Symbolic transfer entropy rate is equal to transfer entropy rate for bivariate finite-alphabet stationary ergodic Markov processes

Transfer entropy is a measure of the magnitude and the direction of information flow between jointly distributed stochastic processes. In recent years, its permutation analogues are considered in the literature to estimate the transfer entropy by counting the number of occurrences of orderings of values, not the values themselves. It has been suggested that the method of permutation is easy to implement, computationally low cost and robust to noise when applying to real world time series data. In this paper, we initiate a theoretical treatment of the corresponding rates. In particular, we consider the transfer entropy rate and its permutation analogue, the symbolic transfer entropy rate, and show that they are equal for any bivariate finite-alphabet stationary ergodic Markov process. This result is an illustration of the duality method introduced in [T. Haruna and K. Nakajima, Physica D 240, 1370 (2011)]. We also discuss the relationship among the transfer entropy rate, the time-delayed mutual information rate and their permutation analogues.Comment: 18 page

Symbolic local information transfer

Recently, the permutation-information theoretic approach has been used in a broad range of research fields. In particular, in the study of highdimensional dynamical systems, it has been shown that this approach can be effective in characterizing global properties, including the complexity of their spatiotemporal dynamics. Here, we show that this approach can also be applied to reveal local spatiotemporal profiles of distributed computations existing at each spatiotemporal point in the system. J. T. Lizier et al. have recently introduced the concept of local information dynamics, which consists of information storage, transfer, and modification. This concept has been intensively studied with regard to cellular automata, and has provided quantitative evidence of several characteristic behaviors observed in the system. In this paper, by focusing on the local information transfer, we demonstrate that the application of the permutation-information theoretic approach, which introduces natural symbolization methods, makes the concept easily extendible to systems that have continuous states. We propose measures called symbolic local transfer entropies, and apply these measures to two test models, the coupled map lattice (CML) system and the Bak-Sneppen model (BS-model), to show their relevance to spatiotemporal systems that have continuous states.Comment: 20 pages, 7 figure

Symbolic local information transfer

Recently, the permutation-information theoretic approach has been used in a broad range of research fields. In particular, in the study of high-dimensional dynamical systems, it has been shown that this approach can be effective in characterizing global properties, including the complexity of their spatiotemporal dynamics. Here, we show that this approach can also be applied to reveal local spatiotemporal profiles of distributed computations existing at each spatiotemporal point in the system. J. T. Lizier et al. have recently introduced the concept of local information dynamics, which consists of information storage, transfer, and modification. This concept has been intensively studied with regard to cellular automata, and has provided quantitative evidence of several characteristic behaviors observed in the system. In this paper, by focusing on the local information transfer, we demonstrate that the application of the permutation-information theoretic approach, which introduces natural symbolization methods, makes the concept easily extendible to systems that have continuous states. We propose measures called symbolic local transfer entropies, and apply these measures to two test models, the coupled map lattice (CML) system and the Bak-Sneppen model (BS-model), to show their relevance to spatiotemporal systems that have continuous states. In the CML, we demonstrate that it can be successfully used as a spatiotemporal filter to stress a coherent structure buried in the system. In particular, we show that the approach can clearly stress out defect turbulences or Brownian motion of defects from the background, which gives quantitative evidence suggesting that these moving patterns are the information transfer substrate in the spatiotemporal system. We then show that these measures reveal qualitatively different properties from the conventional approach using the sliding window method, and are also robust against external noise. In the BS-model, we demonstrate that these measures can provide novel insight to the model, featuring how symbolic local information transfer is related to the dynamical properties of the elements involved in a spatiotemporal dynamic

Permutation Complexity and Coupling Measures in Hidden Markov Models

In [Haruna, T. and Nakajima, K., 2011. Physica D 240, 1370-1377], the authors introduced the duality between values (words) and orderings (permutations) as a basis to discuss the relationship between information theoretic measures for finite-alphabet stationary stochastic processes and their permutation analogues. It has been used to give a simple proof of the equality between the entropy rate and the permutation entropy rate for any finite-alphabet stationary stochastic process and show some results on the excess entropy and the transfer entropy for finite-alphabet stationary ergodic Markov processes. In this paper, we extend our previous results to hidden Markov models and show the equalities between various information theoretic complexity and coupling measures and their permutation analogues. In particular, we show the following two results within the realm of hidden Markov models with ergodic internal processes: the two permutation analogues of the transfer entropy, the symbolic transfer entropy and the transfer entropy on rank vectors, are both equivalent to the transfer entropy if they are considered as the rates, and the directed information theory can be captured by the permutation entropy approach.Comment: 26 page

Permutation Complexity via Duality between Values and Orderings

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and the entropy rate for a finite-state stationary stochastic processes first proved in [Amigo, J.M., Kennel, M. B., Kocarev, L., 2005. Physica D 210, 77-95]. Third, we show that further information on the relationship between the structure of values and the structure of orderings for finite-state stationary stochastic processes beyond the entropy rate can be obtained from the established duality. In particular, we prove that the permutation excess entropy is equal to the excess entropy, which is a measure of global correlation present in a stationary stochastic process, for finite-state stationary ergodic Markov processes.Comment: 26 page

Oral pathobiont induces systemic inflammation and metabolic changes associated with alteration of gut microbiota.

