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We prove that for the two-dimensional steady complete compressible Euler system, with given uniform upcoming supersonic flows, the following three fundamental flow patterns (special solutions) in gas dynamics involving transonic shocks are all unique in the class of piecewise $C^1$ smooth functions, under appropriate conditions on the downstream subsonic flows: $(\rmnum{1})$ the normal transonic shocks in a straight duct with finite or infinite length, after fixing a point the shock-front passing through; $(\rmnum{2})$ the oblique transonic shocks attached to an infinite wedge; $(\rmnum{3})$ a flat Mach configuration containing one supersonic shock, two transonic shocks, and a contact discontinuity, after fixing the point the four discontinuities intersect. These special solutions are constructed traditionally under the assumption that they are piecewise constant, and they have played important roles in the studies of mathematical gas dynamics. Our results show that the assumption of piecewise constant can be replaced by some more weaker assumptions on the downstream subsonic flows, which are sufficient to uniquely determine these special solutions. Mathematically, these are uniqueness results on solutions of free boundary problems of a quasi-linear system of elliptic-hyperbolic composite-mixed type in bounded or unbounded planar domains, without any assumptions on smallness. The proof relies on an elliptic system of pressure $p$ and the tangent of the flow angle $w=v/u$ obtained by decomposition of the Euler system in Lagrangian coordinates, and a newly developed method for the $L^{\infty}$ estimate that is independent of the free boundaries, by combining the maximum principles of elliptic equations, and careful analysis of shock polar applied on the (maybe curved) shock-fronts.
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arxiv:1004.2002
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It has recently been argued by Alday et al that the inclusion of surface operators in 4d N=2 SU(2) quiver gauge theories should correspond to insertions of certain degenerate operators in the dual Liouville theory. So far only the insertion of a single surface operator has been treated (in a semi-classical limit). In this paper we study and generalise this proposal. Our approach relies on the use of topological string theory techniques. On the B-model side we show that the effects of multiple surface operator insertions in 4d N=2 gauge theories can be calculated using the B-model topological recursion method, valid beyond the semi-classical limit. On the mirror A-model side we find by explicit computations that the 5d lift of the SU(N) gauge theory partition function in the presence of (one or many) surface operators is equal to an A-model topological string partition function with the insertion of (one or many) toric branes. This is in agreement with an earlier proposal by Gukov. Our A-model results were motivated by and agree with what one obtains by combining the AGT conjecture with the dual interpretation in terms of degenerate operators. The topological string theory approach also opens up new possibilities in the study of 2d Toda field theories.
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arxiv:1004.2025
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In recent years argument has been made that a high fraction of early-type galaxies in the local universe experience low levels (< 1 M_sun/yr) of star formation (SF) that causes strong excess in UV flux, yet leaves the optical colors red. Many of these studies were based on GALEX imaging of SDSS galaxies (z~0.1), and were thus limited by its 5" FWHM. Poor UV resolution left other possibilities for UV excess open, such as the old populations or an AGN. Here we study high-resolution far-ultraviolet HST/ACS images of optically quiescent early-type galaxies with strong UV excess. The new images show that three-quarters of these moderately massive (~5x10^10 M_sun) early-type galaxies shows clear evidence of extended SF, usually in form of wide or concentric UV rings, and in some cases, striking spiral arms. SDSS spectra probably miss these features due to small fiber size. UV-excess early-type galaxies have on average less dust and larger UV sizes (D>40 kpc) than other green-valley galaxies, which argues for an external origin for the gas that is driving the SF. Thus, most of these galaxies appear `rejuvenated' (e.g., through minor gas-rich mergers or IGM accretion). For a smaller subset of the sample, the declining SF (from the original internal gas) cannot be ruled out. SF is rare in very massive early-types (M_* > 10^11 M_sun), a possible consequence of AGN feedback. In addition to extended UV emission, many galaxies show a compact central source, which may be a weak, optically inconspicuous AGN.
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arxiv:1004.2041
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We have investigated the nanoscale switching properties of strain-engineered BiFeO3 thin films deposited on LaAlO3 substrates using a combination of scanning probe techniques. Polarized Raman spectral analysis indicate that the nearly-tetragonal films have monoclinic (Cc) rather than P4mm tetragonal symmetry. Through local switching-spectroscopy measurements and piezoresponse force microscopy we provide clear evidence of ferroelectric switching of the tetragonal phase but the polarization direction, and therefore its switching, deviates strongly from the expected (001) tetragonal axis. We also demonstrate a large and reversible, electrically-driven structural phase transition from the tetragonal to the rhombohedral polymorph in this material which is promising for a plethora of applications.
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arxiv:1004.2052
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This paper deals with the dimension reduction for high-dimensional time series based on common factors. In particular we allow the dimension of time series $p$ to be as large as, or even larger than, the sample size $n$. The estimation for the factor loading matrix and the factor process itself is carried out via an eigenanalysis for a $p\times p$ non-negative definite matrix. We show that when all the factors are strong in the sense that the norm of each column in the factor loading matrix is of the order $p^{1/2}$, the estimator for the factor loading matrix, as well as the resulting estimator for the precision matrix of the original $p$-variant time series, are weakly consistent in $L_2$-norm with the convergence rates independent of $p$. This result exhibits clearly that the `curse' is canceled out by the `blessings' in dimensionality. We also establish the asymptotic properties of the estimation when not all factors are strong. For the latter case, a two-step estimation procedure is preferred accordingly to the asymptotic theory. The proposed methods together with their asymptotic properties are further illustrated in a simulation study. An application to a real data set is also reported.
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arxiv:1004.2138
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The Dirichlet series $L_m(s)$ are of fundamental importance in number theory. Shanks defined the generalized Euler and class numbers in connection with these Dirichlet series, denoted by $\{s_{m,n}\}_{n\geq 0}$. We obtain a formula for the exponential generating function $s_m(x)$ of $s_{m,n}$, where m is an arbitrary positive integer. In particular, for m>1, say, $m=bu^2$, where b is square-free and u>1, we prove that $s_m(x)$ can be expressed as a linear combination of the four functions $w(b,t)\sec (btx)(\pm \cos ((b-p)tx)\pm \sin (ptx))$, where p is an integer satisfying $0\leq p\leq b$, $t|u^2$ and $w(b,t)=K_bt/u$ with $K_b$ being a constant depending on b. Moreover, the Dirichlet series $L_m(s)$ can be easily computed from the generating function formula for $s_m(x)$. Finally, we show that the main ingredient in the formula for $s_{m,n}$ has a combinatorial interpretation in terms of the m-signed permutations defined by Ehrenborg and Readdy. In principle, this answers a question posed by Shanks concerning a combinatorial interpretation for the numbers $s_{m,n}$.
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arxiv:1004.2168
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We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain close enough at later times. For potential less singular than the classical electrostatic kernel, we are able to prove such a result, for initial positions/velocities distributed according to the Gibbs equilibrium of the system.
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arxiv:1004.2177
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We have investigated single grain boundaries (GBs) isolated in coated conductors produced by Metal-Organic Deposition (MOD). When a magnetic field is swept in the film plane, an angle-dependent crossover from boundary to grain limited critical current density Jc is found. In the force-free orientation, even at fields as high as 8 T, the GBs still limit Jc. We deduce that this effect is a direct consequence of GB meandering. We have employed these single GB results to explain the dependence of Jc of polycrystalline tracks on their width: in-plane measurements become flatter as the tracks are narrowed down. This result is consistent with the stronger GB limitation at field configurations close to force-free found from the isolated boundaries. Our study shows that for certain geometries even at high fields the effect of GBs cannot be neglected.
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arxiv:1004.2204
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The dominant part of the difference between the observed and model frequencies of the Sun can be approximated by a power law. We show that when this empirical law is employed to correct the model frequencies and then the small frequency separations are used for solar age determination, the results are consistent with the meteoritic age (4.563 Gyr < t < 4.576 Gyr). We present the results and compare with those obtained by using the ratios of small to large frequency separations.
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arxiv:1004.2215
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Deep observations of the Small Magellanic Cloud (SMC) and region were carried out in the hard X-ray band by the INTEGRAL observatory in 2008-2009. The field of view of the instrument permitted simultaneous coverage of the entire SMC and the eastern end of the Magellanic Bridge. In total, INTEGRAL detected seven sources in the SMC and five in the Magellanic Bridge; the majority of the sources were previously unknown systems. Several of the new sources were detected undergoing bright X- ray outbursts and all the sources exhibited transient behaviour except the supergiant system SMC X-1. They are all thought to be High Mass X-ray Binary (HMXB) systems in which the compact object is a neutron star.
