieval that incorporates optical procedures, are motivated.
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arxiv:1102.4680
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We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous R\"ossler systems reveal that intermediate, partially coherent states represent characteristic spatio-temporal patterns at the transition from coherence to incoherence.
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arxiv:1102.4709
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We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.
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arxiv:1102.4751
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We describe a straightforward, automated line tracking method to visualize within optical resolution the contour of linear macromolecules as they rearrange shape as a function of time by Brownian diffusion and under external fields such as electrophoresis. Three sequential stages of analysis underpin this method: first, "feature finding" to discriminate signal from noise; second, "line tracking" to approximate those shapes as lines; third, "temporal consistency check" to discriminate reasonable from unreasonable fitted conformations in the time domain. The automated nature of this data analysis makes it straightforward to accumulate vast quantities of data while excluding the unreliable parts of it. We implement the analysis on fluorescence images of lambda-DNA molecules in agarose gel to demonstrate its capability to produce large datasets for subsequent statistical analysis.
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arxiv:1102.4770
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Sterile massive neutrinos are a natural extension of the Standard Model of elementary particles. The energy density of the extra sterile massive states affects cosmological measurements in an analogous way to that of active neutrino species. We perform here an analysis of current cosmological data and derive bounds on the masses of the active and the sterile neutrino states as well as on the number of sterile states. The so-called (3+2) models with three sub-eV active massive neutrinos plus two sub-eV massive sterile species is well within the 95% CL allowed regions when considering cosmological data only. If the two extra sterile states have thermal abundances at decoupling, Big Bang Nucleosynthesis bounds compromise the viability of (3+2) models. Forecasts from future cosmological data on the active and sterile neutrino parameters are also presented. Independent measurements of the neutrino mass from tritium beta decay experiments and of the Hubble constant could shed light on sub-eV massive sterile neutrino scenarios.
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arxiv:1102.4774
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The semiconductor-insulator phase transition of the single-layer manganite La0.5Sr1.5MnO4 has been studied by means of high resolution synchrotron x-ray powder diffraction and resonant x-ray scattering at the Mn K edge. We conclude that a concomitant structural transition from tetragonal I4/mmm to orthorhombic Cmcm phases drives this electronic transition. A detailed symmetry-mode analysis reveals that condensation of three soft modes -Delta_2(B2u), X1+(B2u) and X1+(A)- acting on the oxygen atoms accounts for the structural transformation. The Delta_2 mode leads to a pseudo Jahn-Teller distortion (in the orthorhombic bc-plane only) on one Mn site (Mn1) whereas the two X1+ modes produce an overall contraction of the other Mn site (Mn2) and expansion of the Mn1 one. The X1+ modes are responsible for the tetragonal superlattice (1/2,1/2,0)-type reflections in agreement with a checkerboard ordering of two different Mn sites. A strong enhancement of the scattered intensity has been observed for these superlattice reflections close to the Mn K edge, which could be ascribed to some degree of charge disproportion between the two Mn sites of about 0.15 electrons. We also found that the local geometrical anisotropy of the Mn1 atoms and its ordering originated by the condensed Delta_2 mode alone perfectly explains the resonant scattering of forbidden (1/4,1/4,0)-type reflections without invoking any orbital ordering.
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arxiv:1102.4787
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At large baryon number density, it is likely that the ground state of QCD is a color-flavor-locked phase with a K0 condensate. The CFL+K0 phase is known to support superconducting vortex strings, and it has been previously suggested that it may also support vortons, which are superconducting vortex rings. We reexamine the question of the stability of vortons, taking into account electromagnetic effects, which make leading-order contributions to vorton dynamics but were not investigated in previous work. We find that current-carrying and electrically charged vortons can be stabilized either by their angular momentum, by Coulomb repulsion, or by a combination of both effects.
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arxiv:1102.4795
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The Bose-Hubbard model is well-defined description of a Bose solid which may be realistic for cold atoms in a periodic optical lattice. We show that contrary to accepted theories it can never have as a ground state a perfect Mott insulator solid and that it has a low-energy spectrum of vortex-like phase fluctuations. Whether the ground state is necessarily commensurate remains an open question.
