Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

The effect of age at the first mating and herd size on the lifetime productivity of sows

The effect of age at the first mating and herd size were evaluated in the reference Spanish Databank (BDporc) of 37 698 sows born between 1991 and 1995 and with individual lifetime records. The data included dates of births at entrance and culling, first mating, repetitive mating and conception, first farrowing and weaning records. Individual records were validated before the analysis by screening them through a tolerance “filter” in order to eliminate the extreme values from the analysis. The total database of the sows was classified in 7 classes according to age at the first mating (< 210, 210–220, 221–230, 231–240, 241–250, 251–270, and > 270 days) and in 6 classes of herd size (< 200, 200–300, 301–400, 401–600, 601–800, and > 800 sows). The total number of litters and number of weaned piglets obtained from each sow during the lifetime production were significantly (P < 0.05) greater for gilts between 221 and 240 d of age at the first mating. There was a significant (P < 0.001) effect of the herd size on the reproductive performance of the sow, and the best performance was obtained with herds with 401 to 600 sows compared to < 200 or > 800 sow-herds. Furthermore, a significant (P < 0.001) interaction between age at the first mating and herd size was detected and can be associated with a particular pattern for the herd size class 401–600 sows with the best performances obtained for the sows first mated at less than 200 days. For the other herd sizes, the results indicated that sows mated for the first time at the right age, 221–240 days, are more productive, both in the number and size of the parities throughout lifetime production.

Redistributive taxation, public expenditure, and size of governent

We introduce a model of redistributive income taxation and public expenditure. This joint treatment permits analyzing the interdependencies between the two policies: one cannot be chosen independently of the other. Empirical evidence reveals that partisan confrontation essentially falls on expenditure policies rather than on income taxation. We examine the case in which the expenditure policy (or the size of government) is chosen by majority voting and income taxation is consistently adjusted. This adjustment consists of designing the income tax schedule that, given the expenditure policy, achieves consensus among the population. The model determines the consensus in- come tax schedule, the composition of public expenditure and the size of government. The main results are that inequality is negatively related to the size of government and to the pro-rich bias in public expenditure, and positively or negatively related to the marginal income tax, depending on substitutability between government supplied and market goods. These implications are validated using OECD data.

Universality of rain event size distributions

We compare rain event size distributions derived from measurements in climatically different regions, which we find to be well approximated by power laws of similar exponents over broad ranges. Differences can be seen in the large-scale cutoffs of the distributions. Event duration distributions suggest that the scale-free aspects are related to the absence of characteristic scales in the meteorological mesoscale.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Sequential partitioning: an alternative to understanding size distributions of avalanches in first-order phase transitions

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.

Density matrices and momentum distributions in 3He-4He mixtures

We report variational calculations, in the hypernetted-chain (HNC)-Fermi-HNC scheme, of one-body density matrices and one-particle momentum distributions for 3He-4He mixtures described by a Jastrow correlated wave function. The 4He condensate fractions and the 3He strength poles are examined and compared with the Monte Carlo available results. The agreement has been found to be very satisfactory. Their density dependence is also studied.

Reconfigurable beams with arbitrary polarization and shape distributions at a given plane

Methods for generating beams with arbitrary polarization based on the use of liquid crystal displays have recently attracted interest from a wide range of sources. In this paper we present a technique for generating beams with arbitrary polarization and shape distributions at a given plane using a Mach-Zehnder setup. The transverse components of the incident beam are processed independently by means of spatial light modulators placed in each path of the interferometer. The modulators display computer generated holograms designed to dynamically encode any amplitude value and polarization state for each point of the wavefront in a given plane. The steps required to design such beams are described in detail. Several beams performing different polarization and intensity landscapes have been experimentally implemented. The results obtained demonstrate the capability of the proposed technique to tailor the amplitude and polarization of the beam simultaneously.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Disturbance, age and size structure in stands of Pinus uncinata Ram

