Entropy Transfer Research Articles

Adaptive symbolic transfer entropy and its applications in modeling for complex industrial systems.

Directed coupling between variables is the foundation of studying the dynamical behavior of complex systems. We propose an adaptive symbolic transfer entropy (ASTE) method based on the principle of equal probability division. First, the adaptive kernel density method is used to obtain an accurate probability density function for an observation series. Second, the complete phase space of the system can be obtained by using the multivariable phase space reconstruction method. This provides common parameters for symbolizing a time series, including delay time and embedding dimension. Third, an optimization strategy is used to select the appropriate symbolic parameters of a time series, such as the symbol set and partition intervals, which can be used to convert the time series to a symbol sequence. Then the transfer entropy between the symbolic sequences can be carried out. Finally, the proposed method is analyzed and validated using the chaotic Lorenz system and typical complex industrial systems. The results show that the ASTE method is superior to the existing transfer entropy and symbolic transfer entropy methods in terms of measurement accuracy and noise resistance, and it can be applied to the network modeling and performance safety analysis of complex industrial systems.

A new wind turbine health condition monitoring method based on VMD-MPE and feature-based transfer learning

Aimed at the problem that the signal data of wind turbine faulty gearbox is difficult to obtain and the health condition is difficult to diagnose under variable working conditions, a fault diagnosis method based on variational mode decomposition (VMD) multi-scale permutation entropy (MPE) and feature-based transfer learning (FTL) is proposed. According to the vibration signal characteristics of wind turbines, a series of mode components are obtained by transforming the signals under variable conditions. The MPE of the mode components is combined with the signal time domain features as a feature vector to be input into the transfer learning algorithm. The source domain and the target domain data belong to different working conditions, so the traditional machine learning methods are not ideal for fault classification. The method adopted in this paper minimizes the covariance between the source domain and the target domain through a linear transformation matrix, and reduces the difference of data distribution between the source domain and the target domain. Then, the feature vectors of the covariance-aligned source domain and the target domain are input into the support vector machine (SVM) for training and testing. Experiment shows that the proposed covariance alignment (COVAL) of fault features has higher accuracy in rolling bearing multi-state classification under variable working conditions compared with other methods.

Correlation between zonal flow shearing and entropy transfer rates in toroidal ion temperature gradient turbulence

The transfer rate of the entropy variable in the wavenumber space perpendicular to the equilibrium magnetic field is evaluated by means of the gyrokinetic simulations of the toroidal ion temperature gradient turbulence. Fluctuations of the perturbed gyrocenter distribution function of the linearly unstable mode are transferred to those with higher radial wavenumbers through interactions with zonal flows driven by turbulence. The entropy transfer rate coincides with the zonal flow shearing rate in cases with weak ion temperature gradient where the zonal flows effectively regulate the turbulent transport. The obtained result verifies a correlation between the entropy transfer and the zonal flow shearing processes.

Conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations: Adiabatic wall and heat entropy transfer

We present a novel technique for the imposition of non-linear entropy conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations in the presence of an adiabatic wall, or a wall with a prescribed heat entropy flow. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts and simultaneous-approximation-term operators, and is a generalization of previous works on discontinuous interface coupling [1] and solid wall boundary conditions [2]. Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions are coupled with an entropy-conservative or entropy-stable discrete interior operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation operators (mass lumped nodal discontinuous Galerkin operators), on high-order unstructured grids, are used for the purpose of demonstrating the robustness and efficacy of the new procedure for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional subsonic and supersonic flows. The procedure described is compatible with any diagonal-norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction schemes.

Shannon entropy transfer between solar magnetic modes

Based on Shannon entropy transfer estimation technique and Stanford’s solar global magnetic field harmonic coefficients, several new facts about solar magnetic modes have been found. The entropy transferring between most of the modes has been subjected to a steady modulation with a period near 72 solar rotations (5.38 years). As a rule, the amplitudes of entropy transferring modulation were less or equal to 0.1 bit/solar rotation. These modulations had no relations with intensity or configuration of the solar magnetic fields. Besides, Shannon entropy exchanges have been found between some modes—the sign of dependencies of them. Such modes had sector nature. The influence of a magnetic mode on another is strongest with the delay time between the two modes being twenty to forty solar rotations. Special properties have been revealed for zonal modes also.