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arxiv:1102.4797
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In this paper, we define a new bigraded L-homology on finite simplicial complexes and prove that L-homology is a homeomorphism invariant of polyhedra.
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arxiv:1102.4883
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We carry out an analytic study of the early-time motion of a quark in a strongly-coupled maximally-supersymmetric Yang-Mills plasma, using the AdS/CFT correspondence. Our approach extracts the first thermal effects as a small perturbation of the known quark dynamics in vacuum, using a double expansion that is valid for early times and for (moderately) ultrarelativistic quark velocities. The quark is found to lose energy at a rate that differs significantly from the previously derived stationary/late-time result: it scales like T^4 instead of T^2, and is associated with a friction coefficient that is not independent of the quark momentum. Under conditions representative of the quark-gluon plasma as obtained at RHIC, the early energy loss rate is a few times smaller than its late-time counterpart. Our analysis additionally leads to thermally-corrected expressions for the intrinsic energy and momentum of the quark, in which the previously discovered limiting velocity of the quark is found to appear naturally.
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arxiv:1102.4893
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An improvement of the scheme by Brunner and Simon [Phys. Rev. Lett. 105, 010405 (2010)] is proposed in order to show that quantum weak measurements can provide a method to detect ultrasmall longitudinal phase shifts, even with white light. By performing an analysis in the frequency domain, we find that the amplification effect will work as long as the spectrum is large enough, irrespective of the behavior in the time domain. As such, the previous scheme can be notably simplified for experimental implementations.
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arxiv:1102.4902
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Using the data from SNO NCD phase, SuperK, Borexino and KamLAND Solar phase, we derive in a model independent way, bounds on the possible components in the solar neutrino flux. We update the limits on the antineutrino ($\bar\nu_x$) flux and sterile ($\nu_s$) component and compare them with the previous results obtained using SNO Salt phase data and data from SuperKamiokande experiments. It is affirmed that the upper bound on $\bar\nu_x$ is independent of the $\nu_s$ component. We recover the $\nu_s$ and $\bar\nu_x$ upper bounds existing in the literature. We also obtain bounds on $f_B$, the SSM normalization factor and the common parameter range for $f_B$ and the $\nu_s$ components in the light of latest data. In summary, we update, in a model independent way, the previous results existing in literature in the light of latest solar neutrino data.
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arxiv:1102.4917
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For a real reductive linear Lie group G, the space of Whittaker functions is the representation space induced from a non-degenerate unitary character of the Iwasawa nilpotent subgroup. Defined are the standard Whittaker (g,K)-modules, which are K-admissible submodules of the space of Whittaker functions. We first determine the structures of them when the infinitesimal characters characterizing them are generic. As an example of the integral case, we determine the composition series of the standard Whittaker (g,K)-module when G is the group U(n,1) and the infinitesimal character is regular integral.
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arxiv:1102.4966
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Visible and near-infrared spectra of transiting hot Jupiter planets have recently been observed, revealing some of the atmospheric constituents of their atmospheres. In the near future, it is probable that primary and secondary eclipse observations of Earth-like rocky planets will also be achieved. The characterization of the Earth's transmission spectrum has shown that both major and trace atmospheric constituents may present strong absorption features, including important bio-markers such as water, oxygen and methane. Our simulations using a recently published empirical Earth's transmission spectrum, and the stellar spectra for a variety of stellar types, indicate that the new generation of extremely large telescopes, such as the proposed 42-meter European Extremely Large Telescope(E-ELT), could be capable of retrieving the transmission spectrum of an Earth-like planet around very cool stars and brown dwarfs (Teff < 3100 K). For a twin of Earth around a star with Teff around 3100 K (M4), for example, the spectral features of water vapor, methane, carbon dioxide, and oxygen in the wavelength range between 0.9 and 2.4 micron can simultaneously be detected within a hundred hours of observing time, or even less for a late-M star. Such detection would constitute a proof for the existence of life in that planet. The detection time can be reduced to a few hours for a super-Earth type of planet with twice the Earth's radius.
