Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

A time-domain method for the analysis of thermal impedance response preserving the convolution form

The study of the thermal behavior of complex packages as multichip modules (MCM¿s) is usually carried out by measuring the so-called thermal impedance response, that is: the transient temperature after a power step. From the analysis of this signal, the thermal frequency response can be estimated, and consequently, compact thermal models may be extracted. We present a method to obtain an estimate of the time constant distribution underlying the observed transient. The method is based on an iterative deconvolution that produces an approximation to the time constant spectrum while preserving a convenient convolution form. This method is applied to the obtained thermal response of a microstructure as analyzed by finite element method as well as to the measured thermal response of a transistor array integrated circuit (IC) in a SMD package.

Stable one-step technetium-99m labeling of His-tagged recombinant proteins with a novel Tc(I)-carbonyl complex.

We have developed a technetium labeling technology based on a new organometallic chemistry, which involves simple mixing of the novel reagent, a 99m Tc(I)-carbonyl compound, with a His-tagged recombinant protein. This method obviates the labeling of unpaired engineered cysteines, which frequently create problems in large-scale expression and storage of disulfide-containing proteins. In this study, we labeled antibody single-chain Fv fragments to high specific activities (90 mCi/mg), and the label was very stable to serum and all other challenges tested. The pharmacokinetic characteristics were indistinguishable from iodinated scFv fragments, and thus scFV fragments labeled by the new method will be suitable for biodistribution studies. This novel labeling method should be applicable not only to diagnostic imaging with 99mTc, but also to radioimmunotherapy approaches with 186/188 Re, and its use can be easily extended to almost any recombinant protein or synthetic peptide.

A step beyond--the relevance of depressed mood and mastery in the interplay between the number of social roles and alcohol use.

OBJECTIVES: The present study examines whether depressed mood and external control mediate or moderate the relationship between the number of social roles and alcohol use. PARTICIPANTS: The analysis was based on a national representative sample of 25- to 45-year-old male and female drinkers in Switzerland. METHOD: The influence of depressed mood and external control on the relationship between the number of social roles (parenthood, partnership, employment) and alcohol use was examined in linear structural equation models (mediation) and in multiple regressions (moderation) stratified by gender. All analyses were adjusted for age and education level. RESULTS: Holding more roles was associated with lower alcohol use, lower external control and lower depressed mood. The study did not find evidence of depressed mood or external control mediating the social roles-alcohol relationship. A moderation effect was identified among women only, whereby a protective effect of having more roles could not be found among those who scored high on external control. In general, a stronger link was observed between roles and alcohol use, while depressed mood and external control acted independently on drinking. With the exception of women with high external control, the study found no link between a higher number of social roles and greater alcohol use. CONCLUSION: Our results indicate that drinking behaviours are more strongly linked to external control and depressed mood than they are to the number of social roles. The study also demonstrates that in any effective alcohol prevention policy, societal actions that enable individuals to combine more social roles play a central role.

Adaptive tracking of EEG oscillations.

Neuronal oscillations are an important aspect of EEG recordings. These oscillations are supposed to be involved in several cognitive mechanisms. For instance, oscillatory activity is considered a key component for the top-down control of perception. However, measuring this activity and its influence requires precise extraction of frequency components. This processing is not straightforward. Particularly, difficulties with extracting oscillations arise due to their time-varying characteristics. Moreover, when phase information is needed, it is of the utmost importance to extract narrow-band signals. This paper presents a novel method using adaptive filters for tracking and extracting these time-varying oscillations. This scheme is designed to maximize the oscillatory behavior at the output of the adaptive filter. It is then capable of tracking an oscillation and describing its temporal evolution even during low amplitude time segments. Moreover, this method can be extended in order to track several oscillations simultaneously and to use multiple signals. These two extensions are particularly relevant in the framework of EEG data processing, where oscillations are active at the same time in different frequency bands and signals are recorded with multiple sensors. The presented tracking scheme is first tested with synthetic signals in order to highlight its capabilities. Then it is applied to data recorded during a visual shape discrimination experiment for assessing its usefulness during EEG processing and in detecting functionally relevant changes. This method is an interesting additional processing step for providing alternative information compared to classical time-frequency analyses and for improving the detection and analysis of cross-frequency couplings.

How to measure cortical folding from MR images: a step-by-step tutorial to compute local gyrification index.

