Terms Of Entropy Research Articles

Discontinuity in RG flows across dimensions: entanglement, anomaly coefficients and geometry

We study the entanglement entropy associated with a holographic RG flow from AdS7 to AdS4 × ℍ3, where ℍ3 is a 3-dimensional hyperbolic manifold with curvature κ. The dual six-dimensional RG flow is disconnected from Lorentz-invariant flows. In this context we address various notions of central charges and identify a monotonic candidate c-function that captures IR aspects of the flow. The UV behavior of the holographic entanglement entropy and, in particular its universal term, display an interesting dependence on the curvature, κ. We then contrast our holographic results with existing field theory computations in six dimensions and find a series of new corrections in curvature to the universal term in the entanglement entropy.

Entanglement entropy and the boundary action of edge modes

We consider an antisymmetric gauge field in the Minkowski space of d-dimension and decompose it in terms of the antisymmetric tensor harmonics and fix the gauge. The Gauss law implies that the normal component of the field strength on the spherical entangling surface will label the superselection sectors. From the two-point function of the field strength on the sphere, we evaluate the logarithmic divergent term of the entanglement entropy of edge modes of p-form field. We observe that the logarithmic divergent term in entanglement entropy of edge modes coincides with the edge partition function of co-exact p-form on the sphere when expressed in terms of the Harish-Chandra characters. We also develop a boundary path integral of the antisymmetric p-form gauge field. From the boundary path integral, we show that the edge mode partition function corresponds to the co-exact (p − 1)-forms on the boundary. This boundary path integral agrees with the direct evaluation of the entanglement entropy of edge modes extracted from the two-point function of the normal component of the field strength on the entangling surface.

Characterizing the ambiguity in topological entanglement entropy

Topological entanglement entropy (TEE), the sub-leading term in the entanglement entropy of topological order, is the direct evidence of the long-range entanglement. While effective in characterizing topological orders on closed manifolds, TEE is model-dependent when entanglement cuts intersect with physical gapped boundaries. In this paper, we study the origin of this model-dependence by introducing a model-independent picture of partitioning the topological orders with gapped boundaries. In our picture, the entanglement boundaries (EBs), i.e. the virtual boundaries of each subsystem induced by the entanglement cuts, are assumed to be gapped boundaries with boundary defects. At this model-independent stage, there are two choices one has to make manually in defining the bi-partition: the boundary condition on the EBs, and the coherence between certain boundary states. We show that TEE appears because of a constraint on the defect configurations on the EBs, which is choice-dependent in the cases where the EBs touch gapped boundaries. This choice-dependence is known as the ambiguity in entanglement entropy. Different models intrinsically employ different choices, rendering TEE model-dependent. For D(ℤ2) topological order, the ambiguity can be fully characterized by two parameters that respectively quantifies the EB condition and the coherence. In particular, calculations compatible with the folding trick naturally choose EB conditions that respect electric-magnetic duality and set specific parameter values.

A Spectral Gap-Based Topology Control Algorithm for Wireless Backhaul Networks

This paper presents the spectral gap-based topology control algorithm (SGTC) for wireless backhaul networks, a novel approach that employs the Laplacian Spectral Gap (LSG) to find expander-like graphs that optimize the topology of the network in terms of robustness, diameter, energy cost, and network entropy. The latter measures the network’s ability to promote seamless traffic offloading from the Macro Base Stations to smaller cells by providing a high diversity of shortest paths connecting all the stations. Given the practical constraints imposed by cellular technologies, the proposed algorithm uses simulated annealing to search for feasible network topologies with a large LSG. Then, it computes the Pareto front of the set of feasible solutions found during the annealing process when considering robustness, diameter, and entropy as objective functions. The algorithm’s result is the Pareto efficient solution that minimizes energy cost. A set of experimental results shows that by optimizing the LSG, the proposed algorithm simultaneously optimizes the set of desirable topological properties mentioned above. The results also revealed that generating networks with good spectral expansion is possible even under the restrictions imposed by current wireless technologies. This is a desirable feature because these networks have strong connectivity properties even if they do not have a large number of links.

