Large deviations for stochastic Volterra equations

This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Adherence to and effectiveness of highly active antiretroviral treatment for HIV infection: assessing the bidirectional relationship.

BACKGROUND: It is well established that high adherence to HIV-infected patients on highly active antiretroviral treatment (HAART) is a major determinant of virological and immunologic success. Furthermore, psychosocial research has identified a wide range of adherence factors including patients' subjective beliefs about the effectiveness of HAART. Current statistical approaches, mainly based on the separate identification either of factors associated with treatment effectiveness or of those associated with adherence, fail to properly explore the true relationship between adherence and treatment effectiveness. Adherence behavior may be influenced not only by perceived benefits-which are usually the focus of related studies-but also by objective treatment benefits reflected in biological outcomes. METHODS: Our objective was to assess the bidirectional relationship between adherence and response to treatment among patients enrolled in the ANRS CO8 APROCO-COPILOTE study. We compared a conventional statistical approach based on the separate estimations of an adherence and an effectiveness equation to an econometric approach using a 2-equation simultaneous system based on the same 2 equations. RESULTS: Our results highlight a reciprocal relationship between adherence and treatment effectiveness. After controlling for endogeneity, adherence was positively associated with treatment effectiveness. Furthermore, CD4 count gain after baseline was found to have a positive significant effect on adherence at each observation period. This immunologic parameter was not significant when the adherence equation was estimated separately. In the 2-equation model, the covariances between disturbances of both equations were found to be significant, thus confirming the statistical appropriacy of studying adherence and treatment effectiveness jointly. CONCLUSIONS: Our results, which suggest that positive biological results arising as a result of high adherence levels, in turn reinforce continued adherence and strengthen the argument that patients who do not experience rapid improvement in their immunologic and clinical statuses after HAART initiation should be prioritized when developing adherence support interventions. Furthermore, they invalidate the hypothesis that HAART leads to "false reassurance" among HIV-infected patients.

A LC-tandem MS assay for the simultaneous measurement of new antiretroviral agents: Raltegravir, maraviroc, darunavir, and etravirine.

Raltegravir (RAL), maraviroc (MVC), darunavir (DRV), and etravirine (ETV) are new antiretroviral agents with significant potential for drug interactions. This work describes a sensitive and accurate liquid chromatography-tandem mass spectrometry (LC-MS/MS) method for the determination of plasma drug levels. Single-step extraction of RAL, MVC, DRV, ETV and RTV from plasma (100 microl) is performed by protein precipitation using 600 microl of acetonitrile, after the addition of 100 microl darunavir-d(9) (DRV-d(9)) at 1000 ng/ml in MeOH/H(2)O 50/50 as internal standard (I.S.). The mixture is vortexed, sonicated for 10 min, vortex-mixed again and centrifuged. An aliquot of supernatant (150 microl) is diluted 1:1 with a mixture of 20 mM ammonium acetate/MeOH 40/60 and 10 microl is injected onto a 2.1 x 50 mm Waters Atlantis-dC18 3 microm analytical column. Chromatographic separations are performed using a gradient program with 2 mM ammonium acetate containing 0.1% formic acid and acetonitrile with 0.1% formic acid. Analytes quantification is performed by electrospray ionisation-triple quadrupole mass spectrometry using the selected reaction monitoring detection in the positive mode. The method has been validated over the clinically relevant concentrations ranging from 12.5 to 5000 ng/ml, 2.5 to 1000 ng/ml, 25 to 10,000 ng/ml, 10 to 4000 ng/ml, and 5 to 2000 ng/ml for RAL, MRV, DRV, ETV and RTV, respectively. The extraction recovery for all antiretroviral drugs is always above 91%. The method is precise, with mean inter-day CV% within 5.1-9.8%, and accurate (range of inter-day deviation from nominal values -3.3 to +5.1%). In addition our method enables the simultaneous assessment of raltegravir-glucuronide. This is the first analytical method allowing the simultaneous assay of antiretroviral agents targeted to four different steps of HIV replication. The proposed method is suitable for the Therapeutic Drug Monitoring Service of these new regimen combinations administered as salvage therapy to patients having experienced treatment failure, and for whom exposure, tolerance and adherence assessments are critical.

A validated assay by liquid chromatography-tandem mass spectrometry for the simultaneous quantification of elvitegravir and rilpivirine in HIV positive patients.