Cortical folding (gyrification) is determined during the first months of life, so that adverse events occurring during this period leave traces that will be identifiable at any age. As recently reviewed by Mangin and colleagues(2), several methods exist to quantify different characteristics of gyrification. For instance, sulcal morphometry can be used to measure shape descriptors such as the depth, length or indices of inter-hemispheric asymmetry(3). These geometrical properties have the advantage of being easy to interpret. However, sulcal morphometry tightly relies on the accurate identification of a given set of sulci and hence provides a fragmented description of gyrification. A more fine-grained quantification of gyrification can be achieved with curvature-based measurements, where smoothed absolute mean curvature is typically computed at thousands of points over the cortical surface(4). The curvature is however not straightforward to comprehend, as it remains unclear if there is any direct relationship between the curvedness and a biologically meaningful correlate such as cortical volume or surface. To address the diverse issues raised by the measurement of cortical folding, we previously developed an algorithm to quantify local gyrification with an exquisite spatial resolution and of simple interpretation. Our method is inspired of the Gyrification Index(5), a method originally used in comparative neuroanatomy to evaluate the cortical folding differences across species. In our implementation, which we name local Gyrification Index (lGI(1)), we measure the amount of cortex buried within the sulcal folds as compared with the amount of visible cortex in circular regions of interest. Given that the cortex grows primarily through radial expansion(6), our method was specifically designed to identify early defects of cortical development. In this article, we detail the computation of local Gyrification Index, which is now freely distributed as a part of the FreeSurfer Software (http://surfer.nmr.mgh.harvard.edu/, Martinos Center for Biomedical Imaging, Massachusetts General Hospital). FreeSurfer provides a set of automated reconstruction tools of the brain's cortical surface from structural MRI data. The cortical surface extracted in the native space of the images with sub-millimeter accuracy is then further used for the creation of an outer surface, which will serve as a basis for the lGI calculation. A circular region of interest is then delineated on the outer surface, and its corresponding region of interest on the cortical surface is identified using a matching algorithm as described in our validation study(1). This process is repeatedly iterated with largely overlapping regions of interest, resulting in cortical maps of gyrification for subsequent statistical comparisons (Fig. 1). Of note, another measurement of local gyrification with a similar inspiration was proposed by Toro and colleagues(7), where the folding index at each point is computed as the ratio of the cortical area contained in a sphere divided by the area of a disc with the same radius. The two implementations differ in that the one by Toro et al. is based on Euclidian distances and thus considers discontinuous patches of cortical area, whereas ours uses a strict geodesic algorithm and include only the continuous patch of cortical area opening at the brain surface in a circular region of interest.

Two-step chromatographic purification of human plasma alpha(1)-acid glycoprotein: its application to the purification of rare phenotype samples of the protein and their study by chromatography on immobilized metal chelate affinity adsorbent.

Alpha1-Acid glycoprotein (AAG) or orosomucoid was purified to homogeneity from human plasma by a separate two-step method using chromatography on immobilized Cibacron Blue F3G-A to cross-linked agarose and chromatography on hydroxyapatite. The conditions for the pre-purification of AAG by chromatography on immobilized Cibacron Blue F3G-A were first optimized using different buffer systems with different pH values. The overall yield of the combined techniques was 80% and ca. 12 mg of AAG were purified from an initial total amount of ca. 15 mg in a ca. 40 ml sample of human plasma. This method was applied to the purification of AAG samples corresponding to the three main phenotypes of the protein (FI*S/A, F1/A and S/A), from individual human plasma previously phenotyped for AAG. A study by isoelectric focusing with carrier ampholytes showed that the microheterogeneity of the purified F1*S/A, F1/A and S/A AAG samples was similar to that of AAG in the corresponding plasma, thus suggesting that no apparent desialylation of the glycoprotein occurred during the purification steps. This method was also applied to the purification of AAG samples corresponding to rare phenotypes of the protein (F1/A*AD, S/A*X0 and F1/A*C1) and the interactions of these variants with immobilized copper(II) ions were then studied at pH 7, by chromatography on an iminodiacetate Sepharose-Cu(II) gel. It was found that the different variants encoded by the first of the two genes coding for AAG in humans (i.e. the F1 and S variants) interacted non-specifically with the immobilized ligand, whereas those encoded by the second gene of AAG (i.e. the A, AD, X0 and C1 variants) strongly bound to immobilized Cu(II) ions. These results suggested that chromatography on an immobilized affinity Cu(II) adsorbent could be helpful to distinguish between the respective products of the two highly polymorphic genes which code for human AAG.