Generalized weighted permutation entropy analysis of satellite hot-pixel time series in Brazilian biomes

In this work we analyze hot-pixel satellite data, proxy for natural and anthropogenic vegetation and forest fires, using recently proposed method Generalized weighted permutation entropy (GWPE). The current analysis of data from 2002 to 2022 for six Brazilian biomes sheds new light on differences among the biomes in terms of ordinal pattern entropy, for both small and large fluctuations. It is found that for all biomes large fluctuations in fire temporal series show higher complexity level than small fluctuations, small fluctuations being more predictable as indicated by lower entropy values. Moreover, for fire sensitive biomes Amazon and Atlantic Forest the three dimensional complexity entropy curves in the complexity-entropy-scale causality box (CESCB) are rather similar (indicating similar dynamics for both small and large fluctuations), as well as for fire dependent biomes Pantanal and Pampa, while fire independent Caatinga biome shows different, distinct behavior. Finally, the similarity in lower parts of the CESCB curves (corresponding to small fluctuations) between Amazon and Cerrado reflects the changes of fire dynamics due to human activities.

Quantum relative entropy uncertainty relation.

For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and nonthermal environments.

Exploring the expansion of the universe using the Grüneisen parameter

For a perfect fluid, pressure p and energy density ρ are related via the equation of state (EOS) ω=p/ρ, where ω is the EOS parameter, being its interpretation usually constrained to a numerical value for each universe era. Here, based on the Mie–Grüneisen EOS, we show that ω is recognized as the effective Grüneisen parameter Γeff, whose singular contribution, the so-called Grüneisen ratio Γ, quantifies the barocaloric effect. Our analysis suggests that the negative p associated with dark-energy implies a metastable state and that in the dark-energy-dominated era ω is time-dependent, which reinforces recent proposals of a time-dependent cosmological constant. Furthermore, we demonstrate that Γeff is embodied in the energy–momentum stress tensor in the Einstein field equations, enabling us to analyse, in the frame of an imperfect fluid picture, anisotropic effects of the universe expansion. We propose that upon going from decelerated- to accelerated-expansion, a phase transition-like behaviour can be inferred. Yet, our analysis in terms of entropy, Γ, and a by us adapted version of Avramov/Casalini’s model to Cosmology unveil hidden aspects related to the expansion of the universe. Our findings pave the way to interpret cosmological phenomena in connection with concepts of condensed matter Physics via Γeff.

Kondo screening cloud scaling: impurity entanglement and magnetization

The screening of an impurity spin in the Kondo model occurs over a characteristic length scale ξ K , that defines the size of the Kondo screening cloud or ‘mist’. The presence of such a length scale in experimental and numerical results is rather subtle. A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations in terms of the single variable, r/ξK instead of the correlations depending on r and ξ K separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength JK′ . Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, g. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling JK′ is varied, a precise determination of ξ K can then be obtained. The length scale, ξ K , is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain.

From the detection of monitoring anomalies to the probabilistic forecast of the evolution of volcanic unrest: an entropy-based approach

Owing to the current lack of plausible and exhaustive physical pre-eruptive models, often volcanologists rely on the observation of monitoring anomalies to track the evolution of volcanic unrest episodes. Taking advantage from the work made in the development of Bayesian Event Trees (BET), here we formalize an entropy-based model to translate the observation of anomalies into probability of a specific volcanic event of interest. The model is quite general and it could be used as a stand-alone eruption forecasting tool or to set up conditional probabilities for methodologies like the BET and of the Bayesian Belief Network (BBN). The proposed model has some important features worth noting: (i) it is rooted in a coherent logic, which gives a physical sense to the heuristic information of volcanologists in terms of entropy; (ii) it is fully transparent and can be established in advance of a crisis, making the results reproducible and revisable, providing a transparent audit trail that reduces the overall degree of subjectivity in communication with civil authorities; (iii) it can be embedded in a unified probabilistic framework, which provides an univocal taxonomy of different kinds of uncertainty affecting the forecast and handles these uncertainties in a formal way. Finally, for the sake of example, we apply the procedure to track the evolution of the 1982–1984 phase of unrest at Campi Flegrei.

Detection of Blood CO2 Influences on Cerebral Hemodynamics Using Transfer Entropy.

