Optimal importance sampling for overdamped Langevin dynamics

Calculating averages with respect to multimodal probability distributions is often necessary in applications. Markov chain Monte Carlo (MCMC) methods to this end, which are based on time averages along a realization of a Markov process ergodic with respect to the target probability distribution, are usually plagued by a large variance due to the metastability of the process. In this work, we mathematically analyze an importance sampling approach for MCMC methods that rely on the overdamped Langevin dynamics. Specifically, we study an estimator based on an ergodic average along a realization of an overdamped Langevin process for a modified potential. The estimator we consider incorporates a reweighting term in order to rectify the bias that would otherwise be introduced by this modification of the potential. We obtain an explicit expression in dimension 1 for the biasing potential that minimizes the asymptotic variance of the estimator for a given observable, and propose a general numerical approach for approximating the optimal potential in the multi-dimensional setting. We also investigate an alternative approach where, instead of the asymptotic variance for a given observable, a weighted average of the asymptotic variances corresponding to a class of observables is minimized. Finally, we demonstrate the capabilities of the proposed method by means of numerical experiments

Bicrossproduct approach to the Connes-Moscovici Hopf algebra

We give a rigorous proof that the (codimension one) Connes-Moscovici Hopf algebra H_CM is isomorphic to a bicrossproduct Hopf algebra linked to a group factorisation of the group of positively-oriented diffeomorphisms of the real line. We construct a second bicrossproduct U_CM equipped with a nondegenerate dual pairing with H_CM. We give a natural quotient Hopf algebra of H_CM and Hopf subalgebra of U_CM which again are in duality. All these Hopf algebras arise as deformations of commutative or cocommutative Hopf algebras that we describe in each case. Finally we develop the noncommutative differential geometry of the quotient of H_CM by studying covariant first order differential calculi of small dimension over this algebra.Comment: 21 page

Quantum Symmetries and Strong Haagerup Inequalities

In this paper, we consider families of operators $\{x_r\}_{r \in \Lambda}$ in a tracial C$^\ast$-probability space $(\mathcal A, \phi)$, whose joint $\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\{H_n^+\}_{n \in \N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\mathcal B$ generated by $\{x_r\}_{r \in \Lambda}$, which generalizes the strong Haagerup inequalities for $\ast$-free R-diagonal families obtained by Kemp-Speicher \cite{KeSp}. As an application of our result, we show that $\mathcal B$ always has the metric approximation property (MAP). We also apply our techniques to study the reduced C$^\ast$-algebra of the free unitary quantum group $U_n^+$. We show that the non-self-adjoint subalgebra $\mathcal B_n$ generated by the matrix elements of the fundamental corepresentation of $U_n^+$ has the MAP. Additionally, we prove a strong Haagerup inequality for $\mathcal B_n$, which improves on the estimates given by Vergnioux's property RD \cite{Ve}

Comparing impacts of alien plants and animals in Europe using a standard scoring system

© 2015 British Ecological Society. Alien species can change the recipient environment in various ways, and some of them cause considerable damage. Understanding such impacts is crucial to direct management actions. This study addresses the following questions: Is it possible to quantify impact across higher taxa in a comparative manner? Do impacts differ between taxonomic groups? How are environmental and socio-economic impacts related? Can impacts be predicted based on those in other regions? To address these questions, we reviewed literature describing the impacts of 300 species from five major taxonomic groups: mammals, birds, fish, terrestrial arthropods and plants. To make very diverse impact measures comparable, we used the semi-quantitative generic impact scoring system (GISS) which describes environmental and socio-economic impacts using twelve categories. In each category, scores range from zero (no impact known or detectable) to five (the highest possible impact). Using the same scoring system for taxa as diverse as invertebrates, vertebrates and plants, we found that overall, alien mammals in Europe have the highest impact, while fish have the lowest. Terrestrial arthropods were found to have the lowest environmental impact, while fish had relatively low socio-economic impact. Overall, the magnitude of environmental and socio-economic impacts of individual alien species is highly correlated. However, at the species level, major deviations are found. For mammals and birds, the impacts in invaded ranges outside of Europe are broadly similar to those recorded for alien species within Europe, indicating that a consideration of the known impacts of a species in other regions can be generally useful when predicting the impacts of an alien species. However, it should be noted that this pattern is not consistent across all mammal and bird orders, and thus, such information should be considered with caution. Synthesis and applications. Comparing the impacts of alien species across taxa is necessary for prioritizing management efforts and effective allocation of resources. By applying the generic impact scoring system (GISS) to five major taxonomic groups, we provide the basis for a semi-quantitative cross-taxa listing process (e.g. 'black lists' or 100-worst-lists). If more data are collated from different geographical regions and habitats using standard GISS protocols, risk assessments for alien species based on rigorous measures of impact could be improved by taking into account local variation, and context dependence of impacts. This would also allow studies at lower taxonomic levels, and within-taxon analyses of functional groups and guilds. Comparing the impacts of alien species across taxa is necessary for prioritizing management efforts and effective allocation of resources. By applying the generic impact scoring system (GISS) to five major taxonomic groups, we provide the basis for a semi-quantitative cross-taxa listing process (e.g. 'black lists' or 100-worst-lists). If more data are collated from different geographical regions and habitats using standard GISS protocols, risk assessments for alien species based on rigorous measures of impact could be improved by taking into account local variation, and context dependence of impacts. This would also allow studies at lower taxonomic levels, and within-taxon analyses of functional groups and guilds.Peer Reviewe

