A basis function approach to Bayesian inference in diffusion processes

In this paper, we present a framework for Bayesian inference in continuous-time diffusion processes. The new method is directly related to the recently proposed variational Gaussian Process approximation (VGPA) approach to Bayesian smoothing of partially observed diffusions. By adopting a basis function expansion (BF-VGPA), both the time-dependent control parameters of the approximate GP process and its moment equations are projected onto a lower-dimensional subspace. This allows us both to reduce the computational complexity and to eliminate the time discretisation used in the previous algorithm. The new algorithm is tested on an Ornstein-Uhlenbeck process. Our preliminary results show that BF-VGPA algorithm provides a reasonably accurate state estimation using a small number of basis functions.

A longitudinal study of the diffusion of the ISO/IEC information resource dictionary system standard (IRDS.)

The IRDS standard is an international standard produced by the International Organisation for Standardisation (ISO). In this work the process for producing standards in formal standards organisations, for example the ISO, and in more informal bodies, for example the Object Management Group (OMG), is examined. This thesis examines previous models and classifications of standards. The previous models and classifications are then combined to produce a new classification. The IRDS standard is then placed in a class in the new model as a reference anticipatory standard. Anticipatory standards are standards which are developed ahead of the technology in order to attempt to guide the market. The diffusion of the IRDS is traced over a period of eleven years. The economic conditions which affect the diffusion of standards are examined, particularly the economic conditions which prevail in compatibility markets such as the IT and ICT markets. Additionally the consequences of the introduction of gateway or converter devices into a market where a standard has not yet been established is examined. The IRDS standard did not have an installed base and this hindered its diffusion. The thesis concludes that the IRDS standard was overtaken by new developments such as object oriented technologies and middleware. This was partly because of the slow development process of developing standards in traditional organisations which operate on a consensus basis and partly because the IRDS standard did not have an installed base. Also the rise and proliferation of middleware products resulted in exchange mechanisms becoming dominant rather than repository solutions. The research method used in this work is a longitudinal study of the development and diffusion of the ISO/EEC IRDS standard. The research is regarded as a single case study and follows the interpretative epistemological point of view.

Quantitative interpretation of diffusion-ordered NMR spectra:can we rationalize small molecule diffusion coefficients?

Appealingly simple: A new method is described that allows the diffusion coefficient of a small molecule to be estimated given only the molecular weight and the viscosity of the solvent used. This method makes possible the quantitative interpretation of the diffusion domain of diffusion-ordered NMR spectra (see picture). © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Modification of the B2-type matrix of aluminide diffusion coatings on nickel-base superalloys-bulk aluminide analogues

Pack aluminide coating is a useful method for conferring oxidation resistance on nickel-base superalloys. Nominally, these coatings have a matrix composed of a Ni-Al based B2-type phase (commonly denoted as Β). However, following high-temperature exposure in oxidative envi-ronments, aluminum is depleted from the coating. Aluminum depletion in turn, leads to de-stabilization of the Β phase, resulting in the formation of a characteristic lathlike Β-derivative microstructure. This article presents a transmission electron microscopy study of the formation of the lathlike Β-derivative microstructure using bulk nickel aluminides as model alloys. In the bulk nickel aluminides, the lathlike microstructure has been found to correspond to two distinct components: L10-type martensite and a new Β derivative. The new Β derivative is characterized and the conditions associated with the presence of this feature are identified and compared with those leading to the formation of the L10 martensitic phase. © 1995 The Minerals, Metals & Material Society.

Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.

Increasing the Calculation Speed of an Acceleration Scheme for an Age-Structured Diffusion Model

Дойчин Бояджиев, Галена Пеловска - В статията се предлага оптимизиран алгоритъм, който е по-бърз в сравнение с по- рано описаната ускорена (модифицирана STS) диференчна схема за възрастово структуриран популационен модел с дифузия. Запазвайки апроксимацията на модифицирания STS алгоритъм, изчислителното времето се намаля почти два пъти. Това прави оптимизирания метод по-предпочитан за задачи с нелинейност или с по-висока размерност.

