Entropy

Restricted Mean Survival Time ($RMST$), the average time without an event of interest until a specific time point, is a model-free, easy to interpret statistic. The heavy reliance on non-parametric or semi-parametric methods in the survival analysis has drawn criticism, due to the loss of efficacy compared to parametric methods. This assumes that the parametric family used is the true one, otherwise the gain in efficacy might be lost to interpretability problems due to bias. The Focused Information Criterion ($FIC$) considers the trade-off between bias and variance and offers an objective framework for the selection of the optimal non-parametric or parametric estimator for scalar statistics. Herein, we present the $FIC$ framework for the selection of the $RMST$ estimator with the best bias-variance trade-off. The aim is not to identify the true underling distribution that generated the data, but to identify families of distributions that best approximate this process. Through simulation studies and theoretical reasoning, we highlight the effect of censoring on the performance of $FIC$. Applicability is illustrated with a real life example. Censoring has a non-linear effect on $FIC$s performance that can be traced back to the asymptotic relative efficiency of the estimators. $FIC$s performance is sample size dependent; however, with censoring percentages common in practical applications $FIC$ selects the true model at a nominal probability (0.843) even with small or moderate sample sizes. Full article

The accurate prediction of gross box-office markets is of great benefit for investment and management in the movie industry. In this work, we propose a machine learning-based method for predicting the movie box-office revenue of a country based on the empirical comparisons of eight methods with diverse combinations of economic factors. Specifically, we achieved a prediction performance of the relative root mean squared error of 0.056 in the US and of 0.183 in China for the two case studies of movie markets in time-series forecasting experiments from 2013 to 2016. We concluded that the support-vector-machine-based method using gross domestic product reached the best prediction performance and satisfies the easily available information of economic factors. The computational experiments and comparison studies provided evidence for the effectiveness and advantages of our proposed prediction strategy. In the validation process of the predicted total box-office markets in 2017, the error rates were 0.044 in the US and 0.066 in China. In the consecutive predictions of nationwide box-office markets in 2018 and 2019, the mean relative absolute percentage errors achieved were 0.041 and 0.035 in the US and China, respectively. The precise predictions, both in the training and validation data, demonstrate the efficiency and versatility of our proposed method. Full article

Intelligence is a central feature of human beings’ primary and interpersonal experience. Understanding how intelligence originated and scaled during evolution is a key challenge for modern biology. Some of the most important approaches to understanding intelligence are the ongoing efforts to build new intelligences in computer science (AI) and bioengineering. However, progress has been stymied by a lack of multidisciplinary consensus on what is central about intelligence regardless of the details of its material composition or origin (evolved vs. engineered). We show that Buddhist concepts offer a unique perspective and facilitate a consilience of biology, cognitive science, and computer science toward understanding intelligence in truly diverse embodiments. In coming decades, chimeric and bioengineering technologies will produce a wide variety of novel beings that look nothing like familiar natural life forms; how shall we gauge their moral responsibility and our own moral obligations toward them, without the familiar touchstones of standard evolved forms as comparison? Such decisions cannot be based on what the agent is made of or how much design vs. natural evolution was involved in their origin. We propose that the scope of our potential relationship with, and so also our moral duty toward, any being can be considered in the light of Care—a robust, practical, and dynamic lynchpin that formalizes the concepts of goal-directedness, stress, and the scaling of intelligence; it provides a rubric that, unlike other current concepts, is likely to not only survive but thrive in the coming advances of AI and bioengineering. We review relevant concepts in basal cognition and Buddhist thought, focusing on the size of an agent’s goal space (its cognitive light cone) as an invariant that tightly links intelligence and compassion. Implications range across interpersonal psychology, regenerative medicine, and machine learning. The Bodhisattva’s vow (“for the sake of all sentient life, I shall achieve awakening”) is a practical design principle for advancing intelligence in our novel creations and in ourselves. Full article

The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials. The ultraspherical noncentral t, normal N, F, and ${\chi }^2$ distributions are thus found to be associated with the Gegenbauer, Hermite, Jacobi, and Laguerre polynomial families, respectively, with the corresponding central distributions standing for the polynomial family-defining weights. Obtained through an unconstrained minimization of the Gibbs potential, Jaynes’ maximal entropy priors are formally expressed in terms of the empirical densities’ entropic convex duals. Expanding these duals on orthogonal polynomial bases allows for the expedient determination of the Jaynes–Gibbs priors. Invoking the moment problem and the duality principle, modelization can be reduced to the direct determination of the prior moments in parametric space in terms of the Bayes factor’s orthogonal polynomial expansion coefficients in random variable space. Genomics and geophysics examples are provided. Full article

We propose an amplitude shift keying-type asymmetric quantum communication (AQC) system that uses an entangled state. As a first step toward development of this system, we evaluated and considered the communication performance of the proposed receiver when applied to the AQC system using a two-mode squeezed vacuum state (TSVS), the maximum quasi-Bell state, and the non-maximum quasi-Bell state, along with an asymmetric classical communication (ACC) system using the coherent state. Specifically, we derived an analytical expression for the error probability of the AQC system using the quasi-Bell state. Comparison of the error probabilities of the ACC system and the AQC systems when using the TSVS and the quasi-Bell state shows that the AQC system using the quasi-Bell state offers a clear performance advantage under specific conditions. Additionally, it was clarified that there are cases where the universal lower bound on the error probability for the AQC system was almost achieved when using the quasi-Bell state, unlike the case in which the TSVS was used. Full article