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arxiv:1004.2219
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The universe is filled with blackbody millimeter radiation (CMBR), temperature 2.7{\deg} Kelvin[1]. Big-bang cosmology explains this by the initial thermalization of photons scattered by electrons[2]. This explanation requires ad hoc previous existence of photons and thermal electrons. On the other hand most of the mass of the universe is unknown dark matter3. It explains anomalous dynamical properties, like that of stars in galaxies[4,5,6] . Alternatively the anomalies have been explained by adjusting and modifying well known laws ("Modified Newtonian dynamics"[7]). Here we show that millimeter black holes (m.b.h.) explain both: the background radiation, by its partial "evaporation", and the dark matter. Black holes emit blackbody radiation (Hawking[8] evaporation), and this is what is observed in the CMBR. Millimeter size black holes emit blackbody radiation at a temperature of 2.7{\deg} Kelvin, and this is the resulting CMBR . Partial evaporation of ~10^30 m.b.h. gives the observed background field of photons being emitted and absorbed at the same rate by the m.b.h. The number of photons is constant, as observed. Their temperature decreases with time because the mass of the m.b.h. (and therefore its size) increases with time (the mass-boom effect[9]). The total mass of the m.b.h. is the dark matter. Hence dark matter is not so "dark" after all. Two important cosmological items are here identified by only one source: millimeter black holes.
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arxiv:1004.2251
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We derive the capacity of the binary multi-way relay channel, in which multiple users exchange messages at a common rate through a relay. The capacity is achieved using a novel functional-decode-forward coding strategy. In the functional-decode-forward coding strategy, the relay decodes functions of the users' messages without needing to decode individual messages. The functions to be decoded by the relay are defined such that when the relay broadcasts the functions back to the users, every user is able to decode the messages of all other users.
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arxiv:1004.2299
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We investigate the impact of charm mixing on the model-independent gamma measurement using Dalitz plot analysis of the three-body D decay from B+->DK+ process, and show that ignoring the mixing at all stages of the analysis is safe up to a sub-degree level of precision. We also find that in the coherent production of D0-D0* system in e+e- collisions, the effect of charm mixing is enhanced, and propose a model-independent method to measure charm mixing parameters in the time-integrated Dalitz analysis at charm factories.
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arxiv:1004.2350
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Using the updated oscillation spectrum of $\gamma$ Pegasi, we construct a set of seismic models which reproduce two pulsational frequencies corresponding to the $\ell=0$, p$_1$ and $\ell=1$, g$_1$ modes. Then, we single out models which reproduce other well identified modes. Finally, we extend our seismic modelling by a requirement of fitting also values of the complex, nonadiabatic parameter $f$ associated to each mode frequency. Such complex asteroseismology of the B-type pulsators provides a unique test of stellar metallicity and opacities. In contrast to our previous studies, results for $\gamma$ Peg indicate that both opacity tables, OPAL and OP, are equally preferred.
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arxiv:1004.2366
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We study the applications of non-equilibrium relations such as the Jarzynski equality and fluctuation theorem to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result is used to derive a lower bound on the work done during the non-equilibrium process of temperature change. We also prove identities relating equilibrium and non-equilibrium quantities. These identities suggest a method to evaluate equilibrium quantities from non-equilibrium computations, which may be useful to avoid the problem of slow relaxation in spin glasses.
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arxiv:1004.2389
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We generalize the DeWitt-Virasoro (DWV) construction of arXiv:0912.3987 [hep-th] to tensor representations of higher ranks. A rank-$n$ tensor state, which is by itself coordinate invariant, is expanded in terms of position eigenstates that transform as tensors of the same rank. The representation of the momentum operator in these basis states is then obtained by generalizing DeWitt's argument in Phys.Rev.85:653-661,1952. Such a representation is written in terms of certain bi-vector of parallel displacement and its covariant derivatives. With this machinery at hand we find tensor representations of the DWV generators defined in the previous work. The results differ from those in spin-zero representation by additional terms involving the spin connection. However, we show that the DWV algebra found earlier as a scalar expectation value remains the same, as required by consistency, as all the additional contributions conspire to cancel in various ways. In particular, vanishing of the anomaly term requires the same condition of Ricci-flatness for the background.
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arxiv:1004.2396
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Cosmic Microwave Background satellite missions as the on-going Planck experiment are expected to provide the strongest constraints on a wide set of cosmological parameters. Those constraints, however, could be weakened when the assumption of a cosmological constant as the dark energy component is removed. Here we show that it will indeed be the case when there exists a coupling among the dark energy and the dark matter fluids. In particular, the expected errors on key parameters as the cold dark matter density and the angular diameter distance at decoupling are significantly larger when a dark coupling is introduced. We show that it will be the case also for future satellite missions as EPIC, unless CMB lensing extraction is performed.
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arxiv:1004.2410
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We consider the regular balanced model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad, Dubois, Interian, and Selman. We say that a formula is $p$-satisfying if there is a truth assignment satisfying $1-2^{-k}+p 2^{-k}$ fraction of clauses. Using the first moment method we determine upper bound on the threshold clause density such that there are no $p$-satisfying assignments with high probability above this upper bound. There are two aspects in deriving the lower bound using the second moment method. The first aspect is, given any $p \in (0,1)$ and $k$, evaluate the lower bound on the threshold. This evaluation is numerical in nature. The second aspect is to derive the lower bound as a function of $p$ for large enough $k$. We address the first aspect and evaluate the lower bound on the $p$-satisfying threshold using the second moment method. We observe that as $k$ increases the lower bound seems to converge to the asymptotically derived lower bound for uniform model of formula generation by Achlioptas, Naor, and Peres.
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arxiv:1004.2425
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The Ultraviolet/Optical Telescope (UVOT) is one of three instruments onboard the Swift observatory. The photometric calibration has been published, and this paper follows up with details on other aspects of the calibration including a measurement of the point spread function with an assessment of the orbital variation and the effect on photometry. A correction for large scale variations in sensitivity over the field of view is described, as well as a model of the coincidence loss which is used to assess the coincidence correction in extended regions. We have provided a correction for the detector distortion and measured the resulting internal astrometric accuracy of the UVOT, also giving the absolute accuracy with respect to the International Celestial Reference System. We have compiled statistics on the background count rates, and discuss the sources of the background, including instrumental scattered light. In each case we describe any impact on UVOT measurements, whether any correction is applied in the standard pipeline data processing or whether further steps are recommended.
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arxiv:1004.2448
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We have mesured the carrier recombination dynamics in InGaN/GaN multiple quantum wells over an unprecedented range in intensity. We find that at times shorter than 30\,ns, they follow an exponential form, and a power law at times longer than 1\,$\mu$s. To explain these biphasic dynamics, we propose a simple three-level model where a charge-separated state interplays with the radiative state through charge transfer following a tunneling mechanism. We show how the distribution of distances in charge-separated states controls the dynamics at long time. Our results imply that charge recombination happens on nearly-isolated clusters of localization centers.
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arxiv:1004.2463
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Jet vetoes are essential in many Higgs and new-physics analyses at the LHC and Tevatron. The signals are typically characterized by a specific number of hard jets, leptons, or photons, while the backgrounds often have additional jets. In such cases vetoing undesired additional jets is an effective way to discriminate signals and background. Given an inclusive event sample with N or more jets, the veto to have only N energetic jets defines an "exclusive" N-jet cross section. This strongly restricts the phase space of the underlying inclusive N-jet cross section and causes large double logarithms in perturbation theory that must be summed to obtain theory predictions. Jet vetoes are typically implemented using jet algorithms. This yields complicated phase-space restrictions and one often relies on parton-shower Monte Carlos, which are limited to leading-logarithmic accuracy. We introduce a global event shape "N-jettiness", tau_N, which is defined for events with N signal jets and vanishes in the limit of exactly N infinitely narrow jets. Requiring tau_N << 1 constrains radiation between the N signal jets and vetoes additional undesired jets. This provides an inclusive method to veto jets and to define an exclusive N-jet cross section that can be well-controlled theoretically. N-jettiness yields a factorization formula with inclusive jet and beam functions.
