Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equation under the Bardos-Lebeau-Rauch geometric control condition

AbstractWe extend the result of the null controllability property of the heat equation, obtained as limit, when ϵ tends to zero, of the exact controllability of a singularly perturbed damped wave equation depending on a parameter ϵ > 0, described in [1], to bounded domains which satisfy the Bardos-Lebeau-Rauch geometric control condition [2]. We add to the method of Lopez, Zhang and Zuazua in [1] an explicit in ϵ > 0 observability estimate for the singularly perturbed damped wave equation under the Bardos-Lebeau-Rauch geometric control condition. Here the geometric conditions are more optimal than in [1] and the proof is simpler than in [1]. Instead of using global Carleman inequalities as in [1], we apply an integral representation formula

Adjusting Overall Survival Estimates after Treatment Switching: a Case Study in Metastatic Castration-Resistant Prostate Cancer

Background If patients in oncology trials receive subsequent therapy, standard intention-to-treat (ITT) analyses may inaccurately estimate the overall survival (OS) effect of the investigational product. In this context, a post-hoc analysis of the phase 3 PREVAIL study was performed with the aim to compare enzalutamide with placebo in terms of OS, adjusting for potential confounding from switching to antineoplastic therapies that are not part of standard metastatic castration-resistant prostate cancer (mCRPC) treatment pathways in some jurisdictions. Methods The PREVAIL study, which included 1717 chemotherapy-naïve men with mCRPC randomized to treatment with enzalutamide 160 mg/day or placebo, was stopped after a planned interim survival analysis revealed a benefit in favor of enzalutamide. Data from this cutoff point were confounded by switching from both arms and so were evaluated in terms of OS using two switching adjustment methods: the two-stage accelerated failure time model (two-stage method) and inverse probability of censoring weights (IPCW). Results Following adjustment for switching to nonstandard antineoplastic therapies by 14.8 (129/872 patients) and 21.3% (180/845 patients) of patients initially randomized to enzalutamide and placebo, respectively, the two-stage and IPCW methods both resulted in numerical reductions in the hazard ratio (HR) for OS [HR 0.66, 95% confidence interval (CI) 0.57–0.81 and HR 0.63, 95% CI 0.52–0.75, respectively] for enzalutamide compared to placebo versus the unadjusted ITT analysis (HR 0.71, 95% CI 0.60–0.84). These results suggest a slightly greater effect of enzalutamide on OS than originally reported. Conclusion In the PREVAIL study, switching to nonstandard antineoplastic mCRPC therapies resulted in the ITT analysis of primary data underestimating the benefit of enzalutamide on OS

Shigella flexneri serotype 1c derived from serotype 1a by acquisition of gtrIC gene cluster via a bacteriophage

BACKGROUND: Shigella spp. are the primary causative agents of bacillary dysentery. Since its emergence in the late 1980s, the S. flexneri serotype 1c remains poorly understood, particularly with regard to its origin and genetic evolution. This article provides a molecular insight into this novel serotype and the gtrIC gene cluster that determines its unique immune recognition. RESULTS: A PCR of the gtrIC cluster showed that serotype 1c isolates from different geographical origins were genetically conserved. An analysis of sequences flanking the gtrIC cluster revealed remnants of a prophage genome, in particular integrase and tRNAPro genes. Meanwhile, Southern blot analyses on serotype 1c, 1a and 1b strains indicated that all the tested serotype 1c strains may have had a common origin that has since remained distinct from the closely related 1a and 1b serotypes. The identification of prophage genes upstream of the gtrIC cluster is consistent with the notion of bacteriophage-mediated integration of the gtrIC cluster into a pre-existing serotype. CONCLUSIONS: This is the first study to show that serotype 1c isolates from different geographical origins share an identical pattern of genetic arrangement, suggesting that serotype 1c strains may have originated from a single parental strain. Analysis of the sequence around the gtrIC cluster revealed a new site for the integration of the serotype converting phages of S. flexneri. Understanding the origin of new pathogenic serotypes and the molecular basis of serotype conversion in S. flexneri would provide information for developing cross-reactive Shigella vaccines

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

Restructuring of colloidal aggregates in shear flow: Coupling interparticle contact models with Stokesian dynamics

