10,954 research outputs found
Decorrelation of Neutral Vector Variables: Theory and Applications
In this paper, we propose novel strategies for neutral vector variable
decorrelation. Two fundamental invertible transformations, namely serial
nonlinear transformation and parallel nonlinear transformation, are proposed to
carry out the decorrelation. For a neutral vector variable, which is not
multivariate Gaussian distributed, the conventional principal component
analysis (PCA) cannot yield mutually independent scalar variables. With the two
proposed transformations, a highly negatively correlated neutral vector can be
transformed to a set of mutually independent scalar variables with the same
degrees of freedom. We also evaluate the decorrelation performances for the
vectors generated from a single Dirichlet distribution and a mixture of
Dirichlet distributions. The mutual independence is verified with the distance
correlation measurement. The advantages of the proposed decorrelation
strategies are intensively studied and demonstrated with synthesized data and
practical application evaluations
Computationally efficient inference for latent position network models
Latent position models are widely used for the analysis of networks in a
variety of research fields. In fact, these models possess a number of desirable
theoretical properties, and are particularly easy to interpret. However,
statistical methodologies to fit these models generally incur a computational
cost which grows with the square of the number of nodes in the graph. This
makes the analysis of large social networks impractical. In this paper, we
propose a new method characterised by a linear computational complexity, which
can be used to fit latent position models on networks of several tens of
thousands nodes. Our approach relies on an approximation of the likelihood
function, where the amount of noise introduced by the approximation can be
arbitrarily reduced at the expense of computational efficiency. We establish
several theoretical results that show how the likelihood error propagates to
the invariant distribution of the Markov chain Monte Carlo sampler. In
particular, we demonstrate that one can achieve a substantial reduction in
computing time and still obtain a good estimate of the latent structure.
Finally, we propose applications of our method to simulated networks and to a
large coauthorships network, highlighting the usefulness of our approach.Comment: 39 pages, 10 figures, 1 tabl
Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics
Neural activity patterns related to behavior occur at many scales in time and
space from the atomic and molecular to the whole brain. Here we explore the
feasibility of interpreting neurophysiological data in the context of many-body
physics by using tools that physicists have devised to analyze comparable
hierarchies in other fields of science. We focus on a mesoscopic level that
offers a multi-step pathway between the microscopic functions of neurons and
the macroscopic functions of brain systems revealed by hemodynamic imaging. We
use electroencephalographic (EEG) records collected from high-density electrode
arrays fixed on the epidural surfaces of primary sensory and limbic areas in
rabbits and cats trained to discriminate conditioned stimuli (CS) in the
various modalities. High temporal resolution of EEG signals with the Hilbert
transform gives evidence for diverse intermittent spatial patterns of amplitude
(AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize
in the beta and gamma ranges at near zero time lags over long distances. The
dominant mechanism for neural interactions by axodendritic synaptic
transmission should impose distance-dependent delays on the EEG oscillations
owing to finite propagation velocities. It does not. EEGs instead show evidence
for anomalous dispersion: the existence in neural populations of a low velocity
range of information and energy transfers, and a high velocity range of the
spread of phase transitions. This distinction labels the phenomenon but does
not explain it. In this report we explore the analysis of these phenomena using
concepts of energy dissipation, the maintenance by cortex of multiple ground
states corresponding to AM patterns, and the exclusive selection by spontaneous
breakdown of symmetry (SBS) of single states in sequences.Comment: 31 page
Modeling Network Populations via Graph Distances
This article introduces a new class of models for multiple networks. The core
idea is to parametrize a distribution on labelled graphs in terms of a
Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or
graph distance) and a parameter that controls the concentration of this
distribution about its mean. Entropy is the natural parameter for such control,
varying from a point mass concentrated on the Fr\'{e}chet mean itself to a
uniform distribution over all graphs on a given vertex set. We provide a
hierarchical Bayesian approach for exploiting this construction, along with
straightforward strategies for sampling from the resultant posterior
distribution. We conclude by demonstrating the efficacy of our approach via
simulation studies and two multiple-network data analysis examples: one drawn
from systems biology and the other from neuroscience.Comment: 33 pages, 8 figure
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