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Based on the dispersion entropy model, combined with multiscale analysis method and fractional order information entropy theory, this paper proposes new models — the generalized fractional order multiscale dispersion entropy (GMDE) and the generalized fractional order refined composite multiscale dispersion entropy (GRCMDE). The new models take the amplitude value information of the sequence itself into consideration, which can make better use of some key information in the sequence and have a higher stability and accuracy. In addition, extending the algorithm to generalized fractional order can make the model better capture the small evolution of the signal data, which is more advantageous for studying the dynamic characteristics of complex systems. This paper verifies the effectiveness of the new models by combining theoretical analysis with empirical research, and further studies the complexity of the financial system and the nature of its multiple time scales. The results show that the proposed GMDE, GRCMDE can better detect the intrinsic nature of financial time series and can distinguish the financial market complexity of different countries. [ABSTRACT FROM AUTHOR]

Finding influential nodes is of significance to understand and control the spreading capacity of complex systems. This paper aims to find influential nodes of bus networks by a proposed node failure process. Network efficiency and average transfer times are used to measure the performance of bus networks. Six node measures including degree, node strength, line number, betweenness, local triangle centrality (LTC) and a measure considering neighborhood similarity called LSS are introduced to evaluate the importance of nodes. Results show that removing nodes with high betweenness value can effectively decrease the network efficiency, but cannot increase the average transfer times. Furthermore, removing nodes with high values of LTC and LSS considering the neighborhood information can damage the bus networks from the perspectives of both network efficiency and average transfer times. [ABSTRACT FROM AUTHOR]

Aristotle's dictum scio nescio (I know that I don't know) may serve as a source of enhanced performance for organizations. Awareness of nescience sets the direction for further inquiry, as managers tend to move in the direction that they believe will reduce nescience most. However, nescience is difficult to quantify, so, to date, managers have primarily relied on intuition. This paper introduces a theoretical framework for managing nescience that is based on information theory. This framework is tested in three exploratory empirical studies that take place in highly contrasting settings: semiconductor manufacturing, medical diagnostics and social media analytics. All three studies demonstrate that metrics related to information entropy can be used to quantify nescience. However, practitioners value the framework and its metrics more highly in the settings where the quality of or access to information drives successful product development. The problems encountered in these settings tended to be well-structured, or they were converted from being ill-structured to being well-structured. Further study of more highly contrasting practical settings will be required to determine whether frameworks based on information theory can serve as foundations for a broadly based, pragmatic theory for managing nescience. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a quantity which is called ( R, S)-norm entropy and discuss some of its major properties in comparison with Shannon's and other entropies known in the literature. Further, we give an application of ( R, S)-norm entropy in coding theory and a coding theorem analogous to the ordinary coding theorem for a noiseless channel. The theorem states that the proposed entropy is the lower bound of mean code word length. Further, we give an application of ( R, S)-norm entropy and noiseless coding theorem in questionnaire theory. We show that the relationship between noiseless coding theorem and questionnaire theory through a charging scheme based on the resolution of questions and lower bound on the measure of the charge can also be obtained. [ABSTRACT FROM AUTHOR]

In multiple criteria evaluation, criteria weights are of great importance. In practice, subjective criteria weights determined by specialists/experts are commonly used. The types of elements of a decision matrix also play an important role in the evaluation of alternatives. The objective weights help to estimate the structure of data. The entropy method is widely used for determining the weights (significances) of criteria. A new method of the criterion impact loss, CILOS, is used for determining a relative impact loss experienced by the criterion of an alternative, when another criterion is chosen to be the best. The authors of the paper have combined the best features of the entropy method and the CILOS approach to obtain a new method - Integrated Determination of Objective CRIteria Weights, or (IDOCRIW). [ABSTRACT FROM AUTHOR]

