ALBERT

Description: Microvascular perfusion is commonly used to study the peripheral cardiovascular system. Microvascular blood flow can be continuously and non-invasively monitored with laser speckle contrast imaging (LSCI) or with laser Doppler flowmetry (LDF). These two optical-based techniques give perfusion values in arbitrary units. Our goal is to better understand the perfusion time series given by each technique. For this purpose, we propose a nonlinear complexity analysis of LSCI and LDF time series recorded simultaneously in nine healthy subjects. This is performed through the computation of their multiscale compression entropy. The results obtained with LSCI time series computed from different regions of interest (ROI) sizes are examined. Our findings show that, for LSCI and LDF time series, compression entropy values are less than one for all of the scales analyzed. This suggests that, for all scales, there are repetitive structures within the data fluctuations. Moreover, at the largest scales studied, LDF signals seem to have structures that are different from those Entropy 2014, 16 5778 of Gaussian white noise. By opposition, this is not observed for LSCI time series computed from small ROI sizes

Description: We present a global stability analysis of a Curzon–Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilities and a linear heat transfer law at the thermal couplings. The conditions of the global stability are explored for three regimes of performance: maximum power (MP), efficient power (EP) and the so-called ecological function (EF). Moreover, the analytical results were corroborated by means of numerical integrations, which fully validate the properties of the global asymptotic stability.

Description: This paper presents the experimental results the choked flow characteristics of a subcritical refrigerant through a converging-diverging nozzle. A test nozzle with a throat diameter of 2 mm was designed and developed. The influence of operating conditions on the choked flow characteristics, i.e., the pressure profile and mass flow rate under choked flow conditions are investigated. The results indicate that the choked flow occurs in the flow of subcritical refrigerant through nozzles under the normal working conditions of air-conditioners or heat pumps. The pressure drop near the throat is about 80% of the total pressure drop through the nozzle. The critical mass flux is about 19,800 ~ 24,000 kg/(s·m2). The critical mass flow rate increases with increasing the upstream pressure and subcooling. Furthermore, the relative errors between the model predictions and the experimental results for the critical mass flux are also presented. It is found that the deviations of the predictions for homogeneous equilibrium model and Henry-Fauske model from the experimental values are −35% ~ 5% and 15% ~ 35%, respectively

Description: A novel memristor circuit is presented, which is generated from the canonical Chua’s circuit by replacing the Chua’s diode with a first order memristive diode bridge. The circuit dynamical characteristics with the variations of circuit parameters are investigated both theoretically and numerically. It can be found that the circuit has three determined equilibrium points, including a zero saddle point and two nonzero saddle-foci with index 2. Specially, the circuit is non-dissipative in the neighborhood of the zero saddle point, and there exists complex nonlinear phenomena of coexisting bifurcation modes and coexisting chaotic attractors. Experimental observations are performed to verify the numerical simulation results.

Description: Many problems in business and engineering can be modeled as 0-1 knapsack problems. However, the 0-1 knapsack problem is one of the classical NP-hard problems. Therefore, it is valuable to develop effective and efficient algorithms for solving 0-1 knapsack problems. Aiming at the drawbacks of the selection operator in the traditional differential evolution (DE), we present a novel discrete differential evolution (TDDE) for solving 0-1 knapsack problem. In TDDE, an enhanced selection operator inspired by the principle of the minimal free energy in thermodynamics is employed, trying to balance the conflict between the selective pressure and the diversity of population to some degree. An experimental study is conducted on twenty 0-1 knapsack test instances. The comparison results show that TDDE can gain competitive performance on the majority of the test instances.

Description: In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams. Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems.

Description: In this paper, based on fixed entropy, the adiabatic equation of state in fractal flow is discussed. The local fractional wave equation for the velocity potential is also obtained by using the non-differential perturbations for the pressure and density of fractal hydrodynamics.

Description: In this paper, the parameters identification and synchronization problem of fractional-order neural networks with time delays are investigated. Based on some analytical techniques and an adaptive control method, a simple adaptive synchronization controller and parameter update laws are designed to synchronize two uncertain complex networks with time delays. Besides, the system parameters in the uncertain network can be identified in the process of synchronization. To demonstrate the validity of the proposed method, several illustrative examples are presented.

Description: Autonomic activity affects beat-to-beat variability of heart rate and QT interval. The aim of this study was to explore whether entropy measures are suitable to detect changes in neural outflow to the heart elicited by two different stress paradigms. We recorded short-term ECG in 11 normal subjects during an experimental protocol that involved head-up tilt and mental arithmetic stress and computed sample entropy, cross-sample entropy and causal interactions based on conditional entropy from RR and QT interval time series. Head-up tilt resulted in a significant reduction in sample entropy of RR intervals and cross-sample entropy, while mental arithmetic stress resulted in a significant reduction in coupling directed from RR to QT. In conclusion, measures of entropy are suitable to detect changes in neural outflow to the heart and decoupling of repolarisation variability from heart rate variability elicited by orthostatic or mental arithmetic stress.

Description: Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the efficiency of Decision Making Units (DMUs) with multiple inputs and outputs. In the traditional DEA models, the DMU is allowed to use its most favorable multiplier weights to maximize its efficiency. There is usually more than one efficient DMU which cannot be further discriminated. Evaluating DMUs with different multiplier weights would also be somewhat irrational in practice. The common weights DEA model is an effective method for solving these problems. In this paper, we propose a methodology combining the common weights DEA with Shannon’s entropy. In our methodology, we propose a modified weight restricted DEA model for calculating non-zero optimal weights. Then these non-zero optimal weights would be aggregated to be the common weights using Shannon’s entropy. Compared with the traditional models, our proposed method is more powerful in discriminating DMUs, especially when the inputs and outputs are numerous. Our proposed method also keeps in accordance with the basic DEA method considering the evaluation of the most efficient and inefficient DMUs. Numerical examples are provided to examine the validity and effectiveness of our proposed methodology.

Description: This paper presents a scientific basis for the description of the causes of damage within an irreversible thermodynamic framework and the effects of damage as observable variables that signify degradation of structural integrity. The approach relies on the fundamentals of irreversible thermodynamics and specifically the notion of entropy generation as a measure of degradation and damage. We first review the state-of-the-art advances in entropic treatment of damage followed by a discussion on generalization of the entropic concept to damage characterization that may offers a better definition of damage metric commonly used for structural integrity assessment. In general, this approach provides the opportunity to described reliability and risk of structures in terms of fundamental science concepts. Over the years, many studies have focused on materials damage assessment by determining physics-based cause and affect relationships, the goal of this paper is to put this work in perspective and encourage future work of materials damage based on the entropy concept.

Description: We develop a strategy to design and evaluate high-entropy alloys (HEAs) for structural use in the transportation and energy industries. We give HEA goal properties for low (≤150 °C), medium (≤450 °C) and high (≥1,100 °C) use temperatures. A systematic design approach uses palettes of elements chosen to meet target properties of each HEA family and gives methods to build HEAs from these palettes. We show that intermetallic phases are consistent with HEA definitions, and the strategy developed here includes both single-phase, solid solution HEAs and HEAs with intentional addition of a 2nd phase for particulate hardening. A thermodynamic estimate of the effectiveness of configurational entropy to suppress or delay compound formation is given. A 3-stage approach is given to systematically screen and evaluate a vast number of HEAs by integrating high-throughput computations and experiments. CALPHAD methods are used to predict phase equilibria, and high-throughput experiments on materials libraries with controlled composition and microstructure gradients are suggested. Much of this evaluation can be done now, but key components (materials libraries with microstructure gradients and high-throughput tensile testing) are currently missing. Suggestions for future HEA efforts are given.

Description: Branching network is one of the most universal phenomena in living or non-living systems, such as river systems and the bronchial trees of mammals. To topologically characterize the branching networks, the Branch Length Similarity (BLS) entropy was suggested and the statistical methods based on the entropy have been applied to the shape identification and pattern recognition. However, the mathematical properties of the BLS entropy have not still been explored in depth because of the lack of application and utilization requiring advanced mathematical understanding. Regarding the mathematical study, it was reported, as a theorem, that all BLS entropy values obtained for simple networks created by connecting pixels along the boundary of a shape are exactly unity when the shape has infinite resolution. In the present study, we extended the theorem to the network created by linking infinitely many nodes distributed on the bounded or unbounded domain in Rk for k ≥ 1. We proved that all BLS entropies of the nodes in the network go to one as the number of nodes, n, goes to infinite and its convergence rate is 1 - O(1= ln n), which was confirmed by the numerical tests.

Description: Wheel-bearings easily acquire defects due to their high-speed operating conditions and constant metal-metal contact, so defect detection is of great importance for railroad safety. The conventional spectral kurtosis (SK) technique provides an optimal bandwidth for envelope demodulation. However, this technique may cause false detections when processing real vibration signals for wheel-bearings, because of sparse interference impulses. In this paper, a novel defect detection method with entropy, time-spectral kurtosis (TSK) and support vector machine (SVM) is proposed. In this method, the possible outliers in the short time Fourier transform (STFT) amplitude series are first estimated and preprocessed with information entropy. Then the method extends the SK technique to the time-domain, and extracts defective frequencies from reconstructed vibration signals by TSK filtering. Finally, the multi-class SVM was applied to classify bearing defects. The effectiveness of the proposed method is illustrated using real wheel-bearing vibration signals. Experimental results show that the proposed method provides a better performance in defect frequency detection and classification than the conventional SK-based envelope demodulation.

