An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

The potential impact of new effervescent alendronate formulation on compliance and persistence in osteoporosis treatment.

Osteoporotic fractures are a public health problem and their incidence and subsequent economic and social costs are expected to rise in the next future. Different drugs have been developed to reduce osteoporosis and the risk of osteoporotic fractures, and among them, antiresorptive agents, and in particular oral alendronate, are the most widely utilized. However, one of the most common problems with antiresorptive drugs is poor adherence to treatment, which is associated with a high fracture incidence and with an increase in hospitalization costs. One of the main reasons of poor adherence to these treatments is the occurrence of adverse events, mainly at gastrointestinal (GI) level, including dyspepsia, dysphagia, and esophageal ulcers. In light of these considerations the aim of this paper is to perform a literature review to show the pathophysiologic bases of GI alendronate-induced adverse events and how new bisphosphonate formulations like effervescent alendronate can improve compliance and persistence to treatment and decrease the fracture rate incidence in osteoporotic patients.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

A web-based pilot study of inter-pathologist reproducibility using the ISHLT 2004 working formulation for biopsy diagnosis of cardiac allograft rejection: The European experience.

BACKGROUND: The aim of this study was to assess, at the European level and using digital technology, the inter-pathologist reproducibility of the ISHLT 2004 system and to compare it with the 1990 system We also assessed the reproducibility of the morphologic criteria for diagnosis of antibody-mediated rejection detailed in the 2004 grading system. METHODS: The hematoxylin-eosin-stained sections of 20 sets of endomyocardial biopsies were pre-selected and graded by two pathologists (A.A. and M.B.) and digitized using a telepathology digital pathology system (Aperio ImageScope System; for details refer to http://aperio.com/). Their diagnoses were considered the index diagnoses, which covered all grades of acute cellular rejection (ACR), early ischemic lesions, Quilty lesions, late ischemic lesions and (in the 2005 system) antibody-mediated rejection (AMR). Eighteen pathologists from 16 heart transplant centers in 7 European countries participated in the study. Inter-observer reproducibility was assessed using Fleiss's kappa and Krippendorff's alpha statistics. RESULTS: The combined kappa value of all grades diagnosed by all 18 pathologists was 0.31 for the 1990 grading system and 0.39 for the 2005 grading system, with alpha statistics at 0.57 and 0.55, respectively. Kappa values by grade for 1990/2005, respectively, were: 0 = 0.52/0.51; 1A/1R = 0.24/0.36; 1B = 0.15; 2 = 0.13; 3A/2R = 0.29/0.29; 3B/3R = 0.13/0.23; and 4 = 0.18. For the 2 cases of AMR, 6 of 18 pathologists correctly suspected AMR on the hematoxylin-eosin slides, whereas, in each of 17 of the 18 AMR-negative cases a small percentage of pathologists (range 5% to 33%) overinterpreted the findings as suggestive for AMR. CONCLUSIONS: Reproducibility studies of cardiac biopsies by pathologists in different centers at the international level were feasible using digitized slides rather than conventional histology glass slides. There was a small improvement in interobserver agreement between pathologists of different European centers when moving from the 1990 ISHLT classification to the "new" 2005 ISHLT classification. Morphologic suspicion of AMR in the 2004 system on hematoxylin-eosin-stained slides only was poor, highlighting the need for better standardization of morphologic criteria for AMR. Ongoing educational programs are needed to ensure standardization of diagnosis of both acute cellular and antibody-mediated rejection.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Novel birch pollen specific immunotherapy formulation based on contiguous overlapping peptides.

BACKGROUND: Synthetic contiguous overlapping peptides (COPs) may represent an alternative to allergen extracts or recombinant allergens for allergen specific immunotherapy. In combination, COPs encompass the entire allergen sequence, providing all potential T cell epitopes, while preventing IgE conformational epitopes of the native allergen. METHODS: Individual COPs were derived from the sequence of Bet v 1, the major allergen of birch pollen, and its known crystal structure, and designed to avoid IgE binding. Three sets of COPs were tested in vitro in competition ELISA and basophil degranulation assays. Their in vivo reactivity was determined by intraperitoneal challenge in rBet v 1 sensitized mice as well as by skin prick tests in volunteers with allergic rhinoconjunctivitis to birch pollen. RESULTS: The combination, named AllerT, of three COPs selected for undetectable IgE binding in competition assays and for the absence of basophil activation in vitro was unable to induce anaphylaxis in sensitized mice in contrast to rBet v 1. In addition no positive reactivity to AllerT was observed in skin prick tests in human volunteers allergic to birch pollen. In contrast, a second set of COPs, AllerT4-T5 displayed some residual IgE binding in competition ELISA and a weak subliminal reactivity to skin prick testing. CONCLUSIONS: The hypoallergenicity of contiguous overlapping peptides was confirmed by low, if any, IgE binding activity in vitro, by the absence of basophil activation and the absence of in vivo induction of allergic reactions in mouse and human. TRIAL REGISTRATION: ClinicalTrials.gov NCT01719133.

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography.

Tractography is a class of algorithms aiming at in vivo mapping the major neuronal pathways in the white matter from diffusion magnetic resonance imaging (MRI) data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the neuronal connections of the brain. However, unfortunately, the reconstructions recovered with existing tractography algorithms are not really quantitative even though diffusion MRI is a quantitative modality by nature. As a matter of fact, several techniques have been proposed in recent years to estimate, at the voxel level, intrinsic microstructural features of the tissue, such as axonal density and diameter, by using multicompartment models. In this paper, we present a novel framework to reestablish the link between tractography and tissue microstructure. Starting from an input set of candidate fiber-tracts, which are estimated from the data using standard fiber-tracking techniques, we model the diffusion MRI signal in each voxel of the image as a linear combination of the restricted and hindered contributions generated in every location of the brain by these candidate tracts. Then, we seek for the global weight of each of them, i.e., the effective contribution or volume, such that they globally fit the measured signal at best. We demonstrate that these weights can be easily recovered by solving a global convex optimization problem and using efficient algorithms. The effectiveness of our approach has been evaluated both on a realistic phantom with known ground-truth and in vivo brain data. Results clearly demonstrate the benefits of the proposed formulation, opening new perspectives for a more quantitative and biologically plausible assessment of the structural connectivity of the brain.