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

MSC 2010: 35R11, 42A38, 26A33, 33E12

Soot measurements in steady and pulsed ethylene/air diffusion flames using Laser-Induced Incandescence

Combustion-generated carbon black nano particles, or soot, have both positive and negative effects depending on the application. From a positive point of view, it is used as a reinforcing agent in tires, black pigment in inks, and surface coatings. From a negative point of view, it affects performance and durability of many combustion systems, it is a major contributor of global warming, and it is linked to respiratory illness and cancer. Laser-Induced Incandescence (LII) was used in this study to measure soot volume fractions in four steady and twenty-eight pulsed ethylene diffusion flames burning at atmospheric pressure. A laminar coflow diffusion burner combined with a very-high-speed solenoid valve and control circuit provided unsteady flows by forcing the fuel flow with frequencies between 10 Hz and 200 Hz. Periodic flame oscillations were captured by two-dimensional phase-locked LII images and broadband luminosity images for eight phases (0° – 360°) covering each period. A comparison between the steady and pulsed flames and the effect of the pulsation frequency on soot volume fraction in the flame region and the post flame region are presented. The most significant effect of pulsing frequency was observed at 10 Hz. At this frequency, the flame with the lowest mean flow rate had 1.77 times enhancement in peak soot volume fraction and 1.2 times enhancement in total soot volume fraction; whereas the flame with the highest mean flow rate had no significant change in the peak soot volume fraction and 1.4 times reduction in the total soot volume fraction. A correlation (fvRe-1 = a + b·Str) for the total soot volume fraction in the flame region for the unsteady laminar ethylene flames was obtained for the pulsation frequency between 10 Hz and 200 Hz, and the Reynolds number between 37 and 55. The soot primary particle size in steady and unsteady flames was measured using the Time-Resolved Laser-Induced Incandescence (TIRE-LII) and the double-exponential fit method. At maximum frequency (200 Hz), the soot particles were smaller in size by 15% compared to the steady case in the flame with the highest mean flow rate.

Soot Measurements in Steady and Pulsed Ethylene/Air Diffusion Flames Using Laser-Induced Incandescence

Combustion-generated carbon black nano particles, or soot, have both positive and negative effects depending on the application. From a positive point of view, it is used as a reinforcing agent in tires, black pigment in inks, and surface coatings. From a negative point of view, it affects performance and durability of many combustion systems, it is a major contributor of global warming, and it is linked to respiratory illness and cancer. Laser-Induced Incandescence (LII) was used in this study to measure soot volume fractions in four steady and twenty-eight pulsed ethylene diffusion flames burning at atmospheric pressure. A laminar coflow diffusion burner combined with a very-high-speed solenoid valve and control circuit provided unsteady flows by forcing the fuel flow with frequencies between 10 Hz and 200 Hz. Periodic flame oscillations were captured by two-dimensional phase-locked LII images and broadband luminosity images for eight phases (0°- 360°) covering each period. A comparison between the steady and pulsed flames and the effect of the pulsation frequency on soot volume fraction in the flame region and the post flame region are presented. The most significant effect of pulsing frequency was observed at 10 Hz. At this frequency, the flame with the lowest mean flow rate had 1.77 times enhancement in peak soot volume fraction and 1.2 times enhancement in total soot volume fraction; whereas the flame with the highest mean flow rate had no significant change in the peak soot volume fraction and 1.4 times reduction in the total soot volume fraction. A correlation (ƒv Reˉ1 = a+b· Str) for the total soot volume fraction in the flame region for the unsteady laminar ethylene flames was obtained for the pulsation frequency between 10 Hz and 200 Hz, and the Reynolds number between 37 and 55. The soot primary particle size in steady and unsteady flames was measured using the Time-Resolved Laser-Induced Incandescence (TIRE-LII) and the double-exponential fit method. At maximum frequency (200 Hz), the soot particles were smaller in size by 15% compared to the steady case in the flame with the highest mean flow rate.

Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Radiotherapy Assessment Using Diffusion Weighted MRI

Purpose: There are two goals of this study. The first goal of this study is to investigate the feasibility of using classic textural feature extraction in radiotherapy response assessment among a unique cohort of early stage breast cancer patients who received the single-dose preoperative radiotherapy. The second goal of this study is to investigate the clinical feasibility of using classic texture features as potential biomarkers which are supplementary to regional apparent diffusion coefficient in gynecological cancer radiotherapy response assessment.

