2,052 research outputs found
Decomposition of fractional quantum Hall states: New symmetries and approximations
We provide a detailed description of a new symmetry structure of the monomial
(Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall
states first obtained in Ref. 1, which we now extend to spin-singlet states. We
show that the Haldane-Rezayi spin-singlet state can be obtained without exact
diagonalization through a differential equation method that we conjecture to be
generic to other FQH model states. The symmetry rules in Ref. 1 as well as the
ones we obtain for the spin singlet states allow us to build approximations of
FQH states that exhibit increasing overlap with the exact state (as a function
of system size). We show that these overlaps reach unity in the thermodynamic
limit even though our approximation omits more than half of the Hilbert space.
We show that the product rule is valid for any FQH state which can be written
as an expectation value of parafermionic operators.Comment: 22 pages, 8 figure
The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
We deduce a new set of symmetries and relations between the coefficients of
the expansion of Abelian and Non-Abelian Fractional Quantum Hall (FQH) states
in free (bosonic or fermionic) many-body states. Our rules allow to build an
approximation of a FQH model state with an overlap increasing with growing
system size (that may sometimes reach unity!) while using a fraction of the
original Hilbert space. We prove these symmetries by deriving a previously
unknown recursion formula for all the coefficients of the Slater expansion of
the Laughlin, Read Rezayi and many other states (all Jacks multiplied by
Vandermonde determinants), which completely removes the current need for
diagonalization procedures.Comment: modify comment in Ref. 1
Denial-of-service resilience in peer-to-peer file sharing systems
Peer-to-peer (p2p) file sharing systems are characterized by highly replicated content distributed among nodes with enormous aggregate resources for storage and communication. These properties alone are not sufficient, however, to render p2p networks immune to denial-of-service (DoS) attack. In this paper, we study, by means of analytical modeling and simulation, the resilience of p2p file sharing systems against DoS attacks, in which malicious nodes respond to queries with erroneous responses. We consider the filetargeted attacks in current use in the Internet, and we introduce a new class of p2p-network-targeted attacks. In file-targeted attacks, the attacker puts a large number of corrupted versions of a single file on the network. We demonstrate that the effectiveness of these attacks is highly dependent on the clients’ behavior. For the attacks to succeed over the long term, clients must be unwilling to share files, slow in removing corrupted files from their machines, and quick to give up downloading when the system is under attack. In network-targeted attacks, attackers respond to queries for any file with erroneous information. Our results indicate that these attacks are highly scalable: increasing the number of malicious nodes yields a hyperexponential decrease in system goodput, and a moderate number of attackers suffices to cause a near-collapse of the entire system. The key factors inducing this vulnerability are (i) hierarchical topologies with misbehaving “supernodes,” (ii) high path-length networks in which attackers have increased opportunity to falsify control information, and (iii) power-law networks in which attackers insert themselves into high-degree points in the graph. Finally, we consider the effects of client counter-strategies such as randomized reply selection, redundant and parallel download, and reputation systems. Some counter-strategies (e.g., randomized reply selection) provide considerable immunity to attack (reducing the scaling from hyperexponential to linear), yet significantly hurt performance in the absence of an attack. Other counter-strategies yield little benefit (or penalty). In particular, reputation systems show little impact unless they operate with near perfection
On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures
This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev
inequalities for a class of Boltzmann-Gibbs measures with singular interaction.
Such measures allow to model one-dimensional particles with confinement and
singular pair interaction. The functional inequalities come from convexity. We
prove and characterize optimality in the case of quadratic confinement via a
factorization of the measure. This optimality phenomenon holds for all beta
Hermite ensembles including the Gaussian unitary ensemble, a famous exactly
solvable model of random matrix theory. We further explore exact solvability by
reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting
the Hermite-Lassalle orthogonal polynomials as a complete set of
eigenfunctions. We also discuss the consequence of the log-Sobolev inequality
in terms of concentration of measure for Lipschitz functions such as maxima and
linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional
Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics
225
Identification of absolute geometries of cis and trans molecular isomers by Coulomb Explosion Imaging
Citation: Ablikim, U., Bomme, C., Xiong, H., Savelyev, E., Obaid, R., Kaderiya, B., . . . Rolles, D. (2016). Identification of absolute geometries of cis and trans molecular isomers by Coulomb Explosion Imaging. Scientific Reports, 6, 8. doi:10.1038/srep38202An experimental route to identify and separate geometric isomers by means of coincident Coulomb explosion imaging is presented, allowing isomer-resolved photoionization studies on isomerically mixed samples. We demonstrate the technique on cis/trans 1,2-dibromoethene (C2H2Br2). The momentum correlation between the bromine ions in a three-body fragmentation process induced by bromine 3d inner-shell photoionization is used to identify the cis and trans structures of the isomers. The experimentally determined momentum correlations and the isomer-resolved fragment-ion kinetic energies are matched closely by a classical Coulomb explosion model
Asymptotics for products of characteristic polynomials in classical -Ensembles
We study the local properties of eigenvalues for the Hermite (Gaussian),
Laguerre (Chiral) and Jacobi -ensembles of random matrices.
