Bose-Einstein condensation in an optical lattice: A perturbation approach

We derive closed analytical expressions for the order parameter $\Phi (x)$ and for the chemical potential $\mu$ of a Bose-Einstein Condensate loaded into a harmonically confined, one dimensional optical lattice, for sufficiently weak, repulsive or attractive interaction, and not too strong laser intensities. Our results are compared with exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single particle harmonic oscillator wave function

The null energy condition and instability

We extend previous work showing that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. Simple examples are given to illustrate these results. The role of causality in our results is discussed. Finally, we extend the fluid results to more general systems in thermal equilibrium. When applied to the dark energy, our results imply that w is unlikely to be less than -1.Comment: 11 pages, 5 figures, Revte

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.Comment: 55 pages, 53 reference

Metabolic and motor activity effects of microalgae (Chlorella vulgaris) in laboratory mice

In recent years, the microalgae (Chlorella vulgaris) have increasingly attracted great interest as a potential source of pharmacologically active compounds. Showing anticoagulation, antioxidant and antitumor activities of Chlorella revealed its hypotensive properties. The aim of this study was to evaluate the effects of Chlorella suspension on the weight of the animals, their moving activity, and erythropoiesis. The study was performed on males and females of ICR mice. The animals from the experimental group drank only the Chlorella suspension during 3 weeks and were given standard food. Control animals drank during this period only water and had the same food. The body weight of males in the control and the experimental group with Chlorella did not change, while females in the experimental group showed an increase of body weight in a week. A similar pattern was obtained for estimation of animal body weight changes relative to food consumption. The number of red blood cells in females and males from group with Chlorella increased only after 3 weeks after the start of the experiment. Hemoglobin also increased only after 3 weeks after the start of Chlorella consumption, but only for females. All groups of animals had the same motor activity during experiment. Blood sampling resulted in a reduction of activity in control males and females as well as in males with Chlorella. The motor activity of females with Chlorella after blood sampling did not change. So, consumption of the Chlorella suspension by females leads to more effective digestion and resulted in increased body weight, improved erythropoiesis resulted in increased red blood cells and hemoglobin and also increased their resistance to acute stress. The males in the same situation increased only the erythropoiesis

A link between phenotypic robustness and life expectancy in Drosophila melanogaster

Long-lived systems are expected to be stable, i. e. resistant to either external influences, or internal failures. Robustness of biological systems can be defined as a reciprocal value to their phenotypic plasticity expressed through a coefficient of variation (C.V.) for positively distributed phenotypic traits. Considering lifespan as phenotype, which integrates all functions of an organism, we showed that its phenotypic robustness correlates positively with life expectancy. We assessed lifespan parameters for a selection of inbred Drosophila melanogaster strains from Drosophila Genetic Reference Panel (DGRP) reared at 29 ºС. The robustness of lifespan phenotype (C.V.–1) correlated positively with estimated life expectancy for these strains. The same relation also holds for the lifespan of all DGRP strains reared at 25 ºС. Also, in agreement with previous observations, upon temperature change (decrease or increase) the survival curves scaled in time (stretched or shrunk respectively). In other words, the average lifespan decreased for flies reared at elevated temperature, but so did the standard deviation, and thus the coefficients of variation remained in the same range. From this we conclude that coefficients of variation correlate with life expectancies and account for the robustness of lifespan phenotype irrespective of accelerated aging caused by temperature

Numerical Comparison of Cusum and Shiryaev-Roberts Procedures for Detecting Changes in Distributions

The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that occurs at a distant time horizon. As a simpler alternative to the conventional Monte Carlo approach, we propose a numerical method for the systematic comparison of the two detection schemes in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of exact integral equations for the performance metrics, which are then solved numerically. We present detailed numerical results for the problem of detecting a change in the mean of a Gaussian sequence, which show that the difference between the two procedures is significant only when detecting small changes.Comment: 21 pages, 8 figures, to appear in Communications in Statistics - Theory and Method

On integrability of the vector short pulse equation

Using the Painleve analysis preceded by appropriate transformations of nonlinear systems under investigation, we discover two new cases in which the Pietrzyk-Kanattsikov-Bandelow vector short pulse equation must be integrable due to the results of the Painleve test. Those cases are technologically important because they correspond to the propagation of polarized ultra-short light pulses in usual isotropic silica optical fibers.Comment: 10 page

Multi-scale spatio-temporal analysis of human mobility

The recent availability of digital traces generated by phone calls and online logins has significantly increased the scientific understanding of human mobility. Until now, however, limited data resolution and coverage have hindered a coherent description of human displacements across different spatial and temporal scales. Here, we characterise mobility behaviour across several orders of magnitude by analysing ∼850 individuals' digital traces sampled every ∼16 seconds for 25 months with ∼10 meters spatial resolution. We show that the distributions of distances and waiting times between consecutive locations are best described by log-normal and gamma distributions, respectively, and that natural time-scales emerge from the regularity of human mobility. We point out that log-normal distributions also characterise the patterns of discovery of new places, implying that they are not a simple consequence of the routine of modern life