Entropy2015, 17(4), 1814-1849; doi:10.3390/e17041814 (registering DOI) - published 30 March 2015 Show/Hide Abstract
Abstract: Geometry of Fisher metric and geodesics on a space of probability measures defined on a compact manifold is discussed and is applied to geometry of a barycenter map associated with Busemann function on an Hadamard manifold \(X\). We obtain an explicit formula of geodesic and then several theorems on geodesics, one of which asserts that any two probability measures can be joined by a unique geodesic. Using Fisher metric and thus obtained properties of geodesics, a fibre space structure of barycenter map and geodesical properties of each fibre are discussed. Moreover, an isometry problem on an Hadamard manifold \(X\) and its ideal boundary \(\partial X\)—for a given homeomorphism \(\Phi\) of \(\partial X\) find an isometry of \(X\) whose \(\partial X\)-extension coincides with \(\Phi\)—is investigated in terms of the barycenter map.
Entropy2015, 17(4), 1795-1813; doi:10.3390/e17041795 (registering DOI) - published 30 March 2015 Show/Hide Abstract
Abstract: Background: Developing an accurate computer-aided diagnosis (CAD) system of MR brain images is essential for medical interpretation and analysis. In this study, we propose a novel automatic CAD system to distinguish abnormal brains from normal brains in MRI scanning. Methods: The proposed method simplifies the task to a binary classification problem. We used discrete wavelet packet transform (DWPT) to extract wavelet packet coefficients from MR brain images. Next, Shannon entropy (SE) and Tsallis entropy (TE) were harnessed to obtain entropy features from DWPT coefficients. Finally, generalized eigenvalue proximate support vector machine (GEPSVM), and GEPSVM with radial basis function (RBF) kernel, were employed as classifier. We tested the four proposed diagnosis methods (DWPT + SE + GEPSVM, DWPT + TE + GEPSVM, DWPT + SE + GEPSVM + RBF, and DWPT + TE + GEPSVM + RBF) on three benchmark datasets of Dataset-66, Dataset-160, and Dataset-255. Results: The 10 repetition of K-fold stratified cross validation results showed the proposed DWPT + TE + GEPSVM + RBF method excelled not only other three proposed classifiers but also existing state-of-the-art methods in terms of classification accuracy. In addition, the DWPT + TE + GEPSVM + RBF method achieved accuracy of 100%, 100%, and 99.53% on Dataset-66, Dataset-160, and Dataset-255, respectively. For Dataset-255, the offline learning cost 8.4430s and online prediction cost merely 0.1059s. Conclusions: We have proved the effectiveness of the proposed method, which achieved nearly 100% accuracy over three benchmark datasets.
Entropy2015, 17(4), 1775-1794; doi:10.3390/e17041775 (registering DOI) - published 30 March 2015 Show/Hide Abstract
Abstract: In this paper, we apply multidimensional scaling (MDS) and parametric similarity indices (PSI) in the analysis of complex systems (CS). Each CS is viewed as a dynamical system, exhibiting an output time-series to be interpreted as a manifestation of its behavior. We start by adopting a sliding window to sample the original data into several consecutive time periods. Second, we define a given PSI for tracking pieces of data. We then compare the windows for different values of the parameter, and we generate the corresponding MDS maps of ‘points’. Third, we use Procrustes analysis to linearly transform the MDS charts for maximum superposition and to build a globalMDS map of “shapes”. This final plot captures the time evolution of the phenomena and is sensitive to the PSI adopted. The generalized correlation, theMinkowski distance and four entropy-based indices are tested. The proposed approach is applied to the Dow Jones Industrial Average stock market index and the Europe Brent Spot Price FOB time-series.
Entropy2015, 17(4), 1755-1774; doi:10.3390/e17041755 (registering DOI) - published 30 March 2015 Show/Hide Abstract
Abstract: Herein, we present a feasible, general protocol for quantum communication within a network via generalized remote preparation of an arbitrary m-qubit entangled state designed with genuine tripartite Greenberger–Horne–Zeilinger-type entangled resources. During the implementations, we construct novel collective unitary operations; these operations are tasked with performing the necessary phase transfers during remote state preparations. We have distilled our implementation methods into a five-step procedure, which can be used to faithfully recover the desired state during transfer. Compared to previous existing schemes, our methodology features a greatly increased success probability. After the consumption of auxiliary qubits and the performance of collective unitary operations, the probability of successful state transfer is increased four-fold and eight-fold for arbitrary two- and three-qubit entanglements when compared to other methods within the literature, respectively. We conclude this paper with a discussion of the presented scheme for state preparation, including: success probabilities, reducibility and generalizability.
Entropy2015, 17(4), 1734-1754; doi:10.3390/e17041734 - published 27 March 2015 Show/Hide Abstract
Abstract: We propose a new herd mechanism and embed it into an open financial market system, which allows traders to get in and out of the system based on some transition rates. Moreover, the novel mechanism can avoid the volatility disappearance when the population scale increases. There are three kinds of heterogeneous agents in the system: optimistic, pessimistic and fundamental. Interactions especially occur among three different groups of agents instead of two, which makes the artificial financial market more close to the real one. By the simulation results of this complex system, we can explain stylized facts like volatility clustering and find the key parameters of market bubbles and market collapses.
Entropy2015, 17(4), 1701-1733; doi:10.3390/e17041701 - published 27 March 2015 Show/Hide Abstract
Abstract: The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related eventsmysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.