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arxiv:1004.2489
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Aims. The brown dwarf (BD) formation process has not yet been completely understood. To shed more light on the differences and similarities between star and BD formation processes, we study and compare the disk fraction among both kinds of objects over a large angular region in the Taurus cloud. In addition, we examine the spatial distribution of stars and BD relative to the underlying molecular gas Methods. In this paper, we present new and updated photometry data from the Infrared Array Camera (IRAC) aboard the Spitzer Space Telescope on 43 BDs in the Taurus cloud, and recalculate of the BD disk fraction in this region. We also useed recently available CO mm data to study the spatial distribution of stars and BDs relative to the cloud's molecular gas. Results. We find that the disk fraction among BDs in the Taurus cloud is 41 \pm 12%, a value statistically consistent with the one among TTS (58 \pm 9%). We find that BDs in transition from a state where they have a disk to a diskless state are rare, and we study one isolated example of a transitional disk with an inner radius of \approx 0.1 AU (CFHT BD Tau 12, found via its relatively small mid-IR excess compared to most members of Taurus that have disks. We find that BDs are statistically found in regions of similar molecular gas surface density to those associated with stars. Furthermore, we find that the gas column density distribution is almost identical for stellar and substellar objects with and without disks.
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arxiv:1004.2541
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In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible invariant semiclassical measures obtained as limits of Wigner measures corresponding to eigenfunctions. These measures describe simultaneously the concentration and oscillation effects developed by a sequence of eigenfunctions. We present some results showing how to obtain invariant semiclassical measures from eigenfunctions with prescribed symmetries. As an application of these results, we give a simple proof of the fact that in a manifold of constant positive sectional curvature, every measure which is invariant by the geodesic flow is an invariant semiclassical measure.
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arxiv:1004.2596
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We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portions of the line segments x+y=p lying in the positive quadrant. Every coloopless paving matroids is in the class of matroids which contain two disjoint bases or whose ground set is the union of two bases of M*. For this latter class we give a proof that T_M(a,a) <= max {T_M(2a,0), T_M(0,2a)} for a >= 2. We conjecture that T_M(1,1) <= max {T_M(2,0), T_M(0,2)} for the same class of matroids. We also prove this conjecture for some families of graphs and matroids.
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arxiv:1004.2639
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We consider the source-channel separation architecture for lossy source coding in communication networks. It is shown that the separation approach is optimal in two general scenarios, and is approximately optimal in a third scenario. The two scenarios for which separation is optimal complement each other: the first is when the memoryless sources at source nodes are arbitrarily correlated, each of which is to be reconstructed at possibly multiple destinations within certain distortions, but the channels in this network are synchronized, orthogonal and memoryless point-to-point channels; the second is when the memoryless sources are mutually independent, each of which is to be reconstructed only at one destination within a certain distortion, but the channels are general, including multi-user channels such as multiple access, broadcast, interference and relay channels, possibly with feedback. The third scenario, for which we demonstrate approximate optimality of source-channel separation, generalizes the second scenario by allowing each source to be reconstructed at multiple destinations with different distortions. For this case, the loss from optimality by using the separation approach can be upper-bounded when a "difference" distortion measure is taken, and in the special case of quadratic distortion measure, this leads to universal constant bounds.
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arxiv:1004.2648
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In this paper, we prove that on a Fano manifold $M$ which admits a K\"ahler-Ricci soliton $(\om,X)$, if the initial K\"ahler metric $\om_{\vphi_0}$ is close to $\om$ in some weak sense, then the weak K\"ahler-Ricci flow exists globally and converges in Cheeger-Gromov sense. Moreover, if $\vphi_0$ is also $K_X$-invariant, then the weak modified K\"ahler-Ricci flow converges exponentially to a unique K\"ahler-Ricci soliton nearby. Especially, if the Futaki invariant vanishes, we may delete the $K_X$-invariant assumption. The methods based on the metric geometry of the space of the K\"ahler metrics are potentially applicable to other stability problem of geometric flow near a critical metric.
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arxiv:1004.2695
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This paper provides a short and transparent solution for the covering cost of white-grey trees which play a crucial role in the algorithm of Bergeron {\it et al.}\ to compute the rearrangement distance between two multichromosomal genomes in linear time ({\it Theor. Comput. Sci.}, 410:5300-5316, 2009). In the process it introduces a new {\em center} notion for trees, which seems to be interesting on its own.
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arxiv:1004.2735
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We present the Sloan Low-mass Wide Pairs of Kinematically Equivalent Stars (SLoWPoKES), a catalog of 1342 very-wide (projected separation >500 AU), low-mass (at least one mid-K--mid-M dwarf component) common proper motion pairs identified from astrometry, photometry, and proper motions in the Sloan Digital Sky Survey. A Monte Carlo based Galactic model is constructed to assess the probability of chance alignment for each pair; only pairs with a probability of chance alignment </= 0.05 are included in the catalog. The overall fidelity of the catalog is expected to be 98.35%. The selection algorithm is purposely exclusive to ensure that the resulting catalog is efficient for follow-up studies of low-mass pairs. The SLoWPoKES catalog is the largest sample of wide, low-mass pairs to date and is intended as an ongoing community resource for detailed study of bona fide systems. Here we summarize the general characteristics of the SLoWPoKES sample and present preliminary results describing the properties of wide, low-mass pairs. While the majority of the identified pairs are disk dwarfs, there are 70 halo subdwarf pairs and 21 white dwarf-disk dwarf pairs, as well as four triples. Most SLoWPoKES pairs violate the previously defined empirical limits for maximum angular separation or binding energies. However, they are well within the theoretical limits and should prove very useful in putting firm constraints on the maximum size of binary systems and on different formation scenarios. We find a lower limit to the wide binary frequency for the mid-K-mid-M spectral types that constitute our sample to be 1.1%. This frequency decreases as a function of Galactic height, indicating a time evolution of the wide binary frequency. [See text for full abstract.]
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arxiv:1004.2755
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We present an extension of the QCD sum rule method in the external fields so as to determine the induced pseudoscalar coupling constant g_P, which tests the validity of the partially conserved axial current (PCAC) hypothesis. This is essentially that we pick out the "higher-order" effects of both the hadron and quark (QCD) sides. A specific QCD sum rules for g_P is obtained and its prediction is briefly analyzed. It turns out that the final prediction on g_P is extremely stable. In view of the versatile nature of the present QCD sum rule methods, we appendix some discussions on the possible future of the method.
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arxiv:1004.2767
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The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with four most important interlayer interactions taken into account. Since the main features of the wave functions are well depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions.
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arxiv:1004.2800
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This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms; a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie algorithm or the Stochastic simulation algorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term.
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arxiv:1004.2948
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We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius norm of the fit plus a regularization term proportional to the number of parameters in the reduced rank model. The rank of the RSC estimator provides a consistent estimator of the rank of the coefficient matrix; in general, the rank of our estimator is a consistent estimate of the effective rank, which we define to be the number of singular values of the target matrix that are appropriately large. The consistency results are valid not only in the classic asymptotic regime, when $n$, the number of responses, and $p$, the number of predictors, stay bounded, and $m$, the number of observations, grows, but also when either, or both, $n$ and $p$ grow, possibly much faster than $m$. We establish minimax optimal bounds on the mean squared errors of our estimators. Our finite sample performance bounds for the RSC estimator show that it achieves the optimal balance between the approximation error and the penalty term. Furthermore, our procedure has very low computational complexity, linear in the number of candidate models, making it particularly appealing for large scale problems. We contrast our estimator with the nuclear norm penalized least squares (NNP) estimator, which has an inherently higher computational complexity than RSC, for multivariate regression models. We show that NNP has estimation properties similar to those of RSC, albeit under stronger conditions. However, it is not as parsimonious as RSC. We offer a simple correction of the NNP estimator which leads to consistent rank estimation.
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arxiv:1004.2995
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We prove inequalities between the densities of various bipartite subgraphs in signed graphs and graphons. One of the main inequalities is that the density of any bipartite graph with girth r cannot exceed the density of the r-cycle. This study is motivated by Sidorenko's conjecture, which states that the density of a bipartite graph F with m edges in any graph G is at least the m-th power of the edge density of G. Another way of stating this is that the graph G with given edge density minimizing the number of copies of F is, asymptotically, a random graph. We prove that this is true locally, i.e., for graphs G that are "close" to a random graph.
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arxiv:1004.3026
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For a class of divergence type quasi-linear degenerate parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via nonlinear Wolff potentials.