Computer Model of Synapse Loss During an Alzheimer's Disease-Like Pathology in Hippocampal Subregions DG, CA3 and CA1-The Way to Chaos and Information Transfer.

The aim of the study was to compare the computer model of synaptic breakdown in an Alzheimer’s disease-like pathology in the dentate gyrus (DG), CA3 and CA1 regions of the hippocampus with a control model using neuronal parameters and methods describing the complexity of the system, such as the correlative dimension, Shannon entropy and positive maximal Lyapunov exponent. The model of synaptic breakdown (from 13% to 50%) in the hippocampus modeling the dynamics of an Alzheimer’s disease-like pathology was simulated. Modeling consisted in turning off one after the other EC2 connections and connections from the dentate gyrus on the CA3 pyramidal neurons. The pathological model of synaptic disintegration was compared to a control. The larger synaptic breakdown was associated with a statistically significant decrease in the number of spikes (R = −0.79, P < 0.001), spikes per burst (R = −0.76, P < 0.001) and burst duration (R = −0.83, P < 0.001) and an increase in the inter-burst interval (R = 0.85, P < 0.001) in DG-CA3-CA1. The positive maximal Lyapunov exponent in the control model was negative, but in the pathological model had a positive value of DG-CA3-CA1. A statistically significant decrease of Shannon entropy with the direction of information flow DG->CA3->CA1 (R = −0.79, P < 0.001) in the pathological model and a statistically significant increase with greater synaptic breakdown (R = 0.24, P < 0.05) of the CA3-CA1 region was obtained. The reduction of entropy transfer for DG->CA3 at the level of synaptic breakdown of 35% was 35%, compared with the control. Entropy transfer for CA3->CA1 at the level of synaptic breakdown of 35% increased to 95% relative to the control. The synaptic breakdown model in an Alzheimer’s disease-like pathology in DG-CA3-CA1 exhibits chaotic features as opposed to the control. Synaptic breakdown in which an increase of Shannon entropy is observed indicates an irreversible process of Alzheimer’s disease. The increase in synapse loss resulted in decreased information flow and entropy transfer in DG->CA3, and at the same time a strong increase in CA3->CA1.

Mapping individual behavior in financial markets: synchronization and anticipation

In this paper we develop a methodology, based on Mutual Information and Transfer of Entropy, that allows to identify, quantify and map on a network the synchronization and anticipation relationships between financial traders. We apply this methodology to a dataset containing 410text{,}612 real buy and sell operations, made by 566 non-professional investors from a private investment firm on 8 different assets from the Spanish IBEX market during a period of time from 2000 to 2008. These networks present a peculiar topology significantly different from the random networks. We seek alternative features based on human behavior that might explain part of those 12text{,}158 synchronization links and 1031 anticipation links. Thus, we detect that daily synchronization with price (present in 64.90% of investors) and the one-day delay with respect to price (present in 4.38% of investors) play a significant role in the network structure. We find that individuals reaction to daily price changes explains around 20% of the links in the Synchronization Network, and has significant effects on the Anticipation Network. Finally, we show how using these networks we substantially improve the prediction accuracy when Random Forest models are used to nowcast and predict the activity of individual investors.

Ultraviolet completion of a composite asymmetric dark matter model with a dark photon portal

Composite asymmetric dark matter scenarios naturally explain why the dark matter mass density is comparable with the visible matter mass density. Such scenarios generically require some entropy transfer mechanism below the composite scale; otherwise, their late-time cosmology is incompatible with observations. A tiny kinetic mixing between a dark photon and the visible photon is a promising example of the low-energy portal. In this paper, we demonstrate that grand unifications in the dark and the visible sectors explain the origin of the tiny kinetic mixing. We particularly consider an ultraviolet completion of a simple composite asymmetric dark matter model, where asymmetric dark matter carries a B − L charge. In this setup, the longevity of asymmetric dark matter is explained by the B − L symmetry, while the dark matter asymmetry originates from the B−L asymmetry generated by thermal leptogenesis. In our minimal setup, the Standard Model sector and the dark sector are unified into SU(5)GUT × SU(4)DGUT gauge theories, respectively. This model generates required B − L portal operators while suppressing unwanted higher-dimensional operators that could wash out the generated B − L asymmetry.