Cerebral hemodynamics describes an important physiological system affected by components such as blood pressure, CO2 levels, and endothelial factors. Recently, novel techniques have emerged to analyse cerebral hemodynamics based on the calculation of entropies, which quantifies or describes changes in the complexity of this system when it is affected by a pathological or physiological influence. One recently described measure is transfer entropy, which allows for the determination of causality between the various components of a system in terms of their flow of information, and has shown positive results in the multivariate analysis of physiological signals. This study aims to determine whether conditional transfer entropy reflects the causality in terms of entropy generated by hypocapnia on cerebral hemodynamics. To achieve this, non-invasive signals from 28 healthy individuals who undertook a hyperventilation maneuver were analyzed using conditional transfer entropy to assess the variation in the relevance of CO2 levels on cerebral blood velocity. By employing a specific method to discretize the signals, it was possible to differentiate the influence of CO2 levels during the hyperventilation phase (22.0% and 20.3% increase for the left and right hemispheres, respectively) compared to normal breathing, which remained higher during the recovery phase (15.3% and 15.2% increase, respectively).

Mother-infant social gaze dynamics relate to infant brain activity and word segmentation

The ‘social brain’, consisting of areas sensitive to social information, supposedly gates the mechanisms involved in human language learning. Early preverbal interactions are guided by ostensive signals, such as gaze patterns, which are coordinated across body, brain, and environment. However, little is known about how the infant brain processes social gaze in naturalistic interactions and how this relates to infant language development. During free-play of 9-month-olds with their mothers, we recorded hemodynamic cortical activity of ´social brain` areas (prefrontal cortex, temporo-parietal junctions) via fNIRS, and micro-coded mother’s and infant’s social gaze. Infants’ speech processing was assessed with a word segmentation task. Using joint recurrence quantification analysis, we examined the connection between infants’ ´social brain` activity and the temporal dynamics of social gaze at intrapersonal (i.e., infant’s coordination, maternal coordination) and interpersonal (i.e., dyadic coupling) levels. Regression modeling revealed that intrapersonal dynamics in maternal social gaze (but not infant’s coordination or dyadic coupling) coordinated significantly with infant’s cortical activity. Moreover, recurrence quantification analysis revealed that intrapersonal maternal social gaze dynamics (in terms of entropy) were the best predictor of infants’ word segmentation. The findings support the importance of social interaction in language development, particularly highlighting maternal social gaze dynamics.

A convex analysis approach to the metric mean dimension: Limits of scaled pressures and variational principles

We introduce the concept of upper metric mean dimension of a one-parameter family of scaled pressure functions, which extends the corresponding notion for a single potential and satisfies a variational principle. This approach, supported by Convex Analysis, conveys a definition of measure-theoretic upper metric mean dimension, which is concave and upper semi-continuous, and therewith equilibrium states. In the context of dynamical systems, we establish a variational principle for the metric mean dimension with potential in terms of Katok entropy. As an application, we provide a simple formula for the upper metric mean dimension with potential for the shift on the space ([0,1]D)N, for every D∈N, which links mean dimension theory with ergodic optimization.

Small Stochastic Data Compactification Concept Justified in the Entropy Basis.

Measurement is a typical way of gathering information about an investigated object, generalized by a finite set of characteristic parameters. The result of each iteration of the measurement is an instance of the class of the investigated object in the form of a set of values of characteristic parameters. An ordered set of instances forms a collection whose dimensionality for a real object is a factor that cannot be ignored. Managing the dimensionality of data collections, as well as classification, regression, and clustering, are fundamental problems for machine learning. Compactification is the approximation of the original data collection by an equivalent collection (with a reduced dimension of characteristic parameters) with the control of accompanying information capacity losses. Related to compactification is the data completeness verifying procedure, which is characteristic of the data reliability assessment. If there are stochastic parameters among the initial data collection characteristic parameters, the compactification procedure becomes more complicated. To take this into account, this study proposes a model of a structured collection of stochastic data defined in terms of relative entropy. The compactification of such a data model is formalized by an iterative procedure aimed at maximizing the relative entropy of sequential implementation of direct and reverse projections of data collections, taking into account the estimates of the probability distribution densities of their attributes. The procedure for approximating the relative entropy function of compactification to reduce the computational complexity of the latter is proposed. To qualitatively assess compactification this study undertakes a formal analysis that uses data collection information capacity and the absolute and relative share of information losses due to compaction as its metrics. Taking into account the semantic connection of compactification and completeness, the proposed metric is also relevant for the task of assessing data reliability. Testing the proposed compactification procedure proved both its stability and efficiency in comparison with previously used analogues, such as the principal component analysis method and the random projection method.