Because of the large variability in the pharmacokinetics of anti-HIV drugs, therapeutic drug monitoring in patients may contribute to optimize the overall efficacy and safety of antiretroviral therapy. An LC-MS/MS method for the simultaneous assay in plasma of the novel antiretroviral agents rilpivirine (RPV) and elvitegravir (EVG) has been developed to that endeavor. Plasma samples (100 μL) extraction is performed by protein precipitation with acetonitrile, and the supernatant is subsequently diluted 1:1 with 20-mM ammonium acetate/MeOH 50:50. After reverse-phase chromatography, quantification of RPV and EVG, using matrix-matched calibration samples, is performed by electrospray ionization-triple quadrupole mass spectrometry by selected reaction monitoring detection using the positive mode. The stable isotopic-labeled compounds RPV-(13) C6 and EVG-D6 were used as internal standards. The method was validated according to FDA recommendations, including assessment of extraction yield, matrix effects variability (<6.4%), as well as EVG and RPV short and long-term stability in plasma. Calibration curves were validated over the clinically relevant concentrations ranging from 5 to 2500 ng/ml for RPV and from 50 to 5000 ng/ml for EVG. The method is precise (inter-day CV%: 3-6.3%) and accurate (3.8-7.2%). Plasma samples were found to be stable (<15%) in all considered conditions (RT/48 h, +4°C/48 h, -20°C/3 months and 60°C/1 h). Selected metabolite profiles analysis in patients' samples revealed the presence of EVG glucuronide, that was well separated from parent EVG, allowing to exclude potential interferences through the in-source dissociation of glucuronide to parent drug. This new, rapid and robust LCMS/MS assay for the simultaneous quantification of plasma concentrations of these two major new anti-HIV drugs EVG and RPV offers an efficient analytical tool for clinical pharmacokinetics studies and routine therapeutic drug monitoring service. Copyright © 2013 John Wiley & Sons, Ltd.

Assessment of skinfold thickness equations in estimating body composition in children with inflammatory bowel

Introduction: Growth is a central process in paediatrics. Weight and height evaluation are therefore routine exams for every child but in some situation, particularly inflammatory bowel disease (IBD), a wider evaluation of nutritional status needs to be performed. The assessment of body composition is essential in order to maintain acceptable growth using the following techniques: Dual-energy X-ray absorptiometry (DEXA), bio-impedance-analysis (BIA) and anthropometric measurements (skinfold thickness skin), the latter being most easily available and most cost effective. Objectives: To assess the accuracy of skinfold equations in estimating percentage body fat (%BF) in children with inflammatory bowel disease (IBD), compared with assessment of body fat dual energy X-ray absorptiometry (DEXA). Methods: Twenty-one patients (11 females, 10 males; mean age: 14.3 years, range 12 - 16 years) with IBD (Crohn's disease n = 15, ulcerative colitis n = 6)). Estimated%BF was computed using 6 established equations based on the triceps, biceps, subscapular and suprailiac skinfolds (Deurenberg, Weststrate, Slaughter, Durnin & Rahaman, Johnston, Brook) and compared to DEXA. Concordance analysis was performed using Lin's concordance correlation and the Bland-Altman limits of agreement method. Results: Durnin & Rahaman's equation shows a higher Lin's concordance coefficient with a small difference amongst raw values for skinfolds and DEXA compared to the other equations. Correlation coefficient between mean and difference is close to zero with a non-significant Bradley-Blackwood test. Conclusion: Body composition in paediatric IBD patients using the Durnin & Rahaman skinfold-equation adequately reflects values obtained by DEXA.

Pavement Management Performance Modeling: Evaluating the Existing PCI Equations, RB14-013 2014

The work described in this report documents the activities performed for the evaluation, development, and enhancement of the Iowa Department of Transportation (DOT) pavement condition information as part of their pavement management system operation. The study covers all of the Iowa DOT’s interstate and primary National Highway System (NHS) and non-NHS system. A new pavement condition rating system that provides a consistent, unified approach in rating pavements in Iowa is being proposed. The proposed 100-scale system is based on five individual indices derived from specific distress data and pavement properties, and an overall pavement condition index, PCI-2, that combines individual indices using weighting factors. The different indices cover cracking, ride, rutting, faulting, and friction. The Cracking Index is formed by combining cracking data (transverse, longitudinal, wheel-path, and alligator cracking indices). Ride, rutting, and faulting indices utilize the International Roughness Index (IRI), rut depth, and fault height, respectively.

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Simultaneous determination of gross alpha, gross beta and Ra-226 in natural water by liquid scintillation counting.

The determination of gross alpha, gross beta and 226Ra activity in natural waters is useful in a wide range of environmental studies. Furthermore, gross alpha and gross beta parameters are included in international legislation on the quality of drinking water [Council Directive 98/83/EC].1 In this work, a low-background liquid scintillation counter (Wallac, Quantulus 1220) was used to simultaneously determine gross alpha, gross beta and 226Ra activity in natural water samples. Sample preparation involved evaporation to remove 222Rn and its short-lived decay daughters. The evaporation process concentrated the sample ten-fold. Afterwards, a sample aliquot of 8 mL was mixed with 12 mL of Ultima Gold AB scintillation cocktail in low-diffusion vials. In this study, a theoretical mathematical model based on secular equilibrium conditions between 226Ra and its short-lived decay daughters is presented. The proposed model makes it possible to determine 226Ra activity from two measurements. These measurements also allow determining gross alpha and gross beta simultaneously. To validate the proposed model, spiked samples with different activity levels for each parameter were analysed. Additionally, to evaluate the model's applicability in natural water, eight natural water samples from different parts of Spain were analysed. The eight natural water samples were also characterised by alpha spectrometry for the naturally occurring isotopes of uranium (234U, 235U and 238U), radium (224Ra and 226Ra), 210Po and 232Th. The results for gross alpha and 226Ra activity were compared with alpha spectrometry characterization, and an acceptable concordance was obtained.

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations