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.

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.

Impact of an abrupt cooling event on interglacial methane emissions in northern peatlands

Rapid changes in atmospheric methane (CH4), temperature and precipitation are documented by Greenland ice core data both for glacial times (the so called Dansgaard-Oeschger (D-O) events) as well as for a cooling event in the early Holocene (the 8.2 kyr event). The onsets of D-O warm events are paralleled by abrupt increases in CH4 by up to 250 ppb in a few decades. Vice versa, the 8.2 kyr event is accompanied by an intermittent decrease in CH4 of about 80 ppb over 150 yr. The abrupt CH4 changes are thought to mainly originate from source emission variations in tropical and boreal wet ecosystems, but complex process oriented bottom-up model estimates of the changes in these ecosystems during rapid climate changes are still missing. Here we present simulations of CH4 emissions from northern peatlands with the LPJ-Bern dynamic global vegetation model. The model represents CH4 production and oxidation in soils and transport by ebullition, through plant aerenchyma, and by diffusion. Parameters are tuned to represent site emission data as well as inversion-based estimates of northern wetland emissions. The model is forced with climate input data from freshwater hosing experiments using the NCAR CSM1.4 climate model to simulate an abrupt cooling event. A concentration reduction of ~10 ppb is simulated per degree K change of mean northern hemispheric surface temperature in peatlands. Peatland emissions are equally sensitive to both changes in temperature and in precipitation. If simulated changes are taken as an analogy to the 8.2 kyr event, boreal peatland emissions alone could only explain 23 of the 80 ppb decline in atmospheric methane concentration. This points to a significant contribution to source changes from low latitude and tropical wetlands to this event.

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.

Ar-40/Ar-39 Evidence for Middle Proterozoic (1300-1500 Ma) Slow Cooling of the Southern Black Hills, South Dakota, Midcontinent, North America: Implications for Early Proterozoic P-T Evolution and Posttectonic Magmatism

Ar-40/Ar-39 total gas and plateau dates from muscovite and biotite in the southern Black Hills, South Dakota, provide evidence for a period of Middle Proterozoic slow cooling. Early Proterozoic (1600-1650 Ma) mica dates were obtained from metasedimentary rocks located in a synformal structure between the Harney Peak and Bear Mountain domes and also south of Bear Mountain. Metamorphic rocks from the dome areas and undeformed samples of the similar to 1710 Ma Harney Peak Granite (HPG) yield Middle Proterozoic mica dates (similar to 1270-1500 Ma). Two samples collected between the synform and Bear Mountain dome yield intermediate total gas mica dates of similar to 1550 Ma. We suggest two end-member interpretations to explain the map pattern of cooling ages: (1) subhorizontal slow cooling of an area which exhibits variation in mica Ar retention intervals or (2) mild folding of a Middle Proterozoic (similar to 1500 Ma) similar to 300 degrees C isotherm. According to the second interpretation, the preservation of older dates between the domes may reflect reactivation of a preexisting synformal structure (and downwarping of relatively cold rocks) during a period of approximately east-west contraction and slow uplift during the Middle Proterozoic. The mica data, together with hornblende data from the Black Hills published elsewhere, indicate that the ambient country-rock temperature at the 3-4 kbar depth of emplacement of the HPG was between 350 degrees C and 500 degrees C, suggesting that the average upper crustal geothermal gradient was 25 degrees-40 degrees C/km prior to intrusion. The thermochronologic data suggest HPG emplacement was followed by a similar to 200 m.y. period of stability and tectonic quiescence with little uplift. We propose that crust thickened during the Early Proterozoic was uplifted and erosionally(?) thinned prior to similar to 1710 Ma and that the HPG magma was emplaced into isostatically stable crust of relatively normal thickness. We speculate that uplift and crustal thinning prior to HPG intrusion was the result of differential thinning of the subcrustal lithosphere beneath the Black Hills. If so, this process would have also caused an increase in mantle heat flux across the Moho and triggered vapor-absent melting of biotite to produce the HPG magma. This scenario for posttectonic granite generation is supported, in part, by the fact that in the whole of the Black Hills, the HPG is spatially associated with the deepest exposed Early Proterozoic country rock.

Thermochronological Evidence for Late Proterozoic (Vendian) Cooling in Southwest Wedel Jarlsberg Land, Spitsbergen

Two Proterozoic terranes with different metamorphic histories are distinguished from geological mapping in southwestern Wedel Jarlsberg Land: a northern greenschist facies terrane and a southern amphibolite facies terrane which has been overprinted by greenschist facies metamorphism. To better characterize the tectonothermal history of these terranes we have obtained new Ar-40/Ar-39 mineral dates from this area. A muscovite separate from the northern terrane yielded a Caledonian plateau age of 432 +/- 7 Ma. The southern terrane yielded significantly older Ar-40/Ar-39 ages with three muscovite plateau dates of 584 +/- 14 Ma, 575 +/- 15 Ma, and 459 +/- 9 Ma, a 484 +/- 5 Ma biotite plateau date, and a 616 +/- 17 Ma hornblende plateau date. The oldest thermochronological dates are over 300 Ma younger than the age of amphibolite facies metamorphism and therefore probably do not represent uplift-related cooling. Instead, the Vendian dates correlate well with a regionally widespread magmatic and metamorphic/thermal resetting event recognized within Caledonian complexes of northwestern Spitsbergen and Nordaustlandet. The apparent Ordovician dates are interpreted to represent partial resetting, suggesting that late Caledonian greenschist facies overprinting of the southern terrane was of variable intensity.