Description: The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match.

Description: The paper presents a new approach to restoration characteristics randomized models under small amounts of input and output data. This approach proceeds from involving randomized static and dynamic models and estimating the probabilistic characteristics of their parameters. We consider static and dynamic models described by Volterra polynomials. The procedures of robust parametric and non-parametric estimation are constructed by exploiting the entropy concept based on the generalized informational Boltzmann’s and Fermi’s entropies.

Description: A numerical algorithm to compute the topological entropy of multimodal maps is proposed. This algorithm results from a closed formula containing the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore, it simplifies a previous algorithm, also based on min-max symbols, which was originally proposed for twice differentiable multimodal maps. The new algorithm has been benchmarked against the old one with a number of multimodal maps, the results being reported in the paper. The comparison is favorable to the new algorithm, except in the unimodal case.

Description: Chemical composition of interfaces—free surfaces and grain boundaries—is generally described by the Langmuir–McLean segregation isotherm controlled by Gibbs energy of segregation. Various components of the Gibbs energy of segregation, the standard and the excess ones as well as other thermodynamic state functions—enthalpy, entropy and volume—of interfacial segregation are derived and their physical meaning is elucidated. The importance of the thermodynamic state functions of grain boundary segregation, their dependence on volume solid solubility, mutual solute–solute interaction and pressure effect in ferrous alloys is demonstrated.

Description: The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carathéodory, the Keenan School, Lieb and Yngvason, and the present authors. An improvement of the latter method is then presented. Seven basic axioms are employed: three Postulates, which are considered as having a quite general validity, and four Assumptions, which identify the domains of validity of the definitions of energy (Assumption 1) and entropy (Assumptions 2, 3, 4). The domain of validity of the present definition of entropy is not restricted to stable equilibrium states. For collections of simple systems, it coincides with that of the proof of existence and uniqueness of an entropy function which characterizes the relation of adiabatic accessibility proposed by Lieb and Yngvason. However, our treatment does not require the formation of scaled copies so that it applies not only to collections of simple systems, but also to systems contained in electric or magnetic fields and to small and few-particle systems.

Description: In many data envelopment analysis (DEA) applications, the analyst always confronts the difficulty that the selected data set is not suitable to apply traditional DEA models for their poor discrimination. This paper presents an approach using Shannon’s entropy to improve the discrimination of traditional DEA models. In this approach, DEA efficiencies are first calculated for all possible variable subsets and analyzed using Shannon’s entropy theory to calculate the degree of the importance of each subset in the performance measurement, then we combine the obtained efficiencies and the degrees of importance to generate a comprehensive efficiency score (CES), which can observably improve the discrimination of traditional DEA models. Finally, the proposed approach has been applied to some data sets from the prior DEA literature.

Description: Information-theory provides, among others, conceptual methods to quantify the amount of information contained in single random variables and methods to quantify the amount of information contained and shared among two or more variables. Although these concepts have been successfully applied in hydrology and other fields, the evaluation of these quantities is sensitive to different assumptions in the estimation of probabilities. An example is the histogram bin size used to estimate probabilities to calculate Information Theory quantities via frequency methods. The present research aims at introducing a method to take into consideration the uncertainty coming from these parameters in the evaluation of the North Sea’s water level network. The main idea is that the entropy of a random variable can be represented as a probability distribution of possible values, instead of entropy being a deterministic value. The method consists of solving multiple scenarios of Multi-Objective Optimization Problem in which information content is maximized and redundancy is minimized. Results include probabilistic analysis of the chosen parameters on the resulting family of Pareto fronts, providing additional criteria on the selection of the final set of monitoring points.

Description: I explore the reduction of thermodynamics to statistical mechanics by treating the former as a control theory: A theory of which transitions between states can be induced on a system (assumed to obey some known underlying dynamics) by means of operations from a fixed list. I recover the results of standard thermodynamics in this framework on the assumption that the available operations do not include measurements which affect subsequent choices of operations. I then relax this assumption and use the framework to consider the vexed questions of Maxwell’s demon and Landauer’s principle. Throughout, I assume rather than prove the basic irreversibility features of statistical mechanics, taking care to distinguish them from the conceptually distinct assumptions of thermodynamics proper.

Description: The editors of Entropy would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2013

Description: There are two entropy-based methods to deal with linear inverse problems, which we shall call the ordinary method of maximum entropy (OME) and the method of maximum entropy in the mean (MEM). Not only doesMEM use OME as a stepping stone, it also allows for greater generality. First, because it allows to include convex constraints in a natural way, and second, because it allows to incorporate and to estimate (additive) measurement errors from the data. Here we shall see both methods in action in a specific example. We shall solve the discretized version of the problem by two variants of MEM and directly with OME. We shall see that OME is actually a particular instance of MEM, when the reference measure is a Poisson Measure.

Description: This paper addresses the problem of balancing statistical economic data, when data structure is arbitrary and both uncertainty estimates and a ranking of data quality are available. Using a Bayesian approach, the prior configuration is described as a multivariate random vector and the balanced posterior is obtained by application of relative entropy minimization. The paper shows that conventional data balancing methods, such as generalized least squares, weighted least squares and biproportional methods are particular cases of the general method described here. As a consequence, it is possible to determine the underlying assumptions and range of application of each traditional method. In particular, the popular biproportional method is found to assume that all source data has the same relative uncertainty. Finally, this paper proposes a simple linear iterative method that generalizes the biproportional method to the data balancing problem with arbitrary data structure, uncertainty estimates and multiple data quality levels.

Description: Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a) to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b) to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron) from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.

Description: The use of transfer entropy has proven to be helpful in detecting which is the verse of dynamical driving in the interaction of two processes, X and Y . In this paper, we present a different normalization for the transfer entropy, which is capable of better detecting the information transfer direction. This new normalized transfer entropy is applied to the detection of the verse of energy flux transfer in a synthetic model of fluid turbulence, namely the Gledzer–Ohkitana–Yamada shell model. Indeed, this is a fully well-known model able to model the fully developed turbulence in the Fourier space, which is characterized by an energy cascade towards the small scales (large wavenumbers k), so that the application of the information-theory analysis to its outcome tests the reliability of the analysis tool rather than exploring the model physics. As a result, the presence of a direct cascade along the scales in the shell model and the locality of the interactions in the space of wavenumbers come out as expected, indicating the validity of this data analysis tool. In this context, the use of a normalized version of transfer entropy, able to account for the difference of the intrinsic randomness of the interacting processes, appears to perform better, being able to discriminate the wrong conclusions to which the “traditional” transfer entropy would drive.

Description: A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian/Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory, Liouville’s theorem of conservation of phase density distribution must be modified to allow time evolution of phase density and consequently the Boltzmann H theorem. We argue that the gap between the regular Newtonian dynamics and the random dynamics was not considered in the criticisms of the H theorem.

Description: The editors were made aware that a paper published in Entropy in 2004 [1] may have plagiarized an earlier paper by Roman Hric published in 2000 [2]. After checking with specialized plagiarism software, we found that this claim is indeed correct and almost the entire paper is a verbatim copy of the earlier one. After confirmation of this fact, the editors of Entropy have decided to retract the paper immediately. [...]

Description: The nonverbal transmission of information between social animals is a primary driving force behind their actions and, therefore, an important quantity to measure in animal behavior studies. Despite its key role in social behavior, the flow of information has only been inferred by correlating the actions of individuals with a simplifying assumption of linearity. In this paper, we leverage information-theoretic tools to relax this assumption. To demonstrate the feasibility of our approach, we focus on a robotics-based experimental paradigm, which affords consistent and controllable delivery of visual stimuli to zebrafish. Specifically, we use a robotic arm to maneuver a life-sized replica of a zebrafish in a predetermined trajectory as it interacts with a focal subject in a test tank. We track the fish and the replica through time and use the resulting trajectory data to measure the transfer entropy between the replica and the focal subject, which, in turn, is used to quantify one-directional information flow from the robot to the fish. In agreement with our expectations, we find that the information flow from the replica to the zebrafish is significantly more than the other way around. Notably, such information is specifically related to the response of the fish to the replica, whereby we observe that the information flow is reduced significantly if the motion of the replica is randomly delayed in a surrogate dataset. In addition, comparison with a control experiment, where the replica is replaced by a conspecific, shows that the information flow toward the focal fish is significantly more for a robotic than a live stimulus. These findings support the reliability of using transfer entropy as a measure of information flow, while providing indirect evidence for the efficacy of a robotics-based platform in animal behavioral studies.

