Entropy

12 pages, 794 KiB

Open AccessArticle

Weak Scale Supersymmetry Emergent from the String Landscape

by Howard Baer, Vernon Barger, Dakotah Martinez and Shadman Salam

Entropy 2024, 26(3), 275; https://doi.org/10.3390/e26030275 - 21 Mar 2024

Cited by 2 | Viewed by 954

Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different

4 - d

laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological [...] Read more.

Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different

4 - d

laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological constant, it may also predict the form of weak scale supersymmetry which is expected to emerge. Rather general arguments suggest a power-law draw to large soft terms, but these are subject to an anthropic selection of a not-too-large value for the weak scale. The combined selection allows one to compute relative probabilities for the emergence of supersymmetric models from the landscape. Models with weak scale naturalness appear most likely to emerge since they have the largest parameter space on the landscape. For finetuned models such as high-scale SUSY or split SUSY, the required weak scale finetuning shrinks their parameter space to tiny volumes, making them much less likely to appear compared to natural models. Probability distributions for sparticle and Higgs masses from natural models show a preference for Higgs mass

m_{h} \sim 125

GeV, with sparticles typically beyond the present LHC limits, in accord with data. From these considerations, we briefly describe how natural SUSY is expected to be revealed at future LHC upgrades. This article is a contribution to the Special Edition of the journal Entropy, honoring Paul Frampton on his 80th birthday. Full article

(This article belongs to the Special Issue Particle Theory and Theoretical Cosmology—Dedicated to Professor Paul Howard Frampton on the Occasion of His 80th Birthday)

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8 pages, 886 KiB

Open AccessArticle

Hyper-Ballistic Superdiffusion of Competing Microswimmers

by Kristian Stølevik Olsen, Alex Hansen and Eirik Grude Flekkøy

Entropy 2024, 26(3), 274; https://doi.org/10.3390/e26030274 - 21 Mar 2024

Viewed by 1033

Abstract

Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution [...] Read more.

Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis. Full article

(This article belongs to the Special Issue Statistical Mechanics of Porous Media Flow)

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12 pages, 456 KiB

Open AccessArticle

Tsallis Distribution as a Λ-Deformation of the Maxwell–Jüttner Distribution

by Jean-Pierre Gazeau

Entropy 2024, 26(3), 273; https://doi.org/10.3390/e26030273 - 21 Mar 2024

Viewed by 959

Abstract

Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as

β

, is future-directed and time-like, intriguing insights emerge. Specifically, it is demonstrated that the q [...] Read more.

Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as

β

, is future-directed and time-like, intriguing insights emerge. Specifically, it is demonstrated that the q-dependent Tsallis distribution can be conceptualized as a de Sitterian deformation of the relativistic Maxwell–Jüttner distribution. In this context, the curvature of the de Sitter space-time is characterized by

\sqrt{Λ / 3}

, where

Λ

represents the cosmological constant within the

Λ

CDM standard model for cosmology. For a simple gas composed of particles with proper mass m, and within the framework of quantum statistical de Sitterian considerations, the Tsallis parameter q exhibits a dependence on the cosmological constant given by

q = 1 + ℓ_{c} \sqrt{Λ} / n

, where

ℓ_{c} = ℏ / m c

is the Compton length of the particle and

n

is a positive numerical factor, the determination of which awaits observational confirmation. This formulation establishes a novel connection between the Tsallis distribution, quantum statistics, and the cosmological constant, shedding light on the intricate interplay between relativistic thermodynamics and fundamental cosmological parameters. Full article

(This article belongs to the Special Issue Nonadditive Entropies and Nonextensive Statistical Mechanics—Dedicated to Professor Constantino Tsallis on the Occasion of His 80th Birthday)

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18 pages, 7149 KiB

Open AccessArticle

Entanglement Phase Transitions in Non-Hermitian Kitaev Chains

by Longwen Zhou

Entropy 2024, 26(3), 272; https://doi.org/10.3390/e26030272 - 20 Mar 2024

Cited by 2 | Viewed by 1200

Abstract

The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and [...] Read more.

The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and varying hopping and pairing ranges, the bipartite entanglement entropy of steady states is found to scale logarithmically versus the system size in topologically nontrivial phases and become independent of the system size in the trivial phase. Notably, the scaling coefficients of log-law entangled phases are distinguishable when the underlying system resides in different topological phases. Log-law to log-law and log-law to area-law entanglement phase transitions are further identified when the system switches between different topological phases and goes from a topologically nontrivial to a trivial phase, respectively. These findings not only establish the relationships among spectral, topological and entanglement properties in a class of non-Hermitian topological superconductors but also provide an efficient means to dynamically reveal their distinctive topological features. Full article

(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)

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24 pages, 790 KiB

Open AccessArticle

A Measure of Synergy Based on Union Information

by André F. C. Gomes and Mário A. T. Figueiredo

Entropy 2024, 26(3), 271; https://doi.org/10.3390/e26030271 - 19 Mar 2024

Cited by 1 | Viewed by 1170

Abstract

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does [...] Read more.

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. One often overlooked way to achieve this decomposition is using a so-called measure of union information—which quantifies the information that is present in at least one of the sources—from which a synergy measure stems. In this paper, we introduce a new measure of union information based on adopting a communication channel perspective, compare it with existing measures, and study some of its properties. We also include a comprehensive critical review of characterizations of union information and synergy measures that have been proposed in the literature. Full article

(This article belongs to the Special Issue Synergy and Redundancy Measures: Theory and Applications to Characterize Complex Systems and Shape Neural Network Representations)

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14 pages, 12048 KiB

Open AccessArticle

Decoding the News Media Diet of Disinformation Spreaders

by Anna Bertani, Valeria Mazzeo and Riccardo Gallotti

Entropy 2024, 26(3), 270; https://doi.org/10.3390/e26030270 - 19 Mar 2024

Viewed by 1807

Abstract

In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users’ habits within the digital ecosystem is a challenging task that requires, at the [...] Read more.