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arxiv:1102.4989
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We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes and sizes in the presence of nonparametric noise of unknown level. The noise density is assumed to be unknown and can be very irregular. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove strong consistency and scalability of our method in this setup with minimal assumptions.
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arxiv:1102.5019
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Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if it encourages truthful reporting. It is local of order $k$ if the score depends on the predictive density only through its value and the values of its derivatives of order up to $k$ at the realizing event. Complementing fundamental recent work by Parry, Dawid and Lauritzen, we characterize the local proper scoring rules of order 2 relative to a broad class of Lebesgue densities on the real line, using a different approach. In a data example, we use local and nonlocal proper scoring rules to assess statistically postprocessed ensemble weather forecasts.
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arxiv:1102.5031
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Let $P$ be a set of points in general position in the plane. Join all pairs of points in $P$ with straight line segments. The number of segment-crossings in such a drawing, denoted by $\crg(P)$, is the \emph{rectilinear crossing number} of $P$. A \emph{halving line} of $P$ is a line passing though two points of $P$ that divides the rest of the points of $P$ in (almost) half. The number of halving lines of $P$ is denoted by $h(P)$. Similarly, a $k$\emph{-edge}, $0\leq k\leq n/2-1$, is a line passing through two points of $P$ and leaving exactly $k$ points of $P$ on one side. The number of $(\le k)$-edges of $P$ is denoted by $E_{\leq k}(P) $. Let $\rcr(n)$, $h(n)$, and $E_{\leq k}(n) $ denote the minimum of $\crg(P)$, the maximum of $h(P)$, and the minimum of $E_{\leq k}(P) $, respectively, over all sets $P$ of $n$ points in general position in the plane. We show that the previously best known lower bound on $E_{\leq k}(n)$ is tight for $k<\lceil (4n-2) /9\rceil $ and improve it for all $k\geq \lceil (4n-2) /9 \rceil $. This in turn improves the lower bound on $\rcr(n)$ from $0.37968\binom{n} {4}+\Theta(n^{3})$ to {277/729}\binom{n}{4}+\Theta(n^{3})\geq 0.37997\binom{n}{4}+\Theta(n^{3})$. We also give the exact values of $\rcr(n)$ and $h(n) $ for all $n\leq27$. Exact values were known only for $n\leq18$ and odd $n\leq21$ for the crossing number, and for $n\leq14$ and odd $n\leq21$ for halving lines.
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arxiv:1102.5065
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The existence of bright quasars at high redshifts implies that supermassive black holes were able to form in the early Universe. Though a number of mechanisms to achieve this have been proposed, none yet stands out. A recent suggestion is the formation of quasi-stars, initially stellar-mass black holes accreting from hydrostatic giant-like envelopes of gas, formed from the monolithic collapse of pre-galactic gas clouds. In this work, we modify the Cambridge STARS stellar evolution package to construct detailed models of the evolution of these objects. We find that, in all of our models, the black hole inside the envelope is able to reach slightly more than one-tenth of the total mass of the system before hydrostatic equilibrium breaks down. This breakdown occurs after a few million years of evolution. We show that the mechanism which causes the hydrostatic evolution to end is present in polytropic models. We also show that the solutions are highly sensitive to the size of the inner boundary radius and that no physical solutions exist if the inner boundary is chosen to be less than about 0.3 of the Bondi radius.
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arxiv:1102.5098
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We fabricated dye sensitized graphene antidot superlattices with the purpose of elucidating the role of the localized edge state density. The fluorescence from deposited dye molecules was found to strongly quench as a function of increasing antidot filling fraction, whereas it was enhanced in unpatterned but electrically back-gated samples. This contrasting behavior is strongly indicative of a built-in lateral electric field that accounts for fluorescence quenching as well as p-type doping. These findings are of great interest for light-harvesting applications that require field separation of electron-hole pairs.