Development and application of a one-step low cost procedure to concentrate viruses from seawater samples

A novel and simple procedure for concentrating adenoviruses from seawater samples is described. The technique entails the adsorption of viruses to pre-flocculated skimmed milk proteins, allowing the flocs to sediment by gravity, and dissolving the separated sediment in phosphate buffer. Concentrated virus may be detected by PCR techniques following nucleic acid extraction. The method requires no specialized equipment other than that usually available in routine public health laboratories, and due to its straightforwardness it allows the processing of a larger number of water samples simultaneously. The usefulness of the method was demonstrated in concentration of virus in multiple seawater samples during a survey of adenoviruses in coastal waters.

A multilevel multiscale finite volume method

The Multiscale Finite Volume (MsFV) method has been developed to efficiently solve reservoir-scale problems while conserving fine-scale details. The method employs two grid levels: a fine grid and a coarse grid. The latter is used to calculate a coarse solution to the original problem, which is interpolated to the fine mesh. The coarse system is constructed from the fine-scale problem using restriction and prolongation operators that are obtained by introducing appropriate localization assumptions. Through a successive reconstruction step, the MsFV method is able to provide an approximate, but fully conservative fine-scale velocity field. For very large problems (e.g. one billion cell model), a two-level algorithm can remain computational expensive. Depending on the upscaling factor, the computational expense comes either from the costs associated with the solution of the coarse problem or from the construction of the local interpolators (basis functions). To ensure numerical efficiency in the former case, the MsFV concept can be reapplied to the coarse problem, leading to a new, coarser level of discretization. One challenge in the use of a multilevel MsFV technique is to find an efficient reconstruction step to obtain a conservative fine-scale velocity field. In this work, we introduce a three-level Multiscale Finite Volume method (MlMsFV) and give a detailed description of the reconstruction step. Complexity analyses of the original MsFV method and the new MlMsFV method are discussed, and their performances in terms of accuracy and efficiency are compared.

Single-step extraction of fluconazole from plasma by ultra-filtration for the measurement of its free concentration by high performance liquid chromatography.

High performance liquid chromatography (HPLC) is the reference method for measuring concentrations of antimicrobials in blood. This technique requires careful sample preparation. Protocols using organic solvents and/or solid extraction phases are time consuming and entail several manipulations, which can lead to partial loss of the determined compound and increased analytical variability. Moreover, to obtain sufficient material for analysis, at least 1 ml of plasma is required. This constraint makes it difficult to determine drug levels when blood sample volumes are limited. However, drugs with low plasma-protein binding can be reliably extracted from plasma by ultra-filtration with a minimal loss due to the protein-bound fraction. This study validated a single-step ultra-filtration method for extracting fluconazole (FLC), a first-line antifungal agent with a weak plasma-protein binding, from plasma to determine its concentration by HPLC. Spiked FLC standards and unknowns were prepared in human and rat plasma. Samples (240 microl) were transferred into disposable microtube filtration units containing cellulose or polysulfone filters with a 5 kDa cut-off. After centrifugation for 60 min at 15000g, FLC concentrations were measured by direct injection of the filtrate into the HPLC. Using cellulose filters, low molecular weight proteins were eluted early in the chromatogram and well separated from FLC that eluted at 8.40 min as a sharp single peak. In contrast, with polysulfone filters several additional peaks interfering with the FLC peak were observed. Moreover, the FLC recovery using cellulose filters compared to polysulfone filters was higher and had a better reproducibility. Cellulose filters were therefore used for the subsequent validation procedure. The quantification limit was 0.195 mgl(-1). Standard curves with a quadratic regression coefficient > or = 0.9999 were obtained in the concentration range of 0.195-100 mgl(-1). The inter and intra-run accuracies and precisions over the clinically relevant concentration range, 1.875-60 mgl(-1), fell well within the +/-15% variation recommended by the current guidelines for the validation of analytical methods. Furthermore, no analytical interference was observed with commonly used antibiotics, antifungals, antivirals and immunosuppressive agents. Ultra-filtration of plasma with cellulose filters permits the extraction of FLC from small volumes (240 microl). The determination of FLC concentrations by HPLC after this single-step procedure is selective, precise and accurate.