Description: The time evolution during which macroscopic systems reach thermodynamic equilibrium states proceeds as a continuous sequence of contact structure preserving transformations maximizing the entropy. This viewpoint of mesoscopic thermodynamics and dynamics provides a unified setting for the classical equilibrium and nonequilibrium thermodynamics, kinetic theory, and statistical mechanics. One of the illustrations presented in the paper is a new version of extended nonequilibrium thermodynamics with fluxes as extra state variables.

Description: Recommendation systems are information-filtering systems that tailor information to users on the basis of knowledge about their preferences. The ability of these systems to profile users is what enables such intelligent functionality, but at the same time, it is the source of serious privacy concerns. In this paper we investigate a privacy-enhancing technology that aims at hindering an attacker in its efforts to accurately profile users based on the items they rate. Our approach capitalizes on the combination of two perturbative mechanisms—the forgery and the suppression of ratings. While this technique enhances user privacy to a certain extent, it inevitably comes at the cost of a loss in data utility, namely a degradation of the recommendation’s accuracy. In short, it poses a trade-off between privacy and utility. The theoretical analysis of such trade-off is the object of this work. We measure privacy as the Kullback-Leibler divergence between the user’s and the population’s item distributions, and quantify utility as the proportion of ratings users consent to forge and eliminate. Equipped with these quantitative measures, we find a closed-form solution to the problem of optimal forgery and suppression of ratings, an optimization problem that includes, as a particular case, the maximization of the entropy of the perturbed profile. We characterize the optimal trade-off surface among privacy, forgery rate and suppression rate,and experimentally evaluate how our approach could contribute to privacy protection in a real-world recommendation system.

Description: The primordial confrontation underlying the existence of our Universe can be conceived as the battle between entropy and complexity. The law of ever-increasing entropy (Boltzmann H-theorem) evokes an irreversible, one-directional evolution (or rather involution) going uniformly and monotonically from birth to death. Since the 19th century, this concept is one of the cornerstones and in the same time puzzles of statistical mechanics. On the other hand, there is the empirical experience where one witnesses the emergence, growth and diversification of new self-organized objects with ever-increasing complexity. When modeling them in terms of simple discrete elements one finds that the emergence of collective complex adaptive objects is a rather generic phenomenon governed by a new type of laws. These “emergence” laws, not connected directly with the fundamental laws of the physical reality, nor acting “in addition” to them but acting through them were called “More is Different” by Phil Anderson, “das Maass” by Hegel etc. Even though the “emergence laws” act through the intermediary of the fundamental laws that govern the individual elementary agents, it turns out that different systems apparently governed by very different fundamental laws: gravity, chemistry, biology, economics, social psychology, end up often with similar emergence laws and outcomes. In particular the emergence of adaptive collective objects endows the system with a granular structure which in turn causes specific macroscopic cycles of intermittent fluctuations.

Description: Neuroimage registration has an important role in clinical (for both diagnostic and therapeutic purposes) and research applications. In this article we describe the applicability of Tsallis Entropy as a new cost function for neuroimage registration through a comparative analysis based on the performance of the traditional approaches (correlation based: Entropy Correlation Coefficient (ECC) and Normalized Cross Correlation (NCC); and Mutual Information (MI) based: Mutual Information using Shannon Entropy (MIS) and Normalized Mutual Information (NMI)) and the proposed one based on MI using Tsallis entropy (MIT). We created phantoms with known geometric transformations using Single Photon Emission Computed Tomography (SPECT) and Magnetic Resonance Imaging from 3 morphologically normal subjects. The simulated volumes were registered to the original ones using both the proposed and traditional approaches. The comparative analysis of the Relative Error (RE) showed that MIT was more accurate in the intra-modality registration, whereas for inter-modality registration, MIT presented the lowest RE for rotational transformations, and the ECC the lowest RE for translational transformations. In conclusion, we have shown that, with certain limitations, Tsallis Entropy has application as a better cost function for reliable neuroimage registration.

Description: This paper considers the four-node relay-eavesdropper channel, where a relay node helps the source to send secret messages to the destination in the presence of a passive eavesdropper. For the discrete memoryless case, we propose a hybrid cooperative coding scheme, which is based on the combination of the partial decode-forward scheme, the noise-forward scheme and the random binning scheme. The key feature of the proposed hybrid cooperative scheme is that the relay integrates the explicit cooperation strategy and the implicit cooperation strategy by forwarding source messages and additional interference at the same time. The derived achievable secrecy rate shows that some existing works can be viewed as special cases of the proposed scheme. Then, the achievable secrecy rate is extended to the Gaussian channel based on Gaussian codebooks, and the optimal power policy is also identified in the high power region. Both the analysis and numerical results are provided to demonstrate that the proposed hybrid cooperative coding scheme outperforms the comparable ones, especially in the high power region.

Description: We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.

Description: Specific heat was systematically measured by the heat flow method in Ni50-xCoxMn50-yAly metamagnetic shape memory alloys near the martensitic transformation temperatures. Martensitic transformation and ferromagnetic–paramagnetic transition for the parent phase were directly observed via the specific heat measurements. On the basis of the experimental results, the entropy change was estimated and it was found to show an abrupt decrease below the Curie temperature. The results were found to be consistent with those of earlier studies on Ni-Co-Mn-Al alloys.

Description: Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I – IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

Description: This study applies a new method and technology to measure the discharge in a lined canal in Taiwan. An Acoustic Digital Current Meter mounted on a measurement platform is used to measure the velocities over the full cross-section for establishing the measurement method. The proposed method primarily employs Chiu’s Equation which is based on entropy to establish a constant ratio the relation between the maximum and mean velocities in an irrigation canal, and compute the maximum velocity by the observed velocity profile. In consequence, the mean velocity of the lined canal can be rapidly determined by the maximum velocity and the constant ratio. The cross-sectional area of the artificial irrigation canal can be calculated for the water stage. Finally, the discharge in the lined canal can be efficiently determined by the estimated mean velocity and the cross-sectional area. Using the data of discharges and stages collected in the Wan-Dan Canal, the correlation of stage and discharge is also developed for remote real-time monitoring and estimating discharge from the pumping station. Overall, Chiu’s Equation is demonstrated to reliably and accurately measure discharge in a lined canal, and can serve as reference for future calibration for a stage-discharge rating curve.

Description: As an important research subject, district heating with combined heat and power (CHP) has significant potential for energy conservation. This paper utilised a 200 MW air-cooled unit as an actual case and presented a design scheme and energy consumption analysis of three typical CHP modes, including the low vacuum mode (LVM), the extraction condensing mode (ECM), and the absorbing heat pump mode (AHPM). The advantages and disadvantages of each mode (including their practical problems) were analysed, and suggestions for the best mode were proposed. The energy consumption of the three heating modes changed with the heating load. When the heating load was increased, the net power of the entire system decreased to different degrees. In this paper, the energy conservation effect of the LVM was the most ideal, followed by the ECM and the AHPM. Besides, the LVM and AHPM were able to supply larger heat loads than the ECM, which was limited by the minimum cooling flow of the low pressure cylinder. Furthermore, in order to get a more general conclusion, a similar case with an air-cooled 300 MW unit is studied, showing that the fuel consumption levels of ECM and AHPM have changed.

Description: Repeats or Transposable Elements (TEs) are highly repeated sequence stretches, present in virtually all eukaryotic genomes. We explore the distribution of representative TEs from all major classes in entire chromosomes across various organisms. We employ two complementary approaches, the scaling of block entropy and box-counting. Both converge to the conclusion that well-developed fractality is typical of small genomes while in large genomes it appears sporadically and in some cases is rudimentary. The human genome is particularly prone to develop this pattern, as TE chromosomal distributions therein are often highly clustered and inhomogeneous. Comparing with previous works, where occurrence of power-law-like size distributions in inter-repeat distances is studied, we conclude that fractality in entire chromosomes is a more stringent (thus less often encountered) condition. We have formulated a simple evolutionary scenario for the genomic dynamics of TEs, which may account for their fractal distribution in real genomes. The observed fractality and long-range properties of TE genomic distributions have probably contributed to the formation of the “fractal globule”, a model for the confined chromatin organization of the eukaryotic nucleus proposed on the basis of experimental evidence.

Description: Studies of spatial patterns of landscapes are useful to quantify human impact, predict wildlife effects, or describe various landscape features. A robust landscape index should quantify two components of landscape diversity: composition and configuration. One category of landscape index is the contagion index. Some landscape ecologists promote the use of relative contagion indices. It is demonstrated, using simulated landscapes, that relativized contagion indices are mathematically untenable. A new entropy contagion index (Γ) is developed. Distributional properties of Γ^ are derived. It is shown to be asymptotically unbiased, consistent, and asymptotically normally distributed. A variance formula for Γ^ is derived using the delta method. As an application, the pattern and changes in forest types across four soil-geologic landform strata were analyzed on the 80,000 ha Savannah River Site in South Carolina, USA. One-way analysis of variance was used for hypothesis testing of contagion among strata. The differences in contagion across the strata provide insight to managers to meet structural objectives.