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arxiv:1102.5135
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The transport of magnetic flux to outside of collapsing molecular clouds is a required step to allow the formation of stars. Although ambipolar diffusion is often regarded as a key mechanism for that, it has been recently argued that it may not be efficient enough. In this review, we discuss the role that MHD turbulence plays in the transport of magnetic flux in star forming flows. In particular, based on recent advances in the theory of fast magnetic reconnection in turbulent flows, we will show results of three-dimensional numerical simulations that indicate that the diffusion of magnetic field induced by turbulent reconnection can be a very efficient mechanism, especially in the early stages of cloud collapse and star formation. To conclude, we will also briefly discuss the turbulence-star formation connection and feedback in different astrophysical environments: from galactic to cluster of galaxy scales.
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arxiv:1102.5140
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We give a direct and simple proof of Touchard's continued fraction, provide an extension of it, and transform it into similar expansions related to Motzkin and Schroeder numbers. Another proof is then given that uses only induction. We use this machinery on two examples that appear in recent papers of Josuat-Verges; with an additional parameter, these two can be treated simultaneously.
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arxiv:1102.5186
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In this paper we present regular bilayer LDPC convolutional codes for half-duplex relay channels. For the binary erasure relay channel, we prove that the proposed code construction achieves the capacities for the source-relay link and the source-destination link provided that the channel conditions are known when designing the code. Meanwhile, this code enables the highest transmission rate with decode-and-forward relaying. In addition, its regular degree distributions can easily be computed from the channel parameters, which significantly simplifies the code optimization. Numerical results are provided for both binary erasure channels (BEC) and AWGN channels. In BECs, we can observe that the gaps between the decoding thresholds and the Shannon limits are impressively small. In AWGN channels, the bilayer LDPC convolutional code clearly outperforms its block code counterpart in terms of bit error rate.
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arxiv:1102.5204
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We investigate cosmological implications of an energy density contribution arising by elastic dark matter self-interactions. Its scaling behaviour shows that it can be the dominant energy contribution in the early universe. Constraints from primordial nucleosynthesis give an upper limit on the self-interaction strength which allows for the same strength as standard model strong interactions. Furthermore we explore the cosmological consequences of an early self-interaction dominated universe. Chemical dark matter decoupling requires that self-interacting dark matter particles are rather light (keV range) but we find that super-weak inelastic interactions are predicted by strong elastic dark matter self-interactions. Assuming a second, collisionless cold dark matter component, its natural decoupling scale exceeds the weak scale and is in accord with the electron and positron excess observed by PAMELA and Fermi-LAT. Structure formation analysis reveals a linear growing solution during self-interaction domination, enhancing structures up to ~ 10^(-3) solar masses long before the formation of the first stars.
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arxiv:1102.5292
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The dominant phonon wavevectors $q^{*}$ probed by the 2D Raman mode of graphene are highly anisotropic and rotate with the orientation of the polarizer:analyzer direction relative to the lattice. The corresponding electronic transitions connect the electronic equibandgap contours where the product of the ingoing and outgoing optical matrix elements is strongest, showing a finite component along $\bm{K}-\bm{\Gamma}$ that sensitively determines $q^{*}$. We revoke the notion of 'inner' and 'outer' processes. Our findings explain the splitting of the 2D mode of graphene under uniaxial tensile strain. The splitting originates from a strain-induced distortion of the phonon dispersion; changes in the electronic band structure and resonance conditions are negligeable for the 2D Raman spectrum.
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arxiv:1102.5317
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We examine the effects of gas expulsion on initially sub-structured and out-of-equilibrium star clusters. We perform $N$-body simulations of the evolution of star clusters in a static background potential before removing that potential to model gas expulsion. We find that the initial star formation efficiency is not a good measure of the survivability of star clusters. This is because the stellar distribution can change significantly, causing a large change in the relative importance of the stellar and gas potentials. We find that the initial stellar distribution and velocity dispersion are far more important parameters than the initial star formation efficiency, and that clusters with very low star formation efficiencies can survive gas expulsion. We suggest that it is variations in cluster initial conditions rather than in their star formation efficiencies that cause some clusters to be destroyed while a few survive.