Medium-entropy oxide (Ce0.25Sm0.25La0.25Gd0.25)2O3-δ as promising electrolyte for low-temperature solid oxide fuel cells

The development of high-performance electrolyte is crucial for low-temperature solid oxide fuel cells (LT-SOFCs). Traditional ceria-based materials such as Gd0.1Ce0.9O2-δ (GDC) are promising electrolytes in intermediate-temperature range but their performance drop rapidly with decreasing temperature. Recent advances proposed a new concept for SOFC materials design in terms of entropy, indicative of enormous potential. Herein, a medium-entropy ceria-based oxide (Ce0.25Sm0.25La0.25Gd0.25)2O3-δ (CSLG25) is developed via entropy engineering and evaluated as potential electrolyte for LT-SOFCs by comparing with low-entropy electrolyte GDC. The effects of configuration entropy on crystal structure, oxygen vacancy, electrochemical performance, and proton transport characteristic of the materials are systematically investigated. It is found the CSLG25 cell device exhibits a remarkable power density of 747 mW cm−2 at 520 °C, along with a superionic conductivity of 0.1534 S cm−1. Further study via XPS and Raman technology reveals that the higher entropy of CSLG25 creates more oxygen vacancies and contributes to fast proton transport, which leads to promising fuel cell performance at 430–520 °C. The CSLG25 cell device also delivers the 55.5 h durability performance at 520 °C. This study thus provides a novel electrolyte material for LT-SOFCs and points out a feasible entropy engineering strategy for developing ionic conductors.

Study on Structural Stability of ZrO2 and YSZ: Doping-Induced Phase Transitions and Fermi Level Shift

This work summarizes the results of structural stability, electronic properties and phonon dispersion studies of biocompatible ZrO2 compound in its cubic (c-ZrO2), tetragonal (t-ZrO2) and monoclinic (m-ZrO2) phases. The authors found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The presence of rather weak frequencies for m-ZrO2 also confirms the monoclinic phase as a stable conformation of zirconia. Our analysis of the electronic properties showed that during the m-t phase transformation of ZrO2, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t-c cross-section. The band gaps for c-ZrO2, t-ZrO2, and m-ZrO2 are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations to study the effect of 3.23, 6.67, 10.35 and 16.15 mol%Y2O3 on the structure and properties of m-ZrO2 showed that the enthalpy of m-YSZ decreases linearly and accompanies further stabilization of zirconium dioxide. Doping-induced phase transitions of ZrO2 were discovered under the influence of Y2O3 doping, due to which the position of the Fermi level changes and the band gap decreases. It has been established that, not only for pure systems but including those doped with Y2O3, the main contribution to the formation of the conduction band is made by the p-states of electrons.

High-dimensional memristive neural network and its application in commercial data encryption communication

With the development of economic globalization, demands for digital business data sharing among different subsidiary companies are constantly emerging. How to achieve secure transmission of commercial data in the Internet of Things (IoT) is a challenging task. In this paper, we propose a memristive neural network-based method for encrypted communication of commercial data. First, a high-dimensional memristive Hopfield neural network (MMHNN) model with three memristive synapses and seven neurons is proposed and its complex dynamical behaviors are deeply analyzed. The results of theoretical analysis and numerical simulations show that the proposed MMHNN can generate quasi-periodic, periodic, chaotic and hyperchaotic attractors, as well as some controllable 1-direction (1D), 2D, 3D hyperchaotic multi-scroll attractors and other types of parametric regulatory dynamics and initial value regulation dynamics. In addition, an analog equivalent circuit for the MMHNN is constructed, and the circuit simulations experimental results demonstrate the correctness and feasibility of the multi-scroll attractors phenomena. Finally, a novel MMHNN-based encryption scheme for IoT commercial data images is proposed by applying hyperchaotic spatial multi-scroll attractors, and the performance analysis shows that the proposed system achieves good encryption performances, especially in terms of keyspace, information entropy, correlation and differential attacks. The hardware experiments further verify the effectiveness and superiority of the proposed commercial data encryption scheme based on the MMHNN.

