A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

Performance assessment of exponential Rosenbrock method for large systems of ODE

This paper studies time integration methods for large stiff systems of ordinary differential equations (ODEs) of the form u'(t) = g(u(t)). For such problems, implicit methods generally outperform explicit methods, since the time step is usually less restricted by stability constraints. Recently, however, explicit so-called exponential integrators have become popular for stiff problems due to their favourable stability properties. These methods use matrix-vector products involving exponential-like functions of the Jacobian matrix, which can be approximated using Krylov subspace methods that require only matrix-vector products with the Jacobian. In this paper, we implement exponential integrators of second, third and fourth order and demonstrate that they are competitive with well-established approaches based on the backward differentiation formulas and a preconditioned Newton-Krylov solution strategy.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Secondary curve behavior in Lenke Type 1C adolescent idiopathic scoliosis after thoracoscopic selective anterior thoracic fusion

Study Design. Analysis of a case series of 24 Lenke 1C adolescent idiopathic scoliosis (AIS) patients receiving selective thoracoscopic anterior scoliosis correction. Objective. To report the behaviour of the compensatory lumbar curve in a group of Lenke IC AIS patients following thoracoscopic anterior scoliosis correction, and to compare the results of this study with previously published data. Summary of Background Data. Several prior studies have reported spontaneous lumbar curve correction for both anterior and posterior selective fusion in Lenke 1C/King-Moe II patients; however to our knowledge no previous studies have reported outcomes of thoracoscopic anterior correction for this curve type. Methods. All AIS patients with a curve classification of Lenke 1C and a minimum of 24 months follow-up were retrieved from a consecutive series of 190 AIS patients who underwent thoracoscopic anterior instrumented fusion. Cobb angles of the major curve, instrumented levels, compensatory lumbar curve, and T5-T12 kyphosis were recorded, as well as coronal spinal balance, T1 tilt angle and shoulder balance. All radiographic parameters were measured before surgery and at 2, 6, 12 and 24 months after surgery. Results. Twenty-four female patients with right thoracic curves had a mean thoracic Cobb angle of 53.0° before surgery, decreasing to 24.9° two years after surgery. The mean lumbar compensatory Cobb angle was 43.5° before surgery, spontaneously correcting to 25.4° two years after surgery, indicating balance between the thoracic and lumbar scoliotic curves. The lumbar correction achieved (41.8%) compares favourably to previous studies. Conclusions. Selective thoracoscopic anterior fusion allows spontaneous lumbar curve correction and achieves coronal balance of main thoracic and compensatory lumbar curves, good cosmesis and patient satisfaction. Correction and balance are maintained 24 months after surgery.

Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.

Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

Numerical assessment of mass conservation on a MAC-type method for viscoelastic free surface flows

A numerical study of mass conservation of MAC-type methods is presented, for viscoelastic free-surface flows. We use an implicit formulation which allows for greater time steps, and therefore time marching schemes for advecting the free surface marker particles have to be accurate in order to preserve the good mass conservation properties of this methodology. We then present an improvement by using a Runge-Kutta scheme coupled with a local linear extrapolation on the free surface. A thorough study of the viscoelastic impacting drop problem, for both Oldroyd-B and XPP fluid models, is presented, investigating the influence of timestep, grid spacing and other model parameters to the overall mass conservation of the method. Furthermore, an unsteady fountain flow is also simulated to illustrate the low mass conservation error obtained.

Correlation of blood type with thrombosis in pancreatic cancer patients

Objective: The study aimed to identify the risk factors involved in initiating thromboembolism (TE) in pancreatic cancer (PC) patients, with focus on ABO blood type. ^ Methods and Patients: There were 35.7% confirmed cases of TE and 64.3% cases remained free of TE (n=687). There were 12.7% only Pulmonary embolism (PE), 9% only Deep vein thrombosis (DVT), 53.5% only other sites, 3.3% combined PE and DVT, 8.6% combined PE and other sites, 9.8% combined DVT and other sites, and 3.3% all three combined cases. ^ Results: The risk factors for thrombosis identified by multivariate logistic regression were: history of previous anti-thrombotic treatment, tumor site in pancreatic body or tail, large tumor size, maximum glucose category more than 126 and 200 mg/dL. ^ The factors with worse overall survival by multivariate Cox regression and Kaplan Meier analyses were: locally advanced or metastatic stage, worsening performance status, high CA 19-9 levels, and HbA1C levels more than 6 %, at diagnosis. ^ There were 29.1% and 39.1% of the patients with thrombosis in the O and non-O blood type groups respectively. Both Non-O blood type (P=0.02) and the A, B and AB blood types (P= 0.007) were associated with thrombosis as compared to O type. The odds of thrombosis were nearly half in O blood type patients as compared to non-O blood type [OR-0.54 (95% C.I.- 0.37-0.79), P<0.001]. ^ Conclusion: A better understanding of the TE and PC relationship and involved risk factors may provide insights on tumor biology and patient response to prophylactic anticoagulation therapy.^

