Relative Information Measure Research Articles

A New and Effective Classification Method for Complex Time Series Based on Information Measure

The growing importance of time series information measure raises questions about how to effectively cluster a large number of nonlinear complex time series data and accurately extract more hidden information from them. In this paper, a clustering measurement and classification method for complex time series, the symmetrical exponential Tsallis relative information (SETRI) measure, is proposed, which aims to address these problems. The intrinsic characteristics of different types of time series information could be validly identified by this method. The modified multidimensional scaling (MDS) method, based on the SETRI measure, has the ability to display the data in the form of graphs for intuitive exhibition and accomplish the process of dimension reduction. The introduction of weighted permutation patterns allows a higher-accuracy classification not only for the time series dissimilarity quantification, but also for avoiding dispensable errors. Besides, the feasibility of the modified MDS classification method is visually and quantitatively verified by the simulated and real-world data. Compared with other MDS methods, the proposed method has better performance, which is reflected in the validity and rationality of the clustering results, thus further verifying the feasibility of the proposed method. Therefore, the new results will be helpful to develop complex data clustering and dimensionality reduction methods.

Some theoretical results on fractional-order continuous information measures

Abstract By rewriting the differential entropy in a form of a differ-integral function’s limit, and deforming the ordinary derivative to a fractional-order one, we derive in this paper a novel generalized fractional-order differential entropy along with its related information measures. When the order of fractional differentiation α → 1, the ordinary Shannon’s differential entropy is recovered, which corresponds to the results from first-order ordinary differentiation.

Integration of the USSR into the International Patent-Licensing System in the Context of International Technological Cooperation (1950s – early 1970s)

In the 1950s, as the world entered an era of scientific and technological revolution, the leadership of the Soviet Union chose a new economic course based on scientific knowledge, which could enable the USSR to secure technological leadership, a competitive advantage over Western countries and closer integration with the CMEA. A key indicator of the success of this policy has been the country’s incorporation into the evolving system of international patenting and licence selling. In previous years, these processes had not been covered in historical academic publications. The purpose of this study is to explore the Soviet Union's entry into the international patent licensing system and related organizational, legislative and information measures drawing on the archival documents, including the All-Union Research Institute for State Patent Examination (VNIIGPE), introduced into the academic circuit for the first time, as well as on the published reports of the 1965 meeting of the Committee of Experts on Author's Certificates and the Washington Conference of 1970. The author demonstrates that in the 1950s and 1960s the USSR made the transition from a model of institutional and legal incorporation into international patent-licensing activity to an integration model based on patent cooperation and standardisation, in accordance with international norms. The reason for the slow development of technological cooperation, which hindered the achievement of ambitious goals, was the inertia and internal costs of the Soviet economic and administrative system, which fully affected the development of both models. Ultimately, changes in the international environment and the slowdown of economic development in the USSR in the early 1970s prevented the country from gaining even modest benefits from integration.

On ‘Useful’ R-norm Relative Information Measures and Applications

In this communication a new ‘useful’ R-norm relative information measure is introduced and characterized axiomatically. Its inequalities with particular cases are described. This new information measure has also been applied to study the status of the companies with regard to their loss and profit and that has been illustrated by considering empirical data and drawing figures. Ad joint of the relative information measure is also defined with the illustration of its application in share market with examples.

Different emotional profile of health care staff and general population during the COVID-19 outbreak.