Coupling entropy of co-processing model on social networks is investigated in this paper. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are achieved to disclose the formation. In order to understand the evolution of the co-processing and design the optimal routing strategy according to the maximal entropic diffusion on networks, we propose the coupling entropy comprehending the structural characteristics and information propagation on social network. Based on the analysis of the co-processing model, we analyze the coupling impact of the structural factor and information propagating factor on the coupling entropy, where the analytical results fit well with the numerical ones on scale-free social networks. [ABSTRACT FROM AUTHOR]

In this paper we define some new generalized measures of 'useful' relative information and study their particular cases. We also obtain their relations with common entropy measures. Moreover, we define the quantum generalized Tsallis entropy and show that projective measurement does not decrease the quantum generalized Tsallis entropy of a quantum state. Finally, we define generalized quantum Tsallis and Renyi relative entropies and discuss their particular cases. [ABSTRACT FROM AUTHOR]

Bekenstein has obtained an upper limit on the entropy S, and from that, an information number bound N is deduced. In other words, this is the information contained within a given finite region of space that includes a finite amount of energy. Similarly, this can be thought as the maximum amount of information required to perfectly describe a given physical system down to its quantum level. If the energy and the region of space are finite then the number of information N required in describing the physical system is also finite. In this short paper, two information number bounds are derived and compared for two types of universe. First, a universe without a cosmological constant Λ and second a universe with a cosmological constant Λ are investigated. This is achieved with the derivation of two different relations that connect the Hubble constant and cosmological constants to the number of information N. We find that the number of information N involved in the two universes are identical or N2 = N2Λ, and that the total mass of the universe scales as the square root of the information number N, containing. an information number N of the order of 10122. Finally, we expressed Calogero's quantization action as a function of the number of information N. We also have found that in self-gravitating systems the number of information N in nats is the ratio of the total kinetic to total thermal energy of the system. [ABSTRACT FROM AUTHOR]

Sophisticated models of human social behavior are fast becoming highly desirable in an increasingly complex and interrelated world. Here, we propose that rather than taking established theories from the physical sciences and naively mapping them into the social world, the advanced concepts and theories of social psychology should be taken as a starting point, and used to develop a new modeling methodology. In order to illustrate how such an approach might be carried out, we attempt to model the low elaboration attitude changes of a society of agents in an evolving social context. We propose a geometric model of an agent in context, where individual agent attitudes are seen to self-organize to form ideologies, which then serve to guide further agent-based attitude changes. A computational implementation of the model is shown to exhibit a number of interesting phenomena, including a tendency for a measure of the entropy in the system to decrease, and a potential for externally guiding a population of agents toward a new desired ideology. [ABSTRACT FROM AUTHOR]

The chaotic complexity properties of semiconductor lasers in the chaotic synchronization systems are investigated numerically, based on the information theory based quantifier, the permutation entropy (PE). We find that, on the one hand, the degree of complexity for the master laser increases with the feedback strength firstly and then saturate at higher feedback strength, but are hardly affected by the feedback delay. On the other hand, for the slave laser, the complexity degree is closer to that for the master laser when the high quality chaos synchronization is obtained, which shows that, the PE method is a successful quantifier to evaluate the degree of complexity for the chaotic signals in chaos synchronization systems, and can be considered as a complementary tool to observe the synchronization quality. [ABSTRACT FROM AUTHOR]

We use the Falcone-Takesaki non-commutative flow of weights and the resulting theory of non-commutative Lp spaces in order to define the family of relative entropy functionals that naturally generalise the quantum relative entropies of Jenčová-Ojima and classical relative entropies of Zhu-Rohwer, and belong to an intersection of families of Petz relative entropies with Bregman relative entropies. For the purpose of this task, we generalise the notion of Bregman entropy to the infinite-dimensional non-commutative case using the Legendre-Fenchel duality. In addition, we use the Falcone-Takesaki duality to extend the duality between coarse-grainings and Markov maps to the infinite-dimensional non-commutative case. Following the recent result of Amari for the Zhu-Rohwer entropies, we conjecture that the proposed family of relative entropies is uniquely characterised by the Markov monotonicity and the Legendre-Fenchel duality. The role of these results in the foundations and applications of quantum information theory is discussed. [ABSTRACT FROM AUTHOR]