Description: The 2013 cosmology results from the European Space Agency Planck spacecraft provide new limits to the dark energy equation of state parameter. Here we show that Holographic Dark Information Energy (HDIE), a dynamic dark energy model, achieves an optimal fit to the published datasets where Planck data is combined with other astrophysical measurements. HDIE uses Landauer’s principle to account for dark energy by the energy equivalent of information, or entropy, of stellar heated gas and dust. Combining Landauer’s principle with the Holographic principle yields an equation of state parameter determined solely by star formation history, effectively solving the “cosmic coincidence problem”. While HDIE mimics a cosmological constant at low red-shifts, z 〈 1, the small difference from a cosmological constant expected at higher red-shifts will only be resolved by the next generation of dark energy instrumentation. The HDIE model is shown to provide a viable alternative to the main cosmological constant/vacuum energy and scalar field/ quintessence explanations.

Description: In this work we study the distribution function for the total entropy production of a Brownian particle embedded in a non-Markovian thermal bath. The problem is studied in the overdamped approximation of the generalized Langevin equation, which accounts for a friction memory kernel characteristic of a Gaussian colored noise. The problem is studied in two physical situations: (i) when the particle in the harmonic trap is subjected to an arbitrary time-dependent driving force; and (ii) when the minimum of the harmonic trap is arbitrarily dragged out of equilibrium by an external force. By assuming a natural non Markovian canonical distribution for the initial conditions, the distribution function for the total entropy production becomes a non Gaussian one. Its characterization is then given through the first three cumulants.

Description: It is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality. Here, the criticality means that all the three classes of networks are scale-free and, moreover, display a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input) reaction and the free energy-accepting (output) one. The far-from-equilibrium degree of coupling between the output and the input reaction fluxes have been studied both theoretically and by means of the Monte Carlo simulations on model networks. For single input and output gates the degree of coupling cannot exceed unity. Study simulations of random walks on model networks involving more extended gates indicate that the case of the degree of coupling value higher than one is realized on the mentioned above critical branching trees extended by long-range shortcuts.

Description: In this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs) in n-dimensional piecewise-smooth dynamical systems, particularly Continuous PWS and Discontinuous PWS (or Filippov-type PWS) systems. The proposed qualitative approach explicitly includes two main aspects: multiple discontinuity boundaries (DBs) in the phase space and multiple intersections between DBs (or corner manifolds—CMs). Previous classifications of DIBs of limit cycles have been restricted to generic cases with a single DB or a single CM. We use the definition of piecewise topological equivalence in order to synthesize all possibilities of nonsmooth limit cycles. Families, groups and subgroups of cycles are defined depending on smoothness zones and discontinuity boundaries (DB) involved. The synthesized cycles are used to define bifurcation patterns when the system is perturbed with parametric changes. Four families of DIBs of limit cycles are defined depending on the properties of the cycles involved. Well-known and novel bifurcations can be classified using this approach.

Description: Some critical trends in information theory, its role in living systems and utilization in fluctuation theory are discussed. The mutual information of thermodynamic coupling is incorporated into the generalized fluctuation theorem by using information theory and nonequilibrium thermodynamics. Thermodynamically coupled dissipative structures in living systems are capable of degrading more energy, and processing complex information through developmental and environmental constraints. The generalized fluctuation theorem can quantify the hysteresis observed in the amount of the irreversible work in nonequilibrium regimes in the presence of information and thermodynamic coupling.

Description: In a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in these thermal-inductive materials. The control objective is to achieve subtle temperature distribution in space and simultaneously to suppress its transient overshoots in time. This technology concerns safe and accurate heating/cooling treatments in medical operations, polymer processing, and other prevailing modern day practices. Serving for distributed feedback, spatiotemporal H ∞ /μ control is developed by expansion of the conventional 1D-H ∞ /μ control to a 2D version. Therein 2D geometrical isomorphism is constructed with the Laplace-Galerkin transform, which extends the small-gain theorem into the mode-frequency domain, wherein 2D transfer-function controllers are synthesized with graphical methods. Finally, 2D digital-signal processing is programmed to implement 2D transfer-function controllers, possibly of spatial fraction-orders, into DSP-engine embedded microcontrollers.

Description: Projects are an important part of our activities and regardless of their magnitude, scheduling is at the very core of every project. In an ideal world makespan minimization, which is the most commonly sought objective, would give us an advantage. However, every time we execute a project we have to deal with uncertainty; part of it coming from known sources and part remaining unknown until it affects us. For this reason, it is much more practical to focus on making our schedules robust, capable of handling uncertainty, and even to determine a range in which the project could be completed. In this paper we focus on an approach to determine such a range for the Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP), a widely researched, NP-complete problem, but without adding any subjective considerations to its estimation. We do this by using a concept well known in the domain of thermodynamics, entropy and a three-stage approach. First we use Artificial Bee Colony (ABC)—an effective and powerful meta-heuristic—to determine a schedule with minimized makespan which serves as a lower bound. The second stage defines buffer times and creates an upper bound makespan using an entropy function, with the advantage over other methods that it only considers elements which are inherent to the schedule itself and does not introduce any subjectivity to the buffer time generation. In the last stage, we use the ABC algorithm with an objective function that seeks to maximize robustness while staying within the makespan boundaries defined previously and in some cases even below the lower boundary. We evaluate our approach with two different benchmarks sets: when using the PSPLIB for the MRCPSP benchmark set, the computational results indicate that it is possible to generate robust schedules which generally result in an increase of less than 10% of the best known solutions while increasing the robustness in at least 20% for practically every benchmark set. And, in an attempt to solve larger instances with 50 or 100 activities, we also used the MRCPSP/max benchmark sets, where the increase of the makespan is approximately 35% with respect to the best known solutions at the same time as with a 20% increase in robustness.

Description: Entropy generation in adiabatic flow of highly concentrated non-Newtonian emulsions in smooth tubes of five different diameters (7.15–26.54 mm) was investigated experimentally. The emulsions were of oil-in-water type with dispersed-phase concentration (Φ) ranging from 59.61–72.21% vol. The emulsions exhibited shear-thinning behavior in that the viscosity decreased with the increase in shear rate. The shear-stress (τ) versus shear rate (˙γ) data of emulsions could be described well by the power-law model: τ=K˙γn. The flow behavior index n was less than 1 and it decreased sharply with the increase in Φ whereas the consistency index K increased rapidly with the increase in Φ . For a given emulsion and tube diameter, the entropy generation rate per unit tube length increased linearly with the increase in the generalized Reynolds number ( Re_n ) on a log-log scale. For emulsions with Φ ≤65.15 % vol., the entropy generation rate decreased with the increase in tube diameter. A reverse trend in diameter-dependence was observed for the emulsion with Φ of 72.21% vol. New models are developed for the prediction of entropy generation rate in flow of power-law emulsions in smooth tubes. The experimental data shows good agreement with the proposed models.

Description: We introduce the so far most efficient attack against the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange system. This attack utilizes the lack of exact thermal equilibrium in practical applications and is based on cable resistance losses and the fact that the Second Law of Thermodynamics cannot provide full security when such losses are present. The new attack does not challenge the unconditional security of the KLJN scheme, but it puts more stringent demands on the security/privacy enhancing protocol than for any earlier attack. In this paper we present a simple defense protocol to fully eliminate this new attack by increasing the noise-temperature at the side of the smaller resistance value over the noise-temperature at the side with the greater resistance. It is shown that this simple protocol totally removes Eve’s information not only for the new attack but also for the old Bergou-Scheuer-Yariv attack. The presently most efficient attacks against the KLJN scheme are thereby completely nullified.

Description: The droplet evaporation method (DEM) is increasingly used for assessing various characteristics of water. In our research we tried to use DEM to detect a possible self-ordering capability of (spring) water that would be similar to the already found and described autothixotropic phenomenon, namely increasing order of non-distilled water subject to aging. The output of DEM is a droplet remnant pattern (DRP). For analysis of DRP images we used a specially developed computer program that does the frequency distribution analysis of certain parameters of the images. The results of experiments demonstrated statistically significant differences in both aging of water as well as in the glass exposed surface/volume ratio of the aged water. The most important result supporting the self-ordering character of water was found in an increasing dependence between two analyzed parameters: distance and frequency, at the peak frequency. As the result concerns mostly aging and shows increasing order it further corroborates other findings concerning increasing order by aging. Such further confirmation of self-ordering capacity of water is not important only for physical chemistry, but also for biology.

Description: The problem  addressed concerns the determination of the average number of successive attempts  of guessing  a word of a certain  length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations  to a natural language are considered.  The guessing strategy used is guessing words in decreasing order of probability. When word and alphabet sizes are large, approximations  are necessary in order to estimate the number of guesses.  Several  kinds of approximations  are discussed demonstrating moderate requirements regarding both memory and central processing unit (CPU) time. When considering realistic  sizes of alphabets and words (100), the number of guesses can be estimated  within minutes with reasonable accuracy (a few percent) and may therefore constitute an alternative to, e.g., various entropy expressions.  For many probability  distributions,  the density of the logarithm of probability products is close to a normal distribution. For those cases, it is possible to derive an analytical expression for the average number of guesses. The proportion  of guesses needed on average compared to the total number  decreases almost exponentially with the word length. The leading term in an asymptotic  expansion can be used to estimate the number of guesses for large word lengths. Comparisons with analytical lower bounds and entropy expressions are also provided.