The K-theory of free quantum groups

In this paper we study the K -theory of free quantum groups in the sense of Wang and Van Daele, more precisely, of free products of free unitary and free orthogonal quantum groups. We show that these quantum groups are K -amenable and establish an analogue of the Pimsner–Voiculescu exact sequence. As a consequence, we obtain in particular an explicit computation of the K -theory of free quantum groups. Our approach relies on a generalization of methods from the Baum–Connes conjecture to the framework of discrete quantum groups. This is based on the categorical reformulation of the Baum–Connes conjecture developed by Meyer and Nest. As a main result we show that free quantum groups have a γ -element and that γ=1 . As an important ingredient in the proof we adapt the Dirac-dual Dirac method for groups acting on trees to the quantum case. We use this to extend some permanence properties of the Baum–Connes conjecture to our setting

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

Recruitment, augmentation and apoptosis of rat osteoclasts in 1,25-(OH)2D3 response to short-term treatment with 1,25-dihydroxyvitamin D3in vivo

Background Although much is known about the regulation of osteoclast (OC) formation and activity, little is known about OC senescence. In particular, the fate of of OC seen after 1,25-(OH)2D3 administration in vivo is unclear. There is evidence that the normal fate of OC is to undergo apoptosis (programmed cell death). We have investigated the effect of short-term application of high dose 1,25-dihydroxyvitamin D3 (1,25-(OH)2D3) on OC apoptosis in an experimental rat model. Methods OC recruitment, augmentation and apoptosis was visualised and quantitated by staining histochemically for tartrate resistant acid phosphatase (TRAP), double staining for TRAP/ED1 or TRAP/DAPI, in situ DNA fragmentation end labelling and histomorphometric analysis. Results Short-term treatment with high-dose 1,25-(OH)2D3 increased the recruitment of OC precursors in the bone marrow resulting in a short-lived increase in OC numbers. This was rapidly followed by an increase in the number of apoptotic OC and their subsequent removal. The response of OC to 1,25-(OH)2D3 treatment was dose and site dependent; higher doses producing stronger, more rapid responses and the response in the tibiae being consistently stronger and more rapid than in the vertebrae. Conclusions This study demonstrates that (1) after recruitment, OC are removed from the resorption site by apoptosis (2) the combined use of TRAP and ED1 can be used to identify OC and their precursors in vivo (3) double staining for TRAP and DAPI or in situ DNA fragmentation end labelling can be used to identify apoptotic OC in vivo

To screen or not to screen for peripheral arterial disease in subjects aged 80 and over in primary health care: a cross-sectional analysis from the BELFRAIL study

