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We searched up to height $10^7$ for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright.
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arxiv:1008.3275
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The testing time for a system-on-chip(SOC) largely depends on the design of test wrappers and the test access mechanism(TAM).Wrapper/TAM co-optimization is therefore necessary to minimize SOC testing time . In this paper, we propose an efficient algorithm to construct wrappers that reduce testing time for cores. We further propose a new approach for wrapper/TAM co-optimization based on two-dimensional rectangle packing. This approach considers the diagonal length of the rectangles to emphasize on both TAM widths required by a core and its corresponding testing time.
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arxiv:1008.3320
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We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum algebra.
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arxiv:1008.3333
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A benchmark CP-violating supersymmetric scenario (known as 'CPX-scenario' in the literature) is studied in the context of the Large Hadron Collider (LHC). It is shown that the LHC, with low to moderate accumulated luminosity, will be able to probe the existing `hole' in the $m_{h_1}$-$\tan\beta$ plane, which cannot be ruled out by the LEP data. We explore the parameter space with cascade decay of third generation squarks and gluino with CP-violating decay branching fractions. We propose a multi-channel analysis to probe this parameter space some of which are background free at an integrated luminosity of 5-10 fb$^{-1}$. Specially, multi-lepton final states ($3\l,\, 4\l$ and like sign di-lepton) are almost background free and have $5\sigma$ reach for the corresponding signals with very early data of LHC for both 14 TeV and 7 TeV center of mass energy.
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arxiv:1008.3339
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Variability is a property shared by practically all AGN. This makes variability selection a possible technique for identifying AGN. Given that variability selection makes no prior assumption about spectral properties, it is a powerful technique for detecting both low-luminosity AGN in which the host galaxy emission is dominating and AGN with unusual spectral properties. In this paper, we will discuss and test different statistical methods for the detection of variability in sparsely sampled data that allow full control over the false positive rates. We will apply these methods to the GOODS North and South fields and present a catalog of variable sources in the z band in both GOODS fields. Out of 11931 objects checked, we find 155 variable sources at a significance level of 99.9%, corresponding to about 1.3% of all objects. After rejection of stars and supernovae, 139 variability selected AGN remain. Their magnitudes reach down as faint as 25.5 mag in z. Spectroscopic redshifts are available for 22 of the variability selected AGN, ranging from 0.046 to 3.7. The absolute magnitudes in the rest-frame z-band range from ~ -18 to -24, reaching substantially fainter than the typical luminosities probed by traditional X-ray and spectroscopic AGN selection in these fields. Therefore, this is a powerful technique for future exploration of the evolution of the faint end of the AGN luminosity function up to high redshifts.
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arxiv:1008.3384
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We used low resolution spectroscopy from VLT/FORS1, and high resolution spectra from VLT/UVES, to estimate the physical conditions in the ORs, using nebular analysis for emission lines such as [O II], [O III], [N II], and [S II]. We also measured the velocity at two positions of the ORs to test a geometrical model for the rings. Additionally, we used data from the HST science archives to check the evolution of the ORs of SN 1987A for a period that covers almost 11 years. We measured the flux in four different regions, two for each outer ring. We chose regions away from the two bright foreground stars, and as far as possible from the ER, and we created light curves for the emission lines of [O III], H{\alpha}, and [N II]. The profiles of the lightcurves display a declining behaviour, which is consistent with the initial supernova flash powering of the ORs. The electron density of the emitting gas in the ORs, as estimated through nebular analysis from forbidden [O II] and [S II] lines, is <= 3*10^3 cm^-3, has not changed over the last ~ 15 years, and also the [N II] temperature remains fairly constant at ~ 1.2*10^4 K. We find no obvious difference in density and temperature for the two ORs. The highest density, as measured from the decay of H{\alpha}, could, however, be ~ 5*10^3 cm^-3, and since the decay is somewhat faster for the southern outer ring than for the northern, the highest density in the ORs may be found in the southern outer ring. For an assumed distance of 50 kpc to the supernova, the distance between the supernova and the closest parts of the ORs could be as short as ~ 1.7*10^18 cm. Interaction between the supernova ejecta and the outer rings could therefore start in less than ~ 20 years. We do not expect the ORs to show the same optical display as the equatorial ring when this happens.
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arxiv:1008.3387
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We obtain the exact nonequilibrium work generating function (NEWGF), for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite time interval. The Jarzynski equality (JE), obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.
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arxiv:1008.3400
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We consider a utility maximization problem over partially observable Markov ON/OFF channels. In this network instantaneous channel states are never known, and at most one user is selected for service in every slot according to the partial channel information provided by past observations. Solving the utility maximization problem directly is difficult because it involves solving partially observable Markov decision processes. Instead, we construct an approximate solution by optimizing the network utility only over a good constrained network capacity region rendered by stationary policies. Using a novel frame-based Lyapunov drift argument, we design a policy of admission control and user selection that stabilizes the network with utility that can be made arbitrarily close to the optimal in the constrained region. Equivalently, we are dealing with a high-dimensional restless bandit problem with a general functional objective over Markov ON/OFF restless bandits. Thus the network control algorithm developed in this paper serves as a new approximation methodology to attack such complex restless bandit problems.
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arxiv:1008.3421
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In this paper, we examine the non-relativistic stationary Schr\"odinger equation from a differential Galois-theoretic perspective. The main algorithmic tools are pullbacks of second order ordinary linear differential operators, so as to achieve rational function coefficients ("algebrization"), and Kovacic's algorithm for solving the resulting equations. In particular, we use this Galoisian approach to analyze Darboux transformations, Crum iterations and supersymmetric quantum mechanics. We obtain the ground states, eigenvalues, eigenfunctions, eigenstates and differential Galois groups of a large class of Schr\"odinger equations, e.g. those with exactly solvable and shape invariant potentials (the terms are defined within). Finally, we introduce a method for determining when exact solvability is possible.
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arxiv:1008.3445
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A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In particular, we prove that the minimal cardinality of a hypercyclcic tuple of operators on $C^n$ (respectively, on $R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $C^3$ such that every operator commuting with each member of the tuple is non-cyclic.
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arxiv:1008.3483
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A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space $\H$ are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.
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arxiv:1008.3490
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Data from the operation of a bubble chamber filled with 3.5 kg of CF$_{3}$I in a shallow underground site are reported. An analysis of ultrasound signals accompanying bubble nucleations confirms that alpha decays generate a significantly louder acoustic emission than single nuclear recoils, leading to an efficient background discrimination. Three dark matter candidate events were observed during an effective exposure of 28.1 kg-day, consistent with a neutron background. This observation provides the strongest direct detection constraint to date on WIMP-proton spin-dependent scattering for WIMP masses $>20$ GeV/c$^{2}$.
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arxiv:1008.3518
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We present a modal approach to calculate finite temperature Casimir interactions between two periodically modulated surfaces. The scattering formula is used and the reflection matrices of the patterned surfaces are calculated decomposing the electromagnetic field into the natural modes of the structures. The Casimir force gradient from a deeply etched silicon grating is evaluated using the modal approach and compared to experiment for validation. The Casimir force from a two dimensional periodic structure is computed and deviations from the proximity force approximation examined.
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arxiv:1008.3580
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The validity of the CES approximation is investigated by comparison with direct diagonalisation of a model vibronic Hamiltonian of $N$ identical monomers interacting electronically. Even for quite short aggregates (N\gtrsim 6) the CES approximation is shown to give results in agreement with direct diagonalisation, for all coupling strengths, except that of intermediate positive coupling (the H-band region). However, previously excellent agreement of CES calculations and measured spectra in the H-band region was obtained [A. Eisfeld, J. S. Briggs, Chem. Phys. 324, 376]. This is shown to arise from use of the measured monomer spectrum which includes implicitly dissipative effects not present in the model calculation.
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arxiv:1008.3623
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Several new experiments have extended studies of the Casimir force into new and interesting regimes. This recent work will be briefly reviewed. With this recent progress, new issues with background electrostatic effects have been uncovered. The myriad of problems associated with both patch potentials and electrostatic calibrations are discussed and the remaining open questions are brought forward.
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arxiv:1008.3640
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Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison of three preconditioning strategies, namely Chebyshev polynomials, strong-coupling approximation and weak-coupling expansion. We use conjugate gradient (CG) on the normal equations as well as stabilized biconjugate gradient (BiCGStab) as solvers and focus on the fermion matrix of the unitary Fermi gas. Our results indicate that BiCGStab is by far the most efficient strategy, both in terms of the number of iterations and matrix-vector operations.
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arxiv:1008.3647
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A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle twists. It is shown in arXiv:1005.0073v2 that the groupoid generated by flips and handle twists acts transitively on admissible double pants decompositions where the class of admissible decompositions has a natural topological and combinatorial description. In this paper, we label the curves of double pants decompositions and show that for all but one surfaces the same groupoid acts transitively on all labeled admissible double pants decompositions. The only exclusion is a sphere with two handles, where the groupoid has 15 orbits.
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arxiv:1008.3679
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It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a representation preserves critical points. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader than the class of face posets of finite regular CW complexes.
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arxiv:1008.3724
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We establish the stability of second-order linear dynamic equations on time scales in the sense of Hyers and Ulam. To wit, if an approximate solution of the second-order linear equation exists, then there exists an exact solution to the dynamic equation that is close to the approximate one.
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arxiv:1008.3726
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Over the last couple of years, "Cloud Computing" or "Elastic Computing" has emerged as a compelling and successful paradigm for internet scale computing. One of the major contributing factors to this success is the elasticity of resources. In spite of the elasticity provided by the infrastructure and the scalable design of the applications, the elephant (or the underlying database), which drives most of these web-based applications, is not very elastic and scalable, and hence limits scalability. In this paper, we propose ElasTraS which addresses this issue of scalability and elasticity of the data store in a cloud computing environment to leverage from the elastic nature of the underlying infrastructure, while providing scalable transactional data access. This paper aims at providing the design of a system in progress, highlighting the major design choices, analyzing the different guarantees provided by the system, and identifying several important challenges for the research community striving for computing in the cloud.
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arxiv:1008.3751
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The planar solution is discussed for an N=3 Chern-Simons-matter theory constructed recently by Gaiotto and Tomasiello. The planar resolvent is obtained in terms of contour integrals. If the sum of two Chern-Simons levels k_1,k_2 is small, the expectation value of a supersymmetric Wilson loop grows exponentially with the total 't Hooft coupling, as is expected from AdS/CFT correspondence. If one of the Chern-Simons levels, say k_2, is taken to infinity, for which one of the 't Hooft coupling constants becomes zero, then the exponential behavior disappears.
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arxiv:1008.3950
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We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all non-adiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.
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arxiv:1008.3968
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I review the current status of the nucleon PDFs determined from global fits with emphasis on the impact of recent experimental data and the remaining theoretical challenges.
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arxiv:1008.3988
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During the 2008 run RHIC provided high luminosity in both p+p and d+Au collisions at $\sqrt{s_{NN}}= 200$ GeV. Electromagnetic calorimeter acceptance in STAR was enhanced by the new Forward Meson Spectrometer (FMS), and is now almost contiguous from $-1<\eta<4$ over the full azimuth. This large acceptance provides sensitivity to the gluon density in the nucleus down to $x\approx 10^{-3}$, as expected for $2\rightarrow 2$ parton scattering. Measurements of the azimuthal correlation between a forward $\pi^{0}$ and an associated particle at large rapidity are sensitive to the low-x gluon density. Data exhibit the qualitative features expected from gluon saturation. A comparison to calculations using the Color Glass Condensate (CGC) model is presented.
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arxiv:1008.3989
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We analyze the propagation of waves in sunspots from the photosphere to the chromosphere using time series of co-spatial Ca II H intensity spectra (including its line blends) and polarimetric spectra of Si I 10827 and the He I 10830 multiplet. From the Doppler shifts of these lines we retrieve the variation of the velocity along the line-of-sight at several heights. Phase spectra are used to obtain the relation between the oscillatory signals. Our analysis reveals standing waves at frequencies lower than 4 mHz and a continuous propagation of waves at higher frequencies, which steepen into shocks in the chromosphere when approaching the formation height of the Ca II H core. The observed non-linearities are weaker in Ca II H than in He I lines. Our analysis suggests that the Ca II H core forms at a lower height than the He I 10830 line: a time delay of about 20 s is measured between the Doppler signal detected at both wavelengths. We fit a model of linear slow magnetoacoustic wave propagation in a stratified atmosphere with radiative losses according to Newton's cooling law to the phase spectra and derive the difference in the formation height of the spectral lines. We show that the linear model describes well the wave propagation up to the formation height of Ca II H, where non-linearities start to become very important.
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arxiv:1008.4004
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FU Orionis is the prototype of a class of eruptive young stars (``FUors'') characterized by strong optical outbursts. We recently completed an exploratory survey of FUors using XMM-Newton to determine their X-ray properties, about which little was previously known. The prototype FU Ori and V1735 Cyg were detected. The X-ray spectrum of FU Ori was found to be unusual, consisting of a cool moderately-absorbed component plus a hotter component viewed through an absorption column density that is an order of magnitude higher. We present here a sensitive (99 ks) follow-up X-ray observation of FU Ori obtained at higher angular resolution with Chandra ACIS-S. The unusual multi-component spectrum is confirmed. The hot component is centered on FU Ori and dominates the emission above 2 keV. It is variable (a signature of magnetic activity) and is probably coronal emission originating close to FU Ori's surface viewed through cool gas in FU Ori's strong wind or accretion stream. In contrast, the X-ray centroid of the soft emission below 2 keV is offset 0.20 arcsec to the southeast of FU Ori, toward the near-IR companion (FU Ori S). This offset amounts to slightly less than half the separation between the two stars. The most likely explanation for the offset is that the companion contributes significantly to the softer X-ray emission below 2 keV (and weakly above 2 keV). The superimposed X-ray contributions from FU Ori and the companion resolve the paradox posed by XMM-Newton of an apparently single X-ray source viewed through two different absorption columns.
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arxiv:1008.4090
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The 4-dimensional effective theory arising from an induced gravity action for a co-dimension greater than one brane consists of multiple galileon fields pi^I, I=1...N, invariant under separate Galilean transformations for each scalar, and under an internal SO(N) symmetry. We study the viability of such models by examining spherically symmetric solutions. We find that for general, non-derivative couplings to matter invariant under the internal symmetry, such solutions exist and exhibit a Vainshtein screening effect. By studying perturbations about such solutions, we find both an inevitable gradient instability and fluctuations propagating at superluminal speeds. These findings suggest that more general, derivative couplings to matter are required for the viability of SO(N) galileon theories.
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arxiv:1008.4128
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We have performed a comprehensive chemical abundance analysis of the extremely metal-poor ([Ar/H]<-2) halo planetary nebula (PN) BoBn 1 based on IUE archive data, Subaru/HDS spectra, VLT/UVES archive data, and Spitzer/IRS spectra. We have detected over 600 lines in total and calculated ionic and elemental abundances of 13 elements using detected optical recombination lines (ORLs) and collisionally excited lines (CELs). The estimations of C, N, O, and Ne abundances from the ORLs and Kr, Xe, and Ba from the CELs are done the first for this nebula, empirically and theoretically. The C, N, O, and Ne abundances from ORLs are systematically larger than those from CELs. The abundance discrepancies apart from O could be explained by a temperature fluctuation model, and that of O might be by a hydrogen deficient cold component model. We have detected 5 fluorine and several s-process elements. The amounts of [F/H], [Kr/H], and [Xe/H] suggest that BoBn 1 is the most F-rich among F detected PNe and is a heavy s-process element rich PN. We have confirmed dust in the nebula that is composed of amorphous carbon and PAHs with a total mass of 5.8 x 10^-6 Msun. The photo-ionization models built with non-LTE theoretical stellar atmospheres indicate that the progenitor was a 1-1.5 Msun star that would evolve into a white dwarf with an ~0.62 Msun core mass and ~0.09 Msun ionized nebula. The derived elemental abundances have been reviewed from the standpoint of theoretical nucleosynthesis models. It is likely that the elemental abundances except N could be explained either by a 1.5 Msun single star model or by a binary model composed of 0.75 Msun + 1.5 Msun stars. Careful examination implies that BoBn 1 has evolved from a 0.75 Msun + 1.5 Msun binary and experienced coalescence during the evolution to become a visible PN, similar to the other extremely metal-poor halo PN, K 648 in M 15.
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arxiv:1008.4175
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Recently, Lembert, Gilson et al proposed a lucid and systematic approach to obtain bilinear B\"{a}cklund transformations and Lax pairs for constant-coefficient soliton equations based on the use of binary Bell polynomials. In this paper, we would like to further develop this method with new applications. We extend this method to systematically investigate complete integrability of nonisospectral and variable-coefficient equations. In addiction, a method is described for deriving infinite conservation laws of nonlinear evolution equations based on the use of binary Bell polynomials. All conserved density and flux are given by explicit recursion formulas. By taking variable-coefficient KdV and KP equations as illustrative examples, their bilinear formulism, bilinear B\"{a}cklund transformations, Lax pairs, Darboux covariant Lax pairs and conservation laws are obtained in a quick and natural manner. In conclusion, though the coefficient functions have influences on a variable-coefficient nonlinear equation, under certain constrains the equation turn out to be also completely integrable, which leads us to a canonical interpretation of their $N$-soliton solutions in theory.
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arxiv:1008.4194
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We study a modified model of the Kardar-Parisi-Zhang equation with quenched disorder, in which the driving force decreases as the interface rises up. A critical state is self-organized, and the anomalous scaling law with roughness exponent alpha=0.63 is numerically obtained.
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arxiv:1008.4211
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We demonstrate experimentally the creation and measurement of an entangled state between a microscopic two level system and a macroscopic superconducting resonator where their indirect interaction is mediated by an artificial atom, a superconducting persistent current qubit (PCQB). We show that the microscopic two level system, formed by a defect in an oxide layer, exhibits an order of magnitude longer dephasing time than the PCQB, while the dephasing time of the entangled states between the microscopic two level system and macroscopic superconducting resonator is significantly longer than the dephasing time in the persistent current qubits. This demonstrates the possibility that a qubit of moderate coherence properties can be used in practice to address low decoherence quantum memories by connecting them to macroscopic circuit QED quantum buses, leading future important implications for quantum information processing tasks.
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arxiv:1008.4212
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Larson (1981) first noted a scaling relation between masses and sizes in molecular clouds that implies that these objects have approximately constant column densities. This original claim, based upon millimeter observations of carbon monoxide lines, has been challenged by many theorists, arguing that the apparent constant column density observed is merely the result of the limited dynamic range of observations, and that in reality clouds have column density variations over two orders of magnitudes. In this letter we investigate a set of nearby molecular clouds with near-infrared excess methods, which guarantee very large dynamic ranges and robust column density measurements, to test the validity of Larson's third law. We verify that different clouds have almost identical average column densities above a given extinction threshold; this holds regardless of the extinction threshold, but the actual average surface mass density is a function of the specific threshold used. We show that a second version of Larson's third law, involving the mass-radius relation for single clouds and cores, does not hold in our sample, indicating that individual clouds are not objects that can be described by constant column density. Our results instead indicate that molecular clouds are characterized by a universal structure. Finally we point out that this universal structure can be linked to the log-normal nature of cloud column density distributions.
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arxiv:1008.4251
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We investigate the gradient flow of the $L^2$ norm of the Riemannian curvature on surfaces. We show long time existence with arbitrary initial data, and exponential convergence of the volume normalized flow to a constant scalar curvature metric when the initial energy is below a constant determined by the Euler characteristic of the underlying surface.
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arxiv:1008.4311
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Using archival VLBI data for 3114 radio-luminous active galactic nuclei, we searched for binary supermassive black holes using a radio spectral index mapping technique which targets spatially resolved, double radio-emitting nuclei. Only one source was detected as a double nucleus. This result is compared with a cosmological merger rate model and interpreted in terms of (1) implications for post-merger timescales for centralisation of the two black holes, (2) implications for the possibility of "stalled" systems, and (3) the relationship of radio activity in nuclei to mergers. Our analysis suggests that the binary evolution of paired supermassive black holes (both of masses >= 1e8 Msun) spends less than 500 Myr in progression from the merging of galactic stellar cores to within the purported stalling radius for supermassive black hole pairs. The data show no evidence for an excess of stalled binary systems at small separations. We see circumstantial evidence that the relative state of radio emission between paired supermassive black holes is correlated within orbital separations of 2.5 kpc.
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arxiv:1008.4382
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We use four years of introductory astronomy scores to analyze the ability of the current population to perform college level work and measure the amount of grade inflation across various majors. Using an objective grading scale, one that is independent of grading curves, we find that 29% of intro astronomy students fail to meet minimal standards for college level work. Of the remaining students, 41% achieve satisfactory work, 30% achieve mastery of the topics. Intro astronomy scores correlate with SAT and college GPA. Sequential mapping of the objective grade scheme onto GPA finds that college grades are inflated by 0.2 for natural sciences majors, 0.3 for social sciences, professional schools and undeclared majors), 0.5 for humanities majors. It is unclear from the data whether grade inflation is due to easier grading curves or depression of course material. Experiments with student motivation tools indicates that poor student performance is due to deficiency in student abilities rather than social factors (such as study time or decreased interest in academics), i.e., more stringent admission standards would resolve grade inflation.
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arxiv:1008.4410
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We study the initial and final state interaction effects in the transverse momentum dependent parton distributions in the small-$x$ saturation region. In particular, we discuss the quark distributions in the semi-inclusive deep inelastic scattering, Drell-Yan lepton pair production and dijet-correlation processes in $pA$ collisions. We calculate the quark distributions in the scalar-QED model and then extend to the color glass condensate formalism in QCD. The quark distributions are found universal between the DIS and Drell-Yan processes. On the other hand, the quark distribution from the $qq'\to qq'$ channel contribution to the dijet-correlation process is not universal. However, we find that it can be related to the quark distribution in DIS process by a convolution with the normalized unintegrated gluon distribution in the color glass condensate formalism in the large $N_c$ limit.
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arxiv:1008.4432
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We study the superheating field of a bulk superconductor within Ginzburg-Landau theory, which is valid near the critical temperature. We calculate, as functions of the Ginzburg-Landau parameter $\kappa$, the superheating field $\Hsh$ and the critical momentum $k_c$ characterizing the wavelength of the instability of the Meissner state to flux penetration. By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for an ordinary differential equation, we solve the problem numerically. We demonstrate agreement between the numerics and analytics, and show convergence to the known results at both small and large $\kappa$. We discuss the implications of the results for superconducting RF cavities used in particle accelerators.
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arxiv:1008.4553
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The present paper is devoted to finding a necessary and sufficient condition on the occurence of scattering for the regularly hyperbolic systems with time-dependent coefficients whose time-derivatives are integrable over the real line. More precisely, it will be shown that the solutions are asymptotically free if the coefficients are stable in the sense of the Riemann integrability as time goes to infinity, while each nontrivial solution is never asymptotically free provided that the coefficients are not R-stable as times goes to infinity. As a by-product, the scattering operator can be constructed. It is expected that the results obtained in the present paper would be brought into the study of the asymptotic behaviour of Kirchhoff systems.
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arxiv:1008.4644
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A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence on the interplate distance [Siber and Buljan, arXiv:1007.4699 (2010)]. The phenomenon has been used as a basis for an experimental problem at the 41st International Physics Olympiad. We show that the corresponding variational problem for the equilibrium energy of the deformed cylinder is equivalent to a minimum action description of a simple gravitational pendulum with an amplitude of 90 degrees. We use this analogy to show that the power-law of the force is exact for distances less than a critical value. An analytical solution for the elastic force is found and confirmed by measurements over a range of deformations covering both linear and non-Hookean behavior.
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arxiv:1008.4649
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In a recent study [C Arita, Phys. Rev. E 80, 051119 (2009)], an extension of the M/M/1 queueing process with the excluded-volume effect as in the totally asymmetric simple exclusion process (TASEP) was introduced. In this paper, we consider its discrete-time version. The update scheme we take is the parallel one. A stationary-state solution is obtained in a slightly arranged matrix product form of the discrete-time open TASEP with the parallel update. We find the phase diagram for the existence of the stationary state. The critical line which separates the parameter space into the regions with and without the stationary state can be written in terms of the stationary current of the open TASEP. We calculate the average length of the system and the average number of particles.
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arxiv:1008.4651
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We present a novel laser mode-locking scheme and discuss its unusual properties and feasibility using a theoretical model. A large set of single-frequency continuous-wave lasers oscillate by amplification in spatially separated gain media. They are mutually phase-locked by nonlinear feedback from a common saturable absorber. As a result, ultra short pulses are generated. The new scheme offers three significant benefits: the light that is amplified in each medium is continuous wave, thereby avoiding issues related to group velocity dispersion and nonlinear effects that can perturb the pulse shape. The set of frequencies on which the laser oscillates, and therefore the pulse repetition rate, is controlled by the geometry of resonator-internal optical elements, not by the cavity length. Finally, the bandwidth of the laser can be controlled by switching gain modules on and off. This scheme offers a route to mode-locked lasers with high average output power, repetition rates that can be scaled into the THz range, and a bandwidth that can be dynamically controlled. The approach is particularly suited for implementation using semiconductor diode laser arrays.
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arxiv:1008.4700
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In this paper we show boundary monotonicity formulae for rectifiable varifolds having a $C^{1,\alpha}$ "boundary". In particular, we show that the area ratios of balls centered at this "boundary'' satisfy a nice monotonicity formula, similar to that for interior balls (proved in Allard's paper "On the first variation of a varifold''). This extends the boundary monotonicity formulae of Allard (see "On the first variation of a varifold- boundary behavior''), which require that the boundary is $C^{1,1}$. As a corollary, Allard's boundary regularity results extend to this case and provide a regularity result for rectifiable varifolds with a $C^{1,\alpha}$ ``boundary''.
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arxiv:1008.4728
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We study the high-energy limit of tree-level string production amplitudes from decaying D-branes in bosonic string theory, interpreting the vertex operators as external charges interacting with a Coulomb gas corresponding to the rolling tachyon background, and performing an electrostatic analysis. In particular, we consider two open string - one closed string amplitudes and four open string amplitudes, and calculate explicit formulas for the leading exponential behavior.
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arxiv:1008.4743
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This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error correction performance, high rates, and low decoding complexity. The proposed method produces infinitely many new codes with a wide variety of parameters and entanglement requirements. Our framework encompasses various codes including the previously known entanglement-assisted quantum LDPC codes having the best error correction performance and many new codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.
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arxiv:1008.4747
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Present contribution represents a significant improvement of our previous calculation of Maxwellian-averaged cross sections and astrophysical reaction rates. Addition of newly-evaluated neutron reaction libraries, such as ROSFOND and Low-Fidelity Covariance Project, and improvements in data processing techniques allowed us to extend it for entire range of s-process nuclei, calculate Maxwellian-averaged cross section uncertainties for the first time, and provide additional insights on all currently available neutron-induced reaction data. Nuclear reaction calculations using ENDF libraries and current Java technologies will be discussed and new results will be presented.
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arxiv:1008.4772
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Prior imaging of the lenticular galaxy, NGC 3998, with the Hubble Space Telescope (HST) revealed a small, highly inclined, nuclear ionized gas disk, the kinematics of which indicate the presence of a 270 million solar mass black hole. Plausible kinematic models are used to constrain the size of the broad line region (BELR) in NGC 3998 by modeling the shape of the broad H-alpha, H-beta and H-gamma emission line profiles. The analysis indicates that the BELR is large with an outer radius ~7 pc, regardless of whether the kinematic model is represented by an accretion disk or a spherically symmetric inflow. The electron temperature in the BELR is < 28,800 K consistent with photoionization by the AGN. Indeed, the AGN is able to sustain the ionization of the BELR, albeit with a high covering factor ranging between 20% and 100% depending on the spectral energy distribution adopted for the AGN. The high covering factor favors a spherical distribution for the gas as opposed to a thin disk. If the gas density is > 7 x 10^3 cm^-3 as indicated by the broad forbidden [S II] emission line ratio, then interpreting the broad H-alpha emission line in terms of a steady state spherically symmetric inflow leads to a rate < 6.5 x 10^-2 Msun/yr which exceeds the inflow requirement to explain the X-ray luminosity in terms of a radiatively inefficient inflow by a factor of < 18.
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arxiv:1008.4775
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Rings are a model system for studying phase coherence in one dimension. Superconducting rings have states with uniform phase windings that are integer multiples of 2$\pi$ called fluxoid states. When the energy difference between these fluxoid states is of order the temperature so that phase slips are energetically accessible, several states contribute to the ring's magnetic response to a flux threading the ring in thermal equilibrium and cause a suppression or downturn in the ring's magnetic susceptibility as a function of temperature. We review the theoretical framework for superconducting fluctuations in rings including a model developed by Koshnick$^1$ which includes only fluctuations in the ring's phase winding number called fluxoid fluctuations and a complete model by von Oppen and Riedel$^2$ that includes all thermal fluctuations in the Ginzburg-Landau framework. We show that for sufficiently narrow and dirty rings the two models predict a similar susceptibility response with a slightly shifted Tc indicating that fluxoid fluctuations are dominant. Finally we present magnetic susceptibility data for rings with different physical parameters which demonstrate the applicability of our models. The susceptibility data spans a region in temperature where the ring transitions from a hysteretic to a non hysteretic response to a periodic applied magnetic field. The magnetic susceptibility data, taken where transitions between fluxoid states are slow compared to the measurement time scale and the ring response was hysteretic, decreases linearly with increasing temperature resembling a mean field response with no fluctuations. At higher temperatures where fluctuations begin to play a larger role a crossover occurs and the non-hysteretic data shows a fluxoid fluctuation induced suppression of diamagnetism below the mean field response that agrees well with the models.