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arxiv:1004.3045
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We present a quantitative analysis of the steady state electronic transport in a resistive switching device. The device is composed of a thin film of Ag$_{2}$S (solid electrolyte) contacted by a Pt nano-contact acting as ion-blocking electrode, and a large area Ag reference electrode. When applying a bias voltage both ionic and electronic transport occurs, and depending on the polarity it causes an accumulation of ions around the nano-contact. At small applied voltages (pre-switching) we observed this as a strongly nonlinear current-voltage curve, which have been modeled using the Hebb-Wagner treatment for polarization of a mixed conductor. This model correctly describes the transport of the electrons within the polarized solid electrolyte in the steady state up until the resistance switching, covering the entire range of non-stoichiometries, and including the supersaturation range just before the deposition of elemental silver. In this way, it is a step towards a quantitative understanding of the processes that lead to resistance switching.
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arxiv:1004.3079
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A multiterminal lossy coding problem, which includes various problems such as the Wyner-Ziv problem and the complementary delivery problem as special cases, is considered. It is shown that any point in the achievable rate-distortion region can be attained even if the source statistics are not known.
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arxiv:1004.3085
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Lensing flux-ratio anomalies have been frequently observed and taken as evidence for the presence of abundant dark matter substructures in lensing galaxies, as predicted by the cold dark matter (CDM) model of cosmogony. In previous work, we examined the cusp-caustic relations of the multiple images of background quasars lensed by galaxy-scale dark matter haloes, using a suite of high-resolution N-body simulations (the Aquarius simulations). In this work, we extend our previous calculations to incorporate both the baryonic and diffuse dark components in lensing haloes. We include in each lensing simulation: (1) a satellite galaxy population derived from a semi-analytic model applied to the Aquarius haloes, (2) an empirical Milky-Way globular cluster population and (3) satellite streams (diffuse dark component) identified in the simulations. Accounting for these extra components, we confirm our earlier conclusion that the abundance of intrinsic substructures (dark or bright, bound or diffuse) is not sufficient to explain the observed frequency of cusp-caustic violations in the CLASS survey. We conclude that the observed effect could be the result of the small number statistics of CLASS, or intergalactic haloes along the line of sight acting as additional sources of lensing flux anomalies. Another possibility is that this discrepancy signals a failure of the CDM model.
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arxiv:1004.3094
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In this paper we generalize to the case of partial flags a result proved both by Spaltenstein and by Steinberg that relates the relative position of two complete flags and the irreducible components of the flag variety in which they lie, using the Robinson-Schensted-Knuth correspondence.
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arxiv:1004.3097
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Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme. In the rather different context of what might be called the 'Computational Universe Programme' -- one which associates the complexity of physical phenomena to the emergent features of models such as cellular automata -- a choice problem arises with respect to the variety of formal systems that, in virtue of their computational universality (Turing-completeness), qualify as equally good candidates for a computational, unified theory of physics. This paper proposes Causal Sets as the only objects of physical significance and relevance to be considered under the 'computational universe' perspective, and as the appropriate abstraction for shielding the unessential details of the many different computationally universal candidate models. At the same time, we propose a fully deterministic, radical alternative to the probabilistic techniques currently considered in the Causal Set Programme for growing discrete spacetimes. We investigate a number of computation models by grouping them into two broad classes, based on the support on which they operate; in one case this is linear, like a tape or a string of symbols; in the other, it is a two-dimensional grid or a planar graph. For each model we identify the causality relation among computation events, implement it, and conduct a possibly exhaustive exploration of the associated causal set space, while examining quantitative and qualitative features such as dimensionality, curvature, planarity, emergence of pseudo-randomness, causal set substructures and particles.
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arxiv:1004.3128
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We show that inducing structural softness in regular magnetoelectric (ME) multiferroics -- i.e., tuning the materials to make their structure strongly reactive to applied fields -- makes it possible to obtain very large ME effects. We present illustrative first-principles results for BiFeO3 thin films.
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arxiv:1004.3152
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Stress vs. strain fluctuations in athermal amorphous solids are an example of `crackling noise' of the type studied extensively in the context of elastic membranes moving through random potentials. Contrary to the latter, we do not have a stochastic equation whose statistics agree with the measured ones. On the other hand we show in this Letter that the statistics of the former exhibit 'density scaling' when the interparticle potential can be well approximated by a power law. The distributions of sizes of dissipative events for a wide range of densities and system sizes follow a single scaling function. We find that both the system-size scaling of energy drops and the entire strain interval statistics are invariant to changes in density. We use this to determine accurately the exponents in the scaling laws, establishing that the present crackling noise belongs to a different universality class.
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arxiv:1004.3193
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Local symmetries of a non-expanding horizon has been investigated in the 1st order formulation of gravity. When applied to a spherically symmetric isolated horizon only a U(1) subgroup of the Lorentz group survives as residual local symmetry that one can make use of in constructing an effective theory on the horizon.
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arxiv:1004.3200
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We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This result answers a question posed by Volkov. For the search problems of finding a shortest reset word and the length of a shortest reset word, we establish membership in the complexity classes FP^NP and FP^NP[log], respectively. Moreover, we show that both these problems are hard for FP^NP[log]. Finally, we observe that computing a reset word of a given length is FNP-complete.
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arxiv:1004.3246
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Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N-dimensional basis representation has just K<<N significant coefficients; in this case, the CS theory maintains that just M = K log N random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to S-sparse signals/images that are convolved with an unknown F-sparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K=SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naive bound based on the total signal sparsity K=SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses. The algorithm alternatively estimates the pulse locations and the pulse shape in a manner reminiscent of classical deconvolution algorithms. Numerical experiments on synthetic and real data demonstrate the advantages of our approach over standard CS.
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arxiv:1004.3273
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With the Blue Channel Spectrograph (BCS) on the MMT telescope, we have obtained spectra to the atmospheric cutoff of quasars previously known to show at least one absorption system at z>1.6 with very strong metal lines (candidate metal-strong damped Lya systems; cMSDLAs). The BCS/MMT spectra yield precise estimates of the HI column densities (NHI) of the systems through Voigt profile analysis of their Lya transitions. Nearly all of the cMSDLAs (41/43) satisfy the NHI criterion of DLAs, 10^20.3. As a population, these systems have systematically higher NHI values than DLAs chosen randomly from quasar sightlines. Combining our NHI measurements with previously measured metal column densities, we estimate metallicities for the MSDLAs. These systems have significantly higher values than randomly selected DLAs; at z~2, the MSDLAs show a median metallicity [M/H] ~ -0.67 that is 0.6dex higher than a corresponding control sample. This establishes MSDLAs as having amongst the most metal-rich gas in the high z universe. Our measurements extend the observed correlation between SiII 1526 equivalent width and the gas metallicity to higher values. If interpreted as a mass-metallicity relation, this implies the MSDLAs are the high mass subset of the DLA population. We demonstrate that dust in the MSDLAs reddens their background quasars, with a median shift in the spectral slope of Da = 0.29. Assuming an SMC extinction law, this implies a median reddening E(B-V)=0.025mag and visual extinction A_V=0.076mag. Future studies of MSDLAs offer the opportunity to study the extinction, nucleosynthesis, and kinematics of the most chemically evolved, gas-rich galaxies at high z. [abridged]
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arxiv:1004.3319
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So far, the Standard Model of particle physics (SM) describes the phenomenology observed in high energy physics. In the Large Hadron Collider (LHC) is expected to find the Higgs boson, which is an essential part of SM; also expects to see new particles or deviations from the SM, which would be evidence of other truly fundamental theory. Consequently, a clear understanding of the SM and, in general, quantum field theory is of great importance for particle physics, however, students face a formalism and a set of concepts with which they are unfamiliar. This paper shows how to make an approach to SM to introduce students to the formalism and some fundamental concepts.