In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users’ habits within the digital ecosystem is a challenging task that requires, at the same time, large databases and accurate methodological approaches. This study contributes to this expanding research landscape by employing network science methodologies and entropic measures to analyze the behavioral patterns of social media users sharing news pieces and dig into the diverse news consumption habits within different online social media user groups. Our analyses reveal that users are more inclined to share news classified as fake when they have previously posted conspiracy or junk science content and vice versa, creating a series of “misinformation hot streaks”. To better understand these dynamics, we used three different measures of entropy to gain insights into the news media habits of each user, finding that the patterns of news consumption significantly differ among users when focusing on disinformation spreaders as opposed to accounts sharing reliable or low-risk content. Thanks to these entropic measures, we quantify the variety and the regularity of the news media diet, finding that those disseminating unreliable content exhibit a more varied and, at the same time, a more regular choice of web-domains. This quantitative insight into the nuances of news consumption behaviors exhibited by disinformation spreaders holds the potential to significantly inform the strategic formulation of more robust and adaptive social media moderation policies. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)

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Figure 1
Classification of the news media categories based on their level of reliability based on the work of Gallotti et al. [<a href="#B23-entropy-26-00270" class="html-bibr">23</a>]. Full article ">Figure 2
The News Media Diet. Network and list of the sequence of web-domains posted by a random user on Twitter. We defined the length of each sequence with the term L. Each sequence is decoded in a list of identified letters. On these lists, we calculate the entropy value to obtain information about the variety of each sequence. In particular, we performed both random entropy <math display="inline"><semantics> <msub> <mi>S</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> </semantics></math> and Shannon entropy <math display="inline"><semantics> <msub> <mi>S</mi> <mrow> <mi>u</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> </semantics></math> calculations for each sequence. Full article ">Figure 3
Overview of the dataset. (A) Distribution of the length sequence of web-domains, respectively, for the entire dataset, for users having posted more than 2 distinctive web-domains (N > 1) and users defined according the categories of reliability. (B) Distribution of the number of messages classified in one of the eight categories of news media types. (C) Distribution of the news media categories used by a particularly active user who has posted reliable and low-risk content, with 6 distinctive categories of news. Full article ">Figure 4
The news media environment. (A) Weighted networks of the interactions among different news media types (also known as intra-relations) for 25 countries in 2020. (B) Heatmap showing the corresponding value of the inter-relations among the eight categories. (C) Weighted networks normalized and compared with a null model accounting for the proportion of the number of news pieces belonging to each category. The chances of sharing conspiracy and fake news by the same users is much higher than the strong relation observed between mainstream media and political news (A). (D) Heatmap showing the corresponding normalized value of the inter-relations among the eight categories. Full article ">Figure 5
Self-loops of web-domains and types of news shared. (A) The percentage distribution of the number of self-loops for different users, pointing to the same web-domains for all the categories considered. (B) The percentage distribution of the number of self-loops of different users pointing to the same category of news, regardless of the different web-domains shared. Full article ">Figure 6
News media diet for different types of users. (A) Random entropy <math display="inline"><semantics> <msub> <mi>S</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> </semantics></math> calculated for different types of accounts: users posting reliable or low-risk content and users posting different levels of high-risk (conspiracy/junk science and/or fake/hoax) content. (B) Shannon entropy <math display="inline"><semantics> <msub> <mi>S</mi> <mrow> <mi>u</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> </semantics></math> calculated for the domain and the type of news shared by different types of users accounts: users posting reliable or low-risk content and users posting different levels of high-risk (conspiracy/junk science and/or fake/hoax) content. (C) The actual entropy S calculated for the domain and news media categories shared by different type of users: those posting reliable or low-risk content and those posting different levels of high-risk (conspiracy/junk science and/or fake/hoax) content. Full article ">Figure 7
Fraction of repeated news media categories and web-domains for users with different N. In these boxplots, we represent the percentage of news media categories (A,B) or web-domains (C,D) repeated in subsequent tweets with respect to the total length of the sequence associated with an individual user. Each boxplot is aggregated over users with the same N. The dashed line shows the random expectation of repeated news media categories with respect to the increasing number of N unique news media categories. (A) Patterns of news media categories, aggregated for users classified as having posted only reliable and/or low-risk content on Twitter. There are 8 box-plots here since we have 6 distinctive categories and 2 are filtered out. (B) Patterns of news media categories, aggregated for users having also posted high-risk content. There are 8 box-plots here since we have all 8 distinctive categories of news media types. (C) Patterns of web-domains, aggregated for users classified as having posted reliable and/or low-risk content. (D) Patterns of web-domains, aggregated for users classified as having also posted high-risk content in their sequence of messages posted. Full article ">

16 pages, 15509 KiB

Open AccessArticle

HAG-NET: Hiding Data and Adversarial Attacking with Generative Adversarial Network

by Haiju Fan and Jinsong Wang

Entropy 2024, 26(3), 269; https://doi.org/10.3390/e26030269 - 19 Mar 2024

Viewed by 1070

Abstract

Recent studies on watermarking techniques based on image carriers have demonstrated new approaches that combine adversarial perturbations against steganalysis with embedding distortions. However, while these methods successfully counter convolutional neural network-based steganalysis, they do not adequately protect the data of the carrier itself. [...] Read more.