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arxiv:1102.5360
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We have used multi-epoch images from the Infrared Array Camera on board the Spitzer Space Telescope to search for substellar companions to stars in the solar neighborhood based on common proper motions. Through this work, we have discovered a faint companion to the white dwarf WD 0806-661. The comoving source has a projected separation of 130", corresponding to 2500 AU at the distance of the primary (19.2 pc). If it is physically associated, then its absolute magnitude at 4.5um is ~1 mag fainter than the faintest known T dwarfs, making it a strong candidate for the coolest known brown dwarf. The combination of M_4.5 and the age of the primary (1.5 Gyr) implies an effective temperature of ~300 K and a mass of ~7 M_Jup according to theoretical evolutionary models. The white dwarf's progenitor likely had a mass of ~2 M_sun, and thus could have been born with a circumstellar disk that was sufficiently massive to produce a companion with this mass. Therefore, the companion could be either a brown dwarf that formed like a binary star or a giant planet that was born within a disk and has been dynamically scattered to a larger orbit.
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arxiv:1102.5411
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A specific structure of doped graphene with substituted silicon impurity is introduced and ab. initio density-functional approach is applied for energy band structure calculation of proposed structure. Using the band structure calculation for different silicon sites in the host graphene, the effect of silicon concentration and unit cell geometry on the bandgap of the proposed structure is also investigated. Chemically silicon doped graphene results in an energy gap as large as 2eV according to DFT calculations. As we will show, in contrast to previous bandgap engineering methods, such structure has significant advantages including wide gap tuning capability and its negligible dependency on lattice geometry.
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arxiv:1102.5422
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The semileptonic $D_{l4}$ decay including $D\to K\pi l\nu$ and $D\to \pi\pi l\nu$ have been extensively studied. In these references, the form factors and differential decay rate are explicitly stated. However, we would like to stress that in these papers the final state interactions are often overlooked, i.e. rescattering effect of the pseudoscalars produced by $D_{l4}$ decay may be very important, at least on the side of phase of form factors due to Watson's theorem. In this short paper, we will display this rescattering effect in the framework of heavy hadron chiral perturbation theory, it thus must be a very useful and indispensable supplement of the previous papers on $D_{l4}$ study.
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arxiv:1102.5426
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Most results in multifractal analysis are obtained using either a thermodynamic approach based on existence and uniqueness of equilibrium states or a saturation approach based on some version of the specification property. A general framework incorporating the most important multifractal spectra was introduced by Barreira and Saussol, who used the thermodynamic approach to establish the multifractal formalism in the uniformly hyperbolic setting, unifying many existing results. We extend this framework to apply to a broad class of non-uniformly hyperbolic systems, including examples with phase transitions. In the process, we compare this thermodynamic approach with the saturation approach and give a survey of many of the multifractal results in the literature.
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arxiv:1102.5427
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A measurement of WW production in pp collisions at sqrt(s) = 7 TeV and a search for the Higgs boson are reported. The WW candidates are selected in events with two leptons, either electrons or muons. The measurement is performed using LHC data recorded with the CMS detector, corresponding to an integrated luminosity of 36 inverse picobarns. The pp to WW cross section is measured to be 41.1 +/- 15.3 (stat) +/- 5.8 (syst) +/- 4.5 (lumi) pb, consistent with the standard model prediction. Limits on WW gamma and WWZ anomalous triple gauge couplings are set. The search for the standard model Higgs boson in the WW decay mode does not reveal any evidence of excess above backgrounds. Limits are set on the production of the Higgs boson in the context of the standard model and in the presence of a sequential fourth family of fermions with high masses. In the latter context, a Higgs boson with mass between 144 and 207 GeV is ruled out at 95% confidence level.
