Large deviation for BSDE with subdifferential operator

In this paper we prove that the solution of a backward stochastic differential equation, which involves a subdifferential operator and associated to a family of reflecting diffusion processes, converges to the solution of a deterministic backward equation and satisfes a large deviation principle.

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.

Hydrodynamic origin of diffusion in nanopores

We study the transport of a subcritical Lennard-Jones fluid in a cylindrical nanopore, using a combination of equilibrium and nonequilibrium as well as dual control volume grand canonical molecular dynamics methods. We show that all three techniques yield the same value of the transport coefficient for diffusely reflecting pore walls, even in the presence of viscous transport. We also demonstrate that the classical Knudsen mechanism is not manifested, and that a combination of viscous flow and momentum exchange at the pore wall governs the transport over a wide range of densities.

Solution to telegrapher's equation in the presence of reflecting and partly reflecting broundaries

We show that the reflecting boundary condition for a one-dimensional telegraphers equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegraphers equation in the presence of these boundaries.

Functional evaluation of transplanted kidneys with diffusion-weighted and BOLD MR imaging: initial experience

PURPOSE: To prospectively evaluate feasibility and reproducibility of diffusion-weighted (DW) and blood oxygenation level-dependent (BOLD) magnetic resonance (MR) imaging in patients with renal allografts, as compared with these features in healthy volunteers with native kidneys. MATERIALS AND METHODS: The local ethics committee approved the study protocol; patients provided written informed consent. Fifteen patients with a renal allograft and in stable condition (nine men, six women; age range, 20-67 years) and 15 age- and sex-matched healthy volunteers underwent DW and BOLD MR imaging. Seven patients with renal allografts were examined twice to assess reproducibility of results. DW MR imaging yielded a total apparent diffusion coefficient including diffusion and microperfusion (ADC(tot)), as well as an ADC reflecting predominantly pure diffusion (ADC(D)) and the perfusion fraction. R2* of BOLD MR imaging enabled the estimation of renal oxygenation. Statistical analysis was performed, and analysis of variance was used for repeated measurements. Coefficients of variation between and within subjects were calculated to assess reproducibility. RESULTS: In patients, ADC(tot), ADC(D), and perfusion fraction were similar in the cortex and medulla. In volunteers, values in the medulla were similar to those in the cortex and medulla of patients; however, values in the cortex were higher than those in the medulla (P < .05). Medullary R2* was higher than cortical R2* in patients (12.9 sec(-1) +/- 2.1 [standard deviation] vs 11.0 sec(-1) +/- 0.6, P < .007) and volunteers (15.3 sec(-1) +/- 1.1 vs 11.5 sec(-1) +/- 0.5, P < .0001). However, medullary R2* was lower in patients than in volunteers (P < .004). Increased medullary R2* was paralleled by decreased diffusion in patients with allografts. A low coefficient of variation in the cortex and medulla within subjects was obtained for ADC(tot), ADC(D), and R2* (<5.2%), while coefficient of variation within subjects was higher for perfusion fraction (medulla, 15.1%; cortex, 8.6%). Diffusion and perfusion indexes correlated significantly with serum creatinine concentrations. CONCLUSION: DW and BOLD MR imaging are feasible and reproducible in patients with renal allografts.

Nonperturbative estimate of the heavy quark momentum diffusion coefficient

We estimate the momentum diffusion coefficient of a heavy quark within a pure SU(3) plasma at a temperature of about 1.5Tc. Large-scale Monte Carlo simulations on a series of lattices extending up to 1923×48 permit us to carry out a continuum extrapolation of the so-called color-electric imaginary-time correlator. The extrapolated correlator is analyzed with the help of theoretically motivated models for the corresponding spectral function. Evidence for a nonzero transport coefficient is found and, incorporating systematic uncertainties reflecting model assumptions, we obtain κ=(1.8–3.4)T3. This implies that the “drag coefficient,” characterizing the time scale at which heavy quarks adjust to hydrodynamic flow, is η−1D=(1.8–3.4)(Tc/T)2(M/1.5  GeV)  fm/c, where M is the heavy quark kinetic mass. The results apply to bottom and, with somewhat larger systematic uncertainties, to charm quarks.

Fluorescence correlation analysis of probe diffusion simplifies quantitative pathogen detection by PCR

A sensitive, labor-saving, and easily automatable nonradioactive procedure named APEX-FCS (amplified probe extension detected by fluorescence correlation spectroscopy) has been established to detect specific in vitro amplification of pathogen genomic sequences. As an example, Mycobacterium tuberculosis genomic DNA was subjected to PCR amplification with the Stoffel fragment of Thermus aquaticus DNA polymerase in the presence of nanomolar concentrations of a rhodamine-labeled probe (third primer), binding to the target in between the micromolar amplification primers. The probe becomes extended only when specific amplification occurs. Its low concentration avoids false-positives due to unspecific hybridization under PCR conditions. With increasing portion of extended probe molecules, the probe’s average translational diffusion properties gradually change over the course of the reaction, reflecting amplification kinetics. Following PCR, this change from a stage of high to a stage of low mobility can directly be monitored during a 30-s measurement using a fluorescence correlation spectroscopy device. Quantitation down to 10 target molecules in a background of 2.5 μg unspecific DNA without post-PCR probe manipulations could be achieved with different primer/probe combinations. The assay holds the promise to concurrently perform amplification, probe hybridization, and specific detection without opening the reaction chamber, if sealable foils are used.