Recent studies on watermarking techniques based on image carriers have demonstrated new approaches that combine adversarial perturbations against steganalysis with embedding distortions. However, while these methods successfully counter convolutional neural network-based steganalysis, they do not adequately protect the data of the carrier itself. Recognizing the high sensitivity of Deep Neural Networks (DNNs) to small perturbations, we propose HAG-NET, a method based on image carriers, which is jointly trained by the encoder, decoder, and attacker. In this paper, the encoder generates Adversarial Steganographic Examples (ASEs) that are adversarial to the target classification network, thereby providing protection for the carrier data. Additionally, the decoder can recover secret data from ASEs. The experimental results demonstrate that ASEs produced by HAG-NET achieve an average success rate of over 99% on both the MNIST and CIFAR-10 datasets. ASEs generated with the attacker exhibit greater robustness in terms of attack ability, with an average increase of about 3.32%. Furthermore, our method, when compared with other generative stego examples under similar perturbation strength, contains significantly more information according to image information entropy measurements. Full article

(This article belongs to the Topic Computational Complex Networks)

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Figure 1
Schematic diagram illustrating the variance in perturbations generated by various generative methods. The string represented beneath these perturbations denotes the secret data or the targeted class of the adversarial attack embedded within. D represents the decoder, responsible for decoding the secret data, while its output represents the decoded secret information. C denotes the target classification network, with its output indicating the classified prediction, and the red section highlights inaccuracies in the prediction. Full article ">Figure 2
The framework of HAG-NET: the encoder E receives the cover image ICO and the secret message MIN to generate encoded image IE; the decoder D recovers MIN from IE and outputs the decoded message MOUT; the attacker generates adversarial example IA. The adversarial discriminator A receives ICO or IA and IE to predict whether the input has been encoded; the target classifier C predicts the classification of IE. The loss function LE is the pixel-level difference between IE and ICO; the loss function LC is used to optimize the ability to resist attacks. The loss function LG provides adversarial loss for E. The loss function LD minimizes the difference between MIN and MOUT. The dashed line indicates that data are transferred according to the settings. Full article ">Figure 3
Schematic diagram of the skip connection of the secret message in middle layers, where secret message is MIN, cover image is ICO, and the expanded secret message will be the same size as ICO and the middle layers data. Full article ">Figure 4
Pre-training of HAG-NET under different experimental settings, where (a,b) show the curves of LE loss and the classification accuracy of target classification network Model A in MNIST dataset, (c,d) show the curves of LE loss and the classification accuracy of the target classification network ResNet32 in the MNIST dataset, (e,f) show curves of LE loss and the classification accuracy of the target classification network ResNet32 in the CIFAR-10 dataset. Full article ">Figure 5
HAG-NET provides line graphs illustrating the variations in different types of data when each component loss function is individually removed. Among these, (a) illustrates the changes in Mean Squared Error (MSE) between ASE and the carrier image under various conditions; (b) displays the variations in Bit Error Rate (BER) of decoded information; and (c) demonstrates the changes in accuracy of target classification network in recognizing ASE. Full article ">Figure 6
The ASE of 0–4 target class in CIFAR-10 and the ASE of 5–9 target class in MNIST. Full article ">Figure 7
(a) shows the ASE of that a dog image has been attacked into remaining nine classes, from top to bottom and left to right they are plane, car, bird, cat, deer, frog, horse, ship, and truck. (b) shows the corresponding adversarial embedded disturbance at the same location. Full article ">

25 pages, 407 KiB

Open AccessFeature PaperArticle

Game Theoretic Clustering for Finding Strong Communities

by Chao Zhao, Ali Al-Bashabsheh and Chung Chan

Entropy 2024, 26(3), 268; https://doi.org/10.3390/e26030268 - 18 Mar 2024

Viewed by 1090

Abstract

We address the challenge of identifying meaningful communities by proposing a model based on convex game theory and a measure of community strength. Many existing community detection methods fail to provide unique solutions, and it remains unclear how the solutions depend on initial [...] Read more.

We address the challenge of identifying meaningful communities by proposing a model based on convex game theory and a measure of community strength. Many existing community detection methods fail to provide unique solutions, and it remains unclear how the solutions depend on initial conditions. Our approach identifies strong communities with a hierarchical structure, visualizable as a dendrogram, and computable in polynomial time using submodular function minimization. This framework extends beyond graphs to hypergraphs or even polymatroids. In the case when the model is graphical, a more efficient algorithm based on the max-flow min-cut algorithm can be devised. Though not achieving near-linear time complexity, the pursuit of practical algorithms is an intriguing avenue for future research. Our work serves as the foundation, offering an analytical framework that yields unique solutions with clear operational meaning for the communities identified. Full article

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8 pages, 218 KiB

Open AccessArticle

(Re)Construction of Quantum Space-Time: Transcribing Hilbert into Configuration Space

by Karl Svozil

Entropy 2024, 26(3), 267; https://doi.org/10.3390/e26030267 - 18 Mar 2024

Viewed by 1032

Abstract

Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. [...] Read more.

Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

13 pages, 281 KiB

Open AccessArticle

Group Structure as a Foundation for Entropies

by Henrik Jeldtoft Jensen and Piergiulio Tempesta

Entropy 2024, 26(3), 266; https://doi.org/10.3390/e26030266 - 18 Mar 2024

Cited by 2 | Viewed by 1135

Abstract

Entropy can signify different things. For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract [...] Read more.