Using Information Theory to Evaluate Directional Precipitation Interactions Over the West Sahel Region in Observations and Models

AbstractWater availability has historically been one of the most significant threats to African regional social and economic well‐being. Over the Sahel region, a megadrought during the 1960s and 1970s induced by an abrupt and substantial rainfall reduction caused widespread famine and death. The postdrought recovery, which is still ongoing, has been characterized by gradual increases in rainfall, but with dramatic fluctuations. The large negative human impacts, slow recovery, and variability raise important questions of why and how rainfall dynamics evolve and interact with other components of the regional climate system. Here we provide an observational assessment of rainfall interactions mechanisms (informed by directional transfer of information entropy) that regulate Sahel rainfall. We quantitatively demonstrate that (1) sea surface temperature over the Gulf of Guinea controls moisture advection and transport to the West Sahel region and (2) strong bidirectional interactions exist between local vegetation dynamics and rainfall patterns. Then we assess the directional interaction patterns from nine state‐of‐the‐art Earth System Models (ESMs). We find that most ESMs are able to represent either the unidirectional control of sea surface temperature on precipitation or the bidirectional interaction between vegetation and precipitation. However, none of the ESMs represents both interactive patterns. The GFDL and IPSL‐CM5A‐LR models successfully reproduced observed patterns over ~50% of the West Sahel region but were not accurate in reproducing observed precipitation regional trends or interannual variation. We propose that the directional information transfer is a powerful mechanistic benchmark to assess model fidelity at the process level.

Strongly interacting massive particles through the axion portal

Dark matter could be a thermal relic comprised of strongly interacting massive particles (SIMPs), where $3 \rightarrow 2$ interactions set the relic abundance. Such interactions generically arise in theories of chiral symmetry breaking via the Wess-Zumino-Witten term. In this work, we show that an axion-like particle can successfully maintain kinetic equilibrium between the dark matter and the visible sector, allowing the requisite entropy transfer that is crucial for SIMPs to be a cold dark matter candidate. Constraints on this scenario arise from beam dump and collider experiments, from the cosmic microwave background, and from supernovae. We find a viable parameter space when the axion-like particle is close in mass to the SIMP dark matter, with strong-scale masses of order a few hundred MeV. Many planned experiments are set to probe the parameter space in the near future.

Exact Entanglement Dynamics in Three Interacting Qubits**Supported by the National Natural Science Foundation of China under Grant No 11534014, and the National Key R&D Program of China under Grant No 2017YFA0304500.

Motivated by recent experimental studies on coherent dynamics transfer in three interacting atoms or electron spins [Phys. Rev. Lett 114 (2015) 113002, Phys. Rev. Lett 120 (2018) 243604], here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. Thus dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer, characterized by the quantum mutual information and concurrence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.

Information Transfer Among the Components in Multi-Dimensional Complex Dynamical Systems

In this paper, a rigorous formalism of information transfer within a multi-dimensional deterministic dynamic system is established for both continuous flows and discrete mappings. The underlying mechanism is derived from entropy change and transfer during the evolutions of multiple components. While this work is mainly focused on three-dimensional systems, the analysis of information transfer among state variables can be generalized to high-dimensional systems. Explicit formulas are given and verified in the classical Lorenz and Chua’s systems. The uncertainty of information transfer is quantified for all variables, with which a dynamic sensitivity analysis could be performed statistically as an additional benefit. The generalized formalisms can be applied to study dynamical behaviors as well as asymptotic dynamics of the system. The simulation results can help to reveal some underlying information for understanding the system better, which can be used for prediction and control in many diverse fields.