The aims of this study were to assess COVID-19 outbreak-related emotions, to identify vulnerable groups within health care workers (HCW) and to study the relationship between the emotional state and some environmental features. We conducted a cross-sectional study on March 29 to April 5, 2020 based on a national online survey using snowball sampling techniques. A list of emotional states was compared in HCW and non-HCW and within HCW roles. The relationship between COVID-19 related symptoms, information, and protective measures and the emotional state was analyzed. Fear (p < .001, φc = .11), irritability (p = .001, φc = .08), frustration (p < .001, φc = .10), anger (p = .013, φc = .06), and helplessness (p < .001, φc = .13) appear significantly more frequently in HCW compared to non-HCW. Within HCW, a higher percentage of physicians, especially the less experienced, significantly perceived uncertainty and frustration (p = .001, φc = .13 and p = .025, φc = .10, respectively), while a higher percentage of nurses significantly experienced sadness (p = .024, φc = .10). Having a confirmatory diagnosis of the disease was related to hypochondria sensation (p = .026, φc = .10). Sadness (p = .035, φc = .09), intolerance (p = .058, φc = .09), anger (p = .024, φc = .10), and helplessness (p = .028, φc = .10) appeared as the most relevant emotions when information was perceived as insufficient. The knowledge of the most prevalent different emotional patterns in HCW, as well as in the general population, will allow the detection of subjects at risk for the development of mental disorders and the implementation of therapeutic approaches in future similar situations of pandemic or outbreak of the current one. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Document Clustering Using Graph Based Fuzzy Association Rule Generation

With the wider growth of web-based documents, the necessity of automatic document clustering and text summarization is increased. Here, document summarization that is extracting the essential task with appropriate information, removal of unnecessary data and providing the data in a cohesive and coherent manner is determined to be a most confronting task. In this research, a novel intelligent model for document clustering is designed with graph model and Fuzzy based association rule generation (gFAR). Initially, the graph model is used to map the relationship among the data (multi-source) followed by the establishment of document clustering with the generation of association rule using the fuzzy concept. This method shows benefit in redundancy elimination by mapping the relevant document using graph model and reduces the time consumption and improves the accuracy using the association rule generation with fuzzy. This framework is provided in an interpretable way for document clustering. It iteratively reduces the error rate during relationship mapping among the data (clusters) with the assistance of weighted document content. Also, this model represents the significance of data features with class discrimination. It is also helpful in measuring the significance of the features during the data clustering process. The simulation is done with MATLAB 2016b environment and evaluated with the empirical standards like Relative Risk Patterns (RRP), ROUGE score, and Discrimination Information Measure (DMI) respectively. Here, DailyMail and DUC 2004 dataset is used to extract the empirical results. The proposed gFAR model gives better trade-off while compared with various prevailing approaches.

Cumulative Residual and Relative Cumulative Residual Fisher Information and Their Properties

In this work, we propose cumulative residual Fisher information and relative cumulative residual Fisher information measures and establish some of their properties. We first show that these cumulative Fisher measures can be expressed based on the hazard function. We then define extended versions of cumulative residual entropy and cumulative residual Fisher information measures based on the Jensen inequality. We also discuss connections between these information measures based on a new version of de Bruijn's identity for survival functions.

Coronavirus Disease-19 and Dentistry: A Review

Novel coronavirus (nCoV) is a novel form of virus with a new strain identified recently in humans. Common clinical signs and symptoms primarily consist of fever, cough, and breathing difficulties. In severe cases, it can results in pneumonia, severe acute respiratory syndrome, kidney failure, and even death. It is important to follow all infection control measures in prevention of the nCoV from spreading and controlling the epidemic situation. The risk of cross infection can be high between dental practitioners and patients due to the features of dental clinical settings. Here, we are summarizing the nCoV related information and infection control measures to be followed in dental practice.

On Black–Scholes option pricing model with stochastic volatility: an information theoretic approach

In this article, we derive the risk-neutral measures of the stock options price and volatility by incorporating a simple constrained minimization of the Kullback measure of relative information. We obtain a second-order parabolic partial differential equation, the generalized Black–Scholes equation based on the theoretical analysis when the underlying financial asset is estimated using a stochastic volatility model. Also to investigate the analytical solution of this generalized Black–Scholes equation we have used Laplace transform homotopy perturbation method.

Global Phase and Magnitude Synchronization of Coupled Oscillators With Application to the Control of Grid-Forming Power Inverters

In this paper, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model, we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a synchronizing feedback based on relative state information and local measurements that induces consensus-like dynamics. We show that, under a mild stability condition, the combination of the synchronizing feedback with a decentralized magnitude control law renders the oscillators’ almost globally asymptotically stable with respect to set points for the phase shift, frequency, and magnitude. We apply these result to rigorously solve an open problem in control of inverter-based ac power systems. In this context, the proposed control strategy can be implemented using purely local information, induces a grid-forming behavior, and ensures that a network of ac power inverters is almost globally asymptotically stable with respect to a prespecified solution of the ac power-flow equations. Moreover, we show that the controller exhibits a droop-like behavior around the standard operating point, thus, making it backward compatible with the existing power system operation.