Entropy can signify different things. For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract sense, as a functional on a probability space, and we review how being able to handle the trivial case of non-interacting systems, together with the subtle requirement of extensivity, allows for a systematic classification of the functional form. Full article

(This article belongs to the Special Issue Nonadditive Entropies and Nonextensive Statistical Mechanics—Dedicated to Professor Constantino Tsallis on the Occasion of His 80th Birthday)

24 pages, 755 KiB

Open AccessArticle

Exact Results for Non-Newtonian Transport Properties in Sheared Granular Suspensions: Inelastic Maxwell Models and BGK-Type Kinetic Model

by Rubén Gómez González and Vicente Garzó

Entropy 2024, 26(3), 265; https://doi.org/10.3390/e26030265 - 15 Mar 2024

Viewed by 1060

Abstract

The Boltzmann kinetic equation for dilute granular suspensions under simple (or uniform) shear flow (USF) is considered to determine the non-Newtonian transport properties of the system. In contrast to previous attempts based on a coarse-grained description, our suspension model accounts for the real [...] Read more.

The Boltzmann kinetic equation for dilute granular suspensions under simple (or uniform) shear flow (USF) is considered to determine the non-Newtonian transport properties of the system. In contrast to previous attempts based on a coarse-grained description, our suspension model accounts for the real collisions between grains and particles of the surrounding molecular gas. The latter is modeled as a bath (or thermostat) of elastic hard spheres at a given temperature. Two independent but complementary approaches are followed to reach exact expressions for the rheological properties. First, the Boltzmann equation for the so-called inelastic Maxwell models (IMM) is considered. The fact that the collision rate of IMM is independent of the relative velocity of the colliding spheres allows us to exactly compute the collisional moments of the Boltzmann operator without the knowledge of the distribution function. Thanks to this property, the transport properties of the sheared granular suspension can be exactly determined. As a second approach, a Bhatnagar–Gross–Krook (BGK)-type kinetic model adapted to granular suspensions is solved to compute the velocity moments and the velocity distribution function of the system. The theoretical results (which are given in terms of the coefficient of restitution, the reduced shear rate, the reduced background temperature, and the diameter and mass ratios) show, in general, a good agreement with the approximate analytical results derived for inelastic hard spheres (IHS) by means of Grad’s moment method and with computer simulations performed in the Brownian limiting case (

m / m_{g} \to \infty

, where

m_{g}

and m are the masses of the particles of the molecular and granular gases, respectively). In addition, as expected, the IMM and BGK results show that the temperature and non-Newtonian viscosity exhibit an S shape in a plane of stress–strain rate (discontinuous shear thickening, DST). The DST effect becomes more pronounced as the mass ratio

m / m_{g}

increases. Full article

(This article belongs to the Special Issue 180th Anniversary of Ludwig Boltzmann)

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18 pages, 10036 KiB

Open AccessArticle

Exploration of Resonant Modes for Circular and Polygonal Chladni Plates

by Amira Val Baker, Mate Csanad, Nicolas Fellas, Nour Atassi, Ia Mgvdliashvili and Paul Oomen

Entropy 2024, 26(3), 264; https://doi.org/10.3390/e26030264 - 15 Mar 2024

Viewed by 1951

Abstract

In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within [...] Read more.

In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability. Full article

(This article belongs to the Section Signal and Data Analysis)

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20 pages, 1465 KiB

Open AccessArticle

A Numerical Study of Quantum Entropy and Information in the Wigner–Fokker–Planck Equation for Open Quantum Systems

by Arash Edrisi, Hamza Patwa and Jose A. Morales Escalante

Entropy 2024, 26(3), 263; https://doi.org/10.3390/e26030263 - 14 Mar 2024

Cited by 1 | Viewed by 1189

Abstract

Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase [...] Read more.

Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space description. We perform a numerical inspection of the Wehrl entropy for the benchmark problem of a harmonic potential, since the existence of a steady state and its analytical formula have been proven theoretically in this case. When there is friction in the noise terms, no theoretical results on the monotonicity of absolute entropy are available. We provide numerical results of the time evolution of the entropy in the case with friction using a stochastic (Euler–Maruyama-based Monte Carlo) numerical solver. For all the chosen initial conditions studied (all of them Gaussian states), up to the inherent numerical error of the method, one cannot disregard the possibility of monotonic behavior even in the case under study, where the noise includes friction terms. Full article

(This article belongs to the Special Issue 180th Anniversary of Ludwig Boltzmann)

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Figure 1
Numerical time evolution of the Wehrl entropy starting from a harmonic groundstate initial condition, until the steady state is achieved numerically. Full article ">Figure 2
Numerical time evolution of the Wehrl entropy starting from a Gaussian state whose covariance is <math display="inline"><semantics> <mrow> <msup> <mn>2.25</mn> <mn>2</mn> </msup> <mo>=</mo> <mn>5.0625</mn> </mrow> </semantics></math> times the harmonic groundstate one, until the steady state is achieved numerically. Error bars were included to also consider the inherent uncertainty of the Monte Carlo method in use. Full article ">Figure 3
Numerical time evolution of the Wehrl entropy starting from the steady state as the initial condition, oscillating around it with the inherent numerical error of Monte Carlo methods. Full article ">Figure 4
Numerical time evolution of the Wehrl entropy starting from a Gaussian state with a covariance matrix 1.5 times the steady-state one, having its entropy converge to the steady-state value. Full article ">Figure 5
Numerical time evolution of the Wehrl entropy starting from a squeezed state such that <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>1</mn> <mo>=</mo> <msub> <mi>σ</mi> <mi>x</mi> </msub> <mo>,</mo> <mspace width="0.166667em"/> <mo>Δ</mo> <mi>p</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>=</mo> <msub> <mi>σ</mi> <mi>p</mi> </msub> </mrow> </semantics></math>, having its entropy converge to the steady-state value. Full article ">Figure 6
Numerical time evolution of the Wehrl entropy starting from a squeezed state such that <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>=</mo> <msub> <mi>σ</mi> <mi>x</mi> </msub> <mo>,</mo> <mspace width="0.166667em"/> <mo>Δ</mo> <mi>p</mi> <mo>=</mo> <mn>1</mn> <mo>=</mo> <msub> <mi>σ</mi> <mi>p</mi> </msub> </mrow> </semantics></math>, having its entropy converge to the steady-state value as well. Full article ">

22 pages, 537 KiB

Open AccessArticle

CNN-HT: A Two-Stage Algorithm Selection Framework

by Siyi Xu, Wenwen Liu, Chengpei Wu and Junli Li

Entropy 2024, 26(3), 262; https://doi.org/10.3390/e26030262 - 14 Mar 2024

Viewed by 1147

Abstract

The No Free Lunch Theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. This paper [...] Read more.

