Hot new directions for quasi-Monte Carlo research in step with applications

This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when $s$ is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications

ITERATED QUASI-REVERSIBILITY METHOD APPLIED TO ELLIPTIC AND PARABOLIC DATA COMPLETION PROBLEMS

International audienceWe study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We demonstrate the convergence of the regularized solution to the exact one, and propose a strategy to deal with noise on the data. We present numerical experiments for both problems: a two-dimensional corrosion detection problem and the one-dimensional heat equation with lateral data. In both cases, the method prove to be efficient even with highly corrupted data

Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary

Role of Factor VII in Correcting Dilutional Coagulopathy and Reducing Re-operations for Bleeding Following Non-traumatic Major Gastrointestinal and Abdominal Surgery

Objective The objective of this study is to evaluate the effectiveness of rfVIIa in reducing blood product requirements and re-operation for postoperative bleeding after major abdominal surgery. Background Hemorrhage is a significant complication after major gastrointestinal and abdominal surgery. Clinically significant bleeding can lead to shock, transfusion of blood products, and re-operation. Recent reports suggest that activated rfVIIa may be effective in correcting coagulopathy and decreasing the need for re-operation. Methods This study was a retrospective review over a 4-year period of 17 consecutive bleeding postoperative patients who received rfVIIa to control hemorrhage and avoid re-operation. Outcome measures were blood and clotting factor transfusions, deaths, thromboembolic complications, and number of re-operations for bleeding. Results Seventeen patients with postoperative hemorrhage following major abdominal gastrointestinal surgery (nine pancreas, four sarcoma, two gastric, one carcinoid, and one fistula) were treated with rfVIIa. In these 17 patients, rfVIIa was administered for 18 episodes of bleeding (dose 2,400-9,600 mcg, 29.8-100.8 mcg/kg). Transfusion requirement of pRBC and FFP were each significantly less than pre-rfVIIa. Out of the 18 episodes, bleeding was controlled in 17 (94%) without surgery, and only one patient returned to the operating room for hemorrhage. There were no deaths and two thrombotic complications. Coagulopathy was corrected by rfVIIa from 1.37 to 0.96 (p<0.0001). Conclusion Use of rfVIIa in resuscitation for hemorrhage after non-traumatic major abdominal and gastrointestinal surgery can correct dilutional coagulopathy, reducing blood product requirements and need for re-operation

Changing patterns in diagnostic strategies and the treatment of blunt injury to solid abdominal organs

Background: In recent years there has been increasing interest shown in the nonoperative management (NOM) of blunt traumatic injury. The growing use of NOM for blunt abdominal organ injury has been made possible because of the progress made in the quality and availability of the multidetector computed tomography (MDCT) scan and the development of minimally invasive intervention options such as angioembolization. Aim: The purpose of this review is to describe the changes that have been made over the past decades in the management of blunt trauma to the liver, spleen and kidney. Results: The management of blunt abdominal injury has changed considerably. Focused assessment with sonography for trauma (FAST) examination has replaced diagnostic peritoneal lavage as diagnostic modality in the primary survey. MDCT scanning with intravenous contrast is now the gold standard diagnostic modality in hemodynamically stable patients with intra-abdominal fluid detected with FAST. One of the current discussions in the l erature is whether a whole body MDCT survey should be implemented in the primary survey. Conclusions The progress in imaging techniques has contributed to NOM being currently the treatment of choice for hemodynamically stable patients. Angioembolization can be used as an adjunct to NOM and has increased the succe

Flux norm approach to finite dimensional homogenization approximations with non-separated scales and high contrast

We consider divergence-form scalar elliptic equations and vectorial equations for elasticity with rough ($L^\infty(\Omega)$, $\Omega \subset \R^d$) coefficients $a(x)$ that, in particular, model media with non-separated scales and high contrast in material properties. We define the flux norm as the $L^2$ norm of the potential part of the fluxes of solutions, which is equivalent to the usual $H^1$-norm. We show that in the flux norm, the error associated with approximating, in a properly defined finite-dimensional space, the set of solutions of the aforementioned PDEs with rough coefficients is equal to the error associated with approximating the set of solutions of the same type of PDEs with smooth coefficients in a standard space (e.g., piecewise polynomial). We refer to this property as the {\it transfer property}. A simple application of this property is the construction of finite dimensional approximation spaces with errors independent of the regularity and contrast of the coefficients and with optimal and explicit convergence rates. This transfer property also provides an alternative to the global harmonic change of coordinates for the homogenization of elliptic operators that can be extended to elasticity equations. The proofs of these homogenization results are based on a new class of elliptic inequalities which play the same role in our approach as the div-curl lemma in classical homogenization.Comment: Accepted for publication in Archives for Rational Mechanics and Analysi

IL-6-Mediated Activation of Stat3α Prevents Trauma/Hemorrhagic Shock-Induced Liver Inflammation

Trauma complicated by hemorrhagic shock (T/HS) is the leading cause of morbidity and mortality in the United States for individuals under the age of 44 years. Initial survivors are susceptible to developing multiple organ failure (MOF), which is thought to be caused, at least in part, by excessive or maladaptive activation of inflammatory pathways. We previously demonstrated in rodents that T/HS results in liver injury that can be prevented by IL-6 administration at the start of resuscitation; however, the contribution of the severity of HS to the extent of liver injury, whether or not resuscitation is required, and the mechanism(s) for the IL-6 protective effect have not been reported. In the experiments described here, we demonstrated that the extent of liver inflammation induced by T/HS depends on the duration of hypotension and requires resuscitation. We established that IL-6 administration at the start of resuscitation is capable of completely reversing liver inflammation and is associated with increased Stat3 activation. Global assessment of the livers showed that the main effect of IL-6 was to normalize the T/HS-induced inflammation transcriptome. Pharmacological inhibition of Stat3 activity within the liver blocked the ability of IL-6 to prevent liver inflammation and to normalize the T/HS-induced liver inflammation transcriptome. Genetic deletion of a Stat3β, a naturally occurring, dominant-negative isoform of the Stat3, attenuated T/HS-induced liver inflammation, confirming a role for Stat3, especially Stat3α, in preventing T/HS-mediated liver inflammation. Thus, T/HS-induced liver inflammation depends on the duration of hypotension and requires resuscitation; IL-6 administration at the start of resuscitation reverses T/HS-induced liver inflammation, through activation of Stat3α, which normalized the T/HS-induced liver inflammation transcriptome

A genomic storm in critically injured humans

Critical injury in humans induces a genomic storm with simultaneous changes in expression of innate and adaptive immunity genes

Multi-omic analysis in injured humans: Patterns align with outcomes and treatment responses

Trauma is a leading cause of death and morbidity worldwide. Here, we present the analysis of a longitudinal multi-omic dataset comprising clinical, cytokine, endotheliopathy biomarker, lipidome, metabolome, and proteome data from severely injured humans. A "systemic storm" pattern with release of 1,061 markers, together with a pattern suggestive of the "massive consumption" of 892 constitutive circulating markers, is identified in the acute phase post-trauma. Data integration reveals two human injury response endotypes, which align with clinical trajectory. Prehospital thawed plasma rescues only endotype 2 patients with traumatic brain injury (30-day mortality: 30.3 versus 75.0%; p = 0.0015). Ubiquitin carboxy-terminal hydrolase L1 (UCHL1) was identified as the most predictive circulating biomarker to identify endotype 2-traumatic brain injury (TBI) patients. These response patterns refine the paradigm for human injury, while the datasets provide a resource for the study of critical illness, trauma, and human stress responses