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arxiv:1004.3331
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In this paper, the holographic dark energy model with new infrared (IR) cut-off for both the flat case and the non-flat case are confronted with the combined constraints of current cosmological observations: type Ia Supernovae, Baryon Acoustic Oscillations, current Cosmic Microwave Background, and the observational hubble data. By utilizing the Markov Chain Monte Carlo (MCMC) method, we obtain the best fit values of the parameters with $1\sigma, 2\sigma$ errors in the flat model: $\Omega_{b}h^2=0.0233^{+0.0009 +0.0013}_{-0.0009 -0.0014}$, $\alpha=0.8502^{+0.0984 +0.1299}_{-0.0875 -0.1064}$, $\beta=0.4817^{+0.0842 +0.1176}_{-0.0773 -0.0955}$, $\Omega_{de0}=0.7287^{+0.0296 +0.0432}_{-0.0294 -0.0429}$, $\Omega_{m0}=0.2713^{+0.0294 +0.0429}_{-0.0296 -0.0432}$, $H_0=66.35^{+2.38 +3.35}_{-2.14 -3.07}$. In the non-flat model, the constraint results are found in $1\sigma, 2\sigma$ regions: $\Omega_{b}h^2=0.0228^{+0.0010 +0.0014}_{-0.0010 -0.0014}$, $\Omega_k=0.0305^{+0.0092 +0.0140}_{-0.0134 -0.0176}$, $\alpha=0.8824^{+0.2180 +0.2213}_{-0.1163 -0.1378}$, $\beta=0.5016^{+0.0973 +0.1247}_{-0.0871 -0.1102}$, $\Omega_{de0}=0.6934^{+0.0364 +0.0495}_{-0.0304 -0.0413}$, $\Omega_{m0}=0.2762^{+0.0278 +0.0402}_{-0.0320 -0.0412}$, $H_0=70.20^{+3.03 +3.58}_{-3.17 -4.00}$. In the best fit holographic dark energy models, the equation of state of dark energy and the deceleration parameter at present are characterized by $w_{de0}=-1.1414\pm0.0608, q_0=-0.7476\pm0.0466$ (flat case) and $w_{de0}=-1.0653\pm0.0661, q_0=-0.6231\pm0.0569$ (non-flat case). Compared to the $\Lambda \textmd{CDM}$ model, it is found the current combined datasets do not favor the holographic dark energy model over the $\Lambda \textmd{CDM}$ model.
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arxiv:1004.3340
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We hope to see how much for a model M of some completion T of PA (Peano Arithmetic) does M restriction {<} determine M, say up to isomorphism. We advance in characterizing for non-standard models M of PA the "minimal" set {(a,b):n < a < b for n in N and the linear orders {c:c <_M a}, {c:c <_M b} are isomorphic}, in particular include {(a,b): for no c in M for every n in N we have M models (forall n in N)(exists c)[2 < c^n < a wedge b < a c^n]} and for some model is equal to {(a,b):a < b < a^n for some n in N}.
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arxiv:1004.3342
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A sample of 427 gamma-ray bursts (GRBs), measured by the RHESSI satellite, is studied statistically to determine the number of GRB groups. Previous studies based on the BATSE Catalog and recently on the Swift data claim the existence of an intermediate GRB group, besides the long and short groups. Using only the GRB durations T90 and chi^2 or F-test, we have not found any statistically significant intermediate group. However, the maximum likelihood ratio test, one-dimensional as well as two-dimensional hardness vs. T90 plane, reveal the reality of an intermediate group. Hence, the existence of this group follows not only from the BATSE and Swift datasets, but also from the RHESSI results.
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arxiv:1004.3389
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We study the control complexity of fallback voting. Like manipulation and bribery, electoral control describes ways of changing the outcome of an election; unlike manipulation or bribery attempts, control actions---such as adding/deleting/partitioning either candidates or voters---modify the participative structure of an election. Via such actions one can try to either make a favorite candidate win ("constructive control") or prevent a despised candidate from winning ("destructive control"). Computational complexity can be used to protect elections from control attempts, i.e., proving an election system resistant to some type of control shows that the success of the corresponding control action, though not impossible, is computationally prohibitive. We show that fallback voting, an election system combining approval with majority voting, is resistant to each of the common types of candidate control and to each common type of constructive control. Among natural election systems with a polynomial-time winner problem, only plurality and sincere-strategy preference-based approval voting (SP-AV) were previously known to be fully resistant to candidate control, and only Copeland voting and SP-AV were previously known to be fully resistant to constructive control. However, plurality has fewer resistances to voter control, Copeland voting has fewer resistances to destructive control, and SP-AV (which like fallback voting has 19 out of 22 proven control resistances) is arguably less natural a system than fallback voting.
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arxiv:1004.3398
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We made deep NIR imaging polarimetry toward the Serpens cloud core. The polarization vector maps enable us to newly detect 24 small IR reflection nebulae with YSOs. Polarization measurements of NIR point sources indicate an hourglass-shaped magnetic field, of which symmetry axis is nearly perpendicular to the elongation of the C18O (J=1-0) or submillimeter continuum emission. The bright part of C18O (J=1-0), submillimeter continuum cores as well as many class 0/I objects are located just toward the constriction region of the hourglass-shaped magnetic field. Applying the CF method, the magnetic field strength was estimated to be ~100 muG, suggesting that the ambient region of the Serpens cloud core is moderately magnetically supercritical. These suggest that the Serpens cloud core first contracted along the magnetic field to be an elongated cloud, which is perpendicular to the magnetic field, and that then the central part contracted cross the magnetic field due to the high density in the central region of the cloud core, where star formation is actively continuing. Comparison of this magnetic field with the previous observations of molecular gas and large-scale outflows suggests a possibility that the cloud dynamics is controlled by the magnetic field, protostellar outflows and gravitational inflows. This appears to be in good agreement with the outflow-driven turbulence model and implies the importance of the magnetic field to continuous star formation in the center region of the cluster forming region.
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arxiv:1004.3409
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Using only the Britto-Cachazo-Feng-Witten(BCFW) on-shell recursion relation we prove color-order reversed relation, $U(1)$-decoupling relation, Kleiss-Kuijf(KK) relation and Bern-Carrasco-Johansson(BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color ordered basis from $(n-2)!$ to $(n-3)!$. Our proof gives also its physical interpretation as the mysterious bonus relation with ${1\over z^2}$ behavior under suitable on-shell deformation for no adjacent pair.
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arxiv:1004.3417
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The study of factoring relations between subshifts or cellular automata is central in symbolic dynamics. Besides, a notion of intrinsic universality for cellular automata based on an operation of rescaling is receiving more and more attention in the literature. In this paper, we propose to study the factoring relation up to rescalings, and ask for the existence of universal objects for that simulation relation. In classical simulations of a system S by a system T, the simulation takes place on a specific subset of configurations of T depending on S (this is the case for intrinsic universality). Our setting, however, asks for every configurations of T to have a meaningful interpretation in S. Despite this strong requirement, we show that there exists a cellular automaton able to simulate any other in a large class containing arbitrarily complex ones. We also consider the case of subshifts and, using arguments from recursion theory, we give negative results about the existence of universal objects in some classes.
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arxiv:1004.3458
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This paper considers the stability of liquid metal drops subject to a high-frequency AC magnetic field. An energy variation principle is derived in terms of the surface integral of the scalar magnetic potential. This principle is applied to a thin perfectly conducting liquid disk, which is used to model the drops constrained in a horizontal gap between two parallel insulating plates. Firstly, the stability of a circular disk is analysed with respect to small-amplitude harmonic edge perturbations. Analytical solution shows that the edge deformations with the azimuthal wavenumbers m=2,3,4... start to develop as the magnetic Bond number exceeds the critical threshold Bm_c=3pi(m+1)/2. The most unstable is m=2 mode, which corresponds to an elliptical deformation. Secondly, strongly deformed equilibrium shapes are modelled numerically by minimising the associated energy in combination with the solution of a surface integral equation for the scalar magnetic potential on an unstructured triangular mesh. The edge instability is found to result in the equilibrium shapes of either two- or threefold rotational symmetry depending on the magnetic field strength and the initial perturbation. The shapes of higher rotational symmetries are unstable and fall back to one of these two basic states. The developed method is both efficient and accurate enough for modelling of strongly deformed drop shapes.
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arxiv:1004.3467
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We solve the problem of beams of phonons and rotons incident on, and interacting with, solid surfaces. Phonons and rotons are the quasiparticles of superfluid helium and have a unique dispersion curve. The dispersion curve controls the transmission, reflection and mode change of these quasiparticles at the interface with another medium. We develop a non-local hydrodynamic theory in a consistent and unified way. The structure of the solutions in the quantum fluid is discussed. The creation probabilities of all quasiparticles are derived when any one of them is incident on the interface. The dependencies on frequency and angular are analysed and the backward reflection and refraction for $R^-$ rotons are discussed.