Description: Decision trees are particularly promising in symbolic representation andreasoning due to their comprehensible nature, which resembles the hierarchical process ofhuman decision making. However, their drawbacks, caused by the single-tree structure,cannot be ignored. A rigid decision path may cause the majority class to overwhelm otherclass when dealing with imbalanced data sets, and pruning removes not only superfluousnodes, but also subtrees. The proposed learning algorithm, flexible hybrid decision forest(FHDF), mines information implicated in each instance to form logical rules on the basisof a chain rule of local mutual information, then forms different decision tree structuresand decision forests later. The most credible decision path from the decision forest canbe selected to make a prediction. Furthermore, functional dependencies (FDs), which areextracted from the whole data set based on association rule analysis, perform embeddedattribute selection to remove nodes rather than subtrees, thus helping to achieve differentlevels of knowledge representation and improve model comprehension in the frameworkof semi-supervised learning. Naive Bayes replaces the leaf nodes at the bottom of thetree hierarchy, where the conditional independence assumption may hold. This techniquereduces the potential for overfitting and overtraining and improves the prediction qualityand generalization. Experimental results on UCI data sets demonstrate the efficacy of theproposed approach.

Description: Self-organisation occurs in natural phenomena when a spontaneous increase inorder is produced by the interactions of elements of a complex system. Thermodynamically,this increase must be offset by production of entropy which, broadly speaking, can beunderstood as a decrease in order. Ideally, self-organisation can be used to guide the systemtowards a desired regime or state, while “exporting” the entropy to the system’s exterior.Thus, Guided Self-Organisation (GSO) attempts to harness the order-inducing potentialof self-organisation for specific purposes. Not surprisingly, general methods developed tostudy entropy can also be applied to guided self-organisation. This special issue covers abroad diversity of GSO approaches which can be classified in three categories: informationtheory, intelligent agents, and collective behavior. The proposals make another step towardsa unifying theory of GSO which promises to impact numerous research fields.

Description: Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data compression and parameter estimation are intimately related, we study the redundancy of Bayes estimators coming from Poisson–Dirichlet priors (or “Chinese restaurant processes”) and the Pitman–Yor prior. This provides an understanding of these estimators in the setting of unknown discrete alphabets from the perspective of universal compression. In particular, we identify relations between alphabet sizes and sample sizes where the redundancy is small, thereby characterizing useful regimes for these estimators.

Description: In order to solve the problems of ill-balanced task allocation, long response time, low throughput rate and poor performance when the cluster system is assigning tasks, we introduce the concept of entropy in thermodynamics into load balancing algorithms. This paper proposes a new load balancing algorithm for homogeneous clusters based on the Maximum Entropy Method (MEM). By calculating the entropy of the system and using the maximum entropy principle to ensure that each scheduling and migration is performed following the increasing tendency of the entropy, the system can achieve the load balancing status as soon as possible, shorten the task execution time and enable high performance. The result of simulation experiments show that this algorithm is more advanced when it comes to the time and extent of the load balance of the homogeneous cluster system compared with traditional algorithms. It also provides novel thoughts of solutions for the load balancing problem of the homogeneous cluster system.

Description: Nonlinear parameters of heart rate variability (HRV) have proven their prognostic value in clinical settings, but their physiological background is not very well established. We assessed the effects of low intensity isometric (ISO) and dynamic (DYN) exercise of the lower limbs on heart rate matched intensity on traditional and entropy measures of HRV. Due to changes of afferent feedback under DYN and ISO a distinct autonomic response, mirrored by HRV measures, was hypothesized. Five-minute inter-beat interval measurements of 43 healthy males (26.0 ± 3.1 years) were performed during rest, DYN and ISO in a randomized order. Blood pressures and rate pressure product were higher during ISO vs. DYN (p 〈 0.001). HRV indicators SDNN as well as low and high frequency power were significantly higher during ISO (p 〈 0.001 for all measures). Compared to DYN, sample entropy (SampEn) was lower during ISO (p 〈 0.001). Concluding, contraction mode itself is a significant modulator of the autonomic cardiovascular response to exercise. Compared to DYN, ISO evokes a stronger blood pressure response and an enhanced interplay between both autonomic branches. Non-linear HRV measures indicate a more regular behavior under ISO. Results support the view of the reciprocal antagonism being only one of many modes of autonomic heart rate control. Under different conditions; the identical “end product” heart rate might be achieved by other modes such as sympathovagal co-activation as well.

Description: Topological measures are crucial to describe, classify and understand complex networks. Lots of measures are proposed to characterize specific features of specific networks, but the relationships among these measures remain unclear. Taking into account that pulling networks from different domains together for statistical analysis might provide incorrect conclusions, we conduct our investigation with data observed from the same network in the form of simultaneously measured time series. We synthesize a transfer entropy-based framework to quantify the relationships among topological measures, and then to provide a holistic scenario of these measures by inferring a drive-response network. Techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy are synthesized to deal with challenges such as time series being non-stationary, finite sample effects and indirect effects. We resort to kernel density estimation to assess significance of the results based on surrogate data. The framework is applied to study 20 measures across 2779 records in the Technology Exchange Network, and the results are consistent with some existing knowledge. With the drive-response network, we evaluate the influence of each measure by calculating its strength, and cluster them into three classes, i.e., driving measures, responding measures and standalone measures, according to the network communities.

Description: Information-theory is being increasingly used to analyze complex, self-organizing processes on networks, predominantly in analytical and numerical studies. Perhaps one of the most paradigmatic complex systems is a network of neurons, in which cognition arises from the information storage, transfer, and processing among individual neurons. In this article we review experimental techniques suitable for validating information-theoretical predictions in simple neural networks, as well as generating new hypotheses. Specifically, we focus on techniques that may be used to measure both network (microcircuit) anatomy as well as neuronal activity simultaneously. This is needed to study the role of the network structure on the emergent collective dynamics, which is one of the reasons to study the characteristics of information processing. We discuss in detail two suitable techniques, namely calcium imaging and the application of multi-electrode arrays to simple neural networks in culture, and discuss their advantages and limitations in an accessible manner for non-experts. In particular, we show that each technique induces a qualitatively different type of error on the measured mutual information. The ultimate goal of this work is to bridge the gap between theorists and experimentalists in their shared goal of understanding the behavior of networks of neurons.

Description: We hypothesize a mechanistic model of how negatively-charged exclusion zones (EZs) are created. While the growth of EZs is known to be associated with the absorption of ambient photonic energy, the molecular dynamics giving rise to this process need greater elucidation. We believe they arise due to the formation of oxy-subhydride structures (OH−)(H2O)4 with a tetrahedral (sp3) (OH−)(H2O)3 core. Five experimental data sets derived by previous researchers were assessed in this regard: (1) water-derived EZ light absorbance at specific infrared wavelengths, (2) EZ negative potential in water and ethanol, (3) maximum EZ light absorbance at 270 nm ultraviolet wavelength, (4) ability of dimethyl sulphoxide but not ether to form an EZ, and (5) transitory nature of melting ice derived EZs. The proposed tetrahedral oxy-subhydride structures (TOSH) appear to adequately account for all of the experimental evidence derived from water or other polar solvents.

Description: The intention of this paper is to evaluate the sensitivity of the Storm Water Management Model (SWMM) output to its input parameters. A global parameter sensitivity analysis is conducted in order to determine which parameters mostly affect the model simulation results. Two different methods of sensitivity analysis are applied in this study. The first one is the partial rank correlation coefficient (PRCC) which measures nonlinear but monotonic relationships between model inputs and outputs. The second one is based on the mutual information which provides a general measure of the strength of the non-monotonic association between two variables. Both methods are based on the Latin Hypercube Sampling (LHS) of the parameter space, and thus the same datasets can be used to obtain both measures of sensitivity. The utility of the PRCC and the mutual information analysis methods are illustrated by analyzing a complex SWMM model. The sensitivity analysis revealed that only a few key input variables are contributing significantly to the model outputs; PRCCs and mutual information are calculated and used to determine and rank the importance of these key parameters. This study shows that the partial rank correlation coefficient and mutual information analysis can be considered effective methods for assessing the sensitivity of the SWMM model to the uncertainty in its input parameters.

