7,014 research outputs found
Entropic Characterization and Time Evolution of Complex Networks
In this thesis, we address problems encountered in complex network analysis using graph theoretic methods. The thesis specifically centers on the challenge of how to characterize the structural properties and time evolution of graphs. We commence by providing a brief roadmap for our research in Chapter 1, followed by a review of the relevant research literature in Chapter 2. The remainder of the thesis is structured as follows.
In Chapter 3, we focus on the graph entropic characterizations and explore whether the von Neumann entropy recently defined only on undirected graphs, can be extended to the domain of directed graphs. The substantial contribution involves a simplified form of the entropy which can be expressed in terms of simple graph statistics, such as graph size and vertex in-degree and out-degree. Chapter 4 further investigates the uses and applications of the von Neumann entropy in order to solve a number of network analysis and machine learning problems. The contribution in this chapter includes an entropic edge assortativity measure and an entropic graph embedding method, which are developed for both undirected and directed graphs.
The next part of the thesis analyzes the time-evolving complex networks using physical and information theoretic approaches. In particular, Chapter 5 provides a thermodynamic framework for handling dynamic graphs using ideas from algebraic graph theory and statistical mechanics. This allows us to derive expressions for a number of thermodynamic functions, including energy, entropy and temperature, which are shown to be efficient in identifying abrupt structural changes and phase transitions in real-world dynamical systems. Chapter 6 develops a novel method for constructing a generative model to analyze the structure of labeled data, which provides a number of novel directions to the study of graph time-series. Finally, in Chapter 7, we provide concluding remarks and discuss the limitations of our methodologies, and point out possible future research directions
Information geometric methods for complexity
Research on the use of information geometry (IG) in modern physics has
witnessed significant advances recently. In this review article, we report on
the utilization of IG methods to define measures of complexity in both
classical and, whenever available, quantum physical settings. A paradigmatic
example of a dramatic change in complexity is given by phase transitions (PTs).
Hence we review both global and local aspects of PTs described in terms of the
scalar curvature of the parameter manifold and the components of the metric
tensor, respectively. We also report on the behavior of geodesic paths on the
parameter manifold used to gain insight into the dynamics of PTs. Going
further, we survey measures of complexity arising in the geometric framework.
In particular, we quantify complexity of networks in terms of the Riemannian
volume of the parameter space of a statistical manifold associated with a given
network. We are also concerned with complexity measures that account for the
interactions of a given number of parts of a system that cannot be described in
terms of a smaller number of parts of the system. Finally, we investigate
complexity measures of entropic motion on curved statistical manifolds that
arise from a probabilistic description of physical systems in the presence of
limited information. The Kullback-Leibler divergence, the distance to an
exponential family and volumes of curved parameter manifolds, are examples of
essential IG notions exploited in our discussion of complexity. We conclude by
discussing strengths, limits, and possible future applications of IG methods to
the physics of complexity.Comment: review article, 60 pages, no figure
Riemannian-geometric entropy for measuring network complexity
A central issue of the science of complex systems is the quantitative
characterization of complexity. In the present work we address this issue by
resorting to information geometry. Actually we propose a constructive way to
associate to a - in principle any - network a differentiable object (a
Riemannian manifold) whose volume is used to define an entropy. The
effectiveness of the latter to measure networks complexity is successfully
proved through its capability of detecting a classical phase transition
occurring in both random graphs and scale--free networks, as well as of
characterizing small Exponential random graphs, Configuration Models and real
networks.Comment: 15 pages, 3 figure
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
A characterization of the scientific impact of Brazilian institutions
In this paper we studied the research activity of Brazilian Institutions for
all sciences and also their performance in the area of physics between 1945 and
December 2008. All the data come from the Web of Science database for this
period. The analysis of the experimental data shows that, within a nonextensive
thermostatistical formalism, the Tsallis \emph{q}-exponential distribution
can constitute a new characterization of the research impact for
Brazilian Institutions. The data examined in the present survey can be fitted
successfully by applying a universal curve namely, with for {\it all} the available citations
, being an "effective temperature". The present analysis ultimately
suggests that via the "effective temperature" , we can provide a new
performance metric for the impact level of the research activity in Brazil,
taking into account the number of the publications and their citations. This
new performance metric takes into account the "quantity" (number of
publications) and the "quality" (number of citations) for different Brazilian
Institutions. In addition we analyzed the research performance of Brazil to
show how the scientific research activity changes with time, for instance
between 1945 to 1985, then during the period 1986-1990, 1991-1995, and so on
until the present. Finally, this work intends to show a new methodology that
can be used to analyze and compare institutions within a given country.Comment: 7 pages, 5 figure
One-class classifiers based on entropic spanning graphs
One-class classifiers offer valuable tools to assess the presence of outliers
in data. In this paper, we propose a design methodology for one-class
classifiers based on entropic spanning graphs. Our approach takes into account
the possibility to process also non-numeric data by means of an embedding
procedure. The spanning graph is learned on the embedded input data and the
outcoming partition of vertices defines the classifier. The final partition is
derived by exploiting a criterion based on mutual information minimization.
Here, we compute the mutual information by using a convenient formulation
provided in terms of the -Jensen difference. Once training is
completed, in order to associate a confidence level with the classifier
decision, a graph-based fuzzy model is constructed. The fuzzification process
is based only on topological information of the vertices of the entropic
spanning graph. As such, the proposed one-class classifier is suitable also for
data characterized by complex geometric structures. We provide experiments on
well-known benchmarks containing both feature vectors and labeled graphs. In
addition, we apply the method to the protein solubility recognition problem by
considering several representations for the input samples. Experimental results
demonstrate the effectiveness and versatility of the proposed method with
respect to other state-of-the-art approaches.Comment: Extended and revised version of the paper "One-Class Classification
Through Mutual Information Minimization" presented at the 2016 IEEE IJCNN,
Vancouver, Canad
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