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

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

Spectral Evolution of the Unusual Slow Nova V5558 Sgr

We report on the spectral evolution of the enigmatic, very slow nova V5558 Sgr, based on the low-resolution spectra obtained at the Fujii-Bisei Observatory and the Bisei Astronomical Observatory, Japan during a period of 2007 April 6 to 2008 May 3. V5558 Sgr shows a pre-maximum halt and then several flare-like rebrightenings, which is similar to another very slow nova V723 Cas. In our observations, the spectral type of V5558 Sgr evolved from the He/N type toward the Fe II type during the pre-maximum halt, and then toward the He/N type again. This course of spectral transition was observed for the first time in the long history of the nova research. In the rebrightening stage after the initial brightness maximum, we could identify many emission lines accompanied by a stronger absorption component of the P-Cygni profile at the brightness maxima. We found that the velocity of the P-Cygni absorption component measured from the emission peak decreased at the brightness maxima. Furthermore, we compared the spectra of V5558 Sgr with V723 Cas, and other novae which exhibited several rebrightenings during the early phase.Comment: 8 pages, 7figures, accepted for publication in PAS

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

Star-Forming Galaxies at z=0.24 in the Subaru Deep Field and the Sloan Digital Sky Survey

We make a search for Halpha emitting galaxies at z=0.24 in the Subaru Deep Field (SDF) using the archival data set obtained with the Subaru Telescope. We carefully select Halpha emitters in the narrowband filter NB816, using B, V, Rc, i', and z' broad-band colors. We obtain a sample of 258 emitting galaxies with observed equivalent widths of (Halpha+[NII]6548,6584) greater than 12 angstrom. We also analyze a sample of Halpha emitters taken from the Sloan Digital Sky Survey (SDSS) to constrain the luminous end of Halpha luminosity function. Using the same selection criteria as for the SDF, and after excluding AGNs, we obtain 317 Halpha emitting star-forming galaxies. Combining these two samples of Halpha emitters found in both SDF and SDSS, we derive a Halpha luminosity function with best-fit Schechter function parameters of alpha = -1.31^+0.17_-0.17, log phi^* = -2.46^+0.34_-0.40 Mpc^-3, log L^* = 41.99^+0.08_-0.07 ergs s^-1. An extinction-corrected Halpha luminosity density is 4.45^+2.96_-1.75 x 10^39 ergs s^-1 Mpc^-3. Using the Kennicutt relation between the Halpha luminosity and star formation rate, the star formation rate density in the survey volume is estimated as 0.035^+0.024_-0.014 M_sun yr^-1 Mpc^-3. The angular two-point correlation function of Halpha emitters over 875 arcmin^2 at z = 0.24 is well fitted by a power-law form with w(theta) = 0.047^+0.017_-0.013 theta^-0.66 +- 0.08, corresponding to the correlation function of xi(r) = (r/2.6^+1.0_-0.8 Mpc)^(-1.66 +- 0.08). The small correlation length of Halpha emitters may imply the weak clustering of active star-forming galaxies.Comment: 22 pages, 10 figures, PASJ, Vol.60, No.6 in pres

SDSS J080434.20+510349.2: Eclipsing WZ Sge-Type Dwarf Nova with Multiple Rebrightenings

We observed the 2006 superoutburst of SDSS J080434.20+510349.2 during its plateau phase, rebrightening phase, and post-superoutburst final decline. We found that this object is a grazing eclipsing system with a period of 0.0590048(2) d. Well-defined eclipses were only observed during the late stage of the superoutburst plateau and the depth decreased during the subsequent stages. We determined the superhump period during the superoutburst plateau to be 0.059539(11) d, giving a fractional superhump excess of 0.90(2)%. During the rebrightening and post-superoutburst phases, persisting superhumps with periods longer than those of superhumps during the plateau phase: 0.059632(6) during the rebrightening phase and 0.05969(4) d during the final fading. This phenomenon is very well in line with the previously known long-period "late superhumps" in GW Lib, V455 And and WZ Sge. The amplitudes of orbital humps between different states of rebrightenings suggest that these humps do not arise from the classical hot spot, but are more likely a result of projection effect in a high-inclination system. There was no clear evidence for the enhanced hot spot during the rebrightening phase. We also studied previously reported "mini-outbursts" in the quiescent state and found evidence that superhumps were transiently excited during these mini-outbursts. The presence of grazing eclipses and distinct multiple rebrightenings in SDSS J080434.20+510349.2 would provide a unique opportunity to understanding the mechanism of rebrightenings in WZ Sge-type dwarf novae.Comment: 14 pages, 12 figures, PASJ accepte

Discovery of a new dwarf nova, TSS J022216.4+412259.9: WZ Sge-type dwarf novae breaking the shortest superhump period record

We report on the time-resolved CCD photometry of a newly discovered variable star, TSS J022216.4+412259.9 during the outburst in 2005 November-December brightening. The obtained light curves unambiguously showed 0.2-0.3 mag modulations, which we confirmed to be the superhump observed among SU UMa-type dwarf novae. We also performed a period search for the data obtained during the outburst plateau phase, and revealed the existence of the two periodicities: 0.054868(98) days for the first two nights and 0.055544(26) days for the following plateau phase. This bi-periodicity is hardly observed in usual SU UMa-type dwarf novae, but characteristic of WZ Sge-type stars. We undoubtedly detected a rebrightening in the post-outburst stage, which is typical of short-period SU UMa-type dwarf novae including WZ Sge-type stars. These observations suggests that TSS J022216.4+412259.9 may be a new WZ Sge stars breaking the shortest superhump period of 0.05648 days for V592 Her among this class with a known superhump period so far.Comment: 5 pages, 6 figures, accepted for PASJ lette