Muscle synergy analysis is a kind of modularized decomposition of muscles during exercise controlled by the central nervous system (CNS). It can not only extract the synergistic muscles in exercise, but also obtain the activation states of muscles to reflect the coordination and control relationship between muscles. However, previous studies have mainly focused on the time-domain synergy without considering the frequency-specific characteristics within synergy structures. Therefore, this study proposes a novel method, named time-frequency non-negative matrix factorization (TF-NMF), to explore the time-varying regularity of muscle synergy characteristics of multi-channel surface electromyogram (sEMG) signals at different frequency bands. In this method, the wavelet packet transform (WPT) is used to transform the time-scale signals into time-frequency dimension. Then, the NMF method is calculated in each time-frequency window to extract the synergy modules. Finally, this method is used to analyze the sEMG signals recorded from 8 muscles during the conversion between wrist flexion (WF stage) and wrist extension (WE stage) movements in 12 healthy people. The experimental results show that the number of synergy modules in wrist flexion transmission to wrist extension (Motion Conversion, MC stage) is more than that in the WF stage and WE stage. Furthermore, the number of flexor and extensor muscle synergies in the frequency band of 0–125 Hz during the MC stage is more than that in the frequency band of 125–250 Hz. Further analysis shows that the flexion muscle synergies mostly exist in the frequency band of 140.625–156.25 Hz during the WF stage, and the extension muscle synergies appear in the frequency band of 125–156.25 Hz during the WE stage. These results can help to better understand the time-frequency features of muscle synergy, and expand study perspective related to motor control in nervous system. Full article

The Rényi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Rényi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide the temperature by q. Then the maximum amount of work the system can perform as it moves to equilibrium at the new temperature divided by the change in temperature equals the system’s Rényi entropy in its original state. This result applies to both classical and quantum systems. Mathematically, we can express this result as follows: the Rényi entropy of a system in thermal equilibrium is without the ‘$q^{-1}$-derivative’ of its free energy with respect to the temperature. This shows that Rényi entropy is a q-deformation of the usual concept of entropy. Full article

With the widespread use of emotion recognition, cross-subject emotion recognition based on EEG signals has become a hot topic in affective computing. Electroencephalography (EEG) can be used to detect the brain’s electrical activity associated with different emotions. The aim of this research is to improve the accuracy by enhancing the generalization of features. A Multi-Classifier Fusion method based on mutual information with sequential forward floating selection (MI_SFFS) is proposed. The dataset used in this paper is DEAP, which is a multi-modal open dataset containing 32 EEG channels and multiple other physiological signals. First, high-dimensional features are extracted from 15 EEG channels of DEAP after using a 10 s time window for data slicing. Second, MI and SFFS are integrated as a novel feature-selection method. Then, support vector machine (SVM), k-nearest neighbor (KNN) and random forest (RF) are employed to classify positive and negative emotions to obtain the output probabilities of classifiers as weighted features for further classification. To evaluate the model performance, leave-one-out cross-validation is adopted. Finally, cross-subject classification accuracies of 0.7089, 0.7106 and 0.7361 are achieved by the SVM, KNN and RF classifiers, respectively. The results demonstrate the feasibility of the model by splicing different classifiers’ output probabilities as a portion of the weighted features. Full article

Computing influential nodes gets a lot of attention from many researchers for information spreading in complex networks. It has vast applications, such as viral marketing, social leader creation, rumor control, and opinion monitoring. The information-spreading ability of influential nodes is greater compared with other nodes in the network. Several researchers proposed centrality measures to compute the influential nodes in a complex network, such as degree, betweenness, closeness, semi-local centralities, and PageRank. These centrality methods are defined based on the local and/or global information of nodes in the network. However, due to their high time complexity, centrality measures based on the global information of nodes have become unsuitable for large-scale networks. Very few centrality measures exist that are based on the attributes between nodes and the structure of the network. We propose the nearest neighborhood trust PageRank (NTPR) based on the structural attributes of neighbors and nearest neighbors of nodes. We define the measure based on the degree ratio, the similarity between nodes, the trust values of neighbors, and the nearest neighbors. We computed the influential nodes in various real-world networks using the proposed centrality method. We found the maximum influence by using influential nodes with SIR and independent cascade methods. We also compare the maximum influence of our centrality measure with the existing basic centrality measures. Full article

The local optima network model has proved useful in the past in connection with combinatorial optimization problems. Here we examine its extension to the real continuous function domain. Through a sampling process, the model builds a weighted directed graph which captures the function’s minima basin structure and its interconnection and which can be easily manipulated with the help of complex networks metrics. We show that the model provides a complementary view of function spaces that is easier to analyze and visualize, especially at higher dimensions. In particular, we show that function hardness as represented by algorithm performance is strongly related to several graph properties of the corresponding local optima network, opening the way for a classification of problem difficulty according to the corresponding graph structure and with possible extensions in the design of better metaheuristic approaches. Full article

