25,093 research outputs found

    Performance Limits of Stochastic Sub-Gradient Learning, Part II: Multi-Agent Case

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    The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and involve non-differentiable components. They have been long recognized as being slow converging methods. However, it was revealed in Part I that the rate of convergence becomes linear for stochastic optimization problems, with the error iterate converging at an exponential rate αi\alpha^i to within an O(μ)O(\mu)-neighborhood of the optimizer, for some α(0,1)\alpha \in (0,1) and small step-size μ\mu. The conclusion was established under weaker assumptions than the prior literature and, moreover, several important problems (such as LASSO, SVM, and Total Variation) were shown to satisfy these weaker assumptions automatically (but not the previously used conditions from the literature). These results revealed that sub-gradient learning methods have more favorable behavior than originally thought when used to enable continuous adaptation and learning. The results of Part I were exclusive to single-agent adaptation. The purpose of the current Part II is to examine the implications of these discoveries when a collection of networked agents employs subgradient learning as their cooperative mechanism. The analysis will show that, despite the coupled dynamics that arises in a networked scenario, the agents are still able to attain linear convergence in the stochastic case; they are also able to reach agreement within O(μ)O(\mu) of the optimizer

    The Redshift-Space Cluster-Galaxy Cross-Correlation Function: I. Modeling Galaxy Infall onto Millennium Simulation Clusters and SDSS Groups

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    The large scale infall of galaxies around massive clusters provides a potentially powerful diagnostic of structure growth, dark energy, and cosmological deviations from General Relativity. We develop and test a method to recover galaxy infall kinematics (GIK) from measurements of the redshift-space cluster-galaxy cross-correlation function \xi_{cg}(r_p,r_\pi). Using galaxy and halo samples from the Millennium simulation, we calibrate an analytic model of the galaxy kinematic profiles comprised of a virialized component with an isotropic Gaussian velocity distribution and an infall component described by a skewed 2D t-distribution with a characteristic infall velocity v_r and separate radial and tangential dispersions. We show that convolving the real-space cross-correlation function with this velocity distribution accurately predicts the redshift-space \xi_{cg}, and we show that measurements of \xi_{cg} can be inverted to recover the four distinct elements of the GIK profiles. These in turn provide diagnostics of cluster mass profiles, and we expect the characteristic infall velocity v_r(r) in particular to be insensitive to galaxy formation physics that can affect velocity dispersions within halos. As a proof of concept we measure \xi_{cg} for rich galaxy groups in the Sloan Digital Sky Survey and recover GIK profiles for groups in two bins of central galaxy stellar mass. The higher mass bin has a v_r(r) curve very similar to that of 10^{14} Msun halos in the Millennium simulation, and the recovered kinematics follow the expected trends with mass. GIK modeling of cluster-galaxy cross-correlations can be a valuable complement to stacked weak lensing analyses, allowing novel tests of modified gravity theories that seek to explain cosmic acceleration.Comment: Matched to the published version (adding one figure illustrating the position and velocity vectors). For a brief video explaining the key result of this paper, see https://www.youtube.com/watch?v=7RB49odfSGo, or http://v.youku.com/v_show/id_XNDcxMDY3MTQ0.html in countries where YouTube is not accessibl

    Charged Black Holes with Scalar Hair

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    We consider a class of Einstein-Maxwell-Dilaton theories, in which the dilaton coupling to the Maxwell field is not the usual single exponential function, but one with a stationary point. The theories admit two charged black holes: one is the Reissner-Nordstr{\o}m (RN) black hole and the other has a varying dilaton. For a given charge, the new black hole in the extremal limit has the same AdS2×_2\timesSphere near-horizon geometry as the RN black hole, but it carries larger mass. We then introduce some scalar potentials and obtain exact charged AdS black holes. We also generalize the results to black pp-branes with scalar hair.Comment: Latex, 22 pages, typos corrected and references added, to appear in JHE

