Scale Relativity and Fractal Space-Time: Theory and Applications

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology.     

Informational Branching Universe

This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary for assigning them a probability distribution. The “historical” state of a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed. An age operator computes the informational depth of historical states and its standard deviation can be used to provide a universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence of the subject’s activity of measuring, which defines the flow of time-information.     

The complexity of reconstructing trees from qualitative characters and subtrees

In taxonomy and other branches of classification it is useful to know when tree-like classifications on overlapping sets of labels can be consistently combined into a parent tree. This paper considers the computation complexity of this problem. Recognizing when a consistent parent tree exists is shown to be intractable (NP-complete) for sets of unrooted trees, even when each tree in the set classifies just four labels. Consequently determining the compatibility of qualitative characters and partial binary characters is, in general, also NP-complete. However for sets of rooted trees an algorithm is described which constructs the “strict consensus tree” of all consistent parent trees (when they exist) in polynomial time. The related question of recognizing when a set of subtrees uniquely defines a parent tree is also considered, and a simple necessary and sufficient condition is described for rooted trees. This work was supproted by the Alexander von Humoldt-Stiftung. I wish to thank Andreas Dress, Hans-Jürgen Bandelt and the referees for their helpful comments.     

Concentration level and distribution of polycyclic aromatic hydrocarbons in soil and grass around Mt. Qomolangma, China

High mountains may serve as a condenser for persistent organic pollutants. In the present study, soil and grass samples from Mt. Qomolangma region, China were collected from 4600 to 5620 m a.s.I and were analyzed for polycyclic aromatic hydrocarbons （PAHs） to determine if they are concentrated at colder, more elevated sites and to evaluate their possible resources and fractionation. The total PAHs concentration in soil samples was 〈 600 ng g^-1, the critical value to differentiate PAHs levels in remote and urban regions. This implied the PAHs levels at Mt. Qomolangma are relatively low and what one might expect in such a remote region of the world. These low values may represent a soil background for mid-latitude Northern Hemisphere soils away from the direct influence of an anthropogenic source. As for the distribution pattern, the low molecular weight PAHs were prone to accumulate at higher altitude, while the high molecular weight PAHs inversely related or unrelated with elevation. Based on high concentration of phenanthrene at elevated sample site and the ratios of individual PAHs, we deduced that home-heating combustion and vehicle emission may result in the constitution trait of PAHs in this mountain region. Monsoon traveling over India, Pakistan and other countries with dense population may carry contaminant to Mt. Qomolangma region.     

A model of calcium signaling and degranulation dynamics induced by laser irradiation in mast cells

Recent experiments show that calcium signaling and degranulation dynamics induced by low power laser irradiation in mast cells must rely on extracellular Ca^2＋ influx. An analytical expression of Ca^2＋ flux through TRPV4 cation channel in response to interaction of laser photon energy and extracellular Ca^2＋ is deduced, and a model characterizing dynamics of calcium signaling and degranulation activated by laser irradiation in mast cells is established. The model indicates that the characteristics of calcium signaling and degranulation dynamics are determined by interaction between laser photon energy and Ca^2＋ influx. Extracellular Ca^2＋ concentration is so high that even small photon energy can activate mast cells, thus avoiding the possible injury caused by laser irradiation with shorter wavelengths. The model predicts that there exists a narrow parameter domain of photon energy and extracellular Ca^2＋ concentration of which results in cytosolic Ca^2＋ limit cycle oscillations, and shows that PKC activity is in direct proportion to the frequency of Ca^2＋ oscillations. With the model it is found that sustained and stable maximum plateau of cytosolic Ca^2＋ concentration can get optimal degranulation rate. Furthermore, the idea of introducing the realistic physical energy into model is applicable to modeling other physical signal transduction systems.     

Clustering the rows and columns of a contingency table

A number of ways of investigating heterogeneity in a two-way contingency table are reviewed. In particular, we consider chi-square decompositions of the Pearson chi-square statistic with respect to the nodes of a hierarchical clustering of the rows and/or the columns of the table. A cut-off point which indicates significant clustering may be defined on the binary trees associated with the respective row and column cluster analyses. This approach provides a simple graphical procedure which is useful in interpreting a significant chi-square statistic of a contingency table.The author gratefully acknowledges the constructive comments of the referees and the editor.     

Ultrafast polarization optical switch constructed from one-dimensional photonic crystal and its performance analysis

All-optical switch with the ultrafast optical switching rate is a key device in the next generation optical network. In this article, we propose a polarization switch with ps switching time, which is constructed from one-dimensional resonant photonic crystal （1D RPC）. The model of switch operating at 1.5 μm is established based on the optical stark effect （OSE）. We calculate the performance indices of the switch and the influences of errors of periods and refractive index on the performance characteristics.     

Wolves in sheep’s clothing: three new cases of aggressive mimicry in Red Sea coral reef fishes

ABSTRACT

Here we document three cases of mimicry in coral reef fishes not previously reported in the literature involving two groupers (Epinephelus leucogrammicus and Plectropomus marisrubri) and a soapfish (Diploprion drachi) as mimics, and two wrasses (Larabicus quadrilineatus and Cheilinus quinquecinctus) and a blenny (Meiacanthus nigrolineatus) as models. All three cases are of aggressive mimicry, with a predatory species mimicking a harmless one, and in one of the cases, the mimicry is also Müllerian, where both the predator and harmless species are unpalatable.