The interdependence of financial institutions is primarily responsible for creating a systemic hierarchy in the industry. In this paper, an Adaptive Hierarchical Network Model is proposed to study the problem of hierarchical relationships arising from different individuals in the economic domain. In the presented dynamically evolving network model, new directed edges are generated depending on the existing nodes and the hierarchical structures among the network, and these edges decay over time. When the preference of nodes in the network for higher ranks exceeds a certain threshold value, the equality state in the network becomes unstable and rank states emerge. Meanwhile, we select four real data sets for model evaluation and observe the resilience in the network hierarchy evolution and the differences formed by different patterns of hierarchy preference mechanisms, which help us better understand data science and network dynamics evolution. Full article

As pointed out by many researchers, replication plays a key role in the credibility of applied sciences and the confidence in all research findings. With regard, in particular, to energy finance and economics, replication papers are rare, probably because they are hampered by inaccessible data, but their aim is crucial. We consider two ways to avoid misleading results on the ostensible chaoticity of price series. The first one is represented by the proper mathematical definition of chaos and the related theoretical background, while the latter is represented by the hybrid approach that we propose here—i.e., consisting of considering the dynamical system underlying the price time series as a deterministic system with noise. We find that both chaotic and stochastic features coexist in the energy commodity markets, although the misuse of some tests in the established practice in the literature may say otherwise. Full article

AMC (automatic modulation classification) plays a vital role in spectrum monitoring and electromagnetic abnormal signal detection. Up to now, few studies have focused on the complementarity between features of different modalities and the importance of the feature fusion mechanism in the AMC method. This paper proposes a dual-modal feature fusion convolutional neural network (DMFF-CNN) for AMC to use the complementarity between different modal features fully. DMFF-CNN uses the gram angular field (GAF) image coding and intelligence quotient (IQ) data combined with CNN. Firstly, the original signal is converted into images by GAF, and the GAF images are used as the input of ResNet50. Secondly, it is converted into IQ data and as the complex value network (CV-CNN) input to extract features. Furthermore, a dual-modal feature fusion mechanism (DMFF) is proposed to fuse the dual-modal features extracted by GAF-ResNet50 and CV-CNN. The fusion feature is used as the input of DMFF-CNN for model training to achieve AMC of multi-type signals. In the evaluation stage, the advantages of the DMFF mechanism proposed in this paper and the accuracy improvement compared with other feature fusion algorithms are discussed. The experiment shows that our method performs better than others, including some state-of-the-art methods, and has superior robustness at a low signal-to-noise ratio (SNR), and the average classification accuracy of the dataset signals reaches 92.1%. The DMFF-CNN proposed in this paper provides a new path for the AMC field. Full article

We analyse the fractal nature of geomagnetic field northward and eastward horizontal components with 1 min resolution measured by the four stations Belsk, Hel, Sodankylä and Hornsund during the period of 22 August–1 September, when the 26 August 2018 geomagnetic storm appeared. To reveal and to quantitatively describe the fractal scaling of the considered data, three selected methods, structure function scaling, Higuchi, and detrended fluctuation analysis are applied. The obtained results show temporal variation of the fractal dimension of geomagnetic field components, revealing differences between their irregularity (complexity). The values of fractal dimension seem to be sensitive to the physical conditions connected with the interplanetary shock, the coronal mass ejection, the corotating interaction region, and the high-speed stream passage during the storm development. Especially, just after interplanetary shock occurrence, a decrease in the fractal dimension for all stations is observed, not straightforwardly visible in the geomagnetic field components data. Full article

In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters. The main source for these statistical models resides in the Maximum Entropy framework where we have thermal parameters, corresponding to the natural parameters of an exponential family, and mechanical parameters, here called external parameters. In the first part we we study the geometry of these models introducing a fibration of parameter space over external parameters. In the second part we investigate a class of evolution problems driven by a Fokker-Planck equation whose stationary distribution is an exponential family with external parameters. We discuss applications of these statistical models to thermodynamic length and isentropic evolution of thermodynamic systems and to a problem in the dynamic of quantitative traits in genetics. Full article

Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method. Full article

The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system. Full article

Mathai’s pathway model is playing an increasingly prominent role in statistical distributions. As a generalization of a great variety of distributions, the pathway model allows the studying of several non-linear dynamics of complex systems. Here, we construct a model, called the Pareto–Mathai distribution, using the fact that the earthquakes’ magnitudes of full catalogues are well-modeled by a Mathai distribution. The Pareto–Mathai distribution is used to study artificially induced microseisms in the mining industry. The fitting of a distribution for entire range of magnitudes allow us to calculate the completeness magnitude ($M_c$). Mathematical properties of the new distribution are studied. In addition, applying this model to data recorded at a Chilean mine, the magnitude $M_c$ is estimated for several mine sectors and also the entire mine. Full article