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arxiv:1102.5429
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A sequence $S=s_{1}s_{2}..._{n}$ is \emph{nonrepetitive} if no two adjacent blocks of $S$ are identical. In 1906 Thue proved that there exist arbitrarily long nonrepetitive sequences over 3-element set of symbols. We study a generalization of nonrepetitive sequences involving arithmetic progressions. We prove that for every $k\geqslant 1$ and every $c\geqslant 1$ there exist arbitrarily long sequences over at most $(1+\frac{1}{c})k+18k^{c/c+1}$ symbols whose subsequences indexed by arithmetic progressions with common differences from the set $\{1,2,...,k\}$ are nonrepetitive. This improves a previous bound obtained in \cite{Grytczuk Rainbow}. Our approach is based on a technique introduced recently in \cite{GrytczukKozikMicek}, which was originally inspired by a constructive proof of the Lov\'{a}sz Local Lemma due to Moser and Tardos \cite{MoserTardos}. We also discuss some related problems that can be successfully attacked by this method.
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arxiv:1102.5438
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In an $L_\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures applicable. First we consider equivalent martingale measures with bounds on densities and the corresponding prices bounded by linear minorant and majorant. Then we consider prices bounded by bid-ask dynamics. Finally we study price systems consistent with no-good-deal pricing measures for given bounds on the Sharpe ratio. Within this study we introduce the definition of dynamic no-good-deal pricing measure.
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arxiv:1102.5501
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One of the basic motivations of the KLOE-2 and WASA-at-COSY experiments is the test of fundamental symmetries and the search for phenomena beyond the Standard Model in the hadronic and leptonic decays of ground-state mesons and in particular in decays of the $\eta$ meson. At COSY these mesons are produced in collisions of proton or deuteron beam with hydrogen or deuterium pellet target, and at DA$\Phi$NE $\eta$ mesons originate from radiative decays of $\phi$ meson or from the fusion of virtual gamma quanta exchanged between colliding electrons and positrons. This contribution includes brief description of experimental techniques used by KLOE-2 and WASA-at-COSY as well as some of physics aspects motivating investigations of production and decays of $\eta$ mesons.
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arxiv:1102.5548
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We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one dimension. Although this gauge is not smoothly defined on the two-torus, it respects the T symmetry of the system and allows for a definition of the Z_2 invariant in terms of time-reversal polarization. In 3D we apply the 2D approach to T-invariant planes. We illustrate the method with first-principles calculations on GeTe and on HgTe under [001] and [111] strain. Our approach differs from ones used previously for noncentrosymmetric materials and should be easier to implement in ab initio code packages.
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arxiv:1102.5600
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Sufficient energy resolution is the key issue for the calorimetry in particle and nuclear physics. The calorimeter of the A4 parity violation experiment at MAMI is a segmented calorimeter where the energy of an event is determined by summing the signals of neighbouring channels. In this case the precise matching of the individual modules is crucial to obtain a good energy resolution. We have developped a calibration procedure for our total absorbing electromagnetic calorimeter which consists of 1022 lead fluoride (PbF_2) crystals. This procedure reconstructs the the single-module contributions to the events by solving a linear system of equations, involving the inversion of a 1022 x 1022-matrix. The system has shown its functionality at beam energies between 300 and 1500 MeV and represents a new and fast method to keep the calorimeter permanently in a well-calibrated state.
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arxiv:1102.5640
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The maximal $U(1)_L$ supersymmetric inverse seesaw mechanism (M$L$SIS) provides a natural way to relate asymmetric dark matter (ADM) with neutrino physics. In this paper we point out that, M$L$SIS is a natural outcome if one dynamically realizes the inverse seesaw mechanism in the next-to minimal supersymmetric standard model (NMSSM) via the dimension-five operator $(N)^2S^2/M_*$, with $S$ the NMSSM singlet developing TeV scale VEV; it slightly violates lepton number due to the suppression by the fundamental scale $M_*$, thus preserving $U(1)_L$ maximally. The resulting sneutrino is a distinguishable ADM candidate, oscillating and favored to have weak scale mass. A fairly large annihilating cross section of such a heavy ADM is available due to the presence of singlet.
