Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

Multimodel inference and multimodel averaging in empirical modeling of occupational exposure levels.

Empirical modeling of exposure levels has been popular for identifying exposure determinants in occupational hygiene. Traditional data-driven methods used to choose a model on which to base inferences have typically not accounted for the uncertainty linked to the process of selecting the final model. Several new approaches propose making statistical inferences from a set of plausible models rather than from a single model regarded as 'best'. This paper introduces the multimodel averaging approach described in the monograph by Burnham and Anderson. In their approach, a set of plausible models are defined a priori by taking into account the sample size and previous knowledge of variables influent on exposure levels. The Akaike information criterion is then calculated to evaluate the relative support of the data for each model, expressed as Akaike weight, to be interpreted as the probability of the model being the best approximating model given the model set. The model weights can then be used to rank models, quantify the evidence favoring one over another, perform multimodel prediction, estimate the relative influence of the potential predictors and estimate multimodel-averaged effects of determinants. The whole approach is illustrated with the analysis of a data set of 1500 volatile organic compound exposure levels collected by the Institute for work and health (Lausanne, Switzerland) over 20 years, each concentration having been divided by the relevant Swiss occupational exposure limit and log-transformed before analysis. Multimodel inference represents a promising procedure for modeling exposure levels that incorporates the notion that several models can be supported by the data and permits to evaluate to a certain extent model selection uncertainty, which is seldom mentioned in current practice.

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Validación del delta base déficit como modelo predictor de resultados en pacientes politraumáticos. Hospital Parc Taulí Sabadell. Estudio preliminar

Les escales de valoració al pacient politraumàtic són essencials per al seu maneig i pronòstic. Podem definir índexs de gravetat o probabilitat de supervivència. Segons quins paràmetres analitzi, podem parlar d’escales fisiològiques, anatòmiques, bioquímiques i els índexs de probabilitat de supervivència. El BISS és un model de probabilitat provat a Holanda que ha demostrat ser objectiu. El nostre treball consisteix en la validació del BISS als nostres pacients. Durant dos anys vàrem recollir 354 pacients podent incloure només 167 al nostre estudi. Els resultats van ser significatius amb l’estudi posterior, però degut a la gran pèrdua de pacients no podem afirmar la nostra hipòtesi.

Population pharmacokinetics and clinical response for artemether-lumefantrine in pregnant and nonpregnant women with uncomplicated Plasmodium falciparum malaria in Tanzania.

Artemether-lumefantrine (AL) is the first-line treatment for uncomplicated malaria in the second and third trimesters of pregnancy. Its efficacy during pregnancy has recently been challenged due to altered pharmacokinetic (PK) properties in this vulnerable group. The aim of this study was to determine the PK profile of AL in pregnant and nonpregnant women and assess their therapeutic outcome. Thirty-three pregnant women and 22 nonpregnant women with malaria were treated with AL (80/480 mg) twice daily for 3 days. All patients provided five venous plasma samples for drug quantification at random times over 7 days. Inter- and intraindividual variability was assessed, and the effects of covariates were quantified using a nonlinear mixed-effects modeling approach (NONMEM). A one-compartment model with first-order absorption and elimination with linear metabolism from drug to metabolite fitted the data best for both arthemether (AM) and lumefantrine (LF) and their metabolites. Pregnancy status and diarrhea showed a significant influence on LF PK. The relative bioavailability of lumefantrine and its metabolism rate into desmethyl-lumefantrine were, respectively, 34% lower and 78% higher in pregnant women than in nonpregnant patients. The overall PCR-uncorrected treatment failure rates were 18% in pregnant women and 5% in nonpregnant women (odds ratio [OR] = 4.04; P value of 0.22). A high median day 7 lumefantrine concentration was significantly associated with adequate clinical and parasitological response (P = 0.03). The observed reduction in the relative bioavailability of lumefantrine in pregnant women may explain the higher treatment failure in this group, mostly due to lower posttreatment prophylaxis. Hence, a modified treatment regimen of malaria in pregnancy should be considered.

Best Practice Guidance on Joint Working between the HSC and the Pharmaceutical Industry and other relevant organisations (PDF 260KB)

HSS (GEN) 1) 1/95 update. It is intended to replace the guidance previously provided by former HSSBs and Trusts to assist employers and staff in maintaining strict ethical standards in the conduct of HSC business, in this instance, with the pharmaceutical industry

A Policy to Make Best Use of Resources in Plastic Surgery and Related Specialties (PDF 178 KB)

The purpose of this policy is to introduce a transparent approach to making best use of resources in plastic surgery and related specialties. It was finalised after a formal Public Consultation that included distribution of the Consultation Document to a range of organisations and individuals, meetings with Board representatives as requested and press releases in local and regional media outlets. All responses to the Consultation were considered carefully in developing this final policy. åÊ åÊ