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arxiv:1004.3497
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(Note: this is a shortened version of the original A&A-style structured abstract). The physical nature of the strong photometric variability of T Tau Sa, the more massive member of the Southern "infrared companion" to T Tau, has long been debated. Intrinsic luminosity variations due to variable accretion were originally proposed but later challenged in favor of apparent fluctuations due to time-variable foreground extinction. In this paper we use the timescale of the variability as a diagnostic for the underlying physical mechanism. Because the IR emission emerging from Sa is dominantly thermal emission from circumstellar dust at <=1500K, we can derive a minimum size of the region responsible for the time-variable emission. In the context of the variable foreground extinction scenario, this region must be (un-) covered within the variability timescale, which implies a minimum velocity for the obscuring foreground material. If this velocity supercedes the local Kepler velocity we can reject foreground extinction as a valid variability mechanism. The variable accretion scenario allows for shorter variability timescales since the variations in luminosity occur on much smaller scales, essentially at the surface of the star, and the disk surface can react almost instantly on the changing irradiation with a higher or lower dust temperature and according brightness. We have detected substantial variations at long wavelengths in T Tau S: +26% within four days at 12.8 micron. We show that this short-term variability cannot be due to variable extinction and instead must be due to variable accretion. Using a radiative transfer model of the Sa disk we show that variable accretion can in principle also account for the much larger (several magnitude) variations observed on timescales of several years. For the long-term variability, however, also variable foreground extinction is a viable mechanism.
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arxiv:1004.3502
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In this paper, we present a very important primitive called Information Checking Protocol (ICP) which plays an important role in constructing statistical Verifiable Secret Sharing (VSS) and Weak Secret Sharing (WSS) protocols. Informally, ICP is a tool for authenticating messages in the presence of computationally unbounded corrupted parties. Here we extend the basic bare-bone definition of ICP, introduced by Rabin et al. and then present an ICP that attains the best communication complexity and round complexity among all the existing ICPs in the literature. We also show that our ICP satisfies several interesting properties such as linearity property which is an important requirement in many applications of ICP. Though not presented in this paper, we can design communication and round efficient statistical (i.e involves negligible error probability in computation) VSS and Multiparty Computation (MPC) protocol using our new ICP.
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arxiv:1004.3504
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In this paper we formulate the Least Action Principle for an Organized System as the minimum of the total sum of the actions of all of the elements. This allows us to see how this most basic law of physics determines the development of the system towards states with less action - organized states. Also we state that the metric tensor can describe the specific state of the constraints of the system, which is its actual organization. With this the organization is defined in two ways: 1. A quantitative: the action I. 2. A qualitative: the metric tensor. These two measures can describe the level of development and the specifics of the organization of a system. We consider closed and open systems.
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arxiv:1004.3518
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Major stellar-wind emission features in the spectrum of Eta Car have recently decreased by factors of order 2 relative to the continuum. This is unprecedented in the modern observational record. The simplest, but unproven, explanation is a rapid decrease in the wind density.
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arxiv:1004.3529
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Consider the random walk on the permutation group obtained when the step distribution is uniform on a given conjugacy class. It is shown that there is a critical time at which two phase transitions occur simultaneously. On the one hand, the random walk slows down abruptly (i.e., the acceleration drops from 0 to -\infty at this time as n tends to \infty). On the other hand, the largest cycle size changes from microscopic to giant. The proof of this last result is both considerably simpler and more general than in a previous result of Oded Schramm (2005) for random transpositions. It turns out that in the case of random k-cycles, this critical time is proportional to 1/[k(k-1)], whereas the mixing time is known to be proportional to 1/k.
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arxiv:1004.3530
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In this paper we consider the reconstruction problem on the tree for the hardcore model. We determine new bounds for the non-reconstruction regime on the k-regular tree showing non-reconstruction when lambda < (ln 2-o(1))ln^2(k)/(2 lnln(k)) improving the previous best bound of lambda < e-1. This is almost tight as reconstruction is known to hold when lambda> (e+o(1))ln^2(k). We discuss the relationship for finding large independent sets in sparse random graphs and to the mixing time of Markov chains for sampling independent sets on trees.
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arxiv:1004.3531
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If the orientations of galaxies are correlated with large-scale structure, then anisotropic selection effects such as preferential selection of face-on disc galaxies can contaminate large scale structure observables. Here we consider the effect on the galaxy bispectrum, which has attracted interest as a way to break the degeneracy between galaxy bias and the amplitude of matter fluctuations sigma_8. We consider two models of intrinsic galaxy alignments: one where the probability distribution for the galaxy's orientation contains a term linear in the local tidal field, appropriate for elliptical galaxies; and one with a term quadratic in the local tidal field, which may be applicable to disc galaxies. We compute the correction to the redshift-space bispectrum in the quasilinear regime, and then focus on its effects on parameter constraints from the transverse bispectrum, i.e. using triangles in the plane of the sky. We show that in the linear alignment model, intrinsic alignments result in an error in the galaxy bias parameters, but do not affect the inferred value of sigma_8. In contrast, the quadratic alignment model results in a systematic error in both the bias parameters and sigma_8. However, the quadratic alignment effect has a unique configuration dependence that should enable it to be removed in upcoming surveys.
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arxiv:1004.3611
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In this paper, Lie bialgebra structures on the extended Schrodinger-Virasoro Lie algebra are classified. It is obtained that all the Lie bialgebra structures on L are triangular coboundary. As a by-product, it is derived that the first cohomology group is trivial.
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arxiv:1004.3650
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For a bipartite honeycomb lattice, we show that the Berry phase depends not only on the shape of the system but also on the hopping couplings. Using the entanglement entropy spectra obtained by diagonalizing the block Green's function matrices, the maximal entangled state with the eigenvalue $\lambda_m=1/2$ of the reduced density matrix is shown to have one-to-one correspondence to the zero energy states of the lattice with open boundaries, which depends on the Berry phase. For the systems with finite bearded edges along $x$-direction we find critical hopping couplings: the maximal entangled states (zero-energy states) appear pair by pair if one increases the hopping coupling $h$ over the critical couplings $h_c$s.
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arxiv:1004.3707
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In this paper, based on the user-tag-object tripartite graphs, we propose a recommendation algorithm, which considers social tags as an important role for information retrieval. Besides its low cost of computational time, the experiment results of two real-world data sets, \emph{Del.icio.us} and \emph{MovieLens}, show it can enhance the algorithmic accuracy and diversity. Especially, it can obtain more personalized recommendation results when users have diverse topics of tags. In addition, the numerical results on the dependence of algorithmic accuracy indicates that the proposed algorithm is particularly effective for small degree objects, which reminds us of the well-known \emph{cold-start} problem in recommender systems. Further empirical study shows that the proposed algorithm can significantly solve this problem in social tagging systems with heterogeneous object degree distributions.
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arxiv:1004.3732
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We give a new, elementary proof of a key inequality used by Rudelson in the derivation of his well-known bound for random sums of rank-one operators. Our approach is based on Ahlswede and Winter's technique for proving operator Chernoff bounds. We also prove a concentration inequality for sums of random matrices of rank one with explicit constants.
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arxiv:1004.3821
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It is widely accepted that strong and variable radiation detected over all accessible energy bands in a number of active galaxies arises from a relativistic, Doppler-boosted jet pointing close to our line of sight. The size of the emitting zone and the location of this region relative to the central supermassive black hole are, however, poorly known, with estimates ranging from light-hours to a light-year or more. Here we report the coincidence of a gamma-ray flare with a dramatic change of optical polarization angle. This provides evidence for co-spatiality of optical and gamma-ray emission regions and indicates a highly ordered jet magnetic field. The results also require a non-axisymmetric structure of the emission zone, implying a curved trajectory for the emitting material within the jet, with the dissipation region located at a considerable distance from the black hole, at about 10^5 gravitational radii.
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arxiv:1004.3828
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Sequence organizations are viewed from two points: one is from informational redundancy or informational correlation (IC) and another is from k-mer frequency statistics. Two problems are investigated. The first is how the ICs exceed the fluctuation bound and the order emerges from fluctuation in a genome when the sequence length attains some critical value. We demonstrated that the transition from fluctuation to order takes place at about sequence length 200-300 thousands bases for human and E coli genome. It means that the life emerges from a region between macroscopic and microscopic. The second is about the statistical law of the k-mer organization in a genome under the evolutionary pressure and functional selection. We deduced a sum rule Q(k,N) on the k-mer frequency deviations from the randomness in a N-long sequence of genome and deduced the relations of Q(k,N) with k and N. We found that Q(k,N) increases with length N at a constant rate for most genome sequences and demonstrated that when the functional selection of k-mers is accumulated to some critical value the ordering takes place. An important finding is the sum rule correlated with the evolutionary complexity of the genome.
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arxiv:1004.3843
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Consider a matrix $\Sigma_n$ with random independent entries, each non-centered with a separable variance profile. In this article, we study the limiting behavior of the random bilinear form $u_n^* Q_n(z) v_n$, where $u_n$ and $v_n$ are deterministic vectors, and Q_n(z) is the resolvent associated to $\Sigma_n \Sigma_n^*$ as the dimensions of matrix $\Sigma_n$ go to infinity at the same pace. Such quantities arise in the study of functionals of $\Sigma_n \Sigma_n^*$ which do not only depend on the eigenvalues of $\Sigma_n \Sigma_n^*$, and are pivotal in the study of problems related to non-centered Gram matrices such as central limit theorems, individual entries of the resolvent, and eigenvalue separation.