Salt diffusion and distribution in meat studied by Na-23 nuclear magnetic resonance imaging and relaxometry

This study introduces the use of combined Na-23 magnetic resonance imaging (MRI) and Na-23 NMR relaxometry for the study of meat curing. The diffusion of sodium ions into the meat was measured using Na-23 MRI on a 1 kg meat sample brined in 10% w/w NaCl for 3-100 h. Calculations revealed a diffusion coefficient of 1 x 10(-5) cm(2)/s after 3 h of curing and subsequently decreasing to 8 x 10(-6) cm(2)/s at longer curing times, suggesting that changes occur in the microscopic structure of the meat during curing. The microscopic mobility and distribution of sodium was measured using Na-23 relaxometry. Two sodium populations were observed, and with increasing length of curing time the relaxation times of these changed, reflecting a salt-induced swelling and increase in myofibrillar pore sizes. Accordingly, the present study demonstrated that pore size and thereby salt-induced swelling in meat can be assessed using Na-23 relaxometry.

Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces

Thesis (Ph.D.)--University of Washington, 2016-08

Analysis Of The Dna Fourier Transform-infrared Microspectroscopic Signature Using An All-reflecting Objective.

The Fourier transform-infrared (FT-IR) signature of dry samples of DNA and DNA-polypeptide complexes, as studied by IR microspectroscopy using a diamond attenuated total reflection (ATR) objective, has revealed important discriminatory characteristics relative to the PO2(-) vibrational stretchings. However, DNA IR marks that provide information on the sample's richness in hydrogen bonds have not been resolved in the spectral profiles obtained with this objective. Here we investigated the performance of an all reflecting objective (ARO) for analysis of the FT-IR signal of hydrogen bonds in DNA samples differing in base richness types (salmon testis vs calf thymus). The results obtained using the ARO indicate prominent band peaks at the spectral region representative of the vibration of nitrogenous base hydrogen bonds and of NH and NH2 groups. The band areas at this spectral region differ in agreement with the DNA base richness type when using the ARO. A peak assigned to adenine was more evident in the AT-rich salmon DNA using either the ARO or the ATR objective. It is concluded that, for the discrimination of DNA IR hydrogen bond vibrations associated with varying base type proportions, the use of an ARO is recommended.

Feasibility And Reproducibility Of Diffusion-weighted Magnetic Resonance Imaging Of The Fetal Brain In Twin-twin Transfusion Syndrome.

The aim of this study is to test the feasibility and reproducibility of diffusion-weighted magnetic resonance imaging (DW-MRI) evaluations of the fetal brains in cases of twin-twin transfusion syndrome (TTTS). From May 2011 to June 2012, 24 patients with severe TTTS underwent MRI scans for evaluation of the fetal brains. Datasets were analyzed offline on axial DW images and apparent diffusion coefficient (ADC) maps by two radiologists. The subjective evaluation was described as the absence or presence of water diffusion restriction. The objective evaluation was performed by the placement of 20-mm(2) circular regions of interest on the DW image and ADC maps. Subjective interobserver agreement was assessed by the kappa correlation coefficient. Objective intraobserver and interobserver agreements were assessed by proportionate Bland-Altman tests. Seventy-four DW-MRI scans were performed. Sixty of them (81.1%) were considered to be of good quality. Agreement between the radiologists was 100% for the absence or presence of diffusion restriction of water. For both intraobserver and interobserver agreement of ADC measurements, proportionate Bland-Altman tests showed average percentage differences of less than 1.5% and 95% CI of less than 18% for all sites evaluated. Our data demonstrate that DW-MRI evaluation of the fetal brain in TTTS is feasible and reproducible.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Evaluation of the diffusion capacity of calcium hydroxide pastes through the dentinal tubules

This study aimed to evaluate the diffusion capacity of calcium hydroxide pastes with different vehicles through dentinal tubules. The study was conducted on 60 extracted single-rooted human teeth whose crowns had been removed. The root canals were instrumented and divided into 4 groups according to the vehicle of the calcium hydroxide paste: Group I - distilled water; Group II - propylene glycol; Group III - 0.2% chlorhexidine; Group IV - 2% chlorhexidine. After placement of the root canal dressings, the teeth were sealed and placed in flasks containing deionized water. After 1, 2, 7, 15, 30, 45 and 60 days, the pH of the water was measured to determine the diffusion of calcium hydroxide through the dentinal tubules. The data were recorded and statistically compared by the Tukey test. The results showed that all pastes presented a similar diffusion capacity through dentin. Group IV did not present difference compared to group I. Group II presented difference compared to the other groups, as did Group III. In conclusion, groups I and IV presented a better diffusion capacity through dentin than groups II and III; 2% chlorhexidine can be used as a vehicle in calcium hydroxide pastes.

Anomalous diffusion in non-Markovian walks having amnestically induced persistence

We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.