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arxiv:1008.4821
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Waldmeier [1971] found a very tight relationship between the F10.7 solar radio flux and the sunspot number and suggested using the flux for an objective calibration of the sunspot number. He suggested that if this relationship changed later on, the sunspot number should be re-calibrated, assuming that the calibration must have drifted with time. I repeat his analysis using data up to the present and it is, indeed, clear that the relationship has changed significantly. This could be due to a drift of the calibration or to a secular change in the visibility of sunspots, or both.
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arxiv:1008.4832
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Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches were based on minimizing the maximum error. Recently, Seol and Cheun proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.
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arxiv:1008.4870
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We derive the plasticity equations for convex quadrilaterals on a complete convex surface with bounded specific curvature and prove a plasticity principle which states that: Given four shortest arcs which meet at the weighted Fermat-Torricelli point their endpoints form a convex quadrilateral and the weighted Fermat-Torricelli point belongs to the interior of this convex quadrilateral, an increase of the weight corresponding to a shortest arc causes a decrease of the two weights that correspond to the two neighboring shortest arcs and an increase of the weight corresponding to the opposite shortest arc by solving the inverse weighted Fermat-Torricelli problem for quadrilaterals on a convex surface of bounded specific curvature. Furthermore, we show a connection between the plasticity of convex quadrilaterals on a complete convex surface with bounded specific curvature with the plasticity of some generalized convex quadrilaterals on a manifold which is certainly composed by triangles. We also study some cases of symmetrization of weighted convex quadrilaterals by introducing a new symmetrization technique which transforms some classes of weighted geodesic convex quadrilaterals on a convex surface to parallelograms in the tangent plane at the weighted Fermat-Torricelli point of the corresponding quadrilateral.
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arxiv:1008.4917
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We discuss the possibility of Mathieu group M24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M24. In this paper we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.
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arxiv:1008.4924
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A uniaxial chiral metamaterial is constructed by double-layered four "U" split ring resonators mutually twisted by 90 degrees. It shows a giant optical activity and circular dichroism. The retrieval results reveal that a negative refractive index is realized for circularly polarized waves due to the large chirality. The experimental results are in good agreement with the numerical results.
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arxiv:1008.4950
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We construct classical solutions in quiver gauge theories on D0-branes probing toric del Pezzo singularities in Calabi-Yau manifolds. Our solutions represent D4-branes wrapped around fuzzy del Pezzo surfaces. We study the fluctuation spectrum around the fuzzy CP^2 solution in detail. We also comment on possible applications of our fuzzy del Pezzo surfaces to the fuzzy version of F-theory, dubbed F(uzz) theory.
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arxiv:1008.5012
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By introducing an invariant of loops on a compact oriented surface with one boundary component, we give an explicit formula for the action of Dehn twists on the completed group ring of the fundamental group of the surface. This invariant can be considered as ``the logarithms" of Dehn twists. The formula generalizes the classical formula describing the action on the first homology of the surface, and Morita's explicit computations of the extended first and the second Johnson homomorphisms. For the proof we use a homological interpretation of the Goldman Lie algebra in the framework of Kontsevich's formal symplectic geometry. As an application, we prove the action of the Dehn twist of a simple closed curve on the $k$-th nilpotent quotient of the fundamental group of the surface depends only on the conjugacy class of the curve in the $k$-th quotient.
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arxiv:1008.5017
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Particle impaction in the super heater geometry found in the municipal solid waste incinerator (MSWI) of GKS in Schweinfurt, Germany, has been investigated. By using direct numerical simulations for the fluid flow, inertial particles coupled to the fluid through the classical Stokes' drag law have been tracked. Focus has been on the effect of flow velocity, and it is shown that decreasing the flow velocity will drastically decrease the impaction efficiency for some particle radii. Finally particle size distribution measurements are presented and used to find quantitative mass fluxes both on the front and the back side of the tubes in the super heater tube bundle.
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arxiv:1008.5040
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Measurement of the chemical and isotopic composition of cosmic rays is essential for the precise understanding of their propagation in the galaxy. While the model parameters are mainly determined using the B/C ratio, the study of extended sets of ratios can provide stronger constraints on the propagation models. In this paper the relative abundances of the light nuclei lithium, beryllium, boron and carbon are presented. The secondary to primary ratios Li/C, Be/C and B/C have been measured in the kinetic energy range 0.35-45 GeV/nucleon. The isotopic ratio 7Li/6Li is also determined in the magnetic rigidity interval 2.5-6.3 GV. The secondary to secondary ratios Li/Be, Li/B and Be/B are also reported. These measurements are based on the data collected by the Alpha Magnetic Spectrometer AMS-01 during the STS-91 space shuttle flight in 1998 June. Our experimental results are in substantial agreement with other measurements, where they exist. We describe our light-nuclei data with a diffusive-reacceleration model. A 10-15% overproduction of Be is found in the model predictions and can be attributed to uncertainties in the production cross-section data.
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arxiv:1008.5051
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We prove a Chern-Lashof type formula computing the expected number of critical points of smooth function on a smooth manifold $M$ randomly chosen from a finite dimensional subspace $V\subset C^\infty(M)$ equipped with a Gaussian probability measure. We then use this formula this formula to find the asymptotics of the expected number of critical points of a random linear combination of a large number eigenfunctions of the Laplacian on the round sphere, tori, or a products of two round spheres. In the case $M=S^1$ we show that the number of critical points of a trigonometric polynomial of degree $\leq \nu$ is a random variable $Z_\nu$ with expectation $E(Z_\nu)\sim 2\sqrt{0.6}\,\nu$ and variance $var(Z_\nu)\sim c\nu$ as $\nu\to \infty$, $c\approx 0.35$.
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arxiv:1008.5085
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Degrading performance of indexing schemes for exact similarity search in high dimensions has long since been linked to histograms of distributions of distances and other 1-Lipschitz functions getting concentrated. We discuss this observation in the framework of the phenomenon of concentration of measure on the structures of high dimension and the Vapnik-Chervonenkis theory of statistical learning.
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arxiv:1008.5105
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This paper is devoted to prove the S. L. Singh's common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of Generalized Kannan Con- traction, Generalized Zamfirescu Contraction and Generalized Weak Contraction for a pair of mappings, proving afterward their respective fixed point results.
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arxiv:1008.5141
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We report detailed studies on magnetic properties of Co3O4 nanoparticles of average size 12.5 nm. Temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the particles show some features characteristic of nanoparticle magnetism such as bifurcation of field cooled (FC) and zero field cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at which ZFC magnetization peaks coincides with the bifurcation temperature and does not shift on application of magnetic fields up to 1 kOe, unlike most other nanoparticle systems. Aging effects in these particles are negligible in both FC and ZFC protocol and memory effects are present only in FC protocol. Our results show that Co3O4 nanoparticles constitute a unique system where superparamagnetic blocking starts above the N\'eel temperature, in the paramagnetic state.
