When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

The role of focal therapy in the management of localised prostate cancer: a systematic review.

CONTEXT: The incidence of localised prostate cancer is increasing worldwide. In light of recent evidence, current, radical, whole-gland treatments for organ-confined disease have being questioned with respect to their side effects, cancer control, and cost. Focal therapy may be an effective alternative strategy. OBJECTIVE: To systematically review the existing literature on baseline characteristics of the target population; preoperative evaluation to localise disease; and perioperative, functional, and disease control outcomes following focal therapy. EVIDENCE ACQUISITION: Medline (through PubMed), Embase, Web of Science, and Cochrane Review databases were searched from inception to 31 October 2012. In addition, registered but not yet published trials were retrieved. Studies evaluating tissue-preserving therapies in men with biopsy-proven prostate cancer in the primary or salvage setting were included. EVIDENCE SYNTHESIS: A total of 2350 cases were treated to date across 30 studies. Most studies were retrospective with variable standards of reporting, although there was an increasing number of prospective registered trials. Focal therapy was mainly delivered to men with low and intermediate disease, although some high-risk cases were treated that had known, unilateral, significant cancer. In most of the cases, biopsy findings were correlated to specific preoperative imaging, such as multiparametric magnetic resonance imaging or Doppler ultrasound to determine eligibility. Follow-up varied between 0 and 11.1 yr. In treatment-naïve prostates, pad-free continence ranged from 95% to 100%, erectile function ranged from 54% to 100%, and absence of clinically significant cancer ranged from 83% to 100%. In focal salvage cases for radiotherapy failure, the same outcomes were achieved in 87.2-100%, 29-40%, and 92% of cases, respectively. Biochemical disease-free survival was reported using a number of definitions that were not validated in the focal-therapy setting. CONCLUSIONS: Our systematic review highlights that, when focal therapy is delivered with intention to treat, the perioperative, functional, and disease control outcomes are encouraging within a short- to medium-term follow-up. Focal therapy is a strategy by which the overtreatment burden of the current prostate cancer pathway could be reduced, but robust comparative effectiveness studies are now required.

Health technology assessment in evolution - focal therapy in localised prostate cancer.

Focal therapy in prostate cancer aims to treat only the part of the gland harboring clinically significant disease while preserving the rest of the tissue. This approach may substantially reduce treatment-related toxicity without compromising disease control outcomes. Short- to medium-term functional and oncological results in prospective interventional studies are promising, but comparative effectiveness research against standard of care is required to incorporate focal therapy among standard options. In this review, we discuss the actual stage of assessment and results of sources of energy commonly used to deliver focal therapy. We also provide our viewpoint on how the field will evolve in the near future.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Acute toxicity of curative radiotherapy for intermediate- and high-risk localised prostate cancer in the EORTC trial 22991.

INTRODUCTION: This trial randomly assessed short-term adjuvant hormonal therapy added to radiotherapy (RT) for intermediate- and high-risk (UICC 1997 cT2a or cT1b-c with high PSA or Gleason score) localised prostate cancer. We report acute toxicity (CTCAE v2) assessed weekly during RT in relation to radiation parameters. PATIENTS AND METHODS: Centres selected the RT dose (70, 74 or 78Gy) and RT technique. Statistical significance is at 0.05. RESULTS: Of 791 patients, 652 received 3D-CRT (70Gy: 195, 74Gy: 376, 78Gy: 81) and 139 received IMRT (74Gy: 28, 78Gy: 111). During RT, grade 3 gastrointestinal (GI) and genitourinary (GU) toxicities were reported by 7 (0.8%) and 50 (6.3%) patients, respectively. No grade 4 was reported. The risk of grade 2 GI toxicity increased significantly with increasing D50%-rectum (p=0.004) and that of grade 2 GU toxicity correlated only to Dmax-bladder (p=0.051). 3D-RT technique, increasing total dose and V95% >400 cc increased D50% and Dmax. One month after RT, only 14 patients (1.8%) reported grade 3 toxicity. AST did not seem to influence the risk of GU or GI acute toxicity. CONCLUSION: RT up to 78Gy was well tolerated. Dmax-bladder and D50%-rectum influenced the risk of grade 2 GU toxicity and GI toxicity, respectively. Both were lower with IMRT but remained high for an irradiated RT volume>400 cc for 3D-RT and for a dose of 78Gy. Hormonal treatment did not influence acute toxicity.

Fast Approximation of Nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems

This paper proposes a very fast method for blindly approximating a nonlinear mapping which transforms a sum of random variables. The estimation is surprisingly good even when the basic assumption is not satisfied.We use the method for providing a good initialization for inverting post-nonlinear mixtures and Wiener systems. Experiments show that the algorithm speed is strongly improved and the asymptotic performance is preserved with a very low extra computational cost.

Validity of the acoustic approximation in full-waveform seismic crosshole tomography

Acoustic waveform inversions are an increasingly popular tool for extracting subsurface information from seismic data. They are computationally much more efficient than elastic inversions. Naturally, an inherent disadvantage is that any elastic effects present in the recorded data are ignored in acoustic inversions. We investigate the extent to which elastic effects influence seismic crosshole data. Our numerical modeling studies reveal that in the presence of high contrast interfaces, at which P-to-S conversions occur, elastic effects can dominate the seismic sections, even for experiments involving pressure sources and pressure receivers. Comparisons of waveform inversion results using a purely acoustic algorithm on synthetic data that is either acoustic or elastic, show that subsurface models comprising small low-to-medium contrast (?30%) structures can be successfully resolved in the acoustic approximation. However, in the presence of extended high-contrast anomalous bodies, P-to-S-conversions may substantially degrade the quality of the tomographic images. In particular, extended low-velocity zones are difficult to image. Likewise, relatively small low-velocity features are unresolved, even when advanced a priori information is included. One option for mitigating elastic effects is data windowing, which suppresses later arriving seismic arrivals, such as shear waves. Our tests of this approach found it to be inappropriate because elastic effects are also included in earlier arriving wavetrains. Furthermore, data windowing removes later arriving P-wave phases that may provide critical constraints on the tomograms. Finally, we investigated the extent to which acoustic inversions of elastic data are useful for time-lapse analyses of high contrast engineered structures, for which accurate reconstruction of the subsurface structure is not as critical as imaging differential changes between sequential experiments. Based on a realistic scenario for monitoring a radioactive waste repository, we demonstrated that acoustic inversions of elastic data yield substantial distortions of the tomograms and also unreliable information on trends in the velocity changes.

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose.

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.