More specifically, we calculate scaling limits of the expectation value of
products of characteristic polynomials as . In the bulk of the
spectrum of each -ensemble, the same scaling limit is found to be
whose exact expansion in terms of Jack polynomials is well
known. The scaling limit at the soft edge of the spectrum for the Hermite and
Laguerre -ensembles is shown to be a multivariate Airy function, which
is defined as a generalized Kontsevich integral. As corollaries, when
is even, scaling limits of the -point correlation functions for the three
ensembles are obtained. The asymptotics of the multivariate Airy function for
large and small arguments is also given. All the asymptotic results rely on a
generalization of Watson's lemma and the steepest descent method for integrals
of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article
with new references, simplified demonstations, and improved presentation. To
be published in Constructive Approximation 37 (2013
Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
Using the Coulomb gas method and standard methods of statistical physics, we
compute analytically the joint cumulative probability distribution of the
extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices, in the
limit of large matrices. This allows us to derive the rate functions for the
large fluctuations to the left and the right of the expected values of the
smallest and largest eigenvalues analytically. Our findings are compared with
some available known exact results as well as with numerical simulations
finding good agreement.Comment: 31 pages, 7 figure
A Mathematical model for Astrocytes mediated LTP at Single Hippocampal Synapses
Many contemporary studies have shown that astrocytes play a significant role
in modulating both short and long form of synaptic plasticity. There are very
few experimental models which elucidate the role of astrocyte over Long-term
Potentiation (LTP). Recently, Perea & Araque (2007) demonstrated a role of
astrocytes in induction of LTP at single hippocampal synapses. They suggested a
purely pre-synaptic basis for induction of this N-methyl-D- Aspartate (NMDA)
Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic
induction were not investigated. Here, in this article, we propose a
mathematical model for astrocyte modulated LTP which successfully emulates the
experimental findings of Perea & Araque (2007). Our study suggests the role of
retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically
modulated LTP.Comment: 51 pages, 15 figures, Journal of Computational Neuroscience (to
appear
Measurement of the cross-section and charge asymmetry of bosons produced in proton-proton collisions at TeV with the ATLAS detector
This paper presents measurements of the and cross-sections and the associated charge asymmetry as a
function of the absolute pseudorapidity of the decay muon. The data were
collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with
the ATLAS experiment at the LHC and correspond to a total integrated luminosity
of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements
varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the
1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured
with an uncertainty between 0.002 and 0.003. The results are compared with
predictions based on next-to-next-to-leading-order calculations with various
parton distribution functions and have the sensitivity to discriminate between
them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables,
submitted to EPJC. All figures including auxiliary figures are available at
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13
Search for chargino-neutralino production with mass splittings near the electroweak scale in three-lepton final states in √s=13 TeV pp collisions with the ATLAS detector
A search for supersymmetry through the pair production of electroweakinos with mass splittings near the electroweak scale and decaying via on-shell W and Z bosons is presented for a three-lepton final state. The analyzed proton-proton collision data taken at a center-of-mass energy of √s=13 TeV were collected between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. A search, emulating the recursive jigsaw reconstruction technique with easily reproducible laboratory-frame variables, is performed. The two excesses observed in the 2015–2016 data recursive jigsaw analysis in the low-mass three-lepton phase space are reproduced. Results with the full data set are in agreement with the Standard Model expectations. They are interpreted to set exclusion limits at the 95% confidence level on simplified models of chargino-neutralino pair production for masses up to 345 GeV
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