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Purpose: Flat-detector, cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. Methods: The rich sources of prior information in IGRT are incorporated into a hidden Markov random field (MRF) model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk (OAR). The voxel labels are estimated using the iterated conditional modes (ICM) algorithm. Results: The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom (CIRS, Inc. model 062). The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. Conclusions: By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Finding My Way: Protocol of a randomised controlled trial evaluating an internet self-help program for cancer-related distress

Background A cancer diagnosis elicits greater distress than any other medical diagnosis, and yet very few studies have evaluated the efficacy of structured online self-help therapeutic programs to alleviate this distress. This study aims to assess the efficacy over time of an internet Cognitive Behaviour Therapy (iCBT) intervention (‘Finding My Way’) in improving distress, coping and quality of life for individuals with a recent diagnosis of early stage cancer of any type. Methods/Design The study is a multi-site Randomised Controlled Trial (RCT) seeking to enrol 188 participants who will be randomised to either the Finding My Way Intervention or an attention-control condition. Both conditions are delivered online; with 6 modules released once per week, and an additional booster module released one month after program-completion. Participants complete online questionnaires on 4 occasions: at baseline (immediately prior to accessing the modules); post-treatment (immediately after program-completion); then three and six months later. Primary outcomes are general distress and cancer-specific distress, with secondary outcomes including Health-Related Quality of Life (HRQoL), coping, health service utilisation, intervention adherence, and user satisfaction. A range of baseline measures will be assessed as potential moderators of outcomes. Eligible participants are individuals recently diagnosed with any type of cancer, being treated with curative intent, aged over 18 years with sufficient English language literacy, internet access and an active email account and phone number. Participants are blinded to treatment group allocation. Randomisation is computer generated and stratified by gender. Discussion Compared to the few prior published studies, Finding My Way will be the first adequately powered trial to offer an iCBT intervention to curatively treated patients of heterogeneous cancer types in the immediate post-diagnosis/treatment period. If found efficacious, Finding My Way will assist with overcoming common barriers to face-to-face therapy in a cost-effective and accessible way, thus helping to reduce distress after cancer diagnosis and consequently decrease the cancer burden for individuals and the health system. Trial registration Australian New Zealand Clinical Trials Registry ACTRN12613000001​796 16.10.13

The influence of geometry on jet plume development

Our recent efforts of using large-eddy simulation (LES) type methods to study complex and realistic geometry single stream and co-flow nozzle jets and acoustics are summarized in this paper. For the LES, since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving a numerical type LES (NLES). To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier-Stokes) model is smoothly blended in the LES making a hybrid RANS-NLES approach. Several complex nozzle geometries including the serrated (chevron) nozzle, realistic co-axial nozzles with eccentricity, pylon and wing-flap are discussed. The hybrid RANS-NLES simulations show encouraging predictions for the chevron jets. The chevrons are known to increase the high frequency noise at high polar angles, but decrease the low frequency noise at lower angles. The deflection effect of the potential core has an important mechanism of noise reduction. As for co-axial nozzles, the eccentricity, the pylon and the deployed wing-flap are shown to influence the flow development, especially the former to the length of potential core and the latter two having a significant impact on peak turbulence levels and spreading rates. The studies suggest that complex and real geometry effects are influential and should be taken into count when moving towards real engine simulations. © 2012 Elsevier Ltd. All rights reserved.

The failure of generalized gradient approximations (GGAs) and meta-GGAs for the two-center three-electron bonds in He-2(+), (H2O)(2)(+), and (NH3)(2)(+)

The radical cations He-2(+) (H2O)(2)(+), and (NH3)(2)(+) with two-center three-electron A-A bonds are investigated at the configuration interaction (CI), accurate Kohn-Sham (KS), generalized gradient approximation (GGA), and meta-GGA levels. Assessment of seven different GGA and six meta-GGA methods shows that the A(2)(+) systems remain a difficult case for density functional theory (DFT). All methods tested consistently overestimate the stability of A(2)(+): the corresponding D-e errors decrease for more diffuse valence densities in the series He-2(+) > (H2O)(2)(+) > (NH3)(2)(+). Upon comparison to the energy terms of the accurate Kohn-Sham solutions, the approximate exchange functionals are found to be responsible for the errors of GGA-type methods, which characteristically overestimate the exchange in A(2)(+). These so-called exchange functionals implicitly use localized holes. Such localized holes do occur if there is left-right correlation, i.e., the exchange functionals then also describe nondynamical correlation. However, in the hemibonded A(2)(+) systems the typical molecular (left-right, nondynamical) correlation of the two-electron pair bond is absent. The nondynamical correlation built into the exchange functionals is then spurious and yields too low energies.