The No Free Lunch Theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. This paper introduces an innovative algorithm selection approach called the CNN-HT, which is a two-stage algorithm selection framework. In the first stage, a Convolutional Neural Network (CNN) is employed to classify problems. In the second stage, the Hypothesis Testing (HT) technique is used to suggest the best-performing algorithm based on the statistical analysis of the performance metric of algorithms that address various problem categories. The two-stage approach can adapt to different algorithm combinations without the need to retrain the entire model, and modifications can be made in the second stage only, which is an improvement of one-stage approaches. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as input and utilize feature selection techniques to reduce the redundant ones. In problem classification, the average accuracy of classifying problems using CNN is 96%, which demonstrates the advantages of CNN compared to Random Forest and Support Vector Machines. After feature selection, the accuracy increases to 98.8%, further improving the classification performance while reducing the computational cost. This demonstrates the effectiveness of the first stage of the CNN-HT method, which provides a basis for algorithm selection. In the experiments, CNN-HT shows the advantages of the second stage algorithm as well as good performance with better average rankings in different algorithm combinations compared to the individual algorithms and another algorithm combination approach. Full article

(This article belongs to the Special Issue Swarm Intelligence Optimization: Algorithms and Applications)

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12 pages, 319 KiB

Open AccessArticle

Magnetic Black Hole Thermodynamics in an Extended Phase Space with Nonlinear Electrodynamics

by Sergey Il’ich Kruglov

Entropy 2024, 26(3), 261; https://doi.org/10.3390/e26030261 - 14 Mar 2024

Cited by 1 | Viewed by 1052

Abstract

We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function [...] Read more.

We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed. Full article

(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)

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11 pages, 318 KiB

Open AccessArticle

Restoring the Fluctuation–Dissipation Theorem in Kardar–Parisi–Zhang Universality Class through a New Emergent Fractal Dimension

by Márcio S. Gomes-Filho, Pablo de Castro, Danilo B. Liarte and Fernando A. Oliveira

Entropy 2024, 26(3), 260; https://doi.org/10.3390/e26030260 - 14 Mar 2024

Cited by 1 | Viewed by 1098

Abstract

The Kardar–Parisi–Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth [...] Read more.

The Kardar–Parisi–Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth exponents; and the apparent absence of a fluctuation–dissipation theorem (FDT) for spatial dimension

d > 1

. Notably, these questions were answered exactly only for

1 + 1

dimensions. In this work, we propose a new FDT valid for the KPZ problem in

d + 1

dimensions. This is achieved by rearranging terms and identifying a new correlated noise which we argue to be characterized by a fractal dimension

d_{n}

. We present relations between the KPZ exponents and two emergent fractal dimensions, namely

d_{f}

, of the rough interface, and

d_{n}

. Also, we simulate KPZ growth to obtain values for transient versions of the roughness exponent

α

, the surface fractal dimension

d_{f}

and, through our relations, the noise fractal dimension

d_{n}

. Our results indicate that KPZ may have at least two fractal dimensions and that, within this proposal, an FDT is restored. Finally, we provide new insights into the old question about the upper critical dimension of the KPZ universality class. Full article

(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)

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16 pages, 1798 KiB

Open AccessArticle

Differential Entropy-Based Fault-Detection Mechanism for Power-Constrained Networked Control Systems

by Alejandro J. Rojas

Entropy 2024, 26(3), 259; https://doi.org/10.3390/e26030259 - 14 Mar 2024

Cited by 1 | Viewed by 967

Abstract

In this work, we consider the design of power-constrained networked control systems (NCSs) and a differential entropy-based fault-detection mechanism. For the NCS design of the control loop, we consider faults in the plant gain and unstable plant pole locations, either due to natural [...] Read more.

In this work, we consider the design of power-constrained networked control systems (NCSs) and a differential entropy-based fault-detection mechanism. For the NCS design of the control loop, we consider faults in the plant gain and unstable plant pole locations, either due to natural causes or malicious intent. Since the power-constrained approach utilized in the NCS design is a stationary approach, we then discuss the finite-time approximation of the power constraints for the relevant control loop signals. The network under study is formed by two additive white Gaussian noise (AWGN) channels located on the direct and feedback paths of the closed control loop. The finite-time approximation of the controller output signal allows us to estimate its differential entropy, which is used in our proposed fault-detection mechanism. After fault detection, we propose a fault-identification mechanism that is capable of correctly discriminating faults. Finally, we discuss the extension of the contributions developed here to future research directions, such as fault recovery and control resilience. Full article

(This article belongs to the Special Issue The Application of Information Theory in Fault Detection and Diagnosis)

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16 pages, 3876 KiB

Open AccessArticle

Three-Dimensional Reconstruction Pre-Training as a Prior to Improve Robustness to Adversarial Attacks and Spurious Correlation

by Yutaro Yamada, Fred Weiying Zhang, Yuval Kluger and Ilker Yildirim

Entropy 2024, 26(3), 258; https://doi.org/10.3390/e26030258 - 14 Mar 2024

Viewed by 1176

Abstract

Ensuring robustness of image classifiers against adversarial attacks and spurious correlation has been challenging. One of the most effective methods for adversarial robustness is a type of data augmentation that uses adversarial examples during training. Here, inspired by computational models of human vision, [...] Read more.