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arxiv:1004.3848
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During the evolution of rotating first stars, which initially consisted of only hydrogen and helium, CNO elements may emerge to their surface. These stars may therefore have winds that are driven only by CNO elements. We study weak wind effects (Gayley-Owocki heating and multicomponent effects) in stellar winds of first generation stars driven purely by CNO elements. We apply our NLTE multicomponent models and hydrodynamical simulations. The multicomponent effects (frictional heating and decoupling) are important particularly for low metallicity winds, but they influence mass loss rate only if they cause decoupling for velocities lower than the escape velocity. The multicomponent effects also modify the feedback from first stars. As a result of the decoupling of radiatively accelerated metals from hydrogen and helium, the first low-energy cosmic ray particles are generated. We study the interaction of these particles with the interstellar medium concluding that these particles easily penetrate the interstellar medium of a given minihalo. We discuss the charging of the first stars by means of their winds. Gayley-Owocki heating, frictional heating, and the decoupling of wind components occur in the winds of evolved low-metallicity stars and the solar metallicity main-sequence stars.
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arxiv:1004.3853
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We prove triviality results for Einstein warped products with non-compact bases. These extend previous work by D.-S. Kim and Y.-H. Kim. The proof, from the viewpoint of "quasi-Einstein manifolds" introduced by J. Case, Y.-S. Shu and G. Wei, rely on maximum principles at infinity and Liouville-type theorems.
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arxiv:1004.3866
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We use linear response theory in order to compute the light absorption spectrum, in the terahertz band, of a polariton system composed by excitons in a quantum dot very strongly coupled to the lowest photon mode of a thin micropillar. In a thermalized (Bose condensed) system at low temperatures, the spectral function shows a peak (GDR) associated to a 1s - 2p exciton transition, enhanced by polariton effects. On the other hand, in a non-equilibrium system absorption is peaked at low energies. Thus, a measurement of terahertz absorption could give an indication of the degree of thermalization in the polariton system.
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arxiv:1004.3940
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We show that if a matrix $\Phi$ satisfies the RIP of order $[CK^{1.2}]$ with isometry constant $\dt = c K^{-0.2}$ and has coherence less than $1/(20 K^{0.8})$, then Orthogonal Matching Pursuit (OMP) will recover $K$-sparse signal $x$ from $y=\Phi x$ in at most $[CK^{1.2}]$ iterations. This result implies that $K$-sparse signal can be recovered via OMP by $M=O(K^{1.6}\log N)$ measurements.
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arxiv:1004.3946
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We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass in O(a) improved two-flavour lattice QCD. We employ the Schr\"odinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full relativistic QCD action and renormalization problems in HQET can be solved non-perturbatively by a matching to QCD in finite volume. The other region refers to the common parameter range in large-volume simulations of two-flavour lattice QCD, where our results have particular relevance for charm physics applications.
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arxiv:1004.3978
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We consider the optimal control problem of transferring population between states of a quantum system where the coupling proceeds only via intermediate states that are subject to decay. We pose the question whether it is generally possible to carry out this transfer. For a single intermediate decaying state, we recover the Stimulated Raman Adiabatic Passage (STIRAP) process which we identify as the global optimum in the limit of infinite control time. We also present analytic solutions for the case of transfer that has to proceed via two consecutive intermediate decaying states. We show that in this case, for finite power the optimal control does not approach perfect state transfer even in the infinite time limit. We generalize our findings to characterize the topologies of paths that can be achieved by coherent control under the assumption of finite power.
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arxiv:1004.4050
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We consider invariance of the action of N=1 supersymmetric theories under the change of sign of the fermionic co-ordinate in superspace. We show that the R-parity can be realized as a special implementation of this symmetry. Other implementations in the supersymmetric extension of the standard model can be related to lepton number and baryon number parities.
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arxiv:1004.4055
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We find a parametric resonance in the GHz range of the DNA dynamics, generated by pumping hypersound . There are localized phonon modes caused by the random structure of elastic modulii due to the sequence of base pairs.
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arxiv:1004.4066
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In the anomaly-mediated supersymmetry (SUSY) breaking scenario, neutral gaugino of SU(2)_L multiplet, Wino, can be the lightest SUSY particle and become a candidate for dark matter. We calculated scattering cross section of Wino dark matter with nucleon, which is responsible for direct detection of the dark matter, on the assumption that the SUSY particles and the heavier Higgs bosons have masses of the order of the gravitino mass in the SUSY standard model. In such a case, the Wino-nucleon coupling is generated by loop processes. We have included two-loop contribution to Wino-gluon interaction in the calculation, since it is one of the leading contributions to the Wino-nucleon coupling. It was found that the spin-independent scattering cross section with proton is 10^-(46-48) cm^2. While it is almost independent of the Wino mass, the result is quite sensitive to the Higgs boson mass due to the accidental cancellation.
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arxiv:1004.4090
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Let $G$ be a Lie group and $M$ a smooth proper $G$-manifold. Let $pi:Mto M/G$ denote the natural map to the orbit space. Then there exist a PL manifold $P$, a polyhedron $L$ and homeomorphisms $tau:Pto M$ and $\sigma:M/Gto L$ such that $\sigma\circpi\circ\tau$ is PL. If $M$ and the $G$-action are of analytic class, we can choose subanalytic $\tau$ and then unique $P$ and $L$.
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arxiv:1004.4094
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Using a combination of dielectric spectroscopy and solid-state deuteron NMR, the hydration water dynamics of connective tissue proteins is studied at sub-ambient temperatures. In this range, the water dynamics follows an Arrhenius law. A scaling analysis of dielectric losses, 'two-phase' NMR spectra, and spin-lattice relaxation times consistently yield evidence for a Gaussian distribution of energy barriers. With the dielectric data as input, random-walk simulations of a large-angle, quasi-isotropic water reorientation provide an approximate description of stimulated-echo data on hydrated elastin. This secondary process takes place in an essentially rigid energy landscape, but in contrast to typical {\beta}-relaxations it is quasi-isotropic and delocalized. The delocalization is inferred from previous NMR diffusometry experiments. To emphasize the distinction from conventional {\beta}-processes, for aqueous systems such a matrix-decoupled relaxation was termed a {\nu}-process. It is emphasized that the phenomenology of this time-honored, 'new' process is shared by many non-aqueous binary glasses in which the constituent components exhibit a sufficient dynamical contrast.
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arxiv:1004.4119
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A new kind of contactless pumping mechanism is realized in a layer of ferrofluid via a spatio-temporally modulated magnetic field. The resulting pressure gradient leads to a liquid ramp, which is measured by means of X-rays. The transport mechanism works best if a resonance of the surface waves with the driving is achieved. The behavior can be understood semi-quantitatively by considering the magnetically influenced dispersion relation of the fluid.
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arxiv:1004.4151
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We consider multi-dimensional assignment problems in a probabilistic setting. Our main results are: (i) A new efficient algorithm for the 3-dimensional planar problem, based on enumerating and selecting from a set of "alternating-path trees"; (ii) A new efficient matching-based algorithm for the 3-dimensional axial problem.
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arxiv:1004.4239
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We investigated the electronic structure and lattice dynamics of multiferroic MnWO4 by optical spectroscopy. With variation of polarization, temperature, and magnetic field, we obtained optical responses over a wide range of photon energies. The electronic structure of MnWO4 near to the Fermi level was examined, with inter-band transitions identified in optical conductivity spectra above a band-gap of 2.5 eV. As for the lattice dynamics, we identified all the infrared transverse optical phonon modes available according to the group-theory analysis. Although we did not observe much change in global electronic structure across the phase transition temperatures, an optical absorption at around 2.2 eV showed an evident change depending upon the spin configuration and magnetic field. The behavior of this band-edge absorption indicates that spin-orbit coupling plays an important role in multiferroic MnWO4.
