Phase Information and the Evolution of Cosmological Density Perturbations

The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical techniques. Using a toy model of one-dimensional perturbations evolving under the Zel'dovich approximation as an initial motivation, we develop a statistic that quantifies the information content of the distribution of phases. Using numerical simulations beginning with more realistic Gaussian random-phase initial conditions, we show that the information content of the phases grows from zero in the initial conditions, first slowly and then rapidly when structures become non-linear. This growth of phase information can be expressed in terms of an effective entropy: Gaussian initial conditions are a maximum entropy realisation of the initial power spectrum, gravitational evolution decreases the phase entropy. We show that our definition of phase entropy results in a statistic that explicitly quantifies the information stored in the phases of density perturbations (rather than their amplitudes) and that this statistic displays interesting scaling behaviour for self-similar initial conditions.Comment: Accepted for publication in MNRAS with added comments on future work. For high-resolution Figure 1, or postscript file, please see http://www-star.qmw.ac.uk/~lyc

Size structure and inequality in a commercial stand of the seaweed gelidium-sesquipedale

The temporal dynamics of the frequency distributions of 2 measures of Gelidium sesquipedale frond size, length and weight, was investigated in a subtidal stand under commercial exploitation. Frond weight/length allometry was highly variable, both seasonally and between years, showing that in this species weight and length cannot be used interchangeably as a measure of frond size. Physical disturbances played a fundamental role in allometric variability. The loss of branches due to commercial harvest and storms reduced the slope of the log weight/log length relationship. During spring the slope increased, indicating the production and growth of lateral branches. Size differences among individuals in the population (inequality) were quantified by 3 statistics: the skewness coefficient (g(1)), the coefficient of variation (CV), and the Gini coefficient (G). Highly significant changes in frond length inequality, but not weight, were shown. These correspond to periods when G. sesquipedale length structure varied due to the combined effects of the demographic parameters that regulate the population (frond recruitment, survival, breakage and growth). Graphical analysis of significantly different length structures revealed that a recruitment peak of vegetatively developed fronds occurred during winter, following periods of high frond mortality and breakage caused by both human (summer harvesting) and natural (late fall storms) disturbances. During late spring and summer, the density of smaller fronds decreased due to mortality and growth into higher size classes. To assess density-dependent regulation processes, such as suppressed growth of smaller fronds and self-thinning, the time variation of both relationships, inequality/mean frond weight and biomass/density, was analysed. Inequality/mean frond weight and biomass/density values decreased from summer to winter and increased to the following summer. The increase of inequality while mean frond weight is increasing is consistent with the asymmetric competition theory on the development of crowded plant stands, and supports the hypothesis that the slower growth of smaller fronds during this period (Santos 1994; Mar. Ecol. Prog. Ser. 107: 295-305) is due to intraspecific competition. The time trajectory of the biomass/density relationship is perpendicular to and lies above the theoretical self-thinning line. Evidence for self-thinning was thus not detected. A conceptual model for the functioning of this population is proposed. Thinning and frond breakage caused by disturbances might be keeping intraspecific competition in these G. sesquipedale crowded stands (up to 18 000 fronds m(-2)) at low levels.info:eu-repo/semantics/publishedVersio

Quantifying distortions of the Lagrangian dark-matter mesh in cosmology

We examine the Lagrangian divergence of the displacement field, arguably a more natural object than the density in a Lagrangian description of cosmological large-scale structure. This quantity, which we denote \psi, quantifies the stretching and distortion of the initially homogeneous lattice of dark-matter particles in the universe. \psi\ encodes similar information as the density, but the correspondence has subtleties. It corresponds better to the log-density A than the overdensity \delta. A Gaussian distribution in \psi\ produces a distribution in A with slight skewness; in \delta, we find that in many cases the skewness is further increased by 3. A local spherical-collapse-based (SC) fit found by Bernardeau gives a formula for \psi's particle-by-particle behavior that works quite well, better than applying Lagrangian perturbation theory (LPT) at first or second (2LPT) order. In 2LPT, there is a roughly parabolic relation between initial and final \psi\ that can give overdensities in deep voids, so low-redshift, high-resolution 2LPT realizations should be used with caution. The SC fit excels at predicting \psi\ until streams cross; then, for particles forming haloes, \psi\ plummets as in a waterfall to -3. This gives a new method for producing N-particle realizations. Compared to LPT realizations, such SC realizations give reduced stream-crossing, and better visual and 1-point-PDF correspondence to the results of full gravity. LPT, on the other hand, predicts large-scale flows and the large-scale power-spectrum amplitude better, unless an empirical correction is added to the SC formula.Comment: Changes in presentation to match MNRAS-accepted version, 14 pages, 15 figure

Proposed terminology for the classification and parameters for the quantification of variability in ionosphere morphology

Much uncertainty currently exists in the use by different workers of the term ‘variability’ in describing the results of statistical analyses applied to ionospheric measurement data sets and in their relationships with various existing or new ionospheric models. Often it is not clear whether data for different time periods or different geographical areas, and if so which, are being used to formulate results. Terms are presented in the Annex which it is suggested should be used, at least once in every publication addressing this topic, to describe unambiguously what is talked about. The background to the proposed terminology is discussed. Options for variability parameters are also addressed

Consistency and interpretation of changes in millimeter-scale cortical intrinsic curvature across three independent datasets in schizophrenia.

Several studies have sought to test the neurodevelopmental hypothesis of schizophrenia through analysis of cortical gyrification. However, to date, results have been inconsistent. A possible reason for this is that gyrification measures at the centimeter scale may be insensitive to subtle morphological changes at smaller scales. The lack of consistency in such studies may impede further interpretation of cortical morphology as an aid to understanding the etiology of schizophrenia. In this study we developed a new approach, examining whether millimeter-scale measures of cortical curvature are sensitive to changes in fundamental geometric properties of the cortical surface in schizophrenia. We determined and compared millimeter-scale and centimeter-scale curvature in three separate case-control studies; specifically two adult groups and one adolescent group. The datasets were of different sizes, with different ages and gender-spreads. The results clearly show that millimeter-scale intrinsic curvature measures were more robust and consistent in identifying reduced gyrification in patients across all three datasets. To further interpret this finding we quantified the ratio of expansion in the upper and lower cortical layers. The results suggest that reduced gyrification in schizophrenia is driven by a reduction in the expansion of upper cortical layers. This may plausibly be related to a reduction in short-range connectivity

Random Walks Estimate Land Value

Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time to a place correlates with assessed value of land in that. The method accounting the average number of random turns at junctions on the way to reach any particular place in the city from various starting points could be used to identify isolated neighborhoods in big cities with a complex web of roads, walkways and public transport systems

Sexual selection and sperm competition in the guppy ( Poecilia reticulata)

When differences among individuals in the ability to acquire mates result in evolutionary change, this is known as sexual selection. My goal was to investigate sexual selection on male traits in the guppy (Poecilia reticulata). I assessed reproductive skew and correlates of male reproductive success in a wild population and found that male reproductive success was strongly skewed and correlated with gonopodium length, but not with the relative area of coloured spots, body length, or sperm velocity. I then determined the role of sperm competition in shaping sperm form and function by comparing sperm traits across populations. I found that males in high predation populations, which presumably experience more intense sperm competition, had significantly faster sperm with longer midpieces than males in low predation populations, which experience less intense sperm competition. These results suggest that gonopodium length is a sexually selected trait and that sperm competition selects for sperm velocity