Empirical Estimation of Information Measures: A Literature Guide

We give a brief survey of the literature on the empirical estimation of entropy, differential entropy, relative entropy, mutual information and related information measures. While those quantities are of central importance in information theory, universal algorithms for their estimation are increasingly important in data science, machine learning, biology, neuroscience, economics, language, and other experimental sciences.

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables.

To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here, we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at an arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily increase significantly in order to reach a stationary state with smaller occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely positive divisibility is more subtly signaled by the prohibition of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy, and coherent information.

Sampling Strategies for Uncertainty Reduction in Categorical Random Fields: Formulation, Mathematical Analysis and Application to Multiple-Point Simulations

The task of optimal sampling for the statistical simulation of a discrete random field is addressed from the perspective of minimizing the posterior uncertainty of non-sensed positions given the information of the sensed positions. In particular, information theoretic measures are adopted to formalize the problem of optimal sampling design for field characterization, where concepts such as information of the measurements, average posterior uncertainty, and the resolvability of the field are introduced. The use of the entropy and related information measures are justified by connecting the task of simulation with a source coding problem, where it is well known that entropy offers a fundamental performance limit. On the application, a one-dimensional Markov chain model is explored where the statistics of the random object are known, and then the more relevant case of multiple-point simulations of channelized facies fields is studied, adopting in this case a training image to infer the statistics of a non-parametric model. In both contexts, the superiority of information-driven sampling strategies is proved in different settings and conditions, with respect to random or regular sampling.

Exponential Tsallis-Havrda-Charvat directed-divergence convex function of ‘type α’

In this paper, we propose an exponential Tsallis-Havrda-Charvat relative information measure of ‘type α’ and discuss their special cases. From these special cases new exponential information measures have also been derived and their relations with different measures of entropy have been obtained.

An $$(R',S')$$ ( R ′ , S ′ ) -norm fuzzy relative information measure and its applications in strategic decision-making

In this communication, we propose two quantities named ‘An $$(R', S')$$ -norm directed divergence measure’ and ‘ $$(R', S')$$ -norm fuzzy directed divergence measure’, establish their validity and discuss their properties. Further, the performance of proposed divergence measure is compared with some existing measures through a numerical example. Finally, the application of proposed fuzzy directed divergence measure is given in strategic decision-making and the outcome is compared with other methods in literature.

A Study on the Relative Mutual Information Measures in a Viewpoint of Association Rule

제 4차 산업혁명으로 인하여 새로운 가능성을 여는 기술 중의 하나인 빅 데이터의 중심에 데이터 마이닝 기법이 놓여 있다. 이 중에서도 연관성 규칙은 방대한 데이터베이스에 들어 있는 항목들 간의 상호 관련성을 찾아내는 기법으로 이를 효율적으로 생성하기 위해 많은 평가 기준들이 개발되고 있다. 본 논문에서는 정보이론 기반 측도 중에서 정보량에 의해 정규화된 상호정보량인 상대적 상호정보량을 객관적 흥미도 측도로서 의미가 있는지를 연관성 평가 기준의 관점에서 탐색하고 예제를 이용하여 이들을 비교하였다. 그 결과, 동시발생빈도 또는 동시비발생빈도가 증가함에 따라 연관성 규칙의 기본적인 평가 기준, 상호정보량, 그리고 상대적 상호정보량 모두가 증가하는 반면에 결합정보량은 감소하는 것으로 나타났다. 불일치빈도가 증가하게 되면 결합정보량이 증가하는 반면에 이를 제외한 모든 측도들이 감소하였다. 또한 모든 사례에서 기본적인 연관성 평가 기준들은 항상 양의 값으로 나타난 반면에 상대적 상호정보량들은 모두 양 또는 음의 값으로 나타났다. 따라서 연관성 평가 기준의 관점에서는 연관성의 방향을 나타내는 상대적 상호정보량이 기존의 지지도와 신뢰도 등에 비해 더 바람직한 측도라고 할 수 있다. 마지막으로 상대적 상호정보량에 대해 각 경우의 차이를 계산해보면 평균에 의해 제안된 측도 중에서는 산술평균을 이용한 측도가 가장 큰 것으로 나타났다.Data mining techniques are at the center of big data analysis, which is identified as an important technology that opens new possibilities due to the fourth industrial revolution. Among them, the association rule is a technique for finding the interrelation between items in a big database, and many evaluation criteria are being developed in order to efficiently generate it. In this paper, we investigated whether the relative mutual information measures, which are normalized by the amount of information, are meaningful as objective interestingness measures in a viewpoint of association evaluation criteria. As a result, the basic association thresholds are always positive, while the relative mutual information measures are positive or negative depending on the direction of association rule. Therefore, from the viewpoint of association rule, the relative mutual information measures indicating the direction of association are more preferable than the existing support and confidence. When we calculate the difference between the values of the two cases for the relative mutual information measures, that of the measure by the arithmetic mean is the greatest among those of the relative mutual information measures by the mean.

