Autocorrelation of Random Matrix Polynomials

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions

Conditioned place preference and locomotor activity in response to methylphenidate, amphetamine and cocaine in mice lacking dopamine D4 receptors

Methylphenidate (MP) and amphetamine (AMPH) are the most frequently prescribed medications for the treatment of attention-deficit/hyperactivity disorder (ADHD). Both drugs are believed to derive their therapeutic benefit by virtue of their dopamine (DA)-enhancing effects, yet an explanation for the observation that some patients with ADHD respond well to one medication but not to the other remains elusive. The dopaminergic effects of MP and AMPH are also thought to underlie their reinforcing properties and ultimately their abuse. Polymorphisms in the human gene that codes for the DA D4 receptor (D4R) have been repeatedly associated with ADHD and may correlate with the therapeutic as well as the reinforcing effects of responses to these psychostimulant medications. Conditioned place preference (CPP) for MP, AMPH and cocaine were evaluated in wild-type (WT) mice and their genetically engineered littermates, congenic on the C57Bl/6J background, that completely lack D4Rs (knockout or KO). In addition, the locomotor activity in these mice during the conditioning phase of CPP was tested in the CPP chambers. D4 receptor KO and WT mice showed CPP and increased locomotor activity in response to each of the three psychostimulants tested. D4R differentially modulates the CPP responses to MP, AMPH and cocaine. While the D4R genotype affected CPP responses to MP (high dose only) and AMPH (low dose only) it had no effects on cocaine. Inasmuch as CPP is considered an indicator of sensitivity to reinforcing responses to drugs these data suggest a significant but limited role of D4Rs in modulating conditioning responses to MP and AMPH. In the locomotor test, D4 receptor KO mice displayed attenuated increases in AMPH-induced locomotor activity whereas responses to cocaine and MP did not differ. These results suggest distinct mechanisms for D4 receptor modulation of the reinforcing (perhaps via attenuating dopaminergic signalling) and locomotor properties of these stimulant drugs. Thus, individuals with D4 receptor polymorphisms might show enhanced reinforcing responses to MP and AMPH and attenuated locomotor response to AMPH.Fil: Thanos, P. K.. NIAAA Intramural Program; Estados Unidos. Brookhaven National Laboratory; Estados Unidos. Universidad de Buenos Aires; ArgentinaFil: Bermeo, C.. Brookhaven National Laboratory; Estados UnidosFil: Rubinstein, Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; ArgentinaFil: Suchland, K. L.. Oregon Health & Science University; Estados UnidosFil: Wang, G. J.. Brookhaven National Laboratory; Estados UnidosFil: Grandy, David K.. Oregon Health & Science University; Estados UnidosFil: Volkow, N. D.. NIAAA Intramural Program; Estados Unido

Learning Incoherent Subspaces: Classification via Incoherent Dictionary Learning

In this article we present the supervised iterative projections and rotations (s-ipr) algorithm, a method for learning discriminative incoherent subspaces from data. We derive s-ipr as a supervised extension of our previously proposed iterative projections and rotations (ipr) algorithm for incoherent dictionary learning, and we employ it to learn incoherent sub-spaces that model signals belonging to different classes. We test our method as a feature transform for supervised classification, first by visualising transformed features from a synthetic dataset and from the ‘iris’ dataset, then by using the resulting features in a classification experiment

Spatial and spectral properties of the pulsed second-harmonic generation in a PP-KTP waveguide

Spatial and spectral properties of the pulsed second harmonic generation in a periodically-poled KTP waveguide exploiting simultaneously the first, second, and third harmonics of periodic nonlinear modulation are analyzed. Experimental results are interpreted using a model based on finite elements method. Correlations between spatial and spectral properties of the fundamental and second-harmonic fields are revealed. Individual nonlinear processes can be exploited combining spatial and spectral filtering. Also the influence of waveguide parameters to the second-harmonic spectra is addressed.Comment: 13 pages, 8 figure

Tighter Relations Between Sensitivity and Other Complexity Measures

Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is polynomially related to other major complexity measures. Despite much attention to the problem and major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004. In this work, we present new upper bounds for various complexity measures in terms of sensitivity improving the bounds provided by Kenyon and Kutin. Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1} s(f); these in turn imply various corollaries regarding the relation between sensitivity and other complexity measures, such as block sensitivity, via known results. The gap between sensitivity and other complexity measures remains exponential but these results are the first improvement for this difficult problem that has been achieved in a decade.Comment: This is the merged form of arXiv submission 1306.4466 with another work. Appeared in ICALP 2014, 14 page

Shear flow effects on phase separation of entangled polymer blends

We introduce an entanglement model mixing rule for stress relaxation in a polymer blend to a modified Cahn-Hilliard equation of motion for concentration fluctuations in the presence of shear flow. Such an approach predicts both shear-induced mixing and demixing, depending on the relative relaxation times and plateau moduli of the two components

Static and dynamic friction in sliding colloidal monolayers

In a pioneer experiment, Bohlein et al. realized the controlled sliding of two-dimensional colloidal crystals over laser-generated periodic or quasi-periodic potentials. Here we present realistic simulations and arguments which besides reproducing the main experimentally observed features, give a first theoretical demonstration of the potential impact of colloid sliding in nanotribology. The free motion of solitons and antisolitons in the sliding of hard incommensurate crystals is contrasted with the soliton-antisoliton pair nucleation at the large static friction threshold Fs when the two lattices are commensurate and pinned. The frictional work directly extracted from particles' velocities can be analysed as a function of classic tribological parameters, including speed, spacing and amplitude of the periodic potential (representing respectively the mismatch of the sliding interface, and the corrugation, or "load"). These and other features suggestive of further experiments and insights promote colloid sliding to a novel friction study instrument.Comment: in print in the Proceedings of the National Academy of Sciences U.S.A. This v2 is identical to v1, but includes ancillary material. A few figures were undersampled due to size limits: those in v1 are far sharpe

Role of friction-induced torque in stick-slip motion

We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the periodic stick-slip motion are controlled by the amount of friction-induced torque at the interface. Our model provides a general framework to understand and relate a series of recent experimental observations, in particular the nucleation location of micro-slip instabilities and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure

Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages

In a previous work a random matrix average for the Laguerre unitary ensemble, generalising the generating function for the probability that an interval $(0,s)$ at the hard edge contains $k$ eigenvalues, was evaluated in terms of a Painlev\'e V transcendent in $\sigma$-form. However the boundary conditions for the corresponding differential equation were not specified for the full parameter space. Here this task is accomplished in general, and the obtained functional form is compared against the most general small $s$ behaviour of the Painlev\'e V equation in $\sigma$-form known from the work of Jimbo. An analogous study is carried out for the the hard edge scaling limit of the random matrix average, which we have previously evaluated in terms of a Painlev\'e \IIId transcendent in $\sigma$-form. An application of the latter result is given to the rapid evaluation of a Hankel determinant appearing in a recent work of Conrey, Rubinstein and Snaith relating to the derivative of the Riemann zeta function

Hamiltonian dynamics of homopolymer chain models

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the theta-transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.Comment: 11 pages, 8 figures, accepted for publication in Physical Review