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arxiv:1008.5245
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The incorporation of oxygen atoms has been simulated into either nitrogen or uranium vacancy at the UN(001) surface, sub-surface or central layers. For calculations on the corresponding slab models both the relativistic pseudopotentials and the method of projector augmented-waves (PAW) as implemented in the VASP computer code have been used. The energies of O atom incorporation and solution within the defective UN surface have been calculated and discussed. For different configurations of oxygen ions at vacancies within the UN(001) slab, the calculated density of states and electronic charge re-distribution was analyzed. Considerable energetic preference of O atom incorporation into the N-vacancy as compared to U-vacancy indicates that the observed oxidation of UN is determined mainly by the interaction of oxygen atoms with the surface and sub-surface N vacancies resulting in their capture by the vacancies and formation of O-U bonds with the nearest uranium atoms. Keywords: Density functional calculations, uranium mononitride, surface, defects, N and U vacancies
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arxiv:1008.5311
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The highest exclusive jet multiplicity studied at LEP experiments is five. In this paper we compute the next-to-leading order QCD corrections to e+e- annihilation to five jets, essentially closing the (pure) perturbative QCD studies of exclusive jetty final states at LEP. We compare fixed-order perturbative results with ALEPH data. We estimate hadronization corrections to five-jet observables using the event generator SHERPA, which employs the CKKW procedure to combine a reliable perturbative treatment of high-multiplicity jet final states with parton showers. We show that a competitive value of the strong coupling constant alpha_s(M_Z) = 0.1156 +0.0041 -0.0034 can be extracted from the distribution of the five-jet resolution parameter and the five-jet rate at LEP1 and LEP2.
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arxiv:1008.5313
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Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we propose a novel simple linear graphical model for independent latent random variables, called linear characteristic model (LCM), defined in the characteristic function domain. Using stable distributions, a heavy-tailed family of distributions which is a generalization of Cauchy, L\'evy and Gaussian distributions, we show for the first time, how to compute both exact and approximate inference in such a linear multivariate graphical model. LCMs are not limited to stable distributions, in fact LCMs are always defined for any random variables (discrete, continuous or a mixture of both). We provide a realistic problem from the field of computer networks to demonstrate the applicability of our construction. Other potential application is iterative decoding of linear channels with non-Gaussian noise.
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arxiv:1008.5325
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I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle physics. Noncommutative geometry states that close to the Planck energy scale, space-time has a fine structure and proposes that it is given as the product of a four-dimensional continuum compact Riemaniann manifold by a tiny discrete finite noncommutative space. The spectral action principle, a universal action functional on spectral triples which depends only on the spectrum of the Dirac operator, applied to this almost commutative product geometry, leads to the full Standard Model, including neutrino mixing which has Majorana mass terms and a see-saw mechanism, minimally coupled to gravity. It also makes various predictions at unification scale. I will review some of the phenomenological and cosmological consequences of this beautiful and purely geometrical approach to unification.
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arxiv:1008.5348
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A new implementation of the POWHEG method into the Monte-Carlo event generator Sherpa is presented, focusing on processes with a simple colour structure. Results for a variety of processes, namely e+e- to hadrons, deep-inelastic lepton-nucleon scattering, hadroproduction of single vector bosons and of vector boson pairs as well as the production of Higgs bosons in gluon fusion serve as test cases for the successful realisation. The algorithm is fully automated such that for further processes only virtual matrix elements need to be included.
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arxiv:1008.5399
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We consider isolated compact remnants (ICoRs), i.e. neutrons stars and black holes that do not reside in binary systems and therefore cannot be detected as X-ray binaries. ICoRs may represent $\sim\,5$ percent of the stellar mass budget of the Galaxy, but they are very hard to detect. Here we explore the possibility of using microlensing to identify ICoRs. In a previous paper we described a simulation of neutron star evolution in phase space in the Galaxy, taking into account the distribution of the progenitors and the kick at formation. Here we first reconsider the evolution and distribution of neutron stars and black holes adding a bulge component. From the new distributions we calculate the microlensing optical depth, event rate and distribution of event time scales, comparing and contrasting the case of ICoRs and "normal stars". We find that the contribution of remnants to optical depth is slightly lower than without kinematics, owing to the evaporation from the Galaxy. On the other hand, the relative contribution to the rate of events is a factor $\sim\,5$ higher. In all, $\sim\,6-7$ percent of the events are likely related to ICoRs. In particular, $\sim\,30-40$ percent of the events with duration $>\,100$ days are possibly related to black holes. It seems therefore that microlensing observations are a suitable tool to probe the population of Galactic ICoRs.
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arxiv:1009.0005
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A monochromatic gamma ray line results when dark matter particles in the galactic halo annihilate to produce a two body final state which includes a photon. Such a signal is very distinctive from astrophysical backgrounds, and thus represents an incisive probe of theories of dark matter. We compare the recent null results of searches for gamma ray lines in the galactic center and other regions of the sky with the predictions of effective theories describing the interactions of dark matter particles with the Standard Model. We find that the null results of these searches provide constraints on the nature of dark matter interactions with ordinary matter which are complementary to constraints from other observables, and stronger than collider constraints in some cases.
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arxiv:1009.0008
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We determine the nature of the magnetic quantum critical point in the doped LaFeAsO using a set of constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The system turns out to be remarkably close to a quantum tricritical point, where the nature of the phase transition changes from first to second order. We compare with the effective field theory and discuss the experimental consequences.
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arxiv:1009.0009
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Details of processes through which galaxies convert their gas into stars need to be studied in order to obtain a complete picture of galaxy formation. One way to tackle these phenomena is to relate the HI gas and the stars in galaxies. Here, we present dynamical properties of Damped and sub-Damped Lyman-alpha Systems identified in H-alpha emission with VLT/SINFONI at near infra-red wavelengths. While the DLA towards Q0302-223 is found to be dispersion-dominated, the sub-DLA towards Q1009-0026 shows clear signatures of rotation. We use a proxy to circular velocity to estimate the mass of the halo in which the sub-DLA resides and find M_halo=10^12.6 M_sun. We also derive dynamical masses of these objects, and find M_dyn=10^10.3 M_sun and 10^10.9 M_sun. For one of the two systems (towards Q0302-223), we are able to derive a stellar mass of M_*=10^9.5 M_sun from Spectral Energy Distribution fit. The gas fraction in this object is 1/3rd, comparable to similar objects at these redshifts. Our work illustrates that detailed studies of quasar absorbers can offer entirely new insights into our knowledge of the interaction between stars and the interstellar gas in galaxies.
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arxiv:1009.0027
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For an acyclic quiver Q, we solve the Clebsch-Gordan problem for the projective representations by computing the multiplicity of a given indecomposable projective in the tensor product of two indecomposable projectives. Motivated by this problem for arbitrary representations, we study idempotents in the representation ring of Q (the free abelian group on the indecomposable representations, with multiplication given by tensor product). We give a general technique for constructing such idempotents and for decomposing the representation ring into a direct product of ideals, utilizing morphisms between quivers and categorical Moebius inversion.
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arxiv:1009.0029
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In the interstellar medium the turbulence is believed to be forced mostly through supernova explosions. In a first approximation these flows can be written as a gradient of a potential being thus devoid of vorticity. There are several mechanisms that could lead to vorticity generation, like viscosity and baroclinic terms, rotation, shear and magnetic fields, but it is not clear how effective they are, neither is it clear whether the vorticity is essential in determining the turbulent diffusion acting in the ISM. Here we present a study of the role of rotation, shear and baroclinicity in the generation of vorticity in the ISM.
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arxiv:1009.0147
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A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism.
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arxiv:1009.0174
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The healing of graphene grown from a metallic substrate is investigated using tight-binding Monte Carlo simulations. At temperatures (ranging from 1000 to 2500 K), an isolated graphene sheet can anneal a large number of defects suggesting that their healing are thermally activated. We show that in presence of a nickel substrate we obtain a perfect graphene layer. The nickel-carbon chemical bonds keep breaking and reforming around defected carbon zones, providing a direct interaction, necessary for the healing. Thus, the action of Ni atoms is found to play a key role in the reconstruction of the graphene sheet by annealing defects.