Periodontitis has been implicated as a risk factor for metabolic disorders such as type 2 diabetes, atherosclerotic vascular diseases, and non-alcoholic fatty liver disease. Although bacteremias from dental plaque and/or elevated circulating inflammatory cytokines emanating from the inflamed gingiva are suspected mechanisms linking periodontitis and these diseases, direct evidence is lacking. We hypothesize that disturbances of the gut microbiota by swallowed bacteria induce a metabolic endotoxemia leading metabolic disorders. To investigate this hypothesis, changes in the gut microbiota, insulin and glucose intolerance, and levels of tissue inflammation were analysed in mice after oral administration of Porphyromonas gingivalis, a representative periodontopathogens. Pyrosequencing revealed that the population belonging to Bacteroidales was significantly elevated in P. gingivalis-administered mice which coincided with increases in insulin resistance and systemic inflammation. In P. gingivalis-administered mice blood endotoxin levels tended to be higher, whereas gene expression of tight junction proteins in the ileum was significantly decreased. These results provide a new paradigm for the interrelationship between periodontitis and systemic diseases

Trion confinement in monolayer MoSe2 by carbon nanotube local gating

We have successfully confined trions into a one-dimensional restricted space of a MoSe2 device with CNT gate electrodes. The dry transfer process, including deterministic dry transfer of aligned CNTs, has led to an hBN-encapsulated MoSe2 device with CNT back gate electrodes. In contrast to a location without CNT gate electrodes, applying voltage via CNT gate electrodes significantly alters PL spectra at a location with CNT gate electrodes. PL imaging has revealed that image contrast from trions is linear along the CNT electrode underneath, consistent with 1D confinement of trions in response to the CNT local gating. The confinement width obtained from the PL image is 5.5 x 10^2 nm, consistent with nanoscale 1D confined trions with the diffraction limit broadening. This work has demonstrated electrical control of excitonic states at the nanoscale, leading to novel optoelectronic properties and exciton devices in the future

Non-uniform distribution of the contraction/extension (C–E) in the left ventricular myocardium related to the myocardial function

AbstractObjectiveWe attempted to disclose the microscopic characteristics of the non-uniform distribution of the contraction and extension (C–E) of the left ventricular (LV) myocardium using a new methodology (echo-dynamography).MethodsThe distributions of the “axial strain rate” (aSR) and the intra-mural velocity in the local areas of the free wall including the posterior wall (PW) and interventricular septum (IVS) were microscopically obtained using echo-dynamography with a high accuracy of 821μm in the spatial resolution. The results were shown by the color M-mode echocardiogram or curvilinear graph. Subjects were 10 presumably normal volunteers.Results(1)Both the C–E in the pulsating LV wall showed non-uniformity spatially and time-sequentially.(2)The C–E property was better evaluated by the aSR distribution method rather than the intra-mural velocity distribution method.(3)Two types of non-uniformity of the aSR distribution were observed: i.e. (i) the difference of its (+)SR (contraction: C) or (−)SR (extension: E) was solely the “magnitude”; (ii) the coexistence of both the (+) SR and (−)SR at the same time.(4)The aSR distribution during systole was either “spotted,” or “multi-layered,” or “toned” distribution, whereas “stratified,” “toned,” or “alternating” distributions were observed during diastole.(5)The aSR distribution in the longitudinal section plane was varied in the individual areas of the wall even during the same timing.(6)To the mechanical function of the LV, there was a different behavior between the IVS and PW.ConclusionsThe aSR and its distribution were the major determinants of the C–E property of the LV myocardium. Spatial as well as time-sequential uniformity of either contraction or extension did not exist. The myocardial function changed depending on the assemblage of the aSR distribution, and by the synergistic effect of (+)SR and (−)SR, the non-uniformity itself potentially served to hold the smooth LV mechanical function

On-site underground background measurements for the KASKA reactor-neutrino experiment

On-site underground background measurements were performed for the planned reactor-neutrino oscillation experiment KASKA at Kashiwazaki-Kariwa nuclear power station in Niigata, Japan. A small-diameter boring hole was excavated down to 70m underground level, and a detector unit for $\gamma$-ray and cosmic-muon measurements was placed at various depths to take data. The data were analyzed to obtain abundance of natural radioactive elements in the surrounding soil and rates of cosmic muons that penetrate the overburden. The results will be reflected in the design of the KASKA experiment.Comment: 9 pages, 7 figures, final version for publication. Table 1 and Fig.5 have change