Methods and Materials: For the breast cancer study, 15 patients with early stage breast cancer were enrolled in this retrospective study. Each patient received a single-fraction radiation treatment, and DWI and DCE-MRI scans were conducted before and after the radiotherapy. DWI scans were acquired using a spin-echo EPI sequence with diffusion weighting factors of b = 0 and b = 500 mm2/s, and the apparent diffusion coefficient (ADC) maps were calculated. DCE-MRI scans were acquired using a T1-weighted 3D SPGR sequence with a temporal resolution of about 1 minute. The contrast agent (CA) was intravenously injected with a 0.1 mmol/kg bodyweight dose at 2 ml/s. Two parameters, volume transfer constant (Ktrans) and kep were analyzed using the two-compartment Tofts pharmacokinetic model. For pharmacokinetic parametric maps and ADC maps, 33 textural features were generated from the clinical target volume (CTV) in a 3D fashion using the classic gray level co-occurrence matrix (GLCOM) and gray level run length matrix (GLRLM). Wilcoxon signed-rank test was used to determine the significance of each texture feature’s change after the radiotherapy. The significance was set to 0.05 with Bonferroni correction.

For the gynecological cancer study, 12 female patients with gynecologic cancer treated with fractionated external beam radiotherapy (EBRT) combined with high dose rate (HDR) intracavitary brachytherapy were studied. Each patient first received EBRT treatment followed by five fractions of HDR treatment. Before EBRT and before each fraction of brachytherapy, Diffusion Weighted MRI (DWI-MRI) and CT scans were acquired. DWI scans were acquired in sagittal plane utilizing a spin-echo echo-planar imaging sequence with weighting factors of b = 500 s/mm2 and b = 1000 s/mm2, one set of images of b = 0 s/mm2 were also acquired. ADC maps were calculated using linear least-square fitting method. Distributed diffusion coefficient (DDC) maps and stretching parameter α were calculated. For ADC and DDC maps, 33 classic texture features were generated utilizing the classic gray level run length matrix (GLRLM) and gray level co-occurrence matrix (GLCOM) from high-risk clinical target volume (HR-CTV). Wilcoxon signed-rank statistics test was applied to determine the significance of each feature’s numerical value change after radiotherapy. Significance level was set to 0.05 with multi-comparison correction if applicable.

Results: For the breast cancer study, regarding ADC maps calculated from DWI-MRI, 24 out of 33 CTV features changed significantly after the radiotherapy. For DCE-MRI pharmacokinetic parameters, all 33 CTV features of Ktrans and 33 features of kep changed significantly.

For the gynecological cancer study, regarding ADC maps, 28 out of 33 HR-CTV texture features showed significant changes after the EBRT treatment. 28 out of 33 HR-CTV texture features indicated significant changes after HDR treatments. The texture features that indicated significant changes after HDR treatments are the same as those after EBRT treatment. 28 out of 33 HR-CTV texture features showed significant changes after whole radiotherapy treatment process. The texture features that indicated significant changes for the whole treatment process are the same as those after HDR treatments.

Conclusion: Initial results indicate that certain classic texture features are sensitive to radiation-induced changes. Classic texture features with significant numerical changes can be used in monitoring radiotherapy effect. This might suggest that certain texture features might be used as biomarkers which are supplementary to ADC and DDC for assessment of radiotherapy response in breast cancer and gynecological cancer.

Inter-site and inter-scanner diffusion MRI data harmonization.

We propose a novel method to harmonize diffusion MRI data acquired from multiple sites and scanners, which is imperative for joint analysis of the data to significantly increase sample size and statistical power of neuroimaging studies. Our method incorporates the following main novelties: i) we take into account the scanner-dependent spatial variability of the diffusion signal in different parts of the brain; ii) our method is independent of compartmental modeling of diffusion (e.g., tensor, and intra/extra cellular compartments) and the acquired signal itself is corrected for scanner related differences; and iii) inter-subject variability as measured by the coefficient of variation is maintained at each site. We represent the signal in a basis of spherical harmonics and compute several rotation invariant spherical harmonic features to estimate a region and tissue specific linear mapping between the signal from different sites (and scanners). We validate our method on diffusion data acquired from seven different sites (including two GE, three Philips, and two Siemens scanners) on a group of age-matched healthy subjects. Since the extracted rotation invariant spherical harmonic features depend on the accuracy of the brain parcellation provided by Freesurfer, we propose a feature based refinement of the original parcellation such that it better characterizes the anatomy and provides robust linear mappings to harmonize the dMRI data. We demonstrate the efficacy of our method by statistically comparing diffusion measures such as fractional anisotropy, mean diffusivity and generalized fractional anisotropy across multiple sites before and after data harmonization. We also show results using tract-based spatial statistics before and after harmonization for independent validation of the proposed methodology. Our experimental results demonstrate that, for nearly identical acquisition protocol across sites, scanner-specific differences can be accurately removed using the proposed method.