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arxiv:1009.0192
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In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while we make use of an endofunctor $\mathcal{U}$ on a topos of sets $S$ together with a natural transformation $\upsilon$, instead of the terms as "standard", "internal" or "external". Moreover, we propose a general notion of a space called $\mathcal{U}$-space, and the category $\mathcal{U}space$ whose objects are $\mathcal{U}$-spaces and morphisms are functions called $\mathcal{U}$-spatial morphisms. The category $\mathcal{U}Space$, which is shown to be cartesian closed, will give a unified viewpoint toward topological and coarse geometric structure. It will also useful to study symmetries/asymmetries of the systems with infinite degrees of freedom such as quantum fields.
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arxiv:1009.0234
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We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An $N$-parameter Brownian sheet in $\mathbf{R}^d$ has double points if and only if $d<4N$. In particular, in the critical case where $d=4N$, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning $k$-multiple points in the critical case $k(d-2N)=d$.
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arxiv:1009.0235
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We prove global existence and uniqueness of solutions of Oldroyd-B systems with relatively small data in $\Rr^d$, in a large functional setting ($C^{\alpha}\cap L^1$). This is a stability result, solutions select an equilibrium and converge exponentially to it. Large spatial derivatives of the initial density and stress are allowed, provided the $L^{\infty}$ norm of the density and stress are small enough. We prove global regularity for large data for a model in which the potential responds to high rates of strain in the fluid. We also prove global existence for a class of large data for a didactic scalar model which attempts to capture in the simplest way the essence of the dissipative nature of the coupling to fluid. This latter model has an unexpected cone invariance in function space that is crucial for the global existence.
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arxiv:1009.0249
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Some non perturbative aspects of the pure SU(3) Yang-Mills theory are investigated assuming a specific form of the beta function, based on a recent modification by Ryttov and Sannino of the known one for supersymmetric gauge theories. The characteristic feature is a pole at a particular value of the coupling constant, g. First it is noted, using dimensional analysis, that physical quantities behave smoothly as one travels from one side of the pole to the other. Then it is argued that the form of the integrated beta function g(m), where m is the mass scale, determines the mass gap of the theory. Assuming the usual QCD value one finds it to be 1.67 GeV, which is in surprisingly good agreement with a quenched lattice calculation. A similar calculation is made for the supersymmetric Yang-Mills theory where the corresponding beta function is considered to be exact.
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arxiv:1009.0265
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We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double layer potentials for the wave equation, for the domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.
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arxiv:1009.0288
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We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined by L. Isaev, G. Ortiz, and J. Dukelsky, arXiv:1003.5205, are misplaced.
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arxiv:1009.0296
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We study the joint source-channel coding problem of transmitting a discrete-time analog source over an additive white Gaussian noise (AWGN) channel with interference known at transmitter.We consider the case when the source and the interference are correlated. We first derive an outer bound on the achievable distortion and then, we propose two joint source-channel coding schemes. The first scheme is the superposition of the uncoded signal and a digital part which is the concatenation of a Wyner-Ziv encoder and a dirty paper encoder. In the second scheme, the digital part is replaced by the hybrid digital and analog scheme proposed by Wilson et al. When the channel signal-tonoise ratio (SNR) is perfectly known at the transmitter, both proposed schemes are shown to provide identical performance which is substantially better than that of existing schemes. In the presence of an SNR mismatch, both proposed schemes are shown to be capable of graceful enhancement and graceful degradation. Interestingly, unlike the case when the source and interference are independent, neither of the two schemes outperforms the other universally. As an application of the proposed schemes, we provide both inner and outer bounds on the distortion region for the generalized cognitive radio channel.
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arxiv:1009.0304
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Over the previous decade, many approaches for the modelling of radio emission from cosmic ray air showers have been developed. However, there remained significant deviations between the models, reaching from important qualitative differences such as unipolar versus bipolar pulses to large variations in the predicted absolute amplitudes of up to factors of 20. Only recently, it has been realized that in the many models predicting unipolar pulses, a radio emission contribution due to the time-variation of the number of charged particles or, equivalently, the acceleration of the particles at the beginning and the end of their trajectories, had not been taken into account. We discuss here the nature of the underlying problem and demonstrate that by including the missing contribution in REAS3, the discrepancies are reconciled. Furthermore, we show a direct comparison of REAS3 and MGMR simulations for a set of prototype showers. The results of these two completely independent and very different modelling approaches show a good level of agreement except for regions of parameter space where differences in the underlying air shower model become important. This is the first time that two radio emission models show such close concordance, illustrating that the modelling of radio emission from extensive air showers has indeed made a true breakthrough.
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arxiv:1009.0346
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There were problems encountered in extending the K-slicing of the Schwarzschild and Reissner-Nordstrom (RN) spacetimes [1, 2] to the extreme case, when charge equals mass (in gravitational units). The earlier procedure is here modified so as to allow us to obtain a K-slicing of the region outside the horizon of the extreme metric by spacelike hypersurfaces. We checked this new procedure by applying it to the Schwarzschild and usual RN metrics and recovering the previous foliation with an improved accuracy. We have also checked the asymptotic behaviour of the K-slicing for large K by extrapolation.
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arxiv:1009.0357
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In this note we prove the genus 3 case of a conjecture of G. Farkas and A. Verra on the limit of the Scorza correspondence for curves with a theta-null. Specifically, we show that the limit of the Scorza correspondence for a hyperelliptic genus 3 curve C is the union of the curve ${x,\sigma(x))$ (where $\sigma$ is the hyperelliptic involution), and twice the diagonal. Our proof uses the geometry of the subsystem \Gamma_{00} of the linear system 2\Theta, and Riemann identities for theta constants.
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arxiv:1009.0375
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Any two generating systems of the fundamental group of a closed surface are Nielsen equivalent.
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arxiv:1009.0454
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To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB)model. The typical numerical phasing errors over the $\simeq 22$ GW cycles are $\Delta \phi\simeq \pm 0.24$ rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.
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arxiv:1009.0521
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The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined through the theory of stochastic integration. Here, inspired by the L\'{e}vy-Cieselski construction of the Wiener process, we propose an alternative representation of multidimensional Gauss-Markov processes as expansions on well-chosen Schauder bases, with independent random coefficients of normal law with zero mean and unitary variance. We thereby offer a natural multi-resolution description of Gauss-Markov processes as limits of the finite-dimensional partial sums of the expansion, that are strongly almost-surely convergent. Moreover, such finite-dimensional random processes constitute an optimal approximation of the process, in the sense of minimizing the associated Dirichlet energy under interpolating constraints. This approach allows simpler treatment in many applied and theoretical fields and we provide a short overview of applications we are currently developing.
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arxiv:1009.0533
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Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group for S. More generally, we study superinjective maps from the Torelli complex for S into itself, and show that any finite index subgroup of the Torelli group for S is co-Hopfian.
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arxiv:1009.0568
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I give a proof of the semisimplicity of the action of the geometric frobenius on etale cohomology. This proof is based on the Weil Conjectures.
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arxiv:1009.0596
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A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is a preassigned (natural) number. It is known, already for a long time, that for the optimal policy one needs to compute b position thresholds, for instance via backwards induction. In this paper we study approximate policies, that use just a single or a double position threshold, albeit in conjunction with a level rank. We give exact and asymptotic (as n tends to infinity) results, which show that the double-level policy is an extremely accurate approximation.
