Overlap Fluctuations from Random Overlap Structures

We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Over- lap Structure (ROSt). The concept of ROSt has been introduced recently by Aizenman and coworkers, who developed a variational approach to the Sherrington-Kirkpatrick model. We propose here an iterative procedure to show that, in the so-called Boltzmann ROSt, Aizenman-Contucci (AC) polynomials naturally arise for almost all values of the inverse temperature (not in average over some interval only). The same results can be obtained in any ROSt, including therefore the Parisi structure. The AC polynomials impose restric- tions on the overlap fluctuations in agreement with Parisi theory.Comment: 18 page

The Overlap Package

Camera traps - cameras linked to detectors so that they fire when an animal is present - are a major source of information on the abundance and habitat preferences of rare or shy forest animals. Modern cameras record the time of the photo, and the use of this to investigate diel activity patterns was immediately recognised (Gri?ffiths and van Schaik, 1993). Initially this resulted in broad classfication of taxa as diurnal, nocturnal, crepuscular, or cathemeral (van Schaik and Gri?ths, 1996). More recently, researchers have compared activity patterns among species to see how overlapping patterns may relate to competition or predation (Linkie and Ridout, 2011; Carver et al., 2011; Ramesh et al., 2012; Carter et al., 2012; Kamler et al., 2012; Ross et al., 2013). Ridout and Linkie (2009) presented methods to fit kernel density functions to times of observations of animals and to estimate the coe?cient of overlapping, a quantitative measure ranging from 0 (no overlap) to 1 (identical activity patterns). The code they used forms the basis of the overlap package. Although motivated by the analysis of camera trap data, overlap could be applied to data from other sources such as data loggers, provided data collection is carried out around the clock. Nor is it limited to diel cycles: tidal cycles or seasonal cycles, such as plant flowering or fruiting or animal breeding seasons could also be investigated

Truncated Overlap Fermions

In this talk I propose a new computational scheme with overlap fermions and a fast algorithm to invert the corresponding Dirac operator.Comment: LATTICE99(algorithms

Metric for attractor overlap

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e., ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshots to snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse-graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids, and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by few representative centroids. We employ MAO for two quite different actuated flow configurations: (1) a two-dimensional wake of the fluidic pinball with vortices in a narrow frequency range and (2) three-dimensional wall turbulence with broadband frequency spectrum manipulated by spanwise traveling transversal surface waves. MAO compares and classifies these actuated flows in agreement with physical intuition. For instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.Comment: 33 pages, 20 figure

Packing ellipsoids with overlap

The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. Convergence results are proved and computational experience is described and illustrated. The motivating application - chromosome organization in the human cell nucleus - is discussed briefly, and some illustrative results are presented

Anomalous transport with overlap fermions

Anomalous correlators of vector and axial currents which enter the Kubo formulae for the chiral magnetic and the chiral separation conductivities are explicitly calculated for free overlap fermions on the lattice. The results are confronted with continuum calculations in the finite-temperature regularization, and a subtle point of such regularization for chiral magnetic conductivity related to the correct counting of the chiral states is highlighted. In agreement with some previous claims in the literature, we find that in a lattice regularization which respects gauge invariance, the chiral magnetic conductivity vanishes. We point out that the relation of anomalous transport coefficients to axial anomaly is nontrivial due to the non-commutativity of their infrared limit and the Taylor expansion in baryon or chiral chemical potential. In particular, we argue that the vector and axial Ward identities fix the asymptotic behavior of anomalous current-current correlators in the limit of large momenta. Basing on the work of Knecht et al. on the perturbative non-renormalization of the transverse part of the correlator of two vector and one axial currents, we demonstrate that the relation of the anomalous vector-vector correlator to axial anomaly holds perturbatively in massless QCD but might be subject to non-perturbative corrections. Finally, we identify kinematical regimes in which the anomalous transport coefficients can be extracted from lattice measurements.Comment: 25 pages RevTex, 7 figures; v2: published version, discussion of CME improve