Nonlinear effective connectivity measure based on adaptive Neuro Fuzzy Inference System and Granger Causality

Exploring brain networks is an essential step towards understanding functional organization of the brain, which needs characterization of linear and nonlinear connections based on measurements like EEG or MEG. Conventional measures of connectivity are mostly linear and bivariate. This paper proposes an effective connectivity measure called Adaptive Neuro-Fuzzy Inference System Granger Causality (ANFISGC). The proposed measure is based on the symplectic geometry embedding dimension, Adaptive Neuro-Fuzzy Inference System (ANFIS) predictor, and Granger Causality (GC). It is a powerful predictor that detects both linear and nonlinear causal information flow. It is not bivariate and thus can distinguish between direct and indirect connections. The performance of the proposed method is evaluated and compared with those of the Linear Granger Causality (LGC), Kernel Granger Causality (KGC), combination of Pairwise Granger Causality and Conditional Granger Causality (PwGC + CGC), Transfer Entropy (TE), and Phase Transfer Entropy (PTE) methods using simulated and experimental MEG data. Simulation results show that ANFISGC outperforms the other methods in detecting both linear and nonlinear connections and, by increasing the coupling strength between nodes, the value of ANFISGC increases. In the analysis of the time series of the brain sources of epilepsy patients obtained from the MEG inverse problem, the regions found by ANFISGC were more similar to the clinical findings than those found by the other methods.

Entropy and heat transfer analysis using Cattaneo-Christov heat flux model for a boundary layer flow of Casson nanofluid

Abstract A numerical investigation of Casson nanofluid flow, heat transfer and entropy generation over a horizontal porous stretching surface is carried out in the present research. The simplified flow model includes the effect of Lorentz forces, Cattaneo-Christov heat flux, thermal radiation and non-uniform stretching of porous surface. Similarity technique is employed to reduce the governing nonlinear partial differential equations to a set of nonlinear ordinary differential equations. The resulting set is then solved using finite difference numerical scheme to approximate the solutions for the velocity, temperature and the entropy profiles. Furthermore, the skin friction factor and the heat exchange rate at the boundary have been computed and explored graphically. The numerical computations are carried for Cu - H 2 O and TiO 2 - H 2 O nanofluids. The significant findings of the study are the negative impact of Lorentz forces on the nanofluid motion within the boundary layer and the increase in temperature due to increase in non-Newtonian parameter, thermal radiation parameter and the sheet convection parameter. Moreover Cu - H 2 O nanofluid is detected as superior thermal conductor than TiO 2 - H 2 O nanofluid.

Inter-scale information flow as a surrogate for downward causation that maintains spiral waves.

A rotor, the rotation center of spiral waves, has been proposed as a causal mechanism to maintain atrial fibrillation (AF) in human. However, our current understanding of the causality between rotors and spiral waves remains incomplete. One approach to improving our understanding is to determine the relationship between rotors and downward causation from the macro-scale collective behavior of spiral waves to the micro-scale behavior of individual components in a cardiac system. This downward causation is quantifiable as inter-scale information flow that can be used as a surrogate for the mechanism that maintains spiral waves. We used a numerical model of a cardiac system and generated a renormalization group with system descriptions at multiple scales. We found that transfer entropy quantified the upward and downward inter-scale information flow between micro- and macro-scale descriptions of the cardiac system with spiral waves. In addition, because the spatial profile of transfer entropy and intrinsic transfer entropy was identical, there were no synergistic effects in the system. Furthermore, inter-scale information flow significantly decreased as the description of the system became more macro-scale. Finally, downward information flow was significantly correlated with the number of rotors, but the higher numbers of rotors were not necessarily associated with higher downward information flow. This finding contradicts the concept that the rotors are the causal mechanism that maintains spiral waves, and may account for the conflicting evidence from clinical studies targeting rotors to eliminate AF.

Work required for selective quantum measurement

In quantum mechanics, we define the measuring system M in a selective measurement by two conditions. Firstly, when we define the measured system S as the system in which the non-selective measurement part acts, M is independent from the measured system S as a quantum system in the sense that any time-dependent process in the total system S + M is divisible into parts for S and M. Secondly, when we can separate S and M from each other without changing the unitary equivalence class of the state of S from that obtained by the partial trace of M, the eigenstate selection in the selective measurement cannot be realized. In order for such a system M to exist, we show that in one selective measurement of an observable of a quantum system S0 of particles in S, there exists a negative entropy transfer from M to S that can be directly transformed into an amount of Helmholtz free energy of where T is the thermodynamic temperature of the system S. Equivalently, an extra amount of work, , is required to be done by the system M.