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arxiv:1009.0626
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It is known that two number fields with the same Dedekind zeta function are not necessarily isomorphic. The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical system, which is a C*-algebra with a one parameter group of automorphisms, built from Artin reciprocity. In the first part of this paper, we prove that isomorphism of number fields is the same as isomorphism of these associated systems. Considering the systems as noncommutative analogues of topological spaces, this result can be seen as another version of Grothendieck's "anabelian" program, much like the Neukirch-Uchida theorem characterizes isomorphism of number fields by topological isomorphism of their associated absolute Galois groups. In the second part of the paper, we use these systems to prove the following. If there is an isomorphism of character groups (viz., Pontrjagin duals) of the abelianized Galois groups of the two number fields that induces an equality of all corresponding L-series (not just the zeta function), then the number fields are isomorphic.This is also equivalent to the purely algebraic statement that there exists a topological group isomorphism as a above and a norm-preserving group isomorphism between the ideals of the fields that is compatible with the Artin maps via the other map.
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arxiv:1009.0736
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We present results from numerical simulations of the cooling-core cluster A2199 produced by the two-dimensional (2-D) resistive magnetohydrodynamics (MHD) code MACH2. In our simulations we explore the effect of anisotropic thermal conduction on the energy balance of the system. The results from idealized cases in 2-D axisymmetric geometry underscore the importance of the initial plasma density in ICM simulations, especially the near-core values since the radiation cooling rate is proportional to ${n_e}^2$. Heat conduction is found to be non-effective in preventing catastrophic cooling in this cluster. In addition we performed 2-D planar MHD simulations starting from initial conditions deliberately violating both thermal balance and hydrostatic equilibrium in the ICM, to assess contributions of the convective terms in the energy balance of the system against anisotropic thermal conduction. We find that in this case work done by the pressure on the plasma can dominate the early evolution of the internal energy over anisotropic thermal conduction in the presence of subsonic flows, thereby reducing the impact of the magnetic field. Deviations from hydrostatic equilibrium near the cluster core may be associated with transient activity of a central active galactic nucleus and/or remnant dynamical activity in the ICM and warrant further study in three dimensions.
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arxiv:1009.0751
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A consensus is emerging that interacting galaxies show depressed nuclear gas metallicities compared to isolated star-forming galaxies. Simulations suggest that this nuclear underabundance is caused by interaction-induced inflow of metal-poor gas, and that this inflow concurrently flattens the radial metallicity gradients in strongly interacting galaxies. We present metallicities of over 300 HII regions in a sample of 16 spirals that are members of strongly interacting galaxy pairs with mass ratio near unity. The deprojected radial gradients in these galaxies are about half of those in a control sample of isolated, late-type spirals. Detailed comparison of the gradients with simulations show remarkable agreement in gradient distributions, the relationship between gradients and nuclear underabundances, and the shape of profile deviations from a straight line. Taken together, this evidence conclusively demonstrates that strongly interacting galaxies at the present day undergo nuclear metal dilution due to gas inflow, as well as significant flattening of their gas-phase metallicity gradients, and that current simulations can robustly reproduce this behavior at a statistical level.
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arxiv:1009.0761
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We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger equation in a random delta-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and using control theory.
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arxiv:1009.0782
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Given the monomial ideal I=(x_1^{{\alpha}_1},...,x_{n}^{{\alpha}_{n}})\subset K[x_1,...,x_{n}] where {\alpha}_{i} are positive integers and K a field and let J be the integral closure of I . It is a challenging problem to translate the question of the normality of J into a question about the exponent set {\Gamma}(J) and the Newton polyhedron NP(J). A relaxed version of this problem is to give necessary or sufficient conditions on {\alpha}_1,...,{\alpha}_{n} for the normality of J. We show that if {\alpha}_{i}\epsilon{s,l} with s and l arbitrary positive integers, then J is normal.
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arxiv:1009.0786
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Background: The recent explosion of experimental techniques in single molecule biophysics has generated a variety of novel time series data requiring equally novel computational tools for analysis and inference. This article describes in general terms how graphical modeling may be used to learn from biophysical time series data using the variational Bayesian expectation maximization algorithm (VBEM). The discussion is illustrated by the example of single-molecule fluorescence resonance energy transfer (smFRET) versus time data, where the smFRET time series is modeled as a hidden Markov model (HMM) with Gaussian observables. A detailed description of smFRET is provided as well. Results: The VBEM algorithm returns the model's evidence and an approximating posterior parameter distribution given the data. The former provides a metric for model selection via maximum evidence (ME), and the latter a description of the model's parameters learned from the data. ME/VBEM provide several advantages over the more commonly used approach of maximum likelihood (ML) optimized by the expectation maximization (EM) algorithm, the most important being a natural form of model selection and a well-posed (non-divergent) optimization problem. Conclusions: The results demonstrate the utility of graphical modeling for inference of dynamic processes in single molecule biophysics.
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arxiv:1009.0857
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We summarize, simplify and extend recent work showing that small deviations from exact thermality in Hawking radiation, first uncovered by Kraus and Wilczek, have the capacity to carry off the maximum information content of a black hole. This goes a considerable way toward resolving a long-standing "information-loss paradox".
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arxiv:1009.0879
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We consider the discrete eigenvalues of the operator $H_\eps=-\Delta+V(\x)+\eps^2Q(\eps\x)$, where $V(\x)$ is periodic and $Q(\y)$ is localized on $\R^d,\ \ d\ge1$. For $\eps>0$ and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of the periodic Schr\"odinger operator, $H_0 = -\Delta_\x+V(\x)$, into spectral gaps. The nature of the bifurcation depends on the homogenized Schr\"odinger operator $L_{A,Q}=-\nabla_\y\cdot A \nabla_\y +\ Q(\y)$. Here, $A$ denotes the inverse effective mass matrix, associated with the spectral band edge, which is the site of the bifurcation.
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arxiv:1009.0922
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In this paper we give a complete solution to the Hamilton-Waterloo problem for the case of Hamilton cycles and C4k-factors for all positive integers k.
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arxiv:1009.0965
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Recent structure function results from H1 and ZEUS are presented. The data have been recorded in e+p and e-p collisions for both Neutral Current and Charged Current reactions, covering a wide kinematic range of squared four-momentum transfers Q2, from 0.2GeV2 to 30000GeV2, and Bjorken x between ~5*10-6 and 0.65. Data from both experiments have been combined, leading to significantly reduced experimental uncertainties. The combined measurements are analysed in a NLO QCD fit, and a set of parton density functions, HERAPDF1.0, is extracted from these data alone. New direct measurements of the structure function FL, making use of dedicated low energy runs of the HERA machine, are also presented. The impact of the HERA data on the parton density functions and predictions for LHC is discussed.
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arxiv:1009.0978
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Let $\Theta = (\theta_1,\theta_2,\theta_3)\in \mathbb{R}^3$. Suppose that $1,\theta_1,\theta_2,\theta_3$ are linearly independent over $\mathbb{Z}$. For Diophantine exponents $$ \alpha(\Theta) = \sup \{\gamma >0:\,\,\, \limsup_{t\to +\infty} t^\gamma \psi_\Theta (t) <+\infty \} ,$$ $$\beta(\Theta) = \sup \{\gamma >0:\,\,\, \liminf_{t\to +\infty} t^\gamma \psi_\Theta (t) <+\infty\} $$ we prove $$ \beta (\Theta) \ge {1/2} ({\alpha (\Theta)}/{1-\alpha(\Theta)} +\sqrt{{\alpha(\Theta)}/{1-\alpha(\Theta)})^2 +{4\alpha(\Theta)}/{1-\alpha(\Theta)}}) \alpha (\Theta) $$
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arxiv:1009.0987
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