1,119 research outputs found
Discriminating different classes of biological networks by analyzing the graphs spectra distribution
The brain's structural and functional systems, protein-protein interaction,
and gene networks are examples of biological systems that share some features
of complex networks, such as highly connected nodes, modularity, and
small-world topology. Recent studies indicate that some pathologies present
topological network alterations relative to norms seen in the general
population. Therefore, methods to discriminate the processes that generate the
different classes of networks (e.g., normal and disease) might be crucial for
the diagnosis, prognosis, and treatment of the disease. It is known that
several topological properties of a network (graph) can be described by the
distribution of the spectrum of its adjacency matrix. Moreover, large networks
generated by the same random process have the same spectrum distribution,
allowing us to use it as a "fingerprint". Based on this relationship, we
introduce and propose the entropy of a graph spectrum to measure the
"uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon
divergences between graph spectra to compare networks. We also introduce
general methods for model selection and network model parameter estimation, as
well as a statistical procedure to test the nullity of divergence between two
classes of complex networks. Finally, we demonstrate the usefulness of the
proposed methods by applying them on (1) protein-protein interaction networks
of different species and (2) on networks derived from children diagnosed with
Attention Deficit Hyperactivity Disorder (ADHD) and typically developing
children. We conclude that scale-free networks best describe all the
protein-protein interactions. Also, we show that our proposed measures
succeeded in the identification of topological changes in the network while
other commonly used measures (number of edges, clustering coefficient, average
path length) failed
Reduction of Markov Chains using a Value-of-Information-Based Approach
In this paper, we propose an approach to obtain reduced-order models of
Markov chains. Our approach is composed of two information-theoretic processes.
The first is a means of comparing pairs of stationary chains on different state
spaces, which is done via the negative Kullback-Leibler divergence defined on a
model joint space. Model reduction is achieved by solving a
value-of-information criterion with respect to this divergence. Optimizing the
criterion leads to a probabilistic partitioning of the states in the high-order
Markov chain. A single free parameter that emerges through the optimization
process dictates both the partition uncertainty and the number of state groups.
We provide a data-driven means of choosing the `optimal' value of this free
parameter, which sidesteps needing to a priori know the number of state groups
in an arbitrary chain.Comment: Submitted to Entrop
Likelihood Analysis of Power Spectra and Generalized Moment Problems
We develop an approach to spectral estimation that has been advocated by
Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance
extension problem, by Enqvist and Karlsson. The aim is to determine the power
spectrum that is consistent with given moments and minimizes the relative
entropy between the probability law of the underlying Gaussian stochastic
process to that of a prior. The approach is analogous to the framework of
earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a
generalization of the classical work by Burg and Jaynes on the maximum entropy
method. In the present paper we present a new fast algorithm in the general
case (i.e., for general Gaussian priors) and show that for priors with a
specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure
Non-Extensive Entropy Econometrics for Low Frequency Series
The second edition of Non-extensive Entropy Econometrics for Low Frequency Series provides a new and robust power-law-based, non-extensive entropy econometrics approach to the economic modelling of ill-behaved inverse problems. Particular attention is paid to national account-based general equilibrium models known for their relative complexity. This new proposed approach could extend the frontier of theoretical and applied econometrics
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