We introduce a concept of distance between physical theories described by an action. The definition of the distance is based on the relative entropy. We briefly discuss potential physical applications. [ABSTRACT FROM AUTHOR]

Shannon entropies of the Wigner function are calculated for ground and excited stationary states of the Particle-In-A-Box and Harmonic Oscillator model systems and examined as a measure of the localization of the phase-space distribution. We show that their behavior is consistent with that of the sum of the position and momentum space entropies as a function of quantum number. Position-momentum correlation is then analyzed in these systems by defining mutual information between position and momentum variables. This mutual information yields non-zero values, in contrast to the quantum covariance, and increases with quantum number. [ABSTRACT FROM AUTHOR]

In this paper, we discuss an efficient iterative method for the estimation of the chief dynamical invariants of chaotic systems based on stochastically stable piecewise affine maps (e.g. the invariant measure, the Lyapunov exponent as well as the Kolmogorov–Sinai entropy). The proposed method represents an alternative to the Monte-Carlo methods and to other methods based on the discretization of the Frobenius–Perron operator, such as the well known Ulam's method. The proposed estimation method converges not slower than exponentially and it requires a computation complexity that grows linearly with the iterations. Referring to the theory developed by C. Liverani, we discuss a theoretical tool for calculating a conservative estimation of the convergence rate of the proposed method. The proposed approach can be used to efficiently estimate any order statistics of a symbolic source based on a piecewise affine mixing map. [ABSTRACT FROM AUTHOR]

We show that each weakly mixing group action on a dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, we prove that no nilpotent group action on a dendrite is weakly mixing. At last, we show that each dendrite admits no chaotic group actions. [ABSTRACT FROM AUTHOR]

In the paper, the mixing property of ℤ2 subshift of finite type (SFT) is studied, some checkable conditions are provided to examine the property of mixing. Once the mixing property is checked, a class of examples can be found to show it possesses an entropy conjugacy property proposed in [Quas & Trow, 2000]. Finally, we construct an example of two shift spaces X and Y that are entropy conjugate but not conjugate. [ABSTRACT FROM AUTHOR]

In this paper we have studied the dynamics of thermal broadband noise-driven dynamical system in terms of information entropy at both the nonstationary and stationary states. Here, a unified description of fluctuating force is considered in a thermodynamically closed system. Based on the Fokker–Planck description of stochastic processes and the entropy balance equation, we have calculated the time-dependence of the information entropy production and entropy flux in the presence and absence of nonequilibrium constraint. Our calculation considers how the time evolution of these quantities is affected if the characteristic of noise changes from white to red or green and red to green in a unified scheme. [ABSTRACT FROM AUTHOR]

This investigation elucidates the dense entropy of two-dimensional inhomogeneous cellular neural networks (ICNN) with/without input. It is strongly related to the learning problem (or inverse problem); the necessary and sufficient conditions for the admissibility of local patterns must be characterized. For ICNN with/without input, the entropy function is dense in [0, log 2] with respect to the parameter space and the radius of the interacting cells, indicating that, in some sense, ICNN exhibit a wide range of phenomena. [ABSTRACT FROM AUTHOR]

Based on the intuitionistic knowledge content nature of information gain, the concepts of combination entropy and combination granulation are introduced in rough set theory. The conditional combination entropy and the mutual information are defined and their several useful properties are derived. Furthermore, the relationship between the combination entropy and the combination granulation is established, which can be expressed as CE(R) + CG(R) = 1. All properties of the above concepts are all special instances of those of the concepts in incomplete information systems. These results have a wide variety of applications, such as measuring knowledge content, measuring the significance of an attribute, constructing decision trees and building a heuristic function in a heuristic reduct algorithm in rough set theory. [ABSTRACT FROM AUTHOR]

We use a notion of causal independence based on intervention, which is a fundamental concept of the theory of causal networks, to define a measure for the strength of a causal effect. We call this measure "information flow" and compare it with known information flow measures such as transfer entropy. [ABSTRACT FROM AUTHOR]

