Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Volume, volatility, and leverage: A dynamic analysis

This paper uses dynamic impulse response analysis to investigate the interrelationships among stock price volatility, trading volume, and the leverage effect. Dynamic impulse response analysis is a technique for analyzing the multi-step-ahead characteristics of a nonparametric estimate of the one-step conditional density of a strictly stationary process. The technique is the generalization to a nonlinear process of Sims-style impulse response analysis for linear models. In this paper, we refine the technique and apply it to a long panel of daily observations on the price and trading volume of four stocks actively traded on the NYSE: Boeing, Coca-Cola, IBM, and MMM.

Probabilistic choice: A simple invariance.

When subjects must choose repeatedly between two or more alternatives, each of which dispenses reward on a probabilistic basis (two-armed bandit ), their behavior is guided by the two possible outcomes, reward and nonreward. The simplest stochastic choice rule is that the probability of choosing an alternative increases following a reward and decreases following a nonreward (reward following ). We show experimentally and theoretically that animal subjects behave as if the absolute magnitudes of the changes in choice probability caused by reward and nonreward do not depend on the response which produced the reward or nonreward (source independence ), and that the effects of reward and nonreward are in constant ratio under fixed conditions (effect-ratio invariance )--properties that fit the definition of satisficing . Our experimental results are either not predicted by, or are inconsistent with, other theories of free-operant choice such as Bush-Mosteller, molar maximization, momentary maximizing, and melioration (matching).

Variability of particulate matter concentrations along roads and motorways determined by a moving measurement unit

The spatial variability of aerosol number and mass along roads was determined in different regions (urban, rural and coastal-marine) of the Netherlands. A condensation particle counter (CPC) and an optical aerosol spectrometer (LAS-X) were installed in a van along with a global positioning system (GPS). Concentrations were measured with high-time resolutions while driving allowing investigations not possible with stationary equipment. In particular, this approach proves to be useful to identify those locations where numbers and mass attain high levels ('hot spots'). In general, concentrations of number and mass of particulate matter increase along with the degree of urbanisation, with number concentration being the more sensitive indicator. The lowest particle numbers and PM1-concentrations are encountered in a coastal and rural area: <5000cm-3 and 6μgm-3, respectively. The presence of sea-salt material along the North-Sea coast enhances PM>1-concentrations compared to inland levels. High-particle numbers are encountered on motorways correlating with traffic intensity; the largest average number concentration is measured on the ring motorway around Amsterdam: about 160000cm-3 (traffic intensity 100000vehday-1). Peak values occur in tunnels where numbers exceed 106cm-3. Enhanced PM1 levels (i.e. larger than 9μgm-3) exist on motorways, major traffic roads and in tunnels. The concentrations of PM>1 appear rather uniformly distributed (below 6μgm-3 for most observations). On the urban scale, (large) spatial variations in concentration can be explained by varying intensities of traffic and driving patterns. The highest particle numbers are measured while being in traffic congestions or when behind a heavy diesel-driven vehicle (up to 600×103cm-3). Relatively high numbers are observed during the passages of crossings and, at a decreasing rate, on main roads with much traffic, quiet streets and residential areas with limited traffic. The number concentration exhibits a larger variability than mass: the mass concentration on city roads with much traffic is 12% higher than in a residential area at the edge of the same city while the number of particles changes by a factor of two (due to the presence of the ultrafine particles (aerodynamic diameter <100nm). It is further indicated that people residing at some 100m downwind a major traffic source are exposed to (still) 40% more particles than those living in the urban background areas. © 2004 Elsevier Ltd. All rights reserved.

Outer Membrane Vesicle Production in Escherichia coli Relieves Envelope Stress and is Modulated by Changes in Peptidoglycan