A method to couple interparticle contact models with Stokesian dynamics (SD) is introduced to simulate colloidal aggregates under flow conditions. The contact model mimics both the elastic and plastic behavior of the cohesive connections between particles within clusters. Owing to this, clusters can maintain their structures under low stress while restructuring or even breakage may occur under sufficiently high stress conditions. SD is an efficient method to deal with the long-ranged and many-body nature of hydrodynamic interactions for low Reynolds number flows. By using such a coupled model, the restructuring of colloidal aggregates under stepwise increasing shear flows was studied. Irreversible compaction occurs due to the increase of hydrodynamic stress on clusters. Results show that the greater part of the fractal clusters are compacted to rod-shaped packed structures, while the others show isotropic compaction.Comment: A simulation movie be found at http://www-levich.engr.ccny.cuny.edu/~seto/sites/colloidal_aggregates_shearflow.htm

Hydrodynamic interactions in colloidal ferrofluids: A lattice Boltzmann study

We use lattice Boltzmann simulations, in conjunction with Ewald summation methods, to investigate the role of hydrodynamic interactions in colloidal suspensions of dipolar particles, such as ferrofluids. Our work addresses volume fractions $\phi$ of up to 0.20 and dimensionless dipolar interaction parameters $\lambda$ of up to 8. We compare quantitatively with Brownian dynamics simulations, in which many-body hydrodynamic interactions are absent. Monte Carlo data are also used to check the accuracy of static properties measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic interactions slow down both the long-time and the short-time decays of the intermediate scattering function $S(q,t)$, for wavevectors close to the peak of the static structure factor $S(q)$, by a factor of roughly two. The long-time slowing is diminished at high interaction strengths whereas the short-time slowing (quantified via the hydrodynamic factor $H(q)$) is less affected by the dipolar interactions, despite their strong effect on the pair distribution function arising from cluster formation. Cluster formation is also studied in transient data following a quench from $\lambda = 0$; hydrodynamic interactions slow the formation rate, again by a factor of roughly two

Nonlinear rheology of colloidal dispersions

Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.Comment: Review articl

Clinical outcomes and survival surrogacy studies of prostate-specific antigen declines following enzalutamide in men with metastatic castration-resistant prostate cancer previously treated with docetaxel.

Background In the AFFIRM trial, enzalutamide significantly increased overall survival (OS) for men with metastatic castration-resistant prostate cancer (mCRPC) after chemotherapy versus placebo and significantly decreased prostate-specific antigen (PSA) levels. The goal of this post hoc analysis was to associate levels of PSA decline from baseline after enzalutamide with clinical outcomes in the postchemotherapy mCRPC setting.Methods Men in the AFFIRM trial (n = 1199) were grouped by maximal PSA decline in the first 90 days of treatment. Kaplan-Meier estimates evaluated the association of defined PSA changes from baseline with OS, progression-free survival (PFS), radiographic PFS (rPFS), and pain response. Each PSA decline category was assessed for OS surrogacy using Prentice criteria, proportion of treatment effect explained (PTE), and proportion of variation explained.Results Men treated with enzalutamide had improved OS (hazard ratio, 0.63; P 19.0; P .20).Conclusions PSA declines of any, ≥30%, and ≥50% following enzalutamide were associated with greater clinical and pain response and improvements in PFS and OS. Surrogacy of PSA decline for OS was not fully established, possibly due to lack of PSA declines with placebo, and discordant results between PSA and imaging responses over time, and because some declines were not durable due to rapid resistance development. However, a lack of PSA decline by 90 days following enzalutamide treatment was a poor prognosis indicator in this setting. Conclusions from sensitivity analyses of maximal PSA decline from baseline over the entire treatment period are consistent with PSA declines restricted to the first 90 days. Cancer 2017;123:2303-2311. © 2017 American Cancer Society

Influence of Hydrodynamic Interactions on Mechanical Unfolding of Proteins

We incorporate hydrodynamic interactions in a structure-based model of ubiquitin and demonstrate that the hydrodynamic coupling may reduce the peak force when stretching the protein at constant speed, especially at larger speeds. Hydrodynamic interactions are also shown to facilitate unfolding at constant force and inhibit stretching by fluid flows.Comment: to be published in Journal of Physics: Condensed Matte