An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

Determination of the Enantiomers of Mianserin and its Metabolites in Plasma by Capillary Electrophoresis After Liquid-Liquid Extraction and On-Column Sample Preconcentration

Capillary electrophoresis has drawn considerable attention in the past few years, particularly in the field of chiral separations because of its high separation efficiency. However, its routine use in therapeutic drug monitoring is hampered by its low sensitivity due to a short optical path. We have developed a capillary zone electrophoresis (CZE) method using 2mM of hydroxypropyl-β-cyclodextrin as a chiral selector, which allows base-to-base separation of the enantiomers of mianserin (MIA), desmethylmianserin (DMIA), and 8-hydroxymianserin (OHMIA). Through the use of an on-column sample concentration step after liquid-liquid extraction from plasma and through the presence of an internal standard, the quantitation limits were found to be 5 ng/mL for each enantiomer of MIA and DMIA and 15 ng/mL for each enantiomer of OHMIA. To our knowledge, this is the first published CE method that allows its use for therapeutic monitoring of antidepressants due to its sensitivity down to the low nanogram range. The variability of the assays, as assessed by the coefficients of variation (CV) measured at two concentrations for each substance, ranged from 2 to 14% for the intraday (eight replicates) and from 5 to 14% for the interday (eight replicates) experiments. The deviations from the theoretical concentrations, which represent the accuracy of the method, were all within 12.5%. A linear response was obtained for all compounds within the range of concentrations used for the calibration curves (10-150 ng/mL for each enantiomer of MIA and DMIA and 20-300 ng/mL for each enantiomer of OHMIA). Good correlations were calculated between [(R) + (S)]-MIA and DMIA concentrations measured in plasma samples of 20 patients by a nonchiral gas chromatography method and CZE, and between the (R)- and (S)-concentrations of MIA and DMIA measured in plasma samples of 37 patients by a previously described chiral high-performance liquid chromatography method and CZE. Finally, no interference was noted from more than 20 other psychotropic drugs. Thus, this method, which is both sensitive and selective, can be routinely used for therapeutic monitoring of the enantiomers of MIA and its metabolites. It could be very useful due to the demonstrated interindividual variability of the stereoselective metabolism of MIA.

Satisfaction survey with DNA cards method to collect genetic samples for pharmacogenetics studies

Background: Pharmacogenetic studies are essential in understanding the interindividual variability of drug responses. DNA sample collection for genotyping is a critical step in genetic studies. A method using dried blood samples from finger-puncture, collected on DNA-cards, has been described as an alternative to the usual venepuncture technique. The purpose of this study is to evaluate the implementation of the DNA cards method in a multicentre clinical trial, and to assess the degree of investigators' satisfaction and the acceptance of the patients perceived by the investigators.Methods: Blood samples were collected on DNA-cards. The quality and quantity of DNA recovered were analyzed. Investigators were questioned regarding their general interest, previous experience, safety issues, preferences and perceived patient satisfaction. Results: 151 patients' blood samples were collected. Genotyping of GST polymorphisms was achieved in all samples (100%). 28 investigators completed the survey. Investigators perceived patient satisfaction as very good (60.7%) or good (39.3%), without reluctance to finger puncture. Investigators preferred this method, which was considered safer and better than the usual methods. All investigators would recommend using it in future genetic studies. Conclusion: Within the clinical trial setting, the DNA-cards method was very well accepted by investigators and patients (in perception of investigators), and was preferred to conventional methods due to its ease of use and safety.

Two-step postmortem angiography with a modified heart-lung machine: preliminary results.

OBJECTIVE: The purpose of this study was to adapt and improve a minimally invasive two-step postmortem angiographic technique for use on human cadavers. Detailed mapping of the entire vascular system is almost impossible with conventional autopsy tools. The technique described should be valuable in the diagnosis of vascular abnormalities. MATERIALS AND METHODS: Postmortem perfusion with an oily liquid is established with a circulation machine. An oily contrast agent is introduced as a bolus injection, and radiographic imaging is performed. In this pilot study, the upper or lower extremities of four human cadavers were perfused. In two cases, the vascular system of a lower extremity was visualized with anterograde perfusion of the arteries. In the other two cases, in which the suspected cause of death was drug intoxication, the veins of an upper extremity were visualized with retrograde perfusion of the venous system. RESULTS: In each case, the vascular system was visualized up to the level of the small supplying and draining vessels. In three of the four cases, vascular abnormalities were found. In one instance, a venous injection mark engendered by the self-administration of drugs was rendered visible by exudation of the contrast agent. In the other two cases, occlusion of the arteries and veins was apparent. CONCLUSION: The method described is readily applicable to human cadavers. After establishment of postmortem perfusion with paraffin oil and injection of the oily contrast agent, the vascular system can be investigated in detail and vascular abnormalities rendered visible.

Cross-frequency coupling in EEG revealed by adaptive oscillation tracking.