Informational and Causal Architecture of Continuous-time Renewal Processes

We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and causal-state transitions are described by partial differential equations. Closed-form expressions are given for statistical complexities, excess entropies, and differential information anatomy rates. We present a complete analysis of the {\epsilon}-machines of continuous-time renewal processes and, then, extend this to processes generated by unifilar hidden semi-Markov models and semi-Markov models. Our information-theoretic analysis leads to new expressions for the entropy rate and the rates of related information measures for these very general continuous-time process classes.

Specified‐time containment control of multi‐agent systems over directed topologies

This study addresses the specified-time containment control problem of multi-agent systems over directed topologies. By using motion-planning approaches, a new framework is constructed to solve the containment control problem of multi-agent systems. In this framework, a class of sampled-data-based protocols are proposed to solve the specified-time containment control problem for single-integrator multi-agent systems. These protocols only require relative information measurements at the sampling instants, without requiring information exchange over the sampling interval. Furthermore, the containment protocols are also developed for the multi-agent system with double-integrator dynamics, such that their states converge to the convex hulls formed by those of the target points in a specified settling time over directed topologies. Compared with the existing results, the proposed sampled-data-based protocols have a couple of advantages: first the settling time can be pre-specified, which is very meaningful and consistent with practical needs. Second, the sampling periods, communication topologies and control gains are all decoupled and can be separately designed. This relaxes many restrictions in controllers design. Numerical simulations are provided to demonstrate the effectiveness of the proposed protocols.

Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach.

This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.

Effect of Wavelet Packet Log Energy Entropy on Electroencephalogram (EEG) Signals

The scaling behavior of human electroencephalogram (EEG) signals is well exploited by appropriate extraction of time – frequency domain and entropy based features. Such measurable inherently helps understanding the neurophysiological phenomenon of brain as well as its associated cortical activities. Being a non-linear time series, EEG's are assumed to be fragment of fluctuations. Several attempts have been made to study the EEG signals for clinical applications such as epileptic seizure detection, evoked response potential recognition, tumor detection, identification of alcoholics and so on. In all such applications appropriate selection of feature parameter plays an important role in discriminating normal EEG from abnormal. In the recent past one can find the importance of wavelet and wavelet packet towards EEG analysis. This proposed research work investigates the effect of wavelet packet log energy entropy on EEG signals. Entropy being the measure of relative information, the proposed study attempts to discriminate the normal EEGs from abnormal EEG's by employing the log energy entropy features. For better brevity, this study restricts to the analysis of epileptic seizure from normal EEGs. Different decomposition levels from 2 to 5 were considered for wavelet packets with application of Haar, rbio3.1, sym7, dmey wavelets. A one second windowing was introduced for the data segmentation and Shannon's log energy entropy was estimated. Then the statistical non-parametric Wilcoxon model was employed. The result shows that the application of wavelet packet log energy entropy found to be a potential indicator for discriminating epileptic seizure from normal.