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Book reviews

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Notices bibliographiques

     

Evidence for charge orbital and spin stripe order in an overdoped manganite

Overdoped La0.42Sr1.58MnO4 exhibits a complex ordering of charges, orbitals, and spins. Neutron diffraction experiments reveal three incommensurate and one commensurate order parameters to be tightly coupled. The position and the shape of the distinct superstructure scattering as well as higher-order signals are inconsistent with a harmonic charge and spin-density-wave picture but point to a stripe arrangement in which ferromagnetic zigzag chains are disrupted by excess Mn(4+).     

Dark matter results from 100 live days of XENON100 data

We present results from the direct search for dark matter with the XENON100 detector, installed underground at the Laboratori Nazionali del Gran Sasso of INFN, Italy. XENON100 is a two-phase time-projection chamber with a 62 kg liquid xenon target. Interaction vertex reconstruction in three dimensions with millimeter precision allows the selection of only the innermost 48 kg as the ultralow background fiducial target. In 100.9 live days of data, acquired between January and June 2010, no evidence for dark matter is found. Three candidate events were observed in the signal region with an expected background of (1.8 ± 0.6) events. This leads to the most stringent limit on dark matter interactions today, excluding spin-independent elastic weakly interacting massive particle (WIMP) nucleon scattering cross sections above 7.0 × 10(-45) cm(2) for a WIMP mass of 50 GeV/c(2) at 90% confidence level.     

Multifractal moving average analysis and test of multifractal model with tuned correlations

We address two common major problems in the study of time series characterizing fluctuations in complex systems: multifractal analysis and multifractal modeling. Specifically, we introduce a multi-fractal centered moving average (MF-CMA) analysis, which is computationally easier but equivalently performing compared with the well-established multi-fractal detrended fluctuation analysis (MF-DFA) with linear detrending. In addition, we study in detail a generalized binomial multi-fractal model (GB-MFM) to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long-term persistence. We use the data generated by this model as well as realistic, by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite-size effects as well as limitations due to spurious multifractality.     

On spurious and corrupted multifractality: The effects of additive noise, short-term memory and periodic trends

We study the performance of multifractal detrended fluctuation analysis (MF-DFA) applied to long-term correlated and multifractal data records in the presence of additive white noise, short-term memory and periodicities. Such additions and disturbances that can be typically found in the observational records of various complex systems ranging from climate dynamics to physiology, network traffic, and finance. In monofractal records, we find that (i) additive white noise hardly results in spurious multifractality, but causes underestimated generalized Hurst exponents h(q) for all q values; (ii) short-range correlations lead to pronounced crossovers in the generalized fluctuation functions F_q(s) at positions that decrease with increasing moment q, thus causing significantly overestimated h(q) for small q and spurious multifractality; (iii) periodicities like seasonal trends (with standard deviations comparable with the one of the studied process) result in spurious “reversed” multifractality where h(q) increases with increasing q (except for very short time windows). We also show that in multifractal cascades moderate additions of noise, short-range memory, or periodic trends cause flawed results for h(q) with q<2, while h(q) with q>2 remains nearly unchanged.     

On Two Squares of Opposition: the Leśniewski’s Style Formalization of Synthetic Propositions

In the paper we build up the ontology of Le?niewski’s type for formalizing synthetic propositions. We claim that for these propositions an unconventional square of opposition holds, where a, i are contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a, e (resp. i, o) are said to stand in the subalternation. Further, we construct a non-Archimedean extension of Boolean algebra and show that in this algebra just two squares of opposition are formalized: conventional and the square that we invented. As a result, we can claim that there are only two basic squares of opposition. All basic constructions of the paper (the new square of opposition, the formalization of synthetic propositions within ontology of Le?niewski’s type, the non-Archimedean explanation of square of opposition) are introduced for the first time.