Introduction: Neuronal oscillations have been the focus of increasing interest in the neuroscientific community, in part because they have been considered as a possible integrating mechanism through which internal states can influence stimulus processing in a top-down way (Engel et al., 2001). Moreover, increasing evidence indicates that oscillations in different frequency bands interact with one other through coupling mechanisms (Jensen and Colgin, 2007). The existence and the importance of these cross-frequency couplings during various tasks have been verified by recent studies (Canolty et al., 2006; Lakatos et al., 2007). In this study, we measure the strength and directionality of two types of couplings - phase-amplitude couplings and phase-phase couplings - between various bands in EEG data recorded during an illusory contour experiment that were identified using a recently-proposed adaptive frequency tracking algorithm (Van Zaen et al., 2010). Methods: The data used in this study have been taken from a previously published study examining the spatiotemporal mechanisms of illusory contour processing (Murray et al., 2002). The EEG in the present study were from a subset of nine subjects. Each stimulus was composed of 'pac-man' inducers presented in two orientations: IC, when an illusory contour was present, and NC, when no contour could be detected. The signals recorded by the electrodes P2, P4, P6, PO4 and PO6 were averaged, and filtered into the following bands: 4-8Hz, 8-12Hz, 15-25Hz, 35-45Hz, 45-55Hz, 55-65Hz and 65-75Hz. An adaptive frequency tracking algorithm (Van Zaen et al., 2010) was then applied in each band in order to extract the main oscillation and estimate its frequency. This additional step ensures that clean phase information is obtained when taking the Hilbert transform. The frequency estimated by the tracker was averaged over sliding windows and then used to compare the two conditions. Two types of cross-frequency couplings were considered: phase-amplitude couplings and phase-phase couplings. Both types were measured with the phase locking value (PLV, Lachaux et al., 1999) over sliding windows. The phase-amplitude couplings were computed with the phase of the low frequency oscillation and the phase of the amplitude of the high frequency one. Different coupling coefficients were used when measuring phase-phase couplings in order to estimate different m:n synchronizations (4:3, 3:2, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, 8:1 and 9:1) and to take into account the frequency differences across bands. Moreover, the direction of coupling was estimated with a directionality index (Bahraminasab et al., 2008). Finally, the two conditions IC and NC were compared with ANOVAs with 'subject' as a random effect and 'condition' as a fixed effect. Before computing the statistical tests, the PLV values were transformed into approximately normal variables (Penny et al., 2008). Results: When comparing the mean estimated frequency across conditions, a significant difference was found only in the 4-8Hz band, such that the frequency within this band was significantly higher for IC than NC stimuli starting at ~250ms post-stimulus onset (Fig. 1; solid line shows IC and dashed line NC). Significant differences in phase-amplitude couplings were obtained only when the 4-8 Hz band was taken as the low frequency band. Moreover, in all significant situations, the coupling strength is higher for the NC than IC condition. An example of significant difference between conditions is shown in Fig. 2 for the phase-amplitude coupling between the 4-8Hz and 55-65Hz bands (p-value in top panel and mean PLV values in the bottom panel). A decrease in coupling strength was observed shortly after stimulus onset for both conditions and was greater for the condition IC. This phenomenon was observed with all other frequency bands. The results obtained for the phase-phase couplings were more complex. As for the phase-amplitude couplings, all significant differences were obtained when the 4-8Hz band was considered as the low frequency band. The stimulus condition exhibiting the higher coupling strength depended on the ratio of the coupling coefficients. When this ratio was small, the IC condition exhibited the higher phase-phase coupling strength. When this ratio was large, the NC condition exhibited the higher coupling strength. Fig. 3 shows the phase-phase couplings between the 4-8Hz and 35-45Hz bands for the coupling coefficient 6:1, and the coupling strength was significantly higher for the IC than NC condition. By contrast, for the coupling coefficient 9:1 the NC condition gave the higher coupling strength (Fig. 4). Control analyses verified that it is not a consequence of the frequency difference between the two conditions in the 4-8Hz band. The directionality measures indicated a transfer of information from the low frequency components towards the high frequency ones. Conclusions: Adaptive tracking is a feasible method for EEG analyses, revealing information both about stimulus-related differences and coupling patterns across frequencies. Theta oscillations play a central role in illusory shape processing and more generally in visual processing. The presence vs. absence of illusory shapes was paralleled by faster theta oscillations. Phase-amplitude couplings were decreased more for IC than NC and might be due to a resetting mechanism. The complex patterns in phase-phase coupling between theta and beta/gamma suggest that the contribution of these oscillations to visual binding and stimulus processing are not as straightforward as conventionally held. Causality analyses further suggest that theta oscillations drive beta/gamma oscillations (see also Schroeder and Lakatos, 2009). The present findings highlight the need for applying more sophisticated signal analyses in order to establish a fuller understanding of the functional role of neural oscillations.