scholarly journals On the von Neumann entropy of graphs

2018 ◽  
Vol 7 (4) ◽  
pp. 491-514 ◽  
Author(s):  
Giorgia Minello ◽  
Luca Rossi ◽  
Andrea Torsello
Keyword(s):  
Pattern Recognition ◽  
Graph Laplacian ◽  
Von Neumann Entropy ◽  
Node Degree ◽  
Von Neumann ◽  
Structural Patterns ◽  
Underlying Graph ◽  
Networks Analysis ◽  
Quadratic Approximations

Abstract The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and normalized graph Laplacian, respectively. Due to its computational complexity, previous works have proposed to approximate the von Neumann entropy, effectively reducing it to the computation of simple node degree statistics. Unfortunately, a number of issues surrounding the von Neumann entropy remain unsolved to date, including the interpretation of this spectral measure in terms of structural patterns, understanding the relation between its two variants and evaluating the quality of the corresponding approximations. In this article, we aim to answer these questions by first analysing and comparing the quadratic approximations of the two variants and then performing an extensive set of experiments on both synthetic and real-world graphs. We find that (1) the two entropies lead to the emergence of similar structures, but with some significant differences; (2) the correlation between them ranges from weakly positive to strongly negative, depending on the topology of the underlying graph; (3) the quadratic approximations fail to capture the presence of non-trivial structural patterns that seem to influence the value of the exact entropies; and (4) the quality of the approximations, as well as which variant of the von Neumann entropy is better approximated, depends on the topology of the underlying graph.

scholarly journals A method of evaluating the quality of dual-path entangled quantum microwave signal generated based on von Neumann entropy

2016 ◽  
Vol 65 (11) ◽  
pp. 114204
Author(s):  
Li Xiang ◽  
Wu De-Wei ◽  
Wang Xi ◽  
Miao Qiang ◽  
Chen Kun ◽  
...  
Keyword(s):  
Microwave Signal ◽  
Von Neumann Entropy ◽  
Von Neumann

scholarly journals Instrumental Odour Monitoring System Classification Performance Optimization by Analysis of Different Pattern-Recognition and Feature Extraction Techniques

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 114
Author(s):  
Tiziano Zarra ◽  
Mark Gino K. Galang ◽  
Florencio C. Ballesteros ◽  
Vincenzo Belgiorno ◽  
Vincenzo Naddeo
Keyword(s):  
Pattern Recognition ◽  
Feature Extraction ◽  
Performance Optimization ◽  
Industrial Plant ◽  
Mathematical Treatment ◽  
Extraction Techniques ◽  
Peak Period ◽  
Linear Discriminant ◽  
Artificial Neural

Instrumental odour monitoring systems (IOMS) are intelligent electronic sensing tools for which the primary application is the generation of odour metrics that are indicators of odour as perceived by human observers. The quality of the odour sensor signal, the mathematical treatment of the acquired data, and the validation of the correlation of the odour metric are key topics to control in order to ensure a robust and reliable measurement. The research presents and discusses the use of different pattern recognition and feature extraction techniques in the elaboration and effectiveness of the odour classification monitoring model (OCMM). The effect of the rise, intermediate, and peak period from the original response curve, in collaboration with Linear Discriminant Analysis (LDA) and Artificial Neural Networks (ANN) as a pattern recognition algorithm, were investigated. Laboratory analyses were performed with real odour samples collected in a complex industrial plant, using an advanced smart IOMS. The results demonstrate the influence of the choice of method on the quality of the OCMM produced. The peak period in combination with the Artificial Neural Network (ANN) highlighted the best combination on the basis of high classification rates. The paper provides information to develop a solution to optimize the performance of IOMS.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

Generalized information and entanglement entropy, gravitation and holography

2015 ◽  
Vol 30 (16) ◽  
pp. 1530039 ◽  
Author(s):  
O. Obregón
Keyword(s):  
Entanglement Entropy ◽  
Ideal Gas ◽  
Einstein Equations ◽  
Von Neumann Entropy ◽  
Nonextensive Statistical Mechanics ◽  
Von Neumann ◽  
H Theorem ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Correction Terms

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

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