11,753 research outputs found
Mutual information on the fuzzy sphere
We numerically calculate entanglement entropy and mutual information for a
massive free scalar field on commutative (ordinary) and noncommutative (fuzzy)
spheres. We regularize the theory on the commutative geometry by discretizing
the polar coordinate, whereas the theory on the noncommutative geometry
naturally posseses a finite and adjustable number of degrees of freedom. Our
results show that the UV-divergent part of the entanglement entropy on a fuzzy
sphere does not follow an area law, while the entanglement entropy on a
commutative sphere does. Nonetheless, we find that mutual information (which is
UV-finite) is the same in both theories. This suggests that nonlocality at
short distances does not affect quantum correlations over large distances in a
free field theory.Comment: 16 pages, 10 figures. Fixed minor typos, references updated,
discussion slightly expande
Entanglement entropy on a fuzzy sphere with a UV cutoff
We introduce a UV cutoff into free scalar field theory on the noncommutative
(fuzzy) two-sphere. Due to the IR-UV connection, varying the UV cutoff allows
us to control the effective nonlocality scale of the theory. In the resulting
fuzzy geometry, we establish which degrees of freedom lie within a specific
geometric subregion and compute the associated vacuum entanglement entropy.
Entanglement entropy for regions smaller than the effective nonlocality scale
is extensive, while entanglement entropy for regions larger than the effective
nonlocality scale follows the area law. This reproduces features previously
obtained in the strong coupling regime through holography. We also show that
mutual information is unaffected by the UV cutoff.Comment: Significantly revised with improved methodology, 16 pages, 8 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
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Analysis of a Gibbs sampler method for model based clustering of gene expression data
Over the last decade, a large variety of clustering algorithms have been
developed to detect coregulatory relationships among genes from microarray gene
expression data. Model based clustering approaches have emerged as
statistically well grounded methods, but the properties of these algorithms
when applied to large-scale data sets are not always well understood. An
in-depth analysis can reveal important insights about the performance of the
algorithm, the expected quality of the output clusters, and the possibilities
for extracting more relevant information out of a particular data set. We have
extended an existing algorithm for model based clustering of genes to
simultaneously cluster genes and conditions, and used three large compendia of
gene expression data for S. cerevisiae to analyze its properties. The algorithm
uses a Bayesian approach and a Gibbs sampling procedure to iteratively update
the cluster assignment of each gene and condition. For large-scale data sets,
the posterior distribution is strongly peaked on a limited number of
equiprobable clusterings. A GO annotation analysis shows that these local
maxima are all biologically equally significant, and that simultaneously
clustering genes and conditions performs better than only clustering genes and
assuming independent conditions. A collection of distinct equivalent
clusterings can be summarized as a weighted graph on the set of genes, from
which we extract fuzzy, overlapping clusters using a graph spectral method. The
cores of these fuzzy clusters contain tight sets of strongly coexpressed genes,
while the overlaps exhibit relations between genes showing only partial
coexpression.Comment: 8 pages, 7 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
Entanglement entropy on the fuzzy sphere
We obtain entanglement entropy on the noncommutative (fuzzy) two-sphere. To
define a subregion with a well defined boundary in this geometry, we use the
symbol map between elements of the noncommutative algebra and functions on the
sphere. We find that entanglement entropy is not proportional to the length of
the region's boundary. Rather, in agreement with holographic predictions, it is
extensive for regions whose area is a small (but fixed) fraction of the total
area of the sphere. This is true even in the limit of small noncommutativity.
We also find that entanglement entropy grows linearly with N, where N is the
size of the irreducible representation of SU(2) used to define the fuzzy
sphere.Comment: 18 pages, 7 figures. v3 to appear in JHEP. Clarified statements about
UV/IR mixing and interpretation in terms of degrees of freedom on the fuzzy
sphere vs. matrix degrees of freedom, fixed some typos and added reference
Modeling and Recognition of Smart Grid Faults by a Combined Approach of Dissimilarity Learning and One-Class Classification
Detecting faults in electrical power grids is of paramount importance, either
from the electricity operator and consumer viewpoints. Modern electric power
grids (smart grids) are equipped with smart sensors that allow to gather
real-time information regarding the physical status of all the component
elements belonging to the whole infrastructure (e.g., cables and related
insulation, transformers, breakers and so on). In real-world smart grid
systems, usually, additional information that are related to the operational
status of the grid itself are collected such as meteorological information.
Designing a suitable recognition (discrimination) model of faults in a
real-world smart grid system is hence a challenging task. This follows from the
heterogeneity of the information that actually determine a typical fault
condition. The second point is that, for synthesizing a recognition model, in
practice only the conditions of observed faults are usually meaningful.
Therefore, a suitable recognition model should be synthesized by making use of
the observed fault conditions only. In this paper, we deal with the problem of
modeling and recognizing faults in a real-world smart grid system, which
supplies the entire city of Rome, Italy. Recognition of faults is addressed by
following a combined approach of multiple dissimilarity measures customization
and one-class classification techniques. We provide here an in-depth study
related to the available data and to the models synthesized by the proposed
one-class classifier. We offer also a comprehensive analysis of the fault
recognition results by exploiting a fuzzy set based reliability decision rule
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