Quantum Information Theory is an area of physics which studies both fundamental and applied issues in quantum mechanics from an information-theoretical viewpoint. The underlying techniques are, however, often restricted to the analysis of systems which satisfy a certain independence condition. For example, it is assumed that an experiment can be repeated independently many times or that a large physical system consists of many virtually independent parts. Unfortunately, such assumptions are not always justified. This is particularly the case for practical applications — e.g. in quantum cryptography — where parts of a system might have an arbitrary and unknown behavior. We propose an approach which allows us to study general physical systems for which the above mentioned independence condition does not necessarily hold. It is based on an extension of various information-theoretical notions. For example, we introduce new uncertainty measures, called smooth min- and max-entropy, which are generalizations of the von Neumann entropy. Furthermore, we develop a quantum version of de Finetti's representation theorem, as described below. Consider a physical system consisting of n parts. These might, for instance, be the outcomes of n runs of a physical experiment. Moreover, we assume that the joint state of this n-partite system can be extended to an (n + k)-partite state which is symmetric under permutations of its parts (for some k ≫ 1). The de Finetti representation theorem then says that the original n-partite state is, in a certain sense, close to a mixture of product states. Independence thus follows (approximatively) from a symmetry condition. This symmetry condition can easily be met in many natural situations. For example, it holds for the joint state of n parts, which are chosen at random from an arbitrary (n + k)-partite system. As an application of these techniques, we prove the security of quantum key distribution (QKD), i.e. secret key agreement by communication over a quantum channel. In particular, we show that, in order to analyze QKD protocols, it is generally sufficient to consider so-called collective attacks, where the adversary is restricted to applying the same operation to each particle sent over the quantum channel separately. The proof is generic and thus applies to known protocols such as BB84 and B92 (where better bounds on the secret-key rate and on the the maximum tolerated noise level of the quantum channel are obtained) as well as to continuous variable schemes (where no full security proof has been known). Furthermore, the security holds with respect to a strong so-called universally composable definition. This implies that the keys generated by a QKD protocol can safely be used in any application, e.g. for one-time pad encryption — which, remarkably, is not the case for most standard definitions. [ABSTRACT FROM AUTHOR]

We describe a new adaptive multiwindow Gabor expansion, which dynamically adapts the windows to the signal's features in time-frequency space. The adaptation is based on local time-frequency sparsity criteria, and also yields as by-product an expansion of the signal into layers corresponding to different windows. As an illustration, we show that simply using two different windows with different sizes leads to decompositions of audio signals into transient and tonal layers. We also discuss potential applications to transient detection and denoising. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of how insider trading rules affect price formation in securities markets and suggests the application of information theory to market microstructure theory. We analyze a variant of the setting in [20] by simply introducing a more general criterion for informational efficiency borrowed from information theory — namely maximum information transmission. The analysis shows that both the insider's optimal trading strategy and the market price of the risky security depend on the insider trading restriction. Insider trading restrictions are reported to be detrimental to the liquidity of the securities market. We find that a unique insider trading rule exists which implements semi-strong form informational efficiency of the securities market. Alternative restrictions on insider trading give rise to either underreaction or overreaction in securities prices. Too strict insider trading rules are shown to account for excess volatility in securities prices. Contrary to common notion, the uninformed investors are shown to be hurt by too restrictive insider trading rules. We conclude that loose insider trading rules are preferred by the group of investors as a whole. [ABSTRACT FROM AUTHOR]

The upper entropy of a credal set is the maximum of the entropies of the probabilities belonging to it. Although there are algorithms for computing the upper entropy for the particular cases of credal sets associated to belief functions and probability intervals, there is none for a more general model. In this paper, we shall present an algorithm to obtain the upper entropy for order-2 capacities. Our algorithm is an extension of the one presented for belief functions, and proofs of correctness are provided. By using a counterexample, we shall also prove that this algorithm is not valid for general lower probabilities as it computes a value which is strictly greater than the maximum of entropy. [ABSTRACT FROM AUTHOR]