    SU(2)-Colored (A)dS Black Holes in Conformal Gravity

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    We consider four-dimensional conformal gravity coupled to the U(1) Maxwell and SU(2) Yang-Mills fields. We study the structure of general black hole solutions carrying five independent parameters: the mass, the electric U(1) and magnetic SU(2) charges, the massive spin-2 charge and the thermodynamical pressure associated with the cosmological constant, which is an integration constant in conformal gravity. We derive the thermodynamical first law of the black holes. We obtain some exact solutions including an extremal black hole with vanishing mass and entropy, but with non-trivial SU(2) Yang-Mills charges. We derive the remainder of the first law for this special solution. We also reexamine the colored black holes and derive their first law in Einstein-Yang-Mills gravity with or without a cosmological constant.Comment: Latex, 22 pages, typos corrected and references adde

    Charged Black Holes in Colored Lifshitz Spacetimes

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    We consider Einstein gravities coupled to a cosmological constant and SU(2)SU(2) Yang-Mills fields in four and five dimensions. We find that the theories admit colored Lifshitz solutions with dynamic exponents z>1z>1. We study the wave equations of the SU(2)SU(2) scalar triplet in the bulk, and find that the vacuum color modifies the scaling dimensions of the dual operators. We also introduce a Maxwell field and construct exact solutions of electrically-charged black holes that asymptote to the D=4D=4, z=3z=3 and D=5D=5, z=4z=4 colored Lifshitz spacetimes. We derive the thermodynamical first law for general colored and charged Lifshitz black holes.Comment: Latex, 13 pages, minor corrections and references adde

    Electrically-Charged Lifshitz Spacetimes, and Hyperscaling Violations

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    Electrically-charged Lifshitz spacetimes are hard to come by. In this paper, we construct a class of such solutions in five dimensional Einstein gravity coupled to Maxwell and SU(2)SU(2) Yang-Mills fields. The solutions are electrically-charged under the Maxwell field, whose equation is sourced by the Yang-Mills instanton(-like) configuration living in the hyperbolic four-space of the Lifshitz spacetime. We then introduce a dilaton and construct charged and colored Lifshitz spacetimes with hyperscaling violations. We obtain a class of exact Lifshitz black holes. We also perform similar constructions in four dimensions.Comment: Latex, 14 page

    Heavy Higgs Bosons at 14 TeV and 100 TeV

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    Searching for Higgs bosons beyond the Standard Model (BSM) is one of the most important missions for hadron colliders. As a landmark of BSM physics, the MSSM Higgs sector at the LHC is expected to be tested up to the scale of the decoupling limit of O(1) TeV, except for a wedge region centered around tanβ310\tan\beta \sim 3 -10, which has been known to be difficult to probe. In this article, we present a dedicated study testing the decoupled MSSM Higgs sector, at the LHC and a next-generation pppp-collider, proposing to search in channels with associated Higgs productions, with the neutral and charged Higgs further decaying into tttt and tbtb, respectively. In the case of neutral Higgs we are able to probe for the so far uncovered wedge region via ppbbH/Abbttpp\to bb H/A \to bbtt. Additionally, we cover the the high tanβ\tan\beta range with ppbbH/Abbττpp\to bb H/A \to bb\tau\tau. The combination of these searches with channels dedicated to the low tanβ\tan\beta region, such as ppH/Attpp\to H/A \to tt and ppttH/Attttpp\to tt H/A \to tttt potentially covers the full tanβ\tan\beta range. The search for charged Higgs has a slightly smaller sensitivity for the moderate tanβ\tan\beta region, but additionally probes for the higher and lower tanβ\tan\beta regions with even greater sensitivity, via pptbH±tbtbpp\to tb H^\pm \to tbtb. While the LHC will be able to probe the whole tanβ\tan\beta range for Higgs masses of O(1) TeV by combining these channels, we show that a future 100 TeV pppp-collider has a potential to push the sensitivity reach up to O(10)\sim \mathcal O(10) TeV. In order to deal with the novel kinematics of top quarks produced by heavy Higgs decays, the multivariate Boosted Decision Tree (BDT) method is applied in our collider analyses. The BDT-based tagging efficiencies of both hadronic and leptonic top-jets, and their mutual fake rates as well as the faking rates by other jets (hh, ZZ, WW, bb, etc.) are also presented.Comment: published versio
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