140,001 research outputs found
On the number of non-zero elements of joint degree vectors
Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 ≤ i ≤ j ≤ n-1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree vector as a function of n. This provides an upper bound on the number of estimable parameters in the exponential random graph model with bidegree-distribution as its sufficient statistics.All authors except the second author were supported in part by the U.S. Air Force Office of Scientic Research (AFOSR) and the Defense Advanced Research Projects Agency (DARPA). The last author was supported in part by the NSF DMS contracts no.1300547 and 1600811
On the low dimensional dynamics of structured random networks
Using a generalized random recurrent neural network model, and by extending
our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee,
Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the
network connectivity structure and its low dimensional dynamics. Each
connection in the network is a random number with mean 0 and variance that
depends on pre- and post-synaptic neurons through a sufficiently smooth
function of their identities. We find that these networks undergo a phase
transition from a silent to a chaotic state at a critical point we derive as a
function of . Above the critical point, although unit activation levels are
chaotic, their autocorrelation functions are restricted to a low dimensional
subspace. This provides a direct link between the network's structure and some
of its functional characteristics. We discuss example applications of the
general results to neuroscience where we derive the support of the spectrum of
connectivity matrices with heterogeneous and possibly correlated degree
distributions, and to ecology where we study the stability of the cascade model
for food web structure.Comment: 16 pages, 4 figure
Distribution of roots of random real generalized polynomials
The average density of zeros for monic generalized polynomials,
, with real holomorphic and
real Gaussian coefficients is expressed in terms of correlation functions of
the values of the polynomial and its derivative. We obtain compact expressions
for both the regular component (generated by the complex roots) and the
singular one (real roots) of the average density of roots. The density of the
regular component goes to zero in the vicinity of the real axis like
. We present the low and high disorder asymptotic
behaviors. Then we particularize to the large limit of the average density
of complex roots of monic algebraic polynomials of the form with real independent, identically distributed
Gaussian coefficients having zero mean and dispersion . The average density tends to a simple, {\em universal}
function of and in the domain where nearly all the roots are located for
large .Comment: 17 pages, Revtex. To appear in J. Stat. Phys. Uuencoded gz-compresed
tarfile (.66MB) containing 8 Postscript figures is available by e-mail from
[email protected]
A Discrete Time Presentation of Quantum Dynamics
Inspired by the discrete evolution implied by the recent work on loop quantum
cosmology, we obtain a discrete time description of usual quantum mechanics
viewing it as a constrained system. This description, obtained without any
approximation or explicit discretization, mimics features of the discrete time
evolution of loop quantum cosmology. We discuss the continuum limit, physical
inner product and matrix elements of physical observables to bring out various
issues regarding viability of a discrete evolution. We also point out how a
continuous time could emerge without appealing to any continuum limit.Comment: 20 pages, RevTex, no figures. Additional Clarifications added.
Version accepted for publication in Class. Quant. Gra
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The 3D version of the finite element program FESTER
In this report, a detailed description of the 3-D version finite element pro-gram FESTER is given. This includes: 1. A brief introduction to the package FESTER; 2. Preparing an input data file for the 3D version of FESTER; 3. Principal stress and stress invariant analyses; 4. 2D joint element (surface contact) characterisation and its mathematical formulation; 5. Formulations of the 3D stress-strain analyses for both isotropic and anisotropic materials, plane of weakness and cracking criteria; 6. 3D brick elements, infinity elements and their corresponding shape and mapping functions; 7. Large-displacement formulations; 8. Modifications to the subroutines INVAR, JNTB, TMAT, MOD2 etc; 9. Numerical examples; and 10. Conclusions
A Neural Network Model for Cursive Script Production
This article describes a neural network model, called the VITEWRITE model, for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a. hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The proposed controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in a given synergy is achieved. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. The separate "score" of onset times used in most prior models is hereby replaced by a self-scaling activity-released "motor program" that uses few memory resources, enables each synergy to exhibit a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless. connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data concerning band movements, such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.National Science Foundation (IRI 90-24877, IRI 87-16960); Office of Naval Research (N00014-92-J-1309); Air Force Office of Scientific Research (F49620-92-J-0499); Defense Advanced Research Projects Agency (90-0083
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