The study of minimum entropy of a natural language has been an interesting research subject. For English, great progress has been made, but few reports on other languages have been found in literature. Based on two hypotheses on the conservation of information quantity, we proposed a method which can be used to estimate the minimum entropy of characters in natural languages. With a large quantity of translation corpus, this method enables us to estimate the minimum entropy without calculating the probability. Besides, as the scale of translation corpus increases, the fluctuation of the ratio between character quantities in any two languages becomes negligible. In this paper, we apply this method to the study of two languages of a large character total — Japanese and Chinese. [ABSTRACT FROM AUTHOR]

In order to raise a class discrimination power by the combination of multiple classifiers, the upper bound of Bayes error rate which is bounded by the conditional entropy of a class and decisions should be minimized. Based on the minimization of the upper bound of the Bayes error rate, Wang and Wong proposed only a tree dependence approximation scheme of a high-dimensional probability distribution composed of a class and patterns. This paper extends such a tree dependence approximation scheme to higher order dependency for improving the classification performance and thus optimally approximates the high-dimensional probability distribution with a product of low-dimensional distributions. And then, a new combination method by the proposed approximation scheme is presented and evaluated with classifiers recognizing unconstrained handwritten numerals. [ABSTRACT FROM AUTHOR]

The nature of quantum entropies, and its use in Quantum Information Theory in the form of (i) total entropy, (ii) relative entropy and (iii) conditional entropy is revisited. In this ordering, we first show the correlations existing between the total q-entropy and entanglement, quantified in the form of entanglement of formation. Then, we revisit the use of the quantum relative entropy as a measure of entanglement, and we finally discuss some features of the quantum conditional q-entropies, which are used in turn as a separability criterion. [ABSTRACT FROM AUTHOR]

We analyze how difficult it is to synchronize to a periodic sequence whose structure is known, when an observer is initially unaware of the sequence's phase. We examine the transient information T, a recently introduced information-theoretic quantity that measures the uncertainty an observer experiences while synchronizing to a sequence. We also consider the synchronization time τ, which is the average number of measurements required to infer the phase of a periodic signal. We calculate T and τ for all periodic sequences up to and including period 23. We show which sequences of a given period have the maximum and minimum possible T and τ values, develop analytic expressions for the extreme values, and show that in these cases the transient information is the product of the total phase information and the synchronization time. Despite the latter result, our analyses demonstrate that the transient information and synchronization time capture different and complementary structural properties of individual periodic sequences — properties, moreover, that are distinct from source entropy rate and mutual information measures, such as the excess entropy. [ABSTRACT FROM AUTHOR]

Considering the thermodynamical formalism of dynamical systems, P. Walters showed that for β-transformations all Lipschitz weights define quasi-compact transfer operators and therefore unique equilibrium measures which additionally have positive entropy and good mixing properties. In this note we generalize this to continuous piecewise monotonic maps of the interval. The case of piecewise monotonic maps with discontinuities remains open. [ABSTRACT FROM AUTHOR]

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory. [ABSTRACT FROM AUTHOR]

Heart rate exhibits spontaneous fluctuations that are mainly modulated by control loops within the autonomic nervous system. Assessing the dynamics of heart rate fluctuations can provide valuable information about regulatory processes and patho-physiological behavior. In this paper heart rate fluctuations and its entropy are assessed using an algorithmic information theoretic concept applying a data compressor. First, the beat-to-beat fluctuations of heart rate are binary coded for decreases and increases, respectively. Subsequently, those symbol sequences are compressed using the LZ77 algorithm. The ratio of the length of the compressed sequences to the original length is used as an estimate of entropy. We investigated the compressibility of heart rate fluctuations in athletes before, during, and after a training camp. Heart rate time series were obtained from ECGs recorded over 30 minutes under supine resting conditions. We found a significant entropy reduction during the training camp, reflecting the effects of physical fatigue. In conclusion, the compression entropy seems to be a suitable approach to assess the complexity of heart rate fluctuations. [ABSTRACT FROM AUTHOR]