Ensuring robustness of image classifiers against adversarial attacks and spurious correlation has been challenging. One of the most effective methods for adversarial robustness is a type of data augmentation that uses adversarial examples during training. Here, inspired by computational models of human vision, we explore a synthesis of this approach by leveraging a structured prior over image formation: the 3D geometry of objects and how it projects to images. We combine adversarial training with a weight initialization that implicitly encodes such a prior about 3D objects via 3D reconstruction pre-training. We evaluate our approach using two different datasets and compare it to alternative pre-training protocols that do not encode a prior about 3D shape. To systematically explore the effect of 3D pre-training, we introduce a novel dataset called Geon3D, which consists of simple shapes that nevertheless capture variation in multiple distinct dimensions of geometry. We find that while 3D reconstruction pre-training does not improve robustness for the simplest dataset setting, we consider (Geon3D on a clean background) that it improves upon adversarial training in more realistic (Geon3D with textured background and ShapeNet) conditions. We also find that 3D pre-training coupled with adversarial training improves the robustness to spurious correlations between shape and background textures. Furthermore, we show that the benefit of using 3D-based pre-training outperforms 2D-based pre-training on ShapeNet. We hope that these results encourage further investigation of the benefits of structured, 3D-based models of vision for adversarial robustness. Full article

(This article belongs to the Special Issue Probabilistic Models in Machine and Human Learning)

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14 pages, 737 KiB

Open AccessArticle

Analysis of Quantum Steering Measures

by Lucas Maquedano and Ana C. S. Costa

Entropy 2024, 26(3), 257; https://doi.org/10.3390/e26030257 - 14 Mar 2024

Cited by 2 | Viewed by 1137

Abstract

The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few approaches presented in order to [...] Read more.

The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few approaches presented in order to measure the degree of steerability of a given system. In this work, we are interested in investigating possible ways to quantify quantum steering, where we based our analysis on different criteria presented in the literature. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

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15 pages, 2895 KiB

Open AccessArticle

Patterns in Temporal Networks with Higher-Order Egocentric Structures

by Beatriz Arregui-García, Antonio Longa, Quintino Francesco Lotito, Sandro Meloni and Giulia Cencetti

Entropy 2024, 26(3), 256; https://doi.org/10.3390/e26030256 - 13 Mar 2024

Cited by 2 | Viewed by 1323

Abstract

The analysis of complex and time-evolving interactions, such as those within social dynamics, represents a current challenge in the science of complex systems. Temporal networks stand as a suitable tool for schematizing such systems, encoding all the interactions appearing between pairs of individuals [...] Read more.

The analysis of complex and time-evolving interactions, such as those within social dynamics, represents a current challenge in the science of complex systems. Temporal networks stand as a suitable tool for schematizing such systems, encoding all the interactions appearing between pairs of individuals in discrete time. Over the years, network science has developed many measures to analyze and compare temporal networks. Some of them imply a decomposition of the network into small pieces of interactions; i.e., only involving a few nodes for a short time range. Along this line, a possible way to decompose a network is to assume an egocentric perspective; i.e., to consider for each node the time evolution of its neighborhood. This was proposed by Longa et al. by defining the “egocentric temporal neighborhood”, which has proven to be a useful tool for characterizing temporal networks relative to social interactions. However, this definition neglects group interactions (quite common in social domains), as they are always decomposed into pairwise connections. A more general framework that also allows considering larger interactions is represented by higher-order networks. Here, we generalize the description of social interactions to hypergraphs. Consequently, we generalize their decomposition into “hyper egocentric temporal neighborhoods”. This enables the analysis of social interactions, facilitating comparisons between different datasets or nodes within a dataset, while considering the intrinsic complexity presented by higher-order interactions. Even if we limit the order of interactions to the second order (triplets of nodes), our results reveal the importance of a higher-order representation.In fact, our analyses show that second-order structures are responsible for the majority of the variability at all scales: between datasets, amongst nodes, and over time. Full article

(This article belongs to the Special Issue Topological Data Analysis Meets Information Theory. New Perspectives for the Analysis of Higher-Order Interactions in Complex Systems)

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12 pages, 3364 KiB

Open AccessArticle

Events as Elements of Physical Observation: Experimental Evidence

by J. Gerhard Müller

Entropy 2024, 26(3), 255; https://doi.org/10.3390/e26030255 - 13 Mar 2024

Cited by 2 | Viewed by 2185

Abstract

It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space–time location

\vec{X} = (\vec{x}, t)

. Considering historic experiments, which have been groundbreaking [...] Read more.

It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space–time location

\vec{X} = (\vec{x}, t)

. Considering historic experiments, which have been groundbreaking in the evolution of our modern ideas of matter on the atomic, nuclear, and elementary particle scales, it is shown that such experiments produce as outputs streams of macroscopically observable events which accumulate in the course of time into spatio-temporal patterns of events whose forms allow decisions to be taken concerning conceivable alternatives of explanation. Working towards elucidating the physical and informational characteristics of those elementary observations, we show that these represent hugely amplified images of the initiating micro-events and that the resulting macro-images have a cognitive value of 1 bit and a physical value of

W_{o b s} = E_{o b s} τ_{o b s} ≫ h

. In this latter equation,

E_{o b s}

stands for the energy spent in turning the initiating micro-events into macroscopically observable events,

τ_{o b s}

for the lifetimes during which the generated events remain macroscopically observable, and

h

for Planck’s constant. The relative value

G_{o b s} = W_{o b s} / h

finally represents a measure of amplification that was gained in the observation process. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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23 pages, 36196 KiB

Open AccessArticle

An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images

by Yuli Yang, Ruiyun Chang, Xiufang Feng, Peizhen Li, Yongle Chen and Hao Zhang

Entropy 2024, 26(3), 254; https://doi.org/10.3390/e26030254 - 13 Mar 2024

Cited by 1 | Viewed by 1184

Abstract

The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based [...] Read more.

