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

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

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

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

739 observed NEAs and new 2-4m survey statistics within the EURONEAR network

We report follow-up observations of 477 program Near-Earth Asteroids (NEAs) using nine telescopes of the EURONEAR network having apertures between 0.3 and 4.2 m. Adding these NEAs to our previous results we now count 739 program NEAs followed-up by the EURONEAR network since 2006. The targets were selected using EURONEAR planning tools focusing on high priority objects. Analyzing the resulting orbital improvements suggests astrometric follow-up is most important days to weeks after discovery, with recovery at a new opposition also valuable. Additionally we observed 40 survey fields spanning three nights covering 11 sq. degrees near opposition, using the Wide Field Camera on the 2.5m Isaac Newton Telescope (INT), resulting in 104 discovered main belt asteroids (MBAs) and another 626 unknown one-night objects. These fields, plus program NEA fields from the INT and from the wide field MOSAIC II camera on the Blanco 4m telescope, generated around 12,000 observations of 2,000 minor planets (mostly MBAs) observed in 34 square degrees. We identify Near Earth Object (NEO) candidates among the unknown (single night) objects using three selection criteria. Testing these criteria on the (known) program NEAs shows the best selection methods are our epsilon-miu model which checks solar elongation and sky motion and the MPC's NEO rating tool. Our new data show that on average 0.5 NEO candidates per square degree should be observable in a 2m-class survey (in agreement with past results), while an average of 2.7 NEO candidates per square degree should be observable in a 4m-class survey (although our Blanco statistics were affected by clouds). At opposition just over 100 MBAs (1.6 unknown to every 1 known) per square degree are detectable to R=22 in a 2m survey based on the INT data, while our two best ecliptic Blanco fields away from opposition lead to 135 MBAs (2 unknown to every 1 known) to R=23.Comment: Published in Planetary and Space Sciences (Sep 2013

Fast linear algebra is stable

In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of $n$-by-$n$ matrices can be done by any algorithm in $O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in $O(n^{\omega + \eta})$ operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

Dnmt3a regulates emotional behavior and spine plasticity in the nucleus accumbens.

Despite abundant expression of DNA methyltransferases (Dnmts) in brain, the regulation and behavioral role of DNA methylation remain poorly understood. We found that Dnmt3a expression was regulated in mouse nucleus accumbens (NAc) by chronic cocaine use and chronic social defeat stress. Moreover, NAc-specific manipulations that block DNA methylation potentiated cocaine reward and exerted antidepressant-like effects, whereas NAc-specific Dnmt3a overexpression attenuated cocaine reward and was pro-depressant. On a cellular level, we found that chronic cocaine use selectively increased thin dendritic spines on NAc neurons and that DNA methylation was both necessary and sufficient to mediate these effects. These data establish the importance of Dnmt3a in the NAc in regulating cellular and behavioral plasticity to emotional stimuli

Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

Study of atmospheric pollution and health risk assessment: A case study for the sharjah and ajman emirates (uae)

Dust is a significant pollution source in the United Arab Emirates (UAE) that impacts population health. Therefore, the present study aims to determine the concentration of heavy metals (Cd, Pb, Cr, Cu, Ni, and Zn) in the air in the Sharjah and Ajman emirates’ urban areas and assesses the health risk. Three indicators were used for this purpose: the average daily dose (ADD), the hazard quotient (HQ), and the health index (HI). Data were collected during the period April–August 2020. Moreover, the observation sites were clustered based on the pollutants’ concentration, given that the greater the heavy metal concentration is, the greater is the risk for the population health. The most abundant heavy metal found in the atmosphere was Zn, with a mean concentration of 160.30 mg/kg, the concentrations of other metals being in the following order: Ni \u3e Cr \u3e Cu \u3e Pb \u3e Cd. The mean concentrations of Cd, Pb, and Cr were within the range of background values, while those of Cu, Ni, and Zn were higher than the background values, indicating anthropogenic pollution. For adults, the mean ADD values of heavy metals decreased from Zn to Cd (Zn \u3e Ni \u3e Cr \u3e Cu \u3e Pb \u3e Cd). The HQ (HI) suggested an acceptable (negligible) level of non-carcinogenic harmful health risk to residents’ health. The sites were grouped in three clusters, one of them containing a single location, where the highest concentrations of heavy metals were found