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arxiv:1102.5644
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D.Sullivan (1977) (see also the book by H.Whitney "Geometric Integration Theory",1957) considered a new model for underlying cochain complex for classical cohomologies with rational coefficients for arbitrary simplicial spaces that gives the isomorphism with classical rational cohomologies. We apply the key ideas developed by K.MacKenzie (2005) and J.Kubarski (1991) to generalization of the D.Sullivan model for transitive Lie algebroids. The generalization is based on the existence of the inverse image of the transitive Lie algebroids and on the property of transitive Lie algebroids being trivial over contractible manifolds. Using these properties one can construct an underlying cochain complex of differential forms on simplicial space.
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arxiv:1102.5698
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Recent lattice studies exhibit infrared finite effective QCD charges. Corresponding gluon propagator in Landau gauge is finite and nonzero, suggesting a mechanism of dynamical gluon mass generation is in the operation. In this paper, the analytical continuation of the Euclidean (spacelike) Pinch Technique-Background Field Method (PT-BFM) solution of Schwinger-Dyson equation for gluon propagator to the timelike region of $q^2$ is found. We found the continuation numerically showing good agreement with a generalized Lehman representation for small Schwinger coupling. The associate non-positive spectral function has an unexpected behavior. Albeit infrared Euclidean space solution naively suggests like single scale "massive" propagator, the obtained spectrum of gluon propagator does not correspond to the delta function at single scale $q=m$, instead more possible singularities are generated. The pattern depends on the details of assumed Schwinger mechanism: for stronger coupling there are few maxima and minima which appear at the scale $\Lambda$, while for perturbatively small Schwinger coupling the spectral function shows up two narrow peaks: particle and ghost excitation, which have mutually opposite signs.
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arxiv:1102.5765
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The friends-of-friends algorithm (hereafter, FOF) is a percolation algorithm which is routinely used to identify dark matter halos from N-body simulations. We use results from percolation theory to show that the boundary of FOF halos does not correspond to a single density threshold but to a range of densities close to a critical value that depends upon the linking length parameter, b. We show that for the commonly used choice of b = 0.2, this critical density is equal to 81.62 times the mean matter density. Consequently, halos identified by the FOF algorithm enclose an average overdensity which depends on their density profile (concentration) and therefore changes with halo mass contrary to the popular belief that the average overdensity is ~180. We derive an analytical expression for the overdensity as a function of the linking length parameter b and the concentration of the halo. Results of tests carried out using simulated and actual FOF halos identified in cosmological simulations show excellent agreement with our analytical prediction. We also find that the mass of the halo that the FOF algorithm selects crucially depends upon mass resolution. We find a percolation theory motivated formula that is able to accurately correct for the dependence on number of particles for the mock realizations of spherical and triaxial Navarro-Frenk-White halos. However, we show that this correction breaks down when applied to the real cosmological FOF halos due to presence of substructures. Given that abundance of substructure depends on redshift and cosmology, we expect that the resolution effects due to substructure on the FOF mass and halo mass function will also depend on redshift and cosmology and will be difficult to correct for in general. Finally, we discuss the implications of our results for the universality of the mass function.
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arxiv:1103.0005
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In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum-capacity, the maximum achievable sum-rate drops to that with interference treated as noise. We provide two algorithms (a simple one and a finer one) to translate the optimal schemes in the deterministic channel model to the Gaussian channel model. We also derive two upper bounds on the sum-capacity of the Gaussian Han-Kobayashi schemes, which automatically upper bound the sum-capacity using successive decoding of Gaussian codewords. Numerical evaluations show that, similar to the deterministic channel results, the constrained sum-capacity in the Gaussian channels oscillates between the sum-capacity with Han-Kobayashi schemes and that with single message schemes.
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arxiv:1103.0038
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