The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based chaotic system (nD-CTBCS) with a chaotic coupling model is suggested in this study. To create chaotic maps of any desired dimension, nD-CTBCS can take advantage of already-existing 1D chaotic maps as seed chaotic maps. Three two-dimensional chaotic maps are provided as examples to illustrate the impact. The findings of the evaluation and experiments demonstrate that the newly created chaotic maps function better, have broader chaotic intervals, and display hyperchaotic behavior. To further demonstrate the practicability of nD-CTBCS, a reversible data hiding scheme is proposed for the secure communication of medical images. The experimental results show that the proposed method has higher security than the existing methods. Full article

(This article belongs to the Special Issue Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition)

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15 pages, 681 KiB

Open AccessArticle

Intra-Beam Interference Mitigation for the Downlink Transmission of the RIS-Assisted Hybrid Millimeter Wave System

by Lou Zhao, Yuliang Zhang, Minjie Zhang and Chunshan Liu

Entropy 2024, 26(3), 253; https://doi.org/10.3390/e26030253 - 13 Mar 2024

Viewed by 1110

Abstract

Millimeter-wave (mmWave) communication systems leverage the directional beamforming capabilities of antenna arrays equipped at the base stations (BS) to counteract the inherent high propagation path loss characteristic of mmWave channels. In downlink mmWave transmissions, i.e., from the BS to users, distinguishing users within [...] Read more.

Millimeter-wave (mmWave) communication systems leverage the directional beamforming capabilities of antenna arrays equipped at the base stations (BS) to counteract the inherent high propagation path loss characteristic of mmWave channels. In downlink mmWave transmissions, i.e., from the BS to users, distinguishing users within the same beam direction poses a significant challenge. Additionally, digital baseband precoding techniques are limited in their ability to mitigate inter-user interference within identical beam directions, representing a fundamental constraint in mmWave downlink transmissions. This study introduces an innovative analog beamforming-based interference mitigation strategy for downlink transmissions in reconfigurable intelligent surface (RIS)-assisted hybrid analog–digital (HAD) mmWave systems. This is achieved through the joint design of analog beamformers and the corresponding coefficients at both the RIS and the BS. We first present derived closed-form approximation expressions for the achievable rate performance in the proposed scenario and establish a stringent upper bound on this performance in a large number of RIS elements regimes. The exclusive use of analog beamforming in the downlink phase allows our proposed transmission algorithm to function efficiently when equipped with low-resolution analog-to-digital/digital-to-analog converters (A/Ds) at the BS. The energy efficiency of the downlink transmission is evaluated through the deployment of six-bit A/Ds and six-bit pulse-amplitude modulation (PAM) signals across varying numbers of activated RIS elements. Numerical simulation results validate the effectiveness of our proposed algorithms in comparison to various benchmark schemes. Full article

(This article belongs to the Section Signal and Data Analysis)

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28 pages, 570 KiB

Open AccessReview

To Compress or Not to Compress—Self-Supervised Learning and Information Theory: A Review

by Ravid Shwartz Ziv and Yann LeCun

Entropy 2024, 26(3), 252; https://doi.org/10.3390/e26030252 - 12 Mar 2024

Cited by 28 | Viewed by 6294

Abstract

Deep neural networks excel in supervised learning tasks but are constrained by the need for extensive labeled data. Self-supervised learning emerges as a promising alternative, allowing models to learn without explicit labels. Information theory has shaped deep neural networks, particularly the information bottleneck [...] Read more.

Deep neural networks excel in supervised learning tasks but are constrained by the need for extensive labeled data. Self-supervised learning emerges as a promising alternative, allowing models to learn without explicit labels. Information theory has shaped deep neural networks, particularly the information bottleneck principle. This principle optimizes the trade-off between compression and preserving relevant information, providing a foundation for efficient network design in supervised contexts. However, its precise role and adaptation in self-supervised learning remain unclear. In this work, we scrutinize various self-supervised learning approaches from an information-theoretic perspective, introducing a unified framework that encapsulates the self-supervised information-theoretic learning problem. This framework includes multiple encoders and decoders, suggesting that all existing work on self-supervised learning can be seen as specific instances. We aim to unify these approaches to understand their underlying principles better and address the main challenge: many works present different frameworks with differing theories that may seem contradictory. By weaving existing research into a cohesive narrative, we delve into contemporary self-supervised methodologies, spotlight potential research areas, and highlight inherent challenges. Moreover, we discuss how to estimate information-theoretic quantities and their associated empirical problems. Overall, this paper provides a comprehensive review of the intersection of information theory, self-supervised learning, and deep neural networks, aiming for a better understanding through our proposed unified approach. Full article

(This article belongs to the Special Issue Information-Theoretic Methods in Deep Learning: Theory and Applications)

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17 pages, 8787 KiB

Open AccessArticle

Multipole Approach to the Dynamical Casimir Effect with Finite-Size Scatterers

by Lucas Alonso, Guilherme C. Matos, François Impens, Paulo A. Maia Neto and Reinaldo de Melo e Souza

Entropy 2024, 26(3), 251; https://doi.org/10.3390/e26030251 - 12 Mar 2024

Cited by 1 | Viewed by 1056

Abstract

A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size [...] Read more.

