Local resolution-limit-free Potts model for community detection

We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise. It is also competitive with the best currently available algorithms in terms of speed and size of solvable systems. We find that the computational demand often exhibits superlinear scaling L^1.3 where L is the number of edges in the system, and we have applied the algorithm to synthetic systems as large as 40x10^6 nodes and over 1x10^9 edges. A previous stumbling block encountered by popular community detection methods is the so-called "resolution limit." Being a "local" measure of community structure, our Potts model is free from this resolution-limit effect, and it further remains a local measure on weighted and directed graphs. We also address the mitigation of resolution-limit effects for two other popular Potts models.Comment: 16 pages, 12 figures; title change for Physical Review E, minor editing, updated reference

Notes on SUSY and R-Symmetry Breaking in Wess-Zumino Models

We study aspects of Wess-Zumino models related to SUSY and R-symmetry breaking at tree-level. We present a recipe for constructing a wide class of tree-level SUSY and R-breaking models. We also deduce a general property shared by all tree-level SUSY breaking models that has broad application to model building. In particular, it explains why many models of direct gauge mediation have anomalously light gauginos (even if the R-symmetry is broken spontaneously by an order one amount). This suggests new approaches to dynamical SUSY breaking which can generate large enough gaugino masses.Comment: 23 pages. v2: references added, minor changes. v3: comment on non-renormalizable case adde

Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations

In this work, we illustrate how a Jordan-Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan-Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves, and (v) express the anyonic character of the excitations in this system and the local symmetries that it harbors in terms of fermions.Comment: 14 pages, 7 figure

Avoided Critical Behavior in O(n) Systems

Long-range frustrating interactions, even if their strength is infinitesimal, can give rise to a dramatic proliferations of ground or near-ground states. As a consequence, the ordering temperature can exhibit a discontinuous drop as a function of the frustration. A simple model of the doped Mott insulator, where the short-range tendency of the holes to phase separate competes with long-range Coulomb effects, exhibits this "avoided critical" behavior. This model may serve as a paradigm for many other systems.Comment: 4 pages, 2 figure

The Constraints of Conformal Symmetry on RG Flows

If the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry. We begin the present note by showing that this idea leads to a new proof of Zamolodchikov's theorem. We then review how this simple observation also leads to a derivation of the a-theorem. We exemplify the general procedure in some interacting theories in four space-time dimensions. We concentrate on Banks-Zaks and weakly relevant flows, which can be controlled by ordinary and conformal perturbation theories, respectively. We compute explicitly the dependence of the path integral on the coupling constants and extract the change in the a-anomaly (this agrees with more conventional computations of the same quantity). We also discuss some general properties of the sum rule found in arXiv:1107.3987 and study it in several examples.Comment: 25 pages, 5 figure

Sugarcoated isolation: Evidence that social avoidance is linked to higher basal glucose levels and higher consumption of glucose

Objective: The human brain adjusts its level of effort in coping with various life stressors as a partial function of perceived access to social resources. We examined whether people who avoid social ties maintain a higher fasting basal level of glucose in their bloodstream, reflecting a strategy to draw more on personal resources when threatened.Methods: For Study 1, we obtained fasting blood glucose and adult attachment orientations data from 60 undergraduate women at the University of Virginia. For Study 2, we collected measures of fasting blood glucose, self-reported trait anxiety, DHEA-cortisol, hypertension, and adult attachment orientations from 285 older adults of mixed gender, using a measure of attachment style different from study 1.Results: In study 1, fasting blood glucose levels corresponded with higher attachment avoidance scores after statistically adjusting for interpersonal anxiety. For study 2, fasting blood glucose continued to correspond with higher adult attachment avoidance even after statistically adjusting for interpersonal anxiety, trait anxiety, DHEA-cortisol and hypertension. Conclusions: Results suggest socially avoidant individuals upwardly adjust their basal glucose levels with the expectation of increased personal effort because of limited access to social resources

Local multiresolution order in community detection

Community detection algorithms attempt to find the best clusters of nodes in an arbitrary complex network. Multi-scale ("multiresolution") community detection extends the problem to identify the best network scale(s) for these clusters. The latter task is generally accomplished by analyzing community stability simultaneously for all clusters in the network. In the current work, we extend this general approach to define local multiresolution methods, which enable the extraction of well-defined local communities even if the global community structure is vaguely defined in an average sense. Toward this end, we propose measures analogous to variation of information and normalized mutual information that are used to quantitatively identify the best resolution(s) at the community level based on correlations between clusters in independently-solved systems. We demonstrate our method on two constructed networks as well as a real network and draw inferences about local community strength. Our approach is independent of the applied community detection algorithm save for the inherent requirement that the method be able to identify communities across different network scales, with appropriate changes to account for how different resolutions are evaluated or defined in a particular community detection method. It should, in principle, easily adapt to alternative community comparison measures.Comment: 19 pages, 11 figure

Layer resolved magnetic domain imaging of epitaxial heterostructures in large applied magnetic fields

We use X-ray Excited Luminescence Microscopy to investigate the elemental and layer resolved magnetic reversal in an interlayer exchange coupled (IEC) epitaxial Fe/Cr wedge/Co heterostructure. The transition from strongly coupled parallel Co-Fe reversal for Cr thickness tCr < 0.34 nm to weakly coupled layer independent reversal for tCr > 1.5 nm is punctuated at 0.34 < tCr < 1.5 nm by a combination of IEC guided domain wall motion and stationary zig zag domain walls. Domain walls nucleated at switching field minima are guided by IEC spatial gradients and collapse at switching field maxima.RM acknowledges funding from the European Community under the Seventh Framework Program Contract No. 247368: 3SPIN. DL acknowledges funding from the EPSRC. The work performed at the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-06CH11357.This is the accepted manuscript. The final version is available at http://scitation.aip.org/content/aip/journal/apl/106/7/10.1063/1.4913359

A Bound on the Superpotential

We prove a general bound on the superpotential in theories with broken supersymmetry and broken R-symmetry, 2|W|< f_a F, where f_a and F are the R-axion and Goldstino decay constants, respectively. The bound holds for weakly coupled as well as strongly coupled theories, thereby providing an exact result in theories with broken supersymmetry. We briefly discuss several possible applications.Comment: 20 page

The importance of quantum decoherence in brain processes

Based on a calculation of neural decoherence rates, we argue that that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence timescales ~10^{-13}-10^{-20} seconds are typically much shorter than the relevant dynamical timescales (~0.001-0.1 seconds), both for regular neuron firing and for kink-like polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.Comment: Minor changes to match accepted PRE version. 15 pages with 5 figs included. Color figures and links at http://www.physics.upenn.edu/~max/brain.html or from [email protected]. Physical Review E, in pres