Description: A method is known by which any integer \(\, n\geq2\,\) in a metric Cantor space of right-infinite words \(\,\tilde{A}_{n}^{\,\mathbb N}\,\) gives a construction of a non-injective cellular automaton \(\,(\tilde{A}_{n}^{\,\mathbb N},\,\tilde{F}_{n}),\,\) which is chaotic in Devaney sense, has a radius \(\, r=1,\,\) continuum of fixed points and topological entropy \(\, log(n).\,\) As a generalization of this method we present for any integer \(\, n\geq2,\,\) a construction of a cellular automaton \(\,(A_{n}^{\,\mathbb{N}},\, F_{n}),\,\) which has the listed properties of \(\,(\tilde{A}_{n}^{\,\mathbb N},\,\tilde{F}_{n}),\,\) but has no fixed points and has continuum of periodic points with the period 2. The construction is based on properties of cellular automaton introduced here \(\,(B^{\,\mathbb N},\, F)\,\) with radius \(1\) defined for any prime number \(\, p.\,\) We prove that \(\,(B^{\,\mathbb N},\, F)\,\) is non-injective, chaotic in Devaney sense, has no fixed points, has continuum of periodic points with the period \(2\) and topological entropy \(\, log(p).\,\)

Description: Ni-Co-Mn-Ga ferromagnetic shape memory alloys show metamagnetic transition from ferromagnetic austenite to paramagnetic (or weak-magnetic) martensite for a limited range of Co contents. The temperatures of the structural and magnetic transitions depend strongly on composition and atomic order degree, in such a way that combined composition and thermal treatment allows obtaining martensitic transformation (MT) between any magnetic state of austenite and martensite. The entropy change ΔS measured in the magnetostructural transition comprises a magnetic contribution which depends on the type and degree of magnetic order of the related phases. Consequently, both the magnetization jump across the MT (DM) and DS are composition and atomic order dependent. Both ΔS and ΔM determine the effect of applied magnetic fields on the MT, hence knowledge and understanding of their behavior can help to approach the best conditions for magnetic field induced MT and related effects. In previous papers, we have reported findings regarding the behavior of the transformation entropy in relation to composition and atomic order in Ni50−xCoxMn25+yGa25−y (x = 3–8, y = 5–7) alloys. In the present paper we will review our recent results, summarizing the key findings and drawing general conclusions regarding the magnetic contribution to ΔS and the effect of different factors on the magnetic and structural properties of these metamagnetic alloys.

Description: Due to pervasive communication infrastructures, a plethora of enabling technologies is being developed over mobile and wired networks. Among these, video streaming services over IP are the most challenging in terms of quality, real-time requirements and security. In this paper, we propose a novel scheme to efficiently secure variable length coded (VLC) multimedia bit streams, such as H.264. It is based on code word error diffusion and variable size segment shuffling. The codeword diffusion and the shuffling mechanisms are based on random operations from a secure and computationally efficient chaos-based pseudo-random number generator. The proposed scheme is ubiquitous to the end users and can be deployed at any node in the network. It provides different levels of security, with encrypted data volume fluctuating between 5.5–17%. It works on the compressed bit stream without requiring any decoding. It provides excellent encryption speeds on different platforms, including mobile devices. It is 200% faster and 150% more power efficient when compared with AES software-based full encryption schemes. Regarding security, the scheme is robust to well-known attacks in the literature, such as brute force and known/chosen plain text attacks.

Description: Different techniques originated in information theory and tools from nonlinear systems theory have been applied to the analysis of electro-physiological time series. Several clinically relevant results have emerged from the use of concepts, such as entropy, chaos and complexity, in analyzing electrocardiograms and electroencephalographic (EEG) records. In this work, we develop a method based on permutation entropy (PE) to characterize EEG records from different stages in the treatment of a chronic epileptic patient. Our results show that the PE is useful for clearly quantifying the evolution of the patient along a certain lapse of time and allows visualizing in a very convenient way the effects of the pharmacotherapy.

Description: Flow velocity measurements using point-velocity meters are normally obtained by sampling one, two or three velocity points per vertical profile. During high floods their use is inhibited due to the difficulty of sampling in lower portions of the flow area. Nevertheless, the application of standard methods allows estimation of a parameter, α, which depends on the energy slope and the Manning roughness coefficient. During high floods, monitoring of velocity can be accomplished by sampling the maximum velocity, umax, only, which can be used to estimate the mean flow velocity, um, by applying the linear entropy relationship depending on the parameter, M, estimated on the basis of historical observed pairs (um, umax). In this context, this work attempts to analyze if a correlation between α and M holds, so that the monitoring for high flows can be addressed by exploiting information from standard methods. A methodology is proposed to estimate M from α, by coupling the “historical” information derived by standard methods, and “new” information from the measurement of umax surmised at later times. Results from four gauged river sites of different hydraulic and geometric characteristics have shown the robust estimation of M based on α.

Description: Motifs are small recurring circuits of interactions which constitute the backbone of networked systems. Characterizing motif dynamics is therefore key to understanding the functioning of such systems. Here we propose a method to define and quantify the temporal variability and time scales of electroencephalogram (EEG) motifs of resting brain activity. Given a triplet of EEG sensors, links between them are calculated by means of linear correlation; each pattern of links (i.e., each motif) is then associated to a symbol, and its appearance frequency is analyzed by means of Shannon entropy. Our results show that each motif becomes observable with different coupling thresholds and evolves at its own time scale, with fronto-temporal sensors emerging at high thresholds and changing at fast time scales, and parietal ones at low thresholds and changing at slower rates. Finally, while motif dynamics differed across individuals, for each subject, it showed robustness across experimental conditions, indicating that it could represent an individual dynamical signature.

Description: A comprehensive thermodynamic study is conducted of a diesel based Combined Heat and Power (CHP) system, based on a diesel engine and an Organic Rankine Cycle (ORC). Present research covers both energy and exergy analyses along with a multi-objective optimization. In order to determine the irreversibilities in each component of the CHP system and assess the system performance, a complete parametric study is performed to investigate the effects of major design parameters and operating conditions on the system’s performance. The main contribution of the current research study is to conduct both exergy and multi-objective optimization of a system using different working fluid for low-grade heat recovery. In order to conduct the evolutionary based optimization, two objective functions are considered in the optimization; namely the system exergy efficiency, and the total cost rate of the system, which is a combination of the cost associated with environmental impact and the purchase cost of each component. Therefore, in the optimization approach, the overall cycle exergy efficiency is maximized satisfying several constraints while the total cost rate of the system is minimized. To provide a better understanding of the system under study, the Pareto frontier is shown for multi-objective optimization and also an equation is derived to fit the optimized point. In addition, a closed form relationship between exergy efficiency and total cost rate is derived.

Description: In this paper, we introduce an iterative method with lower positions of true numerical solutions located in the real orbit in order to investigate the property of the logistic map. The basic structure of the logistic map is presented, which consists of the root gene position, the common gene position and the individual gene position. The ergodicity and randomness of the logistic map are dependent on the individual gene position. We find that the lower positions of the true numerical solutions in the real orbits have the property of a half-life.

Description: A new quantum f-divergence for trace class operators in Hilbert Spaces is introduced. It is shown that for normalised convex functions it is nonnegative. Some upper bounds are provided. Applications for some classes of convex functions of interest are also given.

Description: In the last decades of the nineteenth century, different attitudes towards mechanics led to two main theoretical approaches to thermodynamics: an abstract and phenomenological approach, and a very different approach in terms of microscopic models. In reality some intermediate solutions were also put forward. Helmholtz and Planck relied on a mere complementarity between mechanical and thermal variables in the expressions of state functions, and Oettingen explored the possibility of a more demanding symmetry between mechanical and thermal capacities. Planck refused microscopic interpretations of heat, whereas Helmholtz made also recourse to a Lagrangian approach involving fast hidden motions. J.J. Thomson incorporated the two mechanical attitudes in his theoretical framework, and put forward a very general theory for physical and chemical processes. He made use of two sets of Lagrangian coordinates that corresponded to two components of kinetic energy: alongside macroscopic energy, there was a microscopic energy, which was associated with the absolute temperature. Duhem put forward a bold design of unification between physics and chemistry, which was based on the two principles of thermodynamics. From the mathematical point of view, his thermodynamics or energetics consisted of a Lagrangian generalization of mechanics that could potentially describe every kind of irreversible process, explosive chemical reactions included.

Description: Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag–Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

Description: System identification, in practice, is carried out by perturbing processes or plants under operation. That is why in many industrial applications a plant-friendly input signal would be preferred for system identification. The goal of the study is to design the optimal input signal which is then employed in the identification experiment and to examine the relationships between the index of friendliness of this input signal and the accuracy of parameter estimation when the measured output signal is significantly affected by noise. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant (D-optimality) expressed in conventional Bolza form. As setting such conditions of the identification experiment we can only talk about the D-suboptimality, we quantify the plant trajectories using the D-efficiency measure. An additional constraint, imposed on D-efficiency of the solution, should allow one to attain the most adequate information content  from the plant which operating point is perturbed in the least invasive (most friendly) way. A simple numerical example, which clearly demonstrates the idea presented in the paper, is included and discussed.

