Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Urinary oxalate and urate to creatinine ratios in a healthy pediatric population.

The purpose of the study was to determine reference percentiles for the urinary (U) oxalate (Ox) and urate (Ura) to creatinine (Cr) concentration ratios in the second morning urine of healthy infants, children, and adolescents. The urinary oxalate and urate to creatinine ratios were determined in the spontaneously voided second morning urine sample. To test reproducibility, two urine samples were analyzed on 2 consecutive weeks in 63% of the subjects. Three hundred eighty-four healthy children (181 girls, 203 boys), aged 1 month to 17 years, from nurseries, kindergartens, and schools of Lausanne, Switzerland, were studied. The 5th and 95th percentiles were determined from the total number of urine samples (627) after confirmation that there was no order effect between repeated measurements and there were no significant sex differences. A nonlinear regression analysis in terms of age was used to smooth the calculated percentiles. In this manner, curves were obtained from which the reference values can be read at any given age. The 95th percentiles decreased with age: for UOx/Cr from 0.175 mg/mg (0.22 mol/mol) at 1 to 6 months to 0.048 mg/mg (0.06 mol/mol) from 7 years and beyond; and UUra/Cr from 2.378 mg/mg (1.6 mol/mol) at 1 to 6 months to 0.594 mg/mg (0.4 mol/mol) in adolescence. We provide 5th and 95th percentile curves for the UOx/Cr and UUra/Cr ratios determined from the second morning urine samples in a large cohort of healthy infants, children, and adolescents. Values were determined by standard analytical chemical techniques and were analyzed by powerful statistical methods. The calculated 95th percentile for the UOx/Cr values fell rather rapidly and reached normal adult values by the age of 7 years, whereas for UUra/Cr, the 95th percentile decreased slowly and stabilized in adolescence.

Rapid bacterial genome sequencing: methods and applications in clinical microbiology.

The recent advances in sequencing technologies have given all microbiology laboratories access to whole genome sequencing. Providing that tools for the automated analysis of sequence data and databases for associated meta-data are developed, whole genome sequencing will become a routine tool for large clinical microbiology laboratories. Indeed, the continuing reduction in sequencing costs and the shortening of the 'time to result' makes it an attractive strategy in both research and diagnostics. Here, we review how high-throughput sequencing is revolutionizing clinical microbiology and the promise that it still holds. We discuss major applications, which include: (i) identification of target DNA sequences and antigens to rapidly develop diagnostic tools; (ii) precise strain identification for epidemiological typing and pathogen monitoring during outbreaks; and (iii) investigation of strain properties, such as the presence of antibiotic resistance or virulence factors. In addition, recent developments in comparative metagenomics and single-cell sequencing offer the prospect of a better understanding of complex microbial communities at the global and individual levels, providing a new perspective for understanding host-pathogen interactions. Being a high-resolution tool, high-throughput sequencing will increasingly influence diagnostics, epidemiology, risk management, and patient care.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Trypanosoma cruzi: metacyclogenesis in vitro - I. Changes in the properties of metacyclic trypomastigotes maintained in the laboratory by different methods

In this work we have studied the modifications in the biological properties of Trypanosoma cruzi when the parasite is maintained for a long time in axenic culture. The studies were done with a clone from an avirulent strain (Dm30L) and a non-cloned virulent strain (EP) of T. cruzi. Both parasiteswere maintained, for at least three years, by successive triatomine/mouse alternate passage (control condition), or by serial passage in axenic medium (culture condition), or only in the mouse (mouse condition). The comparison between parasites of culture and control condition showed that metacyclogenesis capacity was reduced in the former and that the resulting metacyclics displayed an attenuatedvirulence. In order to compare the virulence of metacyclics from the urine of the insect vector, Rhodnius prolixus were infected by artificial feeding with parasites of the control or culture condition. After three triatomine/triatomine passages, there was observed an almost identical biological behavior for these parasites, hence indicating that the maintenance of T. cruzi for a long time in axenic culture affects the differentiation capacity and the virulence of the parasite. Additionally, it was demonstrated that it is possible to maintain T. cruzi exclusively through passages in the invertebrate host.

The value of selected in vitro and in silico methods to predict acute oral toxicity in a regulatory context: results from the European Project ACuteTox.

ACuteTox is a project within the 6th European Framework Programme which had as one of its goals to develop, optimise and prevalidate a non-animal testing strategy for predicting human acute oral toxicity. In its last 6 months, a challenging exercise was conducted to assess the predictive capacity of the developed testing strategies and final identification of the most promising ones. Thirty-two chemicals were tested blind in the battery of in vitro and in silico methods selected during the first phase of the project. This paper describes the classification approaches studied: single step procedures and two step tiered testing strategies. In summary, four in vitro testing strategies were proposed as best performing in terms of predictive capacity with respect to the European acute oral toxicity classification. In addition, a heuristic testing strategy is suggested that combines the prediction results gained from the neutral red uptake assay performed in 3T3 cells, with information on neurotoxicity alerts identified by the primary rat brain aggregates test method. Octanol-water partition coefficients and in silico prediction of intestinal absorption and blood-brain barrier passage are also considered. This approach allows to reduce the number of chemicals wrongly predicted as not classified (LD50>2000 mg/kg b.w.).

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Reliability of serological methods for detection of leishmaniasis in portuguese domestic and wild reservoirs

A direct agglutination test (DAT) and an immunofluorescence technique (IFAT) were compared for detection of Leishmania infantum infection in 43 dogs and five foxes from Alto-Douro and Arrábida, two known endemic areas in Portugal. In four dogs with proved canine leishmaniasis, both DAT and IFAT showed positive readings (titres >1:320 and >1:128). Of 34 samples collected from apparently healthy dogs, ten were positive by both serological tests and eight were serologically positive by one test or the other. Three foxes out of five captured in this area, scored titres indicative of leishmaniasis in both DAT and IFAT. The concordance between DAT and IFAT in all collected samples (48) was 81.25%. Considering these and previous studies in the adjacent Mediterranean areas, the seroprevalence of L. infantum infection in the canine and vulpine populations appear to be of high magnitude.