Reimercalhoun2890

In this work, we introduce a method for estimating the entropy rate and the entropy production rate from a finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of estimating parameters of a distribution with a censored or truncated sample. We use this point of view to give estimations of the entropy rate and the entropy production rate, assuming that they are parameters of a (limit) distribution. The last statement is actually a consequence of the fact that the distribution of estimations obtained from recurrence-time statistics satisfies the central limit theorem. We test our method using a time series coming from Markov chain models, discrete-time chaotic maps, and a real DNA sequence from the human genome.In this paper, we introduce a novel type of chimera state, characterized by the geometrical distortion of the coherent ring topology of coupled oscillators. The multi-headed loop chimeras are examined for a simple network of locally coupled pendulum clocks, suspended on the vertical platform. We determine the regions of the occurrence of the observed patterns, their structure, and possible co-existence. The representative examples of behaviors are shown, exhibiting the variety of configurations that can be observed. The statistical analysis of the solutions indicates the geometrical regions of the system with the highest probability of the chimeras' occurrence. We investigate the mechanism of the creation of the observed states, showing that the manipulation of the initial positions of chosen pendula may induce the desired patterns. Apart from the study of the isolated network, we also discuss the scenario of the movable platform, showing a possible influence of the global coupling structure on the stability of the observed states. The stability of loop chimeras is examined for varying both the amplitude and the frequency of the oscillations of the platform. We indicate the excitation parameters for which the solutions can survive as well as be destroyed. The bifurcation analysis included in the paper allows us to discuss the transitions between possible behaviors. The appearance of multi-headed loop chimeras is generalized into large networks of oscillators, showing the universal character of the observed patterns. One should expect to observe similar results also in other types of coupled oscillators, especially the mechanical ones.Texture classification is widely used in image analysis and some other related fields. In this paper, we designed a texture classification algorithm, named by TCIVG (Texture Classification based on Image Visibility Graph), based on a newly proposed image visibility graph network constructing method by Lacasa et al. By using TCIVG on a Brodatz texture image database, the whole procedure is illustrated. First, each texture image in the image database was transformed to an associated image natural visibility graph network and an image horizontal visibility graph network. Then, the degree distribution measure [P(k)] was extracted as a key characteristic parameter to different classifiers. Numerical experiments show that for artificial texture images, a 100% classification accuracy can be obtained by means of a quadratic discriminant based on natural TCIVG. For natural texture images, 94.80% classification accuracy can be obtained by a linear SVM (Support Vector Machine) based on horizontal TCIVG. Our results are better than that reported in some existing literature studies based on the same image database.In this paper, a four-dimensional conservative system of Euler equations producing the periodic orbit is constructed and studied. The reason that a conservative system often produces periodic orbit has rarely been studied. By analyzing the Hamiltonian and Casimir functions, three invariants of the conservative system are found. The complete integrability is proved to be the mechanism that the system generates the periodic orbits. The mechanism route from periodic orbit to conservative chaos is found by breaking the conservation of Casimir energy and the integrability through which a chaotic Hamiltonian system is built. The observed chaos is not excited by saddle or center equilibria, so the system has hidden dynamics. It is found that the upgrade in the Hamiltonian energy level violates the order of dynamical behavior and transitions from a low or regular state to a high or an irregular state. From the energy bifurcation associated with different energy levels, rich coexisting orbits are discovered, i.e., the coexistence of chaotic orbits, quasi-periodic orbits, and chaotic quasi-periodic orbits. The coincidence between the two-dimensional diagram of maximum Lyapunov exponents and the bifurcation diagram of Hamiltonian energy is observed. Finally, field programmable gate array implementation, a challenging task for the chaotic Hamiltonian conservative system, is designed to be a Hamiltonian pseudo-random number generator.Extensive clinical and experimental evidence links sleep-wake regulation and state of vigilance (SOV) to neurological disorders including schizophrenia and epilepsy. To understand the bidirectional coupling between disease severity and sleep disturbances, we need to investigate the underlying neurophysiological interactions of the sleep-wake regulatory system (SWRS) in normal and pathological brains. We utilized unscented Kalman filter based data assimilation (DA) and physiologically based mathematical models of a sleep-wake regulatory network synchronized with experimental measurements to reconstruct and predict the state of SWRS in chronically implanted animals. Critical to applying this technique to real biological systems is the need to estimate the underlying model parameters. FIIN-2 molecular weight We have developed an estimation method capable of simultaneously fitting and tracking multiple model parameters to optimize the reconstructed system state. We add to this fixed-lag smoothing to improve reconstruction of random input to the system and those that have a delayed effect on the observed dynamics. To demonstrate application of our DA framework, we have experimentally recorded brain activity from freely behaving rodents and classified discrete SOV continuously for many-day long recordings. These discretized observations were then used as the "noisy observables" in the implemented framework to estimate time-dependent model parameters and then to forecast future state and state transitions from out-of-sample recordings.