Description: One way to increase the thermal efficiency of vehicle diesel engines is to recover waste heat by using an organic Rankine cycle (ORC) system. Tests were conducted to study the running performances of diesel engines in the whole operating range. The law of variation of the exhaust energy rate under various engine operating conditions was also analyzed. A diesel engine-ORC combined system was designed, and relevant evaluation indexes proposed. The variation of the running performances of the combined system under various engine operating conditions was investigated. R245fa and R152a were selected as the components of the mixed working fluid. Thereafter, six kinds of mixed working fluids with different compositions were presented. The effects of mixed working fluids with different compositions on the running performances of the combined system were revealed. Results show that the running performances of the combined system can be improved effectively when mass fraction R152a in the mixed working fluid is high and the engine operates with high power. For the mixed working fluid M1 (R245fa/R152a, 0.1/0.9, by mass fraction), the net power output of the combined system reaches the maximum of 34.61 kW. Output energy density of working fluid (OEDWF), waste heat recovery efficiency (WHRE), and engine thermal efficiency increasing ratio (ETEIR) all reach their maximum values at 42.7 kJ/kg, 10.90%, and 11.29%, respectively.

Description: In medicine, artificial neural networks (ANN) have been extensively applied in many fields to model the nonlinear relationship of multivariate data. Due to the difficulty of selecting input variables, attribute reduction techniques were widely used to reduce data to get a smaller set of attributes. However, to compute reductions from heterogeneous data, a discretizing algorithm was often introduced in dimensionality reduction methods, which may cause information loss. In this study, we developed an integrated method for estimating the medical care costs, obtained from 798 cases, associated with myocardial infarction disease. The subset of attributes was selected as the input variables of ANN by using an entropy-based information measure, fuzzy information entropy, which can deal with both categorical attributes and numerical attributes without discretization. Then, we applied a correction for the Akaike information criterion (ΑICc) to compare the networks. The results revealed that fuzzy information entropy was capable of selecting input variables from heterogeneous data for ANN, and the proposed procedure of this study provided a reasonable estimation of medical care costs, which can be adopted in other fields of medical science.

Description: This paper deals with the leader-following consensus of multi-agent systems with matched nonlinear dynamics. Compared with previous works, the major difficulty here is caused by the simultaneous existence of nonidentical agent dynamics and unknown system parameters, which are more practical in real-world applications. To tackle this difficulty, a distributed adaptive control law for each follower is proposed based on algebraic graph theory and algebraic Riccati equation. By a Lyapunov function method, we show that the designed control law guarantees that each follower asymptotically converges to the leader under connected communication graphs. A simulation example demonstrates the effectiveness of the proposed scheme.

Description: A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i) where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii) with a linear drift term (Ornstein–Uhlenbeck), but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.

Description: This paper describes some underlying principles of multicomponent and high entropy alloys, and gives some examples of these materials. Different types of multicomponent alloy and different methods of accessing multicomponent phase space are discussed. The alloys were manufactured by conventional and high speed solidification techniques, and their macroscopic, microscopic and nanoscale structures were studied by optical, X-ray and electron microscope methods. They exhibit a variety of amorphous, quasicrystalline, dendritic and eutectic structures.

Description: In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for usein particular nonlinear cases. There are some approaches that conclude with these solutions.Optimization in this area means finding the majority of points on the elliptic curve and minimizing the time to compute the solution in contrast with the necessary time to compute the inverse solution. We can compute the positive solution of PDE (partial differentialequation) like oscillations of f(s)/s around the principal eigenvalue λ1 of -Δ in H 0 1 (Ω).Translating mathematics into cryptographic applications will be relevant in everyday life,wherein there are situations in which two parts that communicate need a third part to confirmthis process. For example, if two persons want to agree on something they need an impartialperson to confirm this agreement, like a notary. This third part does not influence in anyway the communication process. It is just a witness to the agreement. We present a systemwhere the communicating parties do not authenticate one another. Each party authenticatesitself to a third part who also sends the keys for the encryption/decryption process. Anotheradvantage of such a system is that if someone (sender) wants to transmit messages to morethan one person (receivers), he needs only one authentication, unlike the classic systemswhere he would need to authenticate himself to each receiver. We propose an authenticationmethod based on zero-knowledge and elliptic curves.

Description: The entropy of a closure operator has been recently proposed for the study ofnetwork coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank functions for a given closure operator, which determine bounds on the entropy of that operator. This yields new axiomsfor matroids based on their closure operators. We also determine necessary conditions fora large class of closure operators to be solvable. We then define the Shannon entropy of aclosure operator and use it to prove that the set of closure entropies is dense. Finally, we justify why we focus on the solvability of closure operators only.

Description: An overview is presented of the recent developments in the application of large eddy simulation (LES) for prediction and analysis of local entropy generation in turbulent reacting flows. A challenging issue in such LES is subgrid-scale (SGS) modeling of filtered entropy generation terms. An effective closure strategy, recently developed, is based on the filtered density function (FDF) methodology with inclusion of entropy variations. This methodology, titled entropy FDF (En-FDF), is the main focus of this article. The En-FDF has been introduced as the joint velocity-scalar-turbulent frequency-entropy FDF and the marginal scalar-entropy FDF. Both formulations contain the chemical reaction and its entropy generation effects in closed forms. The former constitutes the most comprehensive form of the En-FDF and provides closure for all of the unclosed terms in LES transport equations. The latter is the marginal En-FDF and accounts for entropy generation effects, as well as scalar-entropy statistics. The En-FDF methodologies are described, and some of their recent predictions of entropy statistics and entropy generation in turbulent shear flows are presented.

Description: The effect of the internal heat exchanger (IHE) on the performance of the transcritical carbon dioxide refrigeration cycle with an expander is analyzed theoretically on the basis of the first and second laws of thermodynamics. The possible parameters affecting system efficiency such as heat rejection pressure, gas cooler outlet temperature, evaporating temperature, expander isentropic efficiency and IHE effectiveness are investigated. It is found that the IHE addition in the carbon dioxide refrigeration cycle with an expander increases the specific cooling capacity and compression work, and decreases the optimum heat rejection pressure and the expander output power. An IHE addition does not always improve the system performance in the refrigeration cycle with an expander. The throttle valve cycle with IHE provides a 5.6% to 17% increase in maximum COP compared to that of the basic cycle. For the ideal expander cycle with IHE, the maximum COP is approximately 12.3% to 16.1% lower than the maximum COP of the cycle without IHE. Whether the energy efficiency of the cycle by IHE can be improved depends on the isentropic efficiency level of the expander. The use of IHE is only applicable in the cases of lower expander isentropic efficiencies or higher gas cooler exit temperatures for the refrigeration cycle with an expander from the view of energy efficiency.

Description: The purpose of this article is to study the heat transfer characteristics of a voice-coil and permanent magnet for a speaker using nano-sized ferrofluid. In order to investigate the temperature characteristics of the speaker, the speaker power ratings, ambient temperatures of the test chamber, chamber sizes and input signals were tested. As a result, the temperatures of the voice-coil and magnet for the speaker increased with time due to the thermal linearity. The temperature of the voice-coil increased with the decrease of the input signals, but with the increase of the nominal power rating. The voice-coil temperature of Speaker 1 using ferrofluid of an amount of 650 μL at an elapsed time of 10,000 s was 24.5% lower than that of general Speaker 1. In addition, the proper size selection of the enclosure is an important design factor to ensure the sound quality and effective heat transfer of the speaker.

Description: Entropy estimation metrics have become a widely used method to identify subtle changes or hidden features in biomedical records. These methods have been more effective than conventional linear techniques in a number of signal classification applications, specially the healthy–pathological segmentation dichotomy. Nevertheless, a thorough characterization of these measures, namely, how to match metric and signal features, is still lacking. This paper studies a specific characterization problem: the influence of missing samples in biomedical records. The assessment is conducted using four of the most popular entropy metrics: Approximate Entropy, Sample Entropy, Fuzzy Entropy, and Detrended Fluctuation Analysis. The rationale of this study is that missing samples are a signal disturbance that can arise in many cases: signal compression, non-uniform sampling, or data transmission stages. It is of great interest to determine if these real situations can impair the capability of segmenting signal classes using such metrics. The experiments employed several biosignals: electroencephalograms, gait records, and RR time series. Samples of these signals were systematically removed, and the entropy computed for each case. The results showed that these metrics are robust against missing samples: With a data loss percentage of 50% or even higher, the methods were still able to distinguish among signal classes.

Description: Darwinian fitness describes the capacity of an organism to appropriate resources from the environment and to convert these resources into net-offspring production. Studies of competition between related types indicate that fitness is analytically described by entropy, a statistical measure which is positively correlated with population stability, and describes the number of accessible pathways of energy flow between the individuals in the population. Directionality theory is a mathematical model of the evolutionary process based on the concept evolutionary entropy as the measure of fitness. The theory predicts that the changes which occur as a population evolves from one non-equilibrium steady state to another are described by the following directionality principle–fundamental theorem of evolution: (a) an increase in evolutionary entropy when resource composition is diverse, and resource abundance constant; (b) a decrease in evolutionary entropy when resource composition is singular, and resource abundance variable. Evolutionary entropy characterizes the dynamics of energy flow between the individual elements in various classes of biological networks: (a) where the units are individuals parameterized by age, and their age-specific fecundity and mortality; where the units are metabolites, and the transitions are the biochemical reactions that convert substrates to products; (c) where the units are social groups, and the forces are the cooperative and competitive interactions between the individual groups. % This article reviews the analytical basis of the evolutionary entropic principle, and describes applications of directionality theory to the study of evolutionary dynamics in two biological systems; (i) social networks–the evolution of cooperation; (ii) metabolic networks–the evolution of body size. Statistical thermodynamics is a mathematical model of macroscopic behavior in inanimate matter based on entropy, a statistical measure which describes the number of ways the molecules that compose the a material aggregate can be arranged to attain the same total energy. This theory predicts an increase in thermodynamic entropy as the system evolves towards its equilibrium state. We will delineate the relation between directionality theory and statistical thermodynamics, and review the claim that the entropic principle for thermodynamic systems is the limit, as the resource production rate tends to zero, and population size tends to infinity, of the entropic principle for evolutionary systems.

