Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma

The in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound states at finite temperature through a Schrödinger equation with an instantaneous potential. Here we review recent progress in devising a comprehensive approach to define such a potential from first principles QCD and extract its, in general complex, values from non-perturbative lattice QCD simulations. Based on the theory of open quantum systems we will show how to interpret the role of the imaginary part in terms of spatial decoherence by introducing the concept of a stochastic potential. Shortcomings as well as possible paths for improvement are discussed.

Acute effects of stochastic resonance whole body vibration

AIM: To investigate the acute effects of stochastic resonance whole body vibration (SR-WBV) training to identify possible explanations for preventive effects against musculoskeletal disorders. METHODS: Twenty-three healthy, female students participated in this quasi-experimental pilot study. Acute physiological and psychological effects of SR-WBV training were examined using electromyography of descending trapezius (TD) muscle, heart rate variability (HRV), different skin parameters (temperature, redness and blood flow) and self-report questionnaires. All subjects conducted a sham SR-WBV training at a low intensity (2 Hz with noise level 0) and a verum SR-WBV training at a higher intensity (6 Hz with noise level 4). They were tested before, during and after the training. Conclusions were drawn on the basis of analysis of variance. RESULTS: Twenty-three healthy, female students participated in this study (age = 22.4 ± 2.1 years; body mass index = 21.6 ± 2.2 kg/m2). Muscular activity of the TD and energy expenditure rose during verum SR-WBV compared to baseline and sham SR-WBV (all P < 0.05). Muscular relaxation after verum SR-WBV was higher than at baseline and after sham SR-WBV (all P < 0.05). During verum SR-WBV the levels of HRV were similar to those observed during sham SR-WBV. The same applies for most of the skin characteristics, while microcirculation of the skin of the middle back was higher during verum compared to sham SR-WBV (P < 0.001). Skin redness showed significant changes over the three measurement points only in the middle back area (P = 0.022). There was a significant rise from baseline to verum SR-WBV (0.86 ± 0.25 perfusion units; P = 0.008). The self-reported chronic pain grade indicators of pain, stiffness, well-being, and muscle relaxation showed a mixed pattern across conditions. Muscle and joint stiffness (P = 0.018) and muscular relaxation did significantly change from baseline to different conditions of SR-WBV (P < 0.001). Moreover, muscle relaxation after verum SR-WBV was higher than after sham SR-WBV (P < 0.05). CONCLUSION: Verum SR-WBV stimulated musculoskeletal activity in young healthy individuals while cardiovascular activation was low. Training of musculoskeletal capacity and immediate increase in musculoskeletal relaxation are potential mediators of pain reduction in preventive trials.

Mounting behaviour in finishing pigs: Stable individual differences are not due to dominance or stage of sexual development

Every year around 100 million male piglets are castrated in the EU, usually without anaesthesia or post-operative analgesia. This surgical intervention is painful and stressful. Several main players within the pig industry have voluntarily agreed to end the practice of surgical pig castration in the EU by 2018. One alternative to castration is entire male pig production. However, entire males behave differently than castrates, for example, by performing more mounting behaviour, which is suggested to be a welfare problem. The aim of our study was to develop a comprehensive ethogram of different types of mounting and to investigate properties, causes and consequences of mounting behaviour in finishing pigs. The study included 80 entire male and 80 female pigs from two farrowing batches born six weeks apart. Mixed sex and single-sex housing of pigs are both common in pig farming, so to ensure our study was representative, the 160 pigs were assigned to social groups of 20 in three treatments: entire male pigs only (MM, 2 groups, n = 40), entire females only (FF, 2 groups, n = 40) and entire males and females mixed together (MF, 4 groups, n = 80). Measurements took place during the final six weeks before slaughter (between 63.5 and 105.5 kg). Observations of mounting behaviour on 12 days per batch suggested that: (i) males mounted more than females, (ii) within sex, there was no effect of treatment on the amount of mounting (although the statistical power of the study to detect these effects was low), and (iii) there were individual differences in mounting that were stable over time (within sex). Classification of mounting into different categories revealed that sexual mounting was most common overall and in males but only rare in females. Compared to other types of mounting (e.g. caused by crowding or during a fight), sexual mounts lasted longer and provoked more screaming by the recipient. There were no relationships between mounting behaviour on the one hand and dominance rank in food competition tests, the circulating levels of sex hormones (oestradiol, testosterone and progesterone) at the end of the study, the health scores (lameness and scratches) or weight gain on the other hand. The stable individual differences of mounting over time suggest that mounting behaviour is a trait of the individual rather than the appearance of random outbreaks. However, these differences in mounting cannot be explained by dominance behaviour or by differences in sex hormone concentrations that could indicate the onset of puberty. Mounting behaviour and in particular sexual mounting provoked high pitched screaming of the recipients indicating that mounting is a welfare problem. For the welfare assessment of entire male pig production the performance of mounting behaviour should be considered. (C) 2013 Elsevier B.V. All rights reserved.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Dominance of the proximal coordinate frame in determining the locations of hippocampal place cell activity during navigation.

