Permutation Entropy and Bubble Entropy: Possible interactions and synergies between order and sorting relations

[EN] Despite its widely demonstrated usefulness, there is still room for improvement in the basic Permutation Entropy (PE) algorithm, as several subsequent studies have proposed in the recent years. For example, some improved PE variants try to address possible PE weaknesses, such as its only focus on ordinal information, and not on amplitude, or the possible detrimental impact of equal values in subsequences due to motif ambiguity. Other evolved PE methods try to reduce the influence of input parameters. A good representative of this last point is the Bubble Entropy (BE) method. BE is based on sorting relations instead of ordinal patterns, and its promising capabilities have not been extensively assessed yet. The objective of the present study was to comparatively assess the classification performance of this new method, and study and exploit the possible synergies between PE and BE. The claimed superior performance of BE over PE was first evaluated by conducting a series of time series classification tests over a varied and diverse experimental set. The results of this assessment apparently suggested that there is a complementary relationship between PE and BE, instead of a superior/inferior relationship. A second set of experiments using PE and BE simultaneously as the input features of a clustering algorithm, demonstrated that with a proper algorithm configuration, classification accuracy and robustness can benefit from both measures.Cuesta Frau, D.; Vargas-Rojo, B. (2020). Permutation Entropy and Bubble Entropy: Possible interactions and synergies between order and sorting relations. Mathematical Biosciences and Engineering. 17(2):1637-1658. https://doi.org/10.3934/mbe.2020086S163716581721. C. Bandt and B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett., 88 (2002), 174102.2. M. Zanin, L. Zunino, O. A. Rosso and D. 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Measurement of the branching fractions of psi(2S) -> 3(pi+pi-) and J/psi -> 2(pi+pi-)

Using data samples collected at sqrt(s) = 3.686GeV and 3.650GeV by the BESII detector at the BEPC, the branching fraction of psi(2S) -> 3(pi+pi-) is measured to be [4.83 +- 0.38(stat) +- 0.69(syst)] x 10^-4, and the relative branching fraction of J/psi -> 2(pi+pi-) to that of J/psi -> mu+mu- is measured to be [5.86 +- 0.19(stat) +- 0.39(syst)]% via psi(2S) -> (pi+pi-)J/psi, J/psi -> 2(pi+pi-). The electromagnetic form factor of 3(pi+pi-) is determined to be 0.21 +- 0.02 and 0.20 +- 0.01 at sqrt(s) = 3.686GeV and 3.650GeV, respectively.Comment: 17pages, 7 figures, submitted to Phys. Rev.

Measurement of the chi_{c2} Polarization in psi(2S) to gamma chi_{c2}

The polarization of the chi_{c2} produced in psi(2S) decays into gamma chi_{c2} is measured using a sample of 14*10^6 psi(2S) events collected by BESII at the BEPC. A fit to the chi_{c2} production and decay angular distributions in psi(2S) to gamma chi_{c2}, chi_{c2} to pi pi and KK yields values x=A_1/A_0=2.08+/-0.44 and y=A_2/A_0=3.03 +/-0.66, with a correlation rho=0.92 between them, where A_{0,1,2} are the chi_{c2} helicity amplitudes. The measurement agrees with a pure E1 transition, and M2 and E3 contributions do not differ significantly from zero.Comment: 6 pages, 4 figures, 1 tabl

A Unified Approach to the Classical Statistical Analysis of Small Signals

We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battle-ground between classical and Bayesian statistics: Poisson processes with background, and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.Comment: 40 pages, 15 figures. Changes 15-Dec-99 to agree more closely with published version. A few small changes, plus the two substantive changes we made in proof back in 1998: 1) The definition of "sensitivity" in Sec. V(C). It was inconsistent with our actual definition in Sec. VI. 2) "Note added in proof" at end of the Conclusio

Observation of p pbar pi^0 and p pbar eta in psi' decays

The processes psi'-->p pbar pi^0 and psi'-->p pbar eta are studied using a sample of 14 million psi' decays collected with the Beijing Spectrometer at the Beijing Electron-Positron Collider. The branching fraction of psi'-->p pbar pi^0 is measured with improved precision as (13.2\pm 1.0\pm 1.5)\times 10^{-5}, and psi'-->p pbar eta is observed for the first time with a branching fraction of (5.8\pm 1.1\pm 0.7)\times 10^{-5}, where the first errors are statistical and the second ones are systematic.Comment: 15 pages, 8 figures and 3 table

Experimental study of ψ(2S)\psi(2S) decays to \K^+ K^- \pi^+ \pi^- \pi^0 final states

$K^+K^-\pi^+\pi^-\pi^0$ final states are studied using a sample of $14\times10^6$ $\psi(2S)$ decays collected with the Beijing Spectrometer (BESII) at the Beijing Electron-Position Collider. The branching fractions of $\psi(2S)$ decays to $K^+K^-\pi^+\pi^-\pi^0$, $\omega K^+ K^-$, $\omega f_0(1710)$, $K^{\ast}(892)^0 K^- \pi^+\pi^0+c.c.$, $K^{\ast}(892)^{+} K^- \pi^+\pi^- +c.c.$, $K^{\ast}(892)^{+} K^- \rho^0+c.c.$ and $K^{\ast}(892)^0 K^-\rho^+ + c.c.$ are determined. The first two agree with previous measurements, and the last five are first measurements.Comment: 19 pages, 9 figure

First observation of ψ(2S)→pnˉπ−+c.c.\psi(2S) \to p \bar{n} \pi^- +c.c.

Using 14 million $\psi(2S)$ events collected with the Beijing Spectrometer (BESII) at the Beijing Electron-Positron Collider, the branching fractions of $\psi(2S)$ decays to $p \bar{n} \pi^-$ and $\bar{p} n \pi^+$ and the branching fractions of the main background channels $\psi(2S) \to p \bar{n} \pi^-\pi^0$, $\psi(2S) \to \gamma\chi_{c0} \to \gamma p \bar{n} \pi^-$, $\psi(2S) \to \gamma\chi_{c2} \to \gamma p \bar{n} \pi^-$, and $\psi(2S) \to \gamma \chi_{cJ} \to \gamma p \bar{n} \pi^- \pi^0$ are determined. The contributions of the $N^{\ast}$ resonances in $\psi(2S) \to p \bar{n} \pi^- +c.c.$ are also discussed.Comment: 19 pages, 8 figures, add vertex requirement systematic erro

Measurements of J/psi decays into phi pi^0, phi eta, and phi eta^prime

Based on 5.8x10^7 J/psi events detected in BESII, the branching fractions of J/psi--> phi eta and phi eta^prime are measured for different eta and eta^prime decay modes. The results are significantly higher than previous measurements. An upper limit on B(J/psi--> phi pi^0) is also obtained.Comment: 9 pages, 10 figure

Measurements of the continuum RudsR_{\rm uds} and RR values in e+e−e^+e^- annihilation in the energy region between 3.650 and 3.872 GeV

We report measurents of the continuum $R_{\rm uds}$ near the center-of-mass energy of 3.70 GeV, the $R_{{\rm uds(c)}+\psi(3770)}(s)$ and the $R_{\rm had}(s)$ values in $e^+e^-$ annihilation at 68 energy points in the energy region between 3.650 and 3.872 GeV with the BES-II detector at the BEPC Collodier. We obtain the $R_{\rm uds}$ for the continuum light hadron (containing u, d and s quarks) production near the $D\bar D$ threshold to be $R_{\rm uds}=2.141 \pm 0.025 \pm 0.085$.Comment: 5 pages, 3 figure