Description: We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fr and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely \(\chi^2\) \(\chi^2\)and lognormal superstatistics, all maximizing different effective entropy measures. We investigate how the three classes of extreme value theory are related to the three classes of superstatistics. We show that for any superstatistical process whose local equilibrium distribution does not live on a finite support, the Weibull distribution cannot occur. Under the above mild asymptotic independence assumptions, we also show that \(\chi^2\) generally leads an extreme value statistics described by a Fr distribution, whereas inverse \(\chi^2\) as well as lognormal superstatistics, lead to an extreme value statistics associated with the Gumbel distribution.

Description: A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties such as a meaningful structural interpretation and uniqueness. As classical work, many distance-based graph entropies, e.g., the ones due to Bonchev et al. and related quantities have been proposed and studied. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices with distance \(k\) to a given vertex. In particular, we investigate some properties thereof leading to a better understanding of this new information-theoretic quantity.

Description: This study experimentally examined why subjective probability for delayed reward decays non-exponentially (“hyperbolically”, i.e., q ˂ 1 in the q-exponential discount function) in humans. Our results indicate that nonlinear psychophysical time causes hyperbolic time-decay of subjective probability for delayed reward. Implications for econophysics and neuroeconomics are discussed.

Description: In this paper we illustrate the potential of ordinal-patterns-based methods for analysis of real-world data and, especially, of electroencephalogram (EEG) data. We apply already known (empirical permutation entropy, ordinal pattern distributions) and new (empirical conditional entropy of ordinal patterns, robust to noise empirical permutation entropy) methods for measuring complexity, segmentation and classification of time series.

Description: This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively.

Description: Analysis of the characteristics of agricultural product price volatility and trend forecasting are necessary to formulate and implement agricultural price control policies. Taking wholesale cabbage prices as an example, a multiple test methodology has been adopted to identify the nonlinearity, fractality, and chaos of the data. The approaches used include the R/S analysis, the BDS test, the power spectra, the recurrence plot, the largest Lyapunov exponent, the Kolmogorov entropy, and the correlation dimension. The results show that there is chaos in agricultural wholesale price data, which provides a good theoretical basis for selecting reasonable forecasting models as prediction techniques based on chaos theory can be applied to forecasting agricultural prices.

Description: The aim of this paper is to develop a comprehensive study of the geometry involved in combining Bregman divergences with pooling operators over closed convex sets in a discrete probabilistic space. A particular connection we develop leads to an iterative procedure, which is similar to the alternating projection procedure by Csiszár and Tusnády. Although such iterative procedures are well studied over much more general spaces than the one we consider, only a few authors have investigated combining projections with pooling operators. We aspire to achieve here a comprehensive study of such a combination. Besides, pooling operators combining the opinions of several rational experts allows us to discuss possible applications in multi-expert reasoning.

Description: Hubei Province is the hub of communications in central China, which directly determines its strategic position in the country’s development. Additionally, Hubei Province is well-known for its diverse landforms, including mountains, hills, mounds and plains. This area is called “The Province of Thousand Lakes” due to the abundance of water resources. Geographical names are exclusive names given to physical or anthropogenic geographic entities at specific spatial locations and are important signs by which humans understand natural and human activities. In this study, geographic information systems (GIS) technology is adopted to establish a geodatabase of geographical names with particular characteristics in Hubei Province and extract certain geomorphologic and environmental factors. We carry out landscape analysis of mountain-related geographical names and water-related geographical names respectively. In the end, we calculate the information entropy of geographical names of each county to describe the diversity and inhomogeneity of place names in Hubei province. Our study demonstrates that geographical names represent responses to the cultural landscape and physical environment. The geographical names are more interesting in specific landscapes, such as mountains and rivers.

Description: In the present work, the mechanisms, thermochemistry and kinetics of the reaction of SO2 with O3− have been studied using the CCSD(T)/6-31G(d) + CF method. It has been shown that there exist two possible pathways A and B of the SO2 + O3− → SO3− + O2 reaction. The two pathways’ A and B barrier heights are 0.61 kcal mol−1 and 3.40 kcal mol−1, respectively, while the energy of the SO2 + O3− → SO3− + O2 reaction is −25.25 kcal mol−1. The canonical variational transition state theory with small-curvature tunneling (CVT/SCT) has been applied to study the reaction kinetics. The CVT/SCT study shows that the rate constants K for pathways A and B, KA = 1.11 × 10−12exp(−2526.13/T) and KB = 2.7 × 10−14exp(−1029.25/T), respectively, grow as the temperature increases and are much larger than those of the SO2 + O3 → SO3 + O2 reaction over the entire temperature range of 200–1500 K. This indicates that ionization of O3 and high temperatures are favorable for the SO2 oxidation via the reaction with ozone. The new data obtained in the present study can be utilized directly for the evaluation of experiments and model predictions concerning SO2 oxidation and kinetic modeling of gas-phase chemistry of pollutants/nucleation precursors formed in aircraft engines and the Earth’s atmosphere.

Description: The authors wish to make the following corrections to this paper [1]: The correct name of the fourth author is: Ahmed S. Salama. In the Acknowledgment Section, we added the research Project No. 2014/01/2079. Below is the corrected version of the section.[...]

Description: As the early design decision-making structure, a software architecture plays a key role in the final software product quality and the whole project. In the software design and development process, an effective evaluation of the trustworthiness of a software architecture can help making scientific and reasonable decisions on the architecture, which are necessary for the construction of highly trustworthy software. In consideration of lacking the trustworthiness evaluation and measurement studies for software architecture, this paper provides one trustworthy attribute model of software architecture. Based on this model, the paper proposes to use the Principle of Maximum Entropy (POME) and Grey Decision-making Method (GDMM) as the trustworthiness evaluation method of a software architecture and proves the scientificity and rationality of this method, as well as verifies the feasibility through case analysis.

Description: In high-pressure dynamic thermodynamic processes, the pressure is much higher than the air critical pressure, and the temperature can deviate significantly from the Boyle temperature. In such situations, the thermo-physical properties and pneumatic performance can’t be described accurately by the ideal gas law. This paper proposes an approach to evaluate the pneumatic performance of a high-pressure air catapult launch system, in which esidual functions are used to compensate the thermal physical property uncertainties of caused by real gas effects. Compared with the Nelson-Obert generalized compressibility charts, the precision of the improved virial equation of state is better than Soave-Redlich-Kwong (S-R-K) and Peng-Robinson (P-R) equations for high pressure air. In this paper, the improved virial equation of state is further used to establish a compressibility factor database which is applied to evaluate real gas effects. The specific residual thermodynamic energy and specific residual enthalpy of the high-pressure air are also derived using the modified corresponding state equation and improved virial equation of state which are truncated to the third virial coefficient. The pneumatic equations are established on the basis of the derived residual functions. The comparison of the numerical results shows that the real gas effects are strong, and the pneumatic performance analysis indicates that the real dynamic thermodynamic process is obviously different from the ideal one.

Description: Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics) in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed.

Description: Entropy-based complexity of cardiovascular variability at short time scales is largely dependent on the noise and/or action of neural circuits operating at high frequencies. This study proposes a technique for canceling fast variations from cardiovascular variability, thus limiting the effect of these overwhelming influences on entropy-based complexity. The low-pass filtering approach is based on the computation of the fastest intrinsic mode function via empirical mode decomposition (EMD) and its subtraction from the original variability. Sample entropy was exploited to estimate complexity. The procedure was applied to heart period (HP) and QT (interval from Q-wave onset to T-wave end) variability derived from 24-hour Holter recordings in 14 non-mutation carriers (NMCs) and 34 mutation carriers (MCs) subdivided into 11 asymptomatic MCs (AMCs) and 23 symptomatic MCs (SMCs). All individuals belonged to the same family developing long QT syndrome type 1 (LQT1) via KCNQ1-A341V mutation. We found that complexity indexes computed over EMD-filtered QT variability differentiated AMCs from NMCs and detected the effect of beta-blocker therapy, while complexity indexes calculated over EMD-filtered HP variability separated AMCs from SMCs. The EMD-based filtering method enhanced features of the cardiovascular control that otherwise would have remained hidden by the dominant presence of noise and/or fast physiological variations, thus improving classification in LQT1.