Bacterial outer membrane vesicles (OMVs) are spherical buds of the outer membrane (OM) containing periplasmic lumenal components. OMVs have been demonstrated to play a critical part in the transmission of virulence factors, immunologically active compounds, and bacterial survival, however vesiculation also appears to be a ubiquitous physiological process for Gram-negative bacteria. Despite their characterized biological roles, especially for pathogens, very little is known about their importance for the originating organism as well as regulation and mechanism of production. Only when we have established their biogenesis can we fully uncover their roles in pathogenesis and bacterial physiology. The overall goal of this research was to characterize bacterial mutants which display altered vesiculation phenotypes using genetic and biochemical techniques, and thereby begin to elucidate the mechanism of vesicle production and regulation. One part of this work elucidated a synthetic genetic growth defect for a strain with reduced OMV production (ΔnlpA, inner membrane lipoprotein with a minor role in methionine transport) and envelope stress (ΔdegP, dual function periplasmic chaperone/ protease responsible for managing proteinaceous waste). This research showed that the growth defect of ΔnlpAΔdegP correlated with reduced OMV production with respect to the hyprevesiculator ΔdegP and the accumulation of protein in the periplasm and DegP substrates in the lumen of OMVs. We further demonstrated that OMVs do not solely act as a stress response pathway to rid the periplasm of otherwise damaging misfolded protein but also of accumulated peptidoglycan (PG) fragments and lipopolysaccharide (LPS), elucidating OMVs as a general stress response pathway critical for bacterial well-being. The second part of this work, focused on the role of PG structure, turnover and covalent crosslinks to the OM in vesiculation. We established a direct link between PG degradation and vesiculation: Mutations in the OM lipoprotein nlpI had been previously established as a very strong hypervesiculation phenotype. In the literature NlpI had been associated with another OM lipoprotein, Spr that was recently identified as a PG hydrolase. The data presented here suggest that NlpI acts as a negative regulator of Spr and that the ΔnlpI hypervesiculation phenotype is a result of rampantly degraded PG by Spr. Additionally, we found that changes in PG structure and turnover correlate with altered vesiculation levels, as well as non-canonical D-amino acids, which are secreted by numerous bacteria on the onset of stationary phase, being a natural factor to increase OMV production. Furthermore, we discovered an inverse relationship between the concentration of Lpp-mediated, covalent crosslinks and the level of OMV production under conditions of modulated PG metabolism and structure. In contrast, situations that lead to periplasmic accumulation (protein, PG fragments, and LPS) and consequent hypervesiculation the overall OM-PG crosslink concentration appears to be unchanged. Form this work, we conclude that multiple pathways lead to OMV production: Lpp concentration-dependent and bulk driven, Lpp concentration-independent.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

NlpI-mediated modulation of outer membrane vesicle production through peptidoglycan dynamics in Escherichia coli.

Outer membrane vesicles (OMVs) are ubiquitously secreted from the outer membrane (OM) of Gram-negative bacteria. These heterogeneous structures are composed of OM filled with periplasmic content from the site of budding. By analyzing mutants that have vesicle production phenotypes, we can gain insight into the mechanism of OMV budding in wild-type cells, which has thus far remained elusive. In this study, we present data demonstrating that the hypervesiculation phenotype of the nlpI deletion mutant of Escherichia coli correlates with changes in peptidoglycan (PG) dynamics. Our data indicate that in stationary phase cultures the nlpI mutant exhibits increased PG synthesis that is dependent on spr, consistent with a model in which NlpI controls the activity of the PG endopeptidase Spr. In log phase, the nlpI mutation was suppressed by a dacB mutation, suggesting that NlpI regulates penicillin-binding protein 4 (PBP4) during exponential growth. The data support a model in which NlpI negatively regulates PBP4 activity during log phase, and Spr activity during stationary phase, and that in the absence of NlpI, the cell survives by increasing PG synthesis. Further, the nlpI mutant exhibited a significant decrease in covalent outer membrane (OM-PG) envelope stabilizing cross-links, consistent with its high level of OMV production. Based on these results, we propose that one mechanism wild-type Gram-negative bacteria can use to modulate vesiculation is by altering PG-OM cross-linking via localized modulation of PG degradation and synthesis.

Impacts of land use change and climate variations on annual inflow into Miyun Reservoir,Beijing, China

The Miyun Reservoir, the only surface water source for Beijing city, has experienced water supply decline in recent decades. Previous studies suggest that both land use change and climate contribute to the changes of water supply in this critical watershed. However, the specific causes of the decline in the Miyun Reservoir are debatable under a non-stationary climate in the past 4 decades. The central objective of this study was to quantify the separate and collective contributions of land use change and climate variability to the decreasing inflow into the Miyun Reservoir during 1961–2008. Different from previous studies on this watershed, we used a comprehensive approach to quantify the timing of changes in hydrology and associated environmental variables using the long-term historical hydrometeorology and remote-sensing-based land use records. To effectively quantify the different impacts of the climate variation and land use change on streamflow during different sub-periods, an annual water balance model (AWB), the climate elasticity model (CEM), and a rainfall–runoff model (RRM) were employed to conduct attribution analysis synthetically. We found a significant (p  <  0.01) decrease in annual streamflow, a significant positive trend in annual potential evapotranspiration (p  <  0.01), and an insignificant (p  >  0.1) negative trend in annual precipitation during 1961–2008. We identified two streamflow breakpoints, 1983 and 1999, by the sequential Mann–Kendall test and double-mass curve. Climate variability alone did not explain the decrease in inflow to the Miyun Reservoir. Reduction of water yield was closely related to increase in actual evapotranspiration due to the expansion of forestland and reduction in cropland and grassland, and was likely exacerbated by increased water consumption for domestic and industrial uses in the basin. The contribution to the observed streamflow decline from land use change fell from 64–92 % during 1984–1999 to 36–58 % during 2000–2008, whereas the contribution from climate variation climbed from 8–36 % during the 1984–1999 to 42–64 % during 2000–2008. Model uncertainty analysis further demonstrated that climate warming played a dominant role in streamflow reduction in the most recent decade (i.e., 2000s). We conclude that future climate change and variability will further challenge the water supply capacity of the Miyun Reservoir to meet water demand. A comprehensive watershed management strategy needs to consider the climate variations besides vegetation management in the study basin.