The place-specific activity of hippocampal cells provides downstream structures with information regarding an animal's position within an environment and, perhaps, the location of goals within that environment. In rodents, recent research has suggested that distal cues primarily set the orientation of the spatial representation, whereas the boundaries of the behavioral apparatus determine the locations of place activity. The current study was designed to address possible biases in some previous research that may have minimized the likelihood of observing place activity bound to distal cues. Hippocampal single-unit activity was recorded from six freely moving rats as they were trained to perform a tone-initiated place-preference task on an open-field platform. To investigate whether place activity was bound to the room- or platform-based coordinate frame (or both), the platform was translated within the room at an "early" and at a "late" phase of task acquisition (Shift 1 and Shift 2). At both time points, CA1 and CA3 place cells demonstrated room-associated and/or platform-associated activity, or remapped in response to the platform shift. Shift 1 revealed place activity that reflected an interaction between a dominant platform-based (proximal) coordinate frame and a weaker room-based (distal) frame because many CA1 and CA3 place fields shifted to a location intermediate to the two reference frames. Shift 2 resulted in place activity that became more strongly bound to either the platform- or room-based coordinate frame, suggesting the emergence of two independent spatial frames of reference (with many more cells participating in platform-based than in room-based representations).

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.

EVOLUTION OF DOMINANCE UNDER FREQUENCY-DEPENDENT INTRASPECIFIC COMPETITION IN AN ASSORTATIVELY MATING POPULATION

We study the evolution of higher levels of dominance as a response to negative frequency-dependent selection. In contrast to previous studies, we focus on the effect of assortative mating on the evolution of dominance under frequency-dependent intraspecific competition. We analyze a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under a mixture of frequency-independent stabilizing selection, density-dependent selection, and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The second (modifier) locus determines the degree of dominance at the trait level. Additionally, the population mates assortatively with respect to similarities in the ecological trait. Our analysis shows that the parameter region in which dominance can be established decreases if small levels of assortment are introduced. In addition, the degree of dominance that can be established also decreases. In contrast, if assortment is intermediate, sexual selection for extreme types can be established, which leads to evolution of higher levels of dominance than under random mating. For modifiers with large effects, intermediate levels of assortative mating are most favorable for the evolution of dominance. For large modifiers, the speed of fixation can even be higher for intermediate levels of assortative mating than for random mating.

Dominance and the maintenance of polymorphism in multiallelic migration-selection models with two demes

The maintenance of genetic variation in a spatially heterogeneous environment has been one of the main research themes in theoretical population genetics. Despite considerable progress in understanding the consequences of spatially structured environments on genetic variation, many problems remain unsolved. One of them concerns the relationship between the number of demes, the degree of dominance, and the maximum number of alleles that can be maintained by selection in a subdivided population. In this work, we study the potential of maintaining genetic variation in a two-deme model with deme-independent degree of intermediate dominance, which includes absence of G x E interaction as a special case. We present a thorough numerical analysis of a two-deme three-allele model, which allows us to identify dominance and selection patterns that harbor the potential for stable triallelic equilibria. The information gained by this approach is then used to construct an example in which existence and asymptotic stability of a fully polymorphic equilibrium can be proved analytically. Noteworthy, in this example the parameter range in which three alleles can coexist is maximized for intermediate migration rates. Our results can be interpreted in a specialist-generalist context and (among others) show when two specialists can coexist with a generalist in two demes if the degree of dominance is deme independent and intermediate. The dominance relation between the generalist allele and the specialist alleles play a decisive role. We also discuss linear selection on a quantitative trait and show that G x E interaction is not necessary for the maintenance of more than two alleles in two demes.

Male Dominance in the New Zealand Longfin Eel Population of a New Zealand River: Probable Causes and Implications for Management

The endemic New Zealand longfin eel Anguilla dieffenbachi (hereafter, longfin eel), is overfished, and in southern South Island, New Zealand, rivers have recently become predominated by males. This study examined length and age at sexual differentiation in male eels in the Aparima River catchment (area, 1,375 km(2); mean flow, 20 m(3.)s(-1)) and the sex ratio and distribution of eels throughout the catchment. Longfin eels differentiated into males mostly at lengths from 300 to 460 mm and ages from 10 to 25+ years. Females were rare: Of 738 eels examined for sexual differentiation, 466 were males and 5 were females, and a few others, not examined, were large enough to be female. These counts suggest a male : female ratio among differentiated longfin eels of 68:1. Of 31 differentiated shortfin eels A. australis, less common in the Aparima River, 26 were females. Male longfin eels were distributed throughout the main stern and tributaries; undifferentiated eels were more prevalent in lower and middle reaches and in the main stem than in upper reaches and tributaries. In other studies, male longfin eels predominated commercial catches in the Aparima and four other southernmost rivers, by 2.4:1 to 13.6:1 males to females. The Aparima River had the most skewed sex ratio. Longfin eel catches from the Aparima River will become more male predominated because few sublegal-size females were present. The length-frequency distributions of eels in the present samples and in the commercial catches were truncated just above minimum legal size (about 460 mm), showing that few females escape the fishery. Historically, females predominated these rivers. The recent change in sex ratio is attributable partly to selective harvest of females, and partly to changes in the structure of the population from fishing, such that differentiation into males has been favored. Longevity, delayed sexual maturity, semel-parity, and endemism with restricted range make the longfin eel particularly vulnerable to overfishing.