<p>Abstract</p> <p>Background</p> <p>Peripheral arterial disease (PAD) is common in older people. An ankle-brachial index (ABI) < 0.9 can be used as an indicator of PAD. Patients with low ABI have increased mortality and a higher risk of serious cardiovascular morbidity. However, because 80% of the patients are asymptomatic, PAD remains unrecognised in a large group of patients. The aims of this study were 1) to examine the prevalence of reduced ABI in subjects aged 80 and over, 2) to determine the diagnostic accuracy of the medical history and clinical examination for reduced ABI and 3) to investigate the difference in functioning and physical activity between patients with and without reduced ABI.</p> <p>Methods</p> <p>A cross-sectional study embedded within the BELFRAIL study. A general practitioner (GP) centre, located in Hoeilaart, Belgium, recruited 239 patients aged 80 or older. Only three criteria for exclusion were used: urgent medical need, palliative situation and known serious dementia. The GP recorded the medical history and performed a clinical examination. The clinical research assistant performed an extensive examination including Mini-Mental State Examination (MMSE), Geriatric Depression Scale (GDS-15), Activities of Daily Living (ADL), Tinetti test and the LASA Physical Activity Questionnaire (LAPAQ). ABI was measured using an automatic oscillometric appliance.</p> <p>Results</p> <p>In 40% of patients, a reduced ABI was found. Cardiovascular risk factors were unable to identify patients with low ABI. A negative correlation was found between the number of cardiovascular morbidities and ABI. Cardiovascular morbidity had a sensitivity of 65.7% (95% CI 53.4-76.7) and a specificity of 48.6% (95% CI 38.7-58.5). Palpation of the peripheral arteries showed the highest negative predictive value (77.7% (95% CI 71.8-82.9)). The LAPAQ score was significantly lower in the group with reduced ABI.</p> <p>Conclusion</p> <p>The prevalence of PAD is very high in patients aged 80 and over in general practice. The clinical examination, cardiovascular risk factors and the presence of cardiovascular morbidity were not able to identify patients with a low ABI. A screening strategy for PAD by determining ABI could be considered if effective interventions for those aged 80 and over with a low ABI become available through future research.</p

Determination of total and available fractions of PAHs by SPME in oily wastewaters : overcoming interference from NAPL and NOM

Background, aim, and scope Polycyclic aromatic hydrocarbons (PAHs) are often found in oily wastewaters. Their presence is usually the result of human activities and has a negative effect on the environment. One important step in addressing this problem is to evaluate the effectiveness of PAH removal by biological processes since these are the most cost-effective treatments known today. Many techniques are presently available for PAH determination in wastewaters. Solid phase microextracion (SPME) is known to be one of the most effective techniques for this purpose. When analyzing complex matrices with substances such as natural organic matter (NOM) and non-aqueous phase liquids (NAPL), it is important to differentiate the free dissolved PAH from matrix-bonded PAH. PAHs associated with the bonded fraction are less susceptible to biological treatment. The present study concerns the development of a simple and suitable methodology for the determination of the freely dissolved and the total fraction of PAHs present in oily wastewaters. The methodology was then applied to an oily wastewater from a fuel station retention basin. Material and methods Headspace SPME was used for analyzing PAH since the presence of a complex or dirty matrix in direct contact with the fiber may damage it. Four model PAHs—anthracene, fluorene, phenanthrene, and pyrene—were analyzed by GC-MS. Negligible depletion SPME technique was used to determine the free fraction. Total PAH was determined by enhancing the mass transfer from the bonded phase to the freely dissolved phase by temperature optimization and the use of the method of standard additions. The PAH absorption kinetics were determined in order to define the optimal sampling conditions for this method. The fitting of the experimental data to a mathematical model was accomplished using Berkeley Madonna software. Humic acid and silicon oil were used as model NOM and NAPL, respectively, to study the effect of these compounds on the decrease of SPME response. Then, the method was evaluated with wastewater from a fuel station spill retention basin. Results The SPME kinetic parameters—k 1 (uptake rate), k 2 (desorption rate), and K SPME (partition coefficient)—were determined from experimental data modeling. The determination of the free fraction required 15-min sampling to ensure that PAH depletion from sample was below 1%. For total PAH, a 30-min extraction at 100°C ensured the maximum signal response in the GC-MS. For the determination of free and total PAHs, extractions were performed before reaching the SPME equilibrium. The wastewater used in this study had no free fraction of the analyzed PAHs. However, the four studied PAHs were found when the method for total PAH was used. Discussion The addition of NOM and NAPL dramatically decreased the efficiency of the SPME. This decrease was the result of a greater partition of the PAHs to the NAPL and NOM phases. This fact was also observed in the analysis of the fuel station spill retention basin, where no free PAH was measured. However, using the method of standard addition for the determination of total PAH, it was possible to quantify all four PAHs. Conclusions The method developed in the present study was found to be adequate to differentiate between free and total PAH present in oily wastewater. It was determined that the presence of NOM and NAPL had a negative effect on SPME efficiency. Recommendations and perspectives The presence of binding substances had a great influence on SPME kinetics. Therefore, it is of extreme importance to determine their degree of interference when analyzing oily wastewaters or results can otherwise be erroneous. Other factors influencing the total PAH determinations should be considered in further studies.Fundação para a Ciência e a Tecnologia (FCT) - SFRH/BD/ 18816/2004, POCI/AMB/61044/200