Image Encryption Using a New Hybrid Chaotic Map and Spiral Transformation.

Image encryption based on chaotic maps is an important method for ensuring the secure communication of digital multimedia on the Internet. To improve the encryption performance and security of image encryption systems, a new image encryption algorithm is proposed that employs a compound chaotic map and random cyclic shift. First, a new hybrid chaotic system is designed by coupling logistic, ICMIC, Tent, and Chebyshev (HLITC) maps. Comparison tests with previous chaotic maps in terms of chaotic trajectory, Lyapunov exponent, and approximate entropy illustrate that the new hybrid chaotic map has better chaotic performance. Then, the proposed HLITC chaotic system and spiral transformation are used to develop a new chaotic image encryption scheme using the double permutation strategy. The new HLITC chaotic system is used to generate key sequences used in the image scrambling and diffusion stages. The spiral transformation controlled by the chaotic sequence is used to scramble the pixels of the plaintext image, while the XOR operation based on a chaotic map is used for pixel diffusion. Extensive experiments on statistical analysis, key sensitivity, and key space analysis were conducted. Experimental results show that the proposed encryption scheme has good robustness against brute-force attacks, statistical attacks, and differential attacks and is more effective than many existing chaotic image encryption algorithms.

An optimal system for increasing the contrast resolution qualities of histopathology images in the wavelet domain

AbstractIn the field of histopathology, it has been observed that most images are of poor quality as a result of inadequate luminance and contrast. The first step in identifying and analyzing them is to enhance their quality while maintaining their inherent characteristics. This paper presents a novel method for enhancing histopathology images' important features, brightness preservation, and contrast by utilizing the adaptive intensity transformation gamma function in the wavelet domain. The RGB histopathological color image is first converted to the HSV color model. The V component is then stretched in order to compensate for any color distortion. In the proposed scheme, the stretched V component is split into four sub‐bands using discrete wavelet transform (DWT). Next, it determines the optimal value of the gamma correction function in the DWT lower sub‐band. A correction factor is applied using the singular value decomposition (SVD) technique to determine the optimal gamma function value using the nature‐inspired particle swarm optimization method (NIPSO). The corrected LL sub‐band is then applied to the inverse DWT (IDWT) together with the other unprocessed sub‐bands. In addition, the contrast of each feature is enhanced by employing an adaptive histogram equalization model that is contrast‐limited. The proposed method was evaluated through experiments and validations on a variety of histopathology images retrieved from multiple databases. Several quantitative studies have demonstrated that the proposed method outperforms existing enhancement techniques in terms of entropy, edge preservation index, contrast ratio, and Universal Image Quality Index (UIQI). This proposed technique increases contrast, while preserving the inherent characteristics of the original image, resulting in better quality histopathology images that can be used in disease diagnosis and inspection.

A new image encryption method based on memristive hyperchaos

This paper reports an effective image encryption method based on a novel two-dimensional memristive-coupled hyperchaotic Sine map. The performance analysis shows that the proposed map is easier to form hyperchaotic phenomenon in multiple parameter regions than some existing chaotic maps, and is suitable for image encryption. The new image encryption algorithm contains permutation and diffusion processes. The permutation process can make the pixel arrangement of the digital image disorderly, and the diffusion process can propagate small changes from the original image to the entire cipher-image with the help of a new bit-based double-loop-shift exclusive-OR (XOR) mechanism. The encryption and decryption effects are numerically investigated, and the security of the proposed algorithm is fully evaluated. Performance evaluations demonstrate that the proposed algorithm has well key sensitivity and robustness, and it has several advantages in terms of information entropy, correlation coefficient and the ability of defending differential attack, compared with the related algorithms.

Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario

One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when they are obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. In this paper, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to provide lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. We compare experimental setups providing Bell violations close to the Tsirelson’s bound with lower rates of events, with setups having slightly worse levels of violation but higher event rates. Our results demonstrate the first experiment that certifies close to two bits of randomness from binary measurements of two parties. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation theorem and show its advantages compared to existing solutions.