Designing labeled graph classifiers by exploiting the R\'enyi entropy of the dissimilarity representation

Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However, the design of effective learning procedures operating in the space of labeled graphs is still a challenging problem, especially from the computational complexity viewpoint. In this paper, we present a major improvement of a general-purpose classifier for graphs, which is conceived on an interplay between dissimilarity representation, clustering, information-theoretic techniques, and evolutionary optimization algorithms. The improvement focuses on a specific key subroutine devised to compress the input data. We prove different theorems which are fundamental to the setting of the parameters controlling such a compression operation. We demonstrate the effectiveness of the resulting classifier by benchmarking the developed variants on well-known datasets of labeled graphs, considering as distinct performance indicators the classification accuracy, computing time, and parsimony in terms of structural complexity of the synthesized classification models. The results show state-of-the-art standards in terms of test set accuracy and a considerable speed-up for what concerns the computing time.Comment: Revised versio

Ergodic Properties of Microcanonical Observables

The problem of the existence of a Strong Stochasticity Threshold in the FPU-beta model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, that results to be indipendent of the number of degrees of freedom.Comment: 19 pages, 6 figure

Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

DNA denaturation and wetting in the presence of disorder

We present a precise equivalence of the Lifson-Poland-Scheraga model with wetting models. Making use of a representation of the former model in terms of random matrices, we obtain, in the limit of weak disorder, a mean--field approximation, that shows a change of the critical behavior due to disorder.Comment: 4 page

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 $\alpha$-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

Manipulating energy and spin currents in nonequilibrium systems of interacting qubits

We consider generic interacting chain of qubits, which are coupled at the edges to baths of fixed polarizations. We can determine the nonequilibrium steady states, described by the fixed point of the Lindblad Master Equation. Under rather general assumptions about local pumping and interactions, symmetries of the reduced density matrix are revealed. The symmetries drastically restrict the form of the steady density matrices in such a way that an exponentially large subset of one--point and many--point correlation functions are found to vanish. As an example we show how in a Heisenberg spin chain a suitable choice of the baths can completely switch off either the spin or the energy current, or both of them, despite the presence of large boundary gradients.Comment: 8 pages, 3 Figure

Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

Demographic shocks: the view from history

The paper will basically deal with four issues. The first one puts current changes or shifts into a historical comparative perspective. The second deals with "traditional" shocks or violent disturbances of the system and their consequences. The third discusses the "seismic" changes experienced in the past, attempts their measurement, and exemplifies their effects on population and society. The fourth deals with the relevance that past experience has for current changes.Demography ; Economic conditions