Disentangling multi-level systems: averaging, correlations and memory

We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way of parameterizing the effect of the coupling as a function of only the variables of a system of interest. Our focus is on describing the impacts of the coupling on the long term statistics rather than on the finite-time behavior. By direct calculation, we find that, at first order, the coupling can be surrogated by adding a deterministic perturbation to the autonomous dynamics of the system of interest. At second order, there are additionally two separate and very different contributions. One is a term taking into account the second-order contributions of the fluctuations in the coupling, which can be parameterized as a stochastic forcing with given spectral properties. The other one is a memory term, coupling the system of interest to its previous history, through the correlations of the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to treat this case, we present an extension to Ruelle's response theory able to deal with integral operators. We discuss our results in the context of other methods previously proposed for disentangling the dynamics of two coupled systems. We emphasize that our results do not rely on assuming a time scale separation, and, if such a separation exists, can be used equally well to study the statistics of the slow variables and that of the fast variables. By recursively applying the technique proposed here, we can treat the general case of multi-level systems.

A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Is there a place for property in the multi-asset portfolio?

The case for property has typically rested on the application of modern portfolio theory (MPT), in that property has been shown to offer increased diversification benefits within a multi asset portfolio without hurting portfolio returns especially for lower risk portfolios. However this view is based upon the use of historic, usually appraisal based, data for property. Recent research suggests strongly that such data significantly underestimates the risk characteristics of property, because appraisals explicitly or implicitly smooth out much of the real volatility in property returns. This paper examines the portfolio diversification effects of including property in a multi-asset portfolio, using UK appraisal based (smoothed) data and several derived de-smoothed series. Having considered the effects of de-smoothing, we then consider the inclusion of a further low risk asset (cash) in order to investigate further whether property's place in a low risk portfolio is maintained. The conclusions of this study are that the previous supposed benefits of including property have been overstated. Although property may still have a place in a 'balanced' institutional portfolio, the case for property needs to be reassessed and not be based simplistically on the application of MPT.

Stabilization of multi-stranded nucleic acid structures using 3'-S-phosphorothiolate linkages

3 '-S-Phosphorothiolate linkages incorporated into an oligodeoxynucleotide have been shown to stabilise duplex formation with a complementary RNA strand, but destabilise a duplex formed with a complementary DNA strand. The four-stranded i-motif structure is also stabilised this modification.

Kinetic multi-layer model of gas-particle interactions in aerosols and clouds (KM-GAP): linking condensation, evaporation and chemical reactions of organics, oxidants and water

We present a novel kinetic multi-layer model for gas-particle interactions in aerosols and clouds (KMGAP) that treats explicitly all steps of mass transport and chemical reaction of semi-volatile species partitioning between gas phase, particle surface and particle bulk. KMGAP is based on the PRA model framework (P¨oschl-Rudich- Ammann, 2007), and it includes gas phase diffusion, reversible adsorption, surface reactions, bulk diffusion and reaction, as well as condensation, evaporation and heat transfer. The size change of atmospheric particles and the temporal evolution and spatial profile of the concentration of individual chemical species can be modeled along with gas uptake and accommodation coefficients. Depending on the complexity of the investigated system and the computational constraints, unlimited numbers of semi-volatile species, chemical reactions, and physical processes can be treated, and the model shall help to bridge gaps in the understanding and quantification of multiphase chemistry and microphysics in atmospheric aerosols and clouds. In this study we demonstrate how KM-GAP can be used to analyze, interpret and design experimental investigations of changes in particle size and chemical composition in response to condensation, evaporation, and chemical reaction. For the condensational growth of water droplets, our kinetic model results provide a direct link between laboratory observations and molecular dynamic simulations, confirming that the accommodation coefficient of water at 270K is close to unity (Winkler et al., 2006). Literature data on the evaporation of dioctyl phthalate as a function of particle size and time can be reproduced, and the model results suggest that changes in the experimental conditions like aerosol particle concentration and chamber geometry may influence the evaporation kinetics and can be optimized for efficient probing of specific physical effects and parameters. With regard to oxidative aging of organic aerosol particles, we illustrate how the formation and evaporation of volatile reaction products like nonanal can cause a decrease in the size of oleic acid particles exposed to ozone.

In vitro evaluation of single- and multi-strain probiotics: inter-species inhibition between probiotic strains, and inhibition of pathogens

Many studies comparing the effects of single- and multi-strain probiotics on pathogen inhibition compare treatments with different concentrations. They also do not examine the possibility of inhibition between probiotic strains with a mixture. We tested the ability of 14 single-species probiotics to inhibit each other using a cross-streak assay, and agar spot test. We then tested the ability of 15 single-species probiotics and 5 probiotic mixtures to inhibit C. difficile, E. coli and S. Typhimurium, using the agar spot test. Testing was done with mixtures created in two ways: one group contained component species incubated together, the other group of mixtures was made using component species which had been incubated separately, equalised to equal optical density, and then mixed in equal volumes. Inhibition was observed for all combinations of probiotics, suggesting that when used as such there may be inhibition between probiotics, potentially reducing efficacy of the mixture. Significant inter-species variation was seen against each pathogen. When single species were tested against mixtures, the multi-species preparations displayed significantly (p<0.05 or less) greater inhibition of pathogens in 12 out of 24 cases. Despite evidence that probiotic species will inhibit each other when incubated together in vitro, in many cases a probiotic mixture was more effective at inhibiting pathogens than its component species when tested at approximately equal concentrations of biomass. This suggests that using a probiotic mixture might be more effective at reducing gastrointestinal infections, and that creating a mixture using species with different effects against different pathogens may have a broader spectrum of action that a single provided by a single strain.

Sources of multi-decadal variability in Arctic sea ice extent

The observed dramatic decrease in September sea ice extent (SIE) has been widely discussed in the scientific literature. Though there is qualitative agreement between observations and ensemble members of the Third Coupled Model Intercomparison Project (CMIP3), it is concerning that the observed trend (1979–2010) is not captured by any ensemble member. The potential sources of this discrepancy include: observational uncertainty, physical model limitations and vigorous natural climate variability. The latter has received less attention and is difficult to assess using the relatively short observational sea ice records. In this study multi-centennial pre-industrial control simulations with five CMIP3 climate models are used to investigate the role that the Arctic oscillation (AO), the Atlantic multi-decadal oscillation (AMO) and the Atlantic meridional overturning circulation (AMOC) play in decadal sea ice variability. Further, we use the models to determine the impact that these sources of variability have had on SIE over both the era of satellite observation (1979–2010) and an extended observational record (1953–2010). There is little evidence of a relationship between the AO and SIE in the models. However, we find that both the AMO and AMOC indices are significantly correlated with SIE in all the models considered. Using sensitivity statistics derived from the models, assuming a linear relationship, we attribute 0.5–3.1%/decade of the 10.1%/decade decline in September SIE (1979–2010) to AMO driven variability.