Information spillover across international real estate investment trusts: Evidence from an entropy-based network analysis

In this study, we unveil information spillover between international real estate markets using an entropy-based network approach for real estate investment trusts (REIT). Our novel approach is simple and yet flexible enough to accommodate the nature and extent of information spillover among several components of the global housing network. For a network of nine leading industrial economies, we unveil static and time-varying information spillover of REIT returns using total transfer entropy, pairwise net transfer entropy and directional (“From”, “To”) transfer entropy. Evidence suggests that the greatest pairwise transfer entropy is from the US to Australia, whereas France, the Netherlands, New Zealand and Singapore are the largest information recipients in the network. The time-varying evolution of total transfer entropy also exhibits a declining trend for the integration of global housing market during our sample period.

Challenges of digitalizing the circular economy: Assessment of the state-of-the-art of metallurgical carrier metal platform for lead and its associated technology elements

Abstract The circular economy (CE) paradigm in its broadest sense is key to our survival as a species. Due to this critical importance, understanding its fundamental limitations is thus of significant importance. Especially understanding the losses to Nature are key as these represent the true limitation to circularity. This requires at the minimum an understanding of the thermodynamics and entropy of the losses. Most CE work as well as the many depictions to date neglect to address this in detail, the many losses are brushed aside. Many texts in CE do not use the words entropy, thermodynamics, mass and heat transfer, technology etc. which all ultimately fundamentally affect both the circularity as well as economic viability of the system. Using lead as carrier for the narrative of this paper, the state-of-the art from technology to the thermodynamics as well as heat and mass transfer, product design, modularity, environmental impact, system simulation etc. will be critically discussed. This will reveal what key knowledge and data is presently missing to achieve the economically viable circularity of materials and products. This paper identifies what should be researched and developed to “close” the circular economy system. It thus provides a “ground zero” or baseline for the evaluation of the true economic viability of the CE paradigm relative to what we are presently achieving in our linear economy paradigm.

Root cause diagnosis of quality-related faults in industrial multimode processes using robust Gaussian mixture model and transfer entropy

Abstract Modern complex industrial processes often have multiple operating modes due to various factors, such as different manufacturing strategies, alterations of feedstock and compositions, etc. In this paper, a practical technology or solution of quality-related fault diagnosis is put forward for industrial multimode processes. Different from traditional data-based fault diagnosis methods, the alternative approach is focused more on root cause diagnosis. The new scheme addresses the quality-related fault detection issue with a developed robust Gaussian mixture model and modified Mahalanobis distance. Then, a Bayesian inference-based robust Gaussian mixture contribution index is designed to analyze the potential root-cause variables. Meanwhile, a combination of transfer entropy and direct transfer entropy-based cause and effect extraction methodologies is proposed for root cause diagnosis of quality-related faults. Finally, the whole proposed framework is applied to a real industrial multimode finishing mill process, where the performance and effectiveness are further demonstrated from real industrial data.

Modelling the generation of temperature inhomogeneities by a premixed flame

The response of a laminar, premixed flame to perturbations of upstream equivalence ratio is investigated and modelled, with emphasis on the generation of ‘entropy waves’, i.e. entropic inhomogeneities of downstream temperature. Transient computational fluid dynamics simulations of two adiabatic lean methane-air flames of different Péclet numbers provide guidance and validation data for subsequent modelling. The respective entropy transfer functions, which describe the production of temperature inhomogeneities, as well as transfer functions for the variation of the heat release, are determined from the computational fluid dynamics time series data by means of system identification. The processes governing the dynamics of the entropy transfer functions are segregated into two sub-problems: (1) heat release due to chemical reaction at the flame front and (2) advective and diffusive transport. By adopting a formulation in terms of a mixture fraction variable, these two sub-problems can be treated independently from each other. Models for both phenomena are derived and analysed using simple 0- and 1-dimensional configurations. The heat release process (1) is represented by a fast-reaction-zone model, which takes into account variations of the specific heat capacity with equivalence ratio in order to evaluate the magnitude of downstream temperature fluctuations with quantitative accuracy. For the transport processes (2), two types of models based on mean field data from the computational fluid dynamics simulation are proposed: A semi-analytical, low-order formulation based on stream lines, and a state-space formulation, which is constructed by Finite Elements discretisation of the transport equation for mixture fraction. Model predictions for the entropy transfer functions are found to agree well with the computational fluid dynamics reference data at very low computational costs.