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arxiv:1004.4254
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Let $U_\zeta$ be the quantum group (Lusztig form) associated to the simple Lie algebra $\mathfrak{g}$, with parameter $\zeta$ specialized to an $\ell$-th root of unity in a field of characteristic $p>0$. In this paper we study certain finite-dimensional normal Hopf subalgebras $U_\zeta(G_r)$ of $U_\zeta$, called Frobenius-Lusztig kernels, which generalize the Frobenius kernels $G_r$ of an algebraic group $G$. When $r=0$, the algebras studied here reduce to the small quantum group introduced by Lusztig. We classify the irreducible $U_\zeta(G_r)$-modules and discuss their characters. We then study the cohomology rings for the Frobenius-Lusztig kernels and for certain nilpotent and Borel subalgebras corresponding to unipotent and Borel subgroups of $G$. We prove that the cohomology ring for the first Frobenius-Lusztig kernel is finitely-generated when $\g$ has type $A$ or $D$, and that the cohomology rings for the nilpotent and Borel subalgebras are finitely-generated in general.
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arxiv:1004.4315
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Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$ that allow its recovery using L1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of $D$ called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given $D$, called the "capacity sets". We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of $D\alpha=s$.
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arxiv:1004.4329
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We show that SL(2,R) cocycles with a positive Lyapunov exponent are dense in all regularity classes and for all non-periodic dynamical systems. For Schr\"odinger cocycles, we show prevalence of potentials for which the Lyapunov exponent is positive for a dense set of energies.
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arxiv:1004.4349
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In this paper, we investigate an equivariant homeomorphism of the boundaries $\partial X$ and $\partial Y$ of two proper CAT(0) spaces $X$ and $Y$ on which a CAT(0) group $G$ acts geometrically. We provide a sufficient condition to obtain a $G$-equivariant homeomorphism of the two boundaries $\partial X$ and $\partial Y$ as a continuous extension of the quasi-isometry $\phi:Gx_0\to Gy_0$ defined by $\phi(gx_0)=gy_0$, where $x_0\in X$ and $y_0\in Y$.
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arxiv:1004.4376
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It has been reported that damage of genome in a living cell by ionizing radiation is about one-third direct and two-thirds indirect. The former which has been introduced in our last paper, concerns direct energy deposition and ionizing reactions in the biomolecules; the latter results from radiation induced reactive species (mainly radicals) in the medium (mainly water) surrounding the biomolecules. In this review, a short description of ion implantation induced radical formation in water is presented. Then we summarize the aqueous radical reaction chemistry of DNA, protein and their components, followed by a brief introduction of biomolecular damage induced by secondary particles (ions and electron). Some downstream biological effects are also discussed.
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arxiv:1004.4394
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The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems had been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sensing (CS) due to its capability to estimate sparse support even with an insufficient number of snapshots, in which case classical array signal processing fails. However, CS guarantees the accurate recovery in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The apparent dichotomy between the {\em probabilistic} CS and {\em deterministic} sensor array signal processing have not been fully understood. The main contribution of the present article is a unified approach that unveils a {missing link} between CS and array signal processing. The new algorithm, which we call {\em compressive MUSIC}, identifies the parts of support using CS, after which the remaining supports are estimated using a novel generalized MUSIC criterion. Using a large system MMV model, we show that our compressive MUSIC requires a smaller number of sensor elements for accurate support recovery than the existing CS methods and can approach the optimal $l_0$-bound with finite number of snapshots.
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arxiv:1004.4398
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We build upon some new ideas in direct transcription methods developed within the Advanced Concepts Team to introduce two improvements to the Sims-Flanagan transcription for low-thrust trajectories. The obtained new algorithm is able to produce an operational trajectory accounting for the real spacecraft dynamics and adapting the segment duration on-line improving the final trajectory optimality.
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arxiv:1004.4539
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We study D0-D0 mixing in the presence of a fourth generation of quarks. In particular, we calculate the size of the allowed CP violation which is found at the observable level well beyond anything possible with CKM dynamics. We calculate the semileptonic asymmetry a_SL and the mixing induced CP asymmetry eta_fS_f which are correlated with each other. We also investigate the correlation of eta_fS_f with a number of prominent observables in other mesonic systems like epsilon'/epsilon, Br(K_L -> pi0 nu nu), Br(K+ -> pi+ nu nu), Br(B_s ->mu+ mu-), Br(B_d -> mu+ mu-) and finally S_psi phi in the B_s system. We identify a clear pattern of flavour and CP violation predicted by the SM4 model: While simultaneous large 4G effects in the K and D systems are possible, accompanying large NP effects in the B_d system are disfavoured. However this behaviour is not as pronounced as found for the LHT and RSc models. In contrast to this, sizeable CP violating effects in the B_s system are possible unless extreme effects in eta_fS_f are found, and Br(B_s ->mu+ mu-) can be strongly enhanced regardless of the situation in the D system. We find that, on the other hand, S_psi phi > 0.2 combined with the measured epsilon'/epsilon significantly diminishes 4G effects within the D system.
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arxiv:1004.4565
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Quantum Monte Carlo simulations of a two-component Bose mixture of trapped dipolar atoms of identical masses and dipole moments, provide numerical evidence of de-mixing at low finite temperatures. De-mixing occurs as a consequence of quantum statistics, which results in an effective attraction between like bosons. Spatial separation of two components takes place at low temperature with the onset of long exchanges of identical particles, underlying Bose-Einstein condensation of both components. Conversely, at higher temperature the system is miscible due to the entropy of mixing. Exchanges are also found to enhance de-mixing in the case of mixtures of non-identical and distinguishable species.
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arxiv:1004.4581
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A global time-discretized scheme for the Navier-Stokes equation system in its Leray projection form is defined. It is shown that the scheme converges to a bounded global classical solution for smooth data which have polynomial decay at infinity. Furthermore, the algorithm proposed is extended to the situation of initial-boundary value problems. Algorithms constructed in a different context (cf. [4, 10, 5, 9]) may be used within the proposed scheme in order to compute the solution of Leray's form of the Navier-Stokes system. The main idea for global existence is to define a control function dynamically and show explicitly that the scheme which solves a controlled Navier-Stokes type equation can control the modulus of velocity and the first derivatives of velocity to be bounded. The method described here can be extended to Navier-Stokes equations on compact manifolds which is done in a subsequent paper.
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arxiv:1004.4589
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Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schroedinger dynamics and irreversible processes of diffusion. Moreover, said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet, as well as Born's rule, are thus all derived solely from classical physics.
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arxiv:1004.4596
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We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of the space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed.
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arxiv:1004.4599
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In this letter we obtain the finite-temperature structure of 180^o domain walls in PbTiO3 using a quasi-harmonic lattice dynamics approach. We obtain the temperature dependence of the atomic structure of domain walls from 0K up to room temperature. We also show that both Pb-centered and Ti-centered 180^o domain walls are thicker at room temperature; domain wall thickness at T=300K is about three times larger than that of T=0K. Our calculations show that Ti-centered domain walls have a lower free energy than Pb-centered domain walls and hence are more likely to be seen at finite temperatures.
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arxiv:1004.4652
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We review the Moyal and Wick-Voros products, and more in general the translation invariant non-commutative products, and apply them to classical and quantum field theory. We investigate phi^4 field theories calculating their Green's functions up to one-loop for the two- and four-point cases. We also review the connections of these theories with Drinfeld twists.
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arxiv:1004.4655
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Coherent control of quantum states is at the heart of implementing solid-state quantum processors and testing quantum mechanics at the macroscopic level. Despite significant progress made in recent years in controlling single- and bi-partite quantum systems, coherent control of quantum wave function in multipartite systems involving artificial solid-state qubits has been hampered due to the relatively short decoherence time and lacking of precise control methods. Here we report the creation and coherent manipulation of quantum states in a tripartite quantum system, which is formed by a superconducting qubit coupled to two microscopic two-level systems (TLSs). The avoided crossings in the system's energy-level spectrum due to the qubit-TLS interaction act as tunable quantum beam splitters of wave functions. Our result shows that the Landau-Zener-St\"{u}ckelberg interference has great potential in the precise control of the quantum states in the tripartite system.
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arxiv:1004.4657
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In this paper, we investigate a novel $(2,2)$-threshold scheme and then generalize this to a $(n,n)$-threshold scheme for quantum secret sharing (QSS) which makes use of the fundamentals of Analytic Geometry. The dealer aptly selects GHZ states related to the coefficients which determine straight lines on a two-dimension plane. Then by computing each two of the lines intercept or not, we obtain a judging matrix whose rank can be used to determine the secret stored in entangled bits. Based on the database technology, authorized participants access to the database to obtain the secret information and hence the secret never appears in the channel. In this way, the eavesdroppers fail to obtain any secret by applying various attack strategies.
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arxiv:1004.4682
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Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.
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arxiv:1004.4717
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