A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size and oscillation frequency), this assumption is inadequate and drastically overestimates the DCE radiation. Taking the opposite limit, we use instead the dipolar approximation to obtain a simpler and more realistic treatment of DCE for macroscopic bodies. Our approach is inspired by a microscopic theory of DCE, which is extended to the macroscopic realm by a suitable effective Hamiltonian description of moving anisotropic scatterers. We illustrate the benefits of our approach by considering the DCE from macroscopic bodies of different geometries. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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33 pages, 506 KiB

Open AccessArticle

Fundamental Limits of Coded Caching in Request-Robust D2D Communication Networks

by Wuqu Wang, Zhe Tao, Nan Liu and Wei Kang

Entropy 2024, 26(3), 250; https://doi.org/10.3390/e26030250 - 12 Mar 2024

Viewed by 1071

Abstract

D2D coded caching, originally introduced by Ji, Caire, and Molisch, significantly improves communication efficiency by applying the multi-cast technology proposed by Maddah-Ali and Niesen to the D2D network. Most prior works on D2D coded caching are based on the assumption that all users [...] Read more.

D2D coded caching, originally introduced by Ji, Caire, and Molisch, significantly improves communication efficiency by applying the multi-cast technology proposed by Maddah-Ali and Niesen to the D2D network. Most prior works on D2D coded caching are based on the assumption that all users will request content at the beginning of the delivery phase. However, in practice, this is often not the case. Motivated by this consideration, this paper formulates a new problem called request-robust D2D coded caching. The considered problem includes K users and a content server with access to N files. Only r users, known as requesters, request a file each at the beginning of the delivery phase. The objective is to minimize the average and worst-case delivery rate, i.e., the average and worst-case number of broadcast bits from all users among all possible demands. For this novel D2D coded caching problem, we propose a scheme based on uncoded cache placement and exploiting common demands and one-shot delivery. We also propose information-theoretic converse results under the assumption of uncoded cache placement. Furthermore, we adapt the scheme proposed by Yapar et al. for uncoded cache placement and one-shot delivery to the request-robust D2D coded caching problem and prove that the performance of the adapted scheme is order optimal within a factor of two under uncoded cache placement and within a factor of four in general. Finally, through numerical evaluations, we show that the proposed scheme outperforms known D2D coded caching schemes applied to the request-robust scenario for most cache size ranges. Full article

(This article belongs to the Special Issue Information Theory and Network Coding II)

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18 pages, 401 KiB

Open AccessArticle

Constrained Reweighting of Distributions: An Optimal Transport Approach

by Abhisek Chakraborty, Anirban Bhattacharya and Debdeep Pati

Entropy 2024, 26(3), 249; https://doi.org/10.3390/e26030249 - 11 Mar 2024

Viewed by 1155

Abstract

We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the [...] Read more.

We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the resulting weight-adjusted empirical distribution. In this article, we substantially enhance the flexibility of such a methodology by introducing a nonparametrically imbued distributional constraint on the weights and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight-adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric, while allowing for subtle departures. The proposed scheme for the re-weighting of observations subject to constraints is reminiscent of the empirical likelihood and related ideas, but offers greater flexibility in applications where parametric distribution-guided constraints arise naturally. The versatility of the proposed framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task—namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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15 pages, 1251 KiB

Open AccessArticle

Network Higher-Order Structure Dismantling

by Peng Peng, Tianlong Fan and Linyuan Lü

Entropy 2024, 26(3), 248; https://doi.org/10.3390/e26030248 - 11 Mar 2024

Viewed by 1512

Abstract

Diverse higher-order structures, foundational for supporting a network’s “meta-functions”, play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, [...] Read more.

Diverse higher-order structures, foundational for supporting a network’s “meta-functions”, play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, with the objective of disrupting not only network connectivity but also eradicating all higher-order structures in each branch, thereby ensuring thorough functional paralysis. Given the diversity and unknown specifics of higher-order structures, identifying and targeting them individually is not practical or even feasible. Fortunately, their close association with k-cores arises from their internal high connectivity. Thus, we transform higher-order structure measurement into measurements on k-cores with corresponding orders. Furthermore, we propose the Belief Propagation-guided Higher-order Dismantling (BPHD) algorithm, minimizing dismantling costs while achieving maximal disruption to connectivity and higher-order structures, ultimately converting the network into a forest. BPHD exhibits the explosive vulnerability of network higher-order structures, counterintuitively showcasing decreasing dismantling costs with increasing structural complexity. Our findings offer a novel approach for dismantling malignant networks, emphasizing the substantial challenges inherent in safeguarding against such malicious attacks. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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1 pages, 381 KiB

Open AccessCorrection

Correction: Zhou et al. Optimal Flow Distribution of Military Supply Transportation Based on Network Analysis and Entropy Measurement. Entropy 2018, 20, 446

by Wei Zhou, Jin Chen and Bingqing Ding

Entropy 2024, 26(3), 247; https://doi.org/10.3390/e26030247 - 11 Mar 2024

Viewed by 832

Abstract

In the original publication [...] Full article

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10 pages, 325 KiB

Open AccessArticle

Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation

by Gilberto M. Kremer

Entropy 2024, 26(3), 246; https://doi.org/10.3390/e26030246 - 10 Mar 2024

Viewed by 998

Abstract

Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner [...] Read more.

Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. Full article

(This article belongs to the Special Issue Statistical Mechanics of Self-Gravitating Systems)

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