Las estructuras de tamaño y edad de dos bosques monoespecificos subalpinos de Pinus uncinata en el Pirineo, fueron estudiadas e interpretadas introduciendo una clasificación sencilla de los árboles según la exposición de su copa a la radiación solar directa. Ambas poblaciones muestran distribuciones de diámetro de J invertida irregulares, cuya Interpretación es incierta. Por el contrario, la estructura de edad en ambos bosques muestra picos visibles, los cuales, si se tienen en cuenta la exposición de la copa, indican que la regeneración se produce en claros del bosque. Se analizaron las series de anillos de crecimiento de los árboles de cada sitio para reconstruir su historia reciente de perturbaciones Identificando los incrementos bruscos del crecimiento. El régimen de perturbaciones en los dos bosques es diferente, y en ambos casos muestra un efecto madelador análogo sobre la estructura de edad. Se concluye que P. uncinata se comporta como una especie heliófila que puede formar bosques maduros o multicohorte bajo determinados regímenes de perturbaciones suaves, gracias a su capacidad para iniciar la regeneración en claros pequeños. Este proceso tiene lugar en un lapso de tiempo corto después de la incidencia de las perturbaciones.

Randomization tests for ABAB designs: Comparing-data-division-specific and common distributions

Monte Carlo simulations were used to generate data for ABAB designs of different lengths. The points of change in phase are randomly determined before gathering behaviour measurements, which allows the use of a randomization test as an analytic technique. Data simulation and analysis can be based either on data-division-specific or on common distributions. Following one method or another affects the results obtained after the randomization test has been applied. Therefore, the goal of the study was to examine these effects in more detail. The discrepancies in these approaches are obvious when data with zero treatment effect are considered and such approaches have implications for statistical power studies. Data-division-specific distributions provide more detailed information about the performance of the statistical technique.

Comparative effects of macro-sized aluminum oxide and aluminum oxide nanoparticles on erythrocyte hemolysis: influence of cell source, temperature and size

Al2O3 is the most abundantly produced nanomaterial and has been used in diverse fields, including the medical, military and industrial sectors. As there are concerns about the health effects of nanoparticles, it is important to understand how they interact with cells, and specifically with red blood cells. The hemolysis induced by three commercial nano-sized aluminum oxide particles (nanopowder 13 nm, nanopowder <50 nm and nanowire 2-6 nm × 200-400 nm) was compared to aluminum oxide and has been studied on erythrocytes from humans, rats and rabbits, in order to elucidate the mechanism of action and the influence of size and shape on hemolytic behavior. The concentrations inducing 50% hemolysis (HC50) were calculated for each compound studied. The most hemolytic aluminum oxide particles were of nanopowder 13, followed by nanowire and nanopowder 50. The addition of albumin to PBS induced a protective effect on hemolysis in all the nano-forms of Al2O3, but not on Al2O3. The drop in HC50 correlated to a decrease in nanomaterial size, which was induced by a reduction of aggregation Aluminum oxide nanoparticles are less hemolytic than other oxide nanoparticles, and behave differently depending on the size and shape of the nanoparticles. The hemolytic behavior of aluminum oxide nanoparticles differs from that of aluminum oxide.

Comparative effects of macro-sized aluminum oxide and aluminum oxide nanoparticles on erythrocyte hemolysis: influence of cell source, temperature and size

Al2O3 is the most abundantly produced nanomaterial and has been used in diverse fields, including the medical, military and industrial sectors. As there are concerns about the health effects of nanoparticles, it is important to understand how they interact with cells, and specifically with red blood cells. The hemolysis induced by three commercial nano-sized aluminum oxide particles (nanopowder 13 nm, nanopowder <50 nm and nanowire 2-6 nm × 200-400 nm) was compared to aluminum oxide and has been studied on erythrocytes from humans, rats and rabbits, in order to elucidate the mechanism of action and the influence of size and shape on hemolytic behavior. The concentrations inducing 50% hemolysis (HC50) were calculated for each compound studied. The most hemolytic aluminum oxide particles were of nanopowder 13, followed by nanowire and nanopowder 50. The addition of albumin to PBS induced a protective effect on hemolysis in all the nano-forms of Al2O3, but not on Al2O3. The drop in HC50 correlated to a decrease in nanomaterial size, which was induced by a reduction of aggregation Aluminum oxide nanoparticles are less hemolytic than other oxide nanoparticles, and behave differently depending on the size and shape of the nanoparticles. The hemolytic behavior of aluminum oxide nanoparticles differs from that of aluminum oxide.