Numerical impulse controllability for parabolic equations by a penalized HUM approach

This work presents a comparative study to numerically compute impulse approximate controls for parabolic equations with various boundary conditions. Theoretical controllability results have been recently investigated using a logarithmic convexity estimate at a single time based on a Carleman commutator approach. We propose a numerical algorithm for computing the impulse controls with minimal $L^2$-norms by adapting a penalized Hilbert Uniqueness Method (HUM) combined with a Conjugate Gradient (CG) method. We consider static boundary conditions (Dirichlet and Neumann) and dynamic boundary conditions. Some numerical experiments based on our developed algorithm are given to validate and compare the theoretical impulse controllability results

Numerical identification of initial temperatures in heat equation with dynamic boundary conditions

We investigate the inverse problem of numerically identifying unknown initial temperatures in a heat equation with dynamic boundary conditions whenever some overdetermination data is provided after a final time. This is a backward parabolic problem which is severely ill-posed. As a first step, the problem is reformulated as an optimization problem with an associated cost functional. Using the weak solution approach, an explicit formula for the Fr\'echet gradient of the cost functional is derived from the corresponding sensitivity and adjoint problems. Then the Lipschitz continuity of the gradient is proved. Next, further spectral properties of the input-output operator are established. Finally, the numerical results for noisy measured data are performed using the regularization framework and the conjugate gradient method. We consider both one- and two-dimensional numerical experiments using finite difference discretization to illustrate the efficiency of the designed algorithm. Aside from dealing with a time derivative on the boundary, the presence of a boundary diffusion makes the analysis more complicated. This issue is handled in the 2-D case by considering the polar coordinate system. The presented method implies fast numerical results

Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T], U(0) & = u_0. {aligned}. {equation} Here $(A(t))_{t\in [0,T]}$ are unbounded operators with domains $(D(A(t)))_{t\in [0,T]}$ which may be time dependent. We assume that $(A(t))_{t\in [0,T]}$ satisfies the conditions of Acquistapace and Terreni. The functions $F$ and $B$ are nonlinear functions defined on certain interpolation spaces and $u_0\in E$ is the initial value. $W_H$ is a cylindrical Brownian motion on a separable Hilbert space $H$. Under Lipschitz and linear growth conditions we show that there exists a unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk, to obtain space-time regularity results for the solution $U$ of \eqref{eq:SEab}. For Hilbert spaces $E$ we obtain a maximal regularity result. The results improve several previous results from the literature. The theory is applied to a second order stochastic partial differential equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to several improvements of their result.Comment: Accepted for publication in Journal of Evolution Equation

Session availability as a result of prior injury impacts the risk of subsequent injury in elite male Australian footballers

Prior injury is a commonly identified risk factor for subsequent injury. However, a binary approach to classifying prior injury (i.e., yes/no) is commonly implemented and may constrain scientific findings, as it is possible that variations in the amount of time lost due to an injury will impact subsequent injury risk to differing degrees. Accordingly, this study investigated whether session availability, a surrogate marker of prior injury, influenced the risk of subsequent non-contact lower limb injury in Australian footballers. Data were collected from 62 male elite Australian footballers throughout the 2015, 2016, and 2017 Australian Football League seasons. Each athlete’s participation status (i.e., full or missed/modified) and any injuries that occurred during training sessions/matches were recorded. As the focus of the current study was prior injury, any training sessions/matches that were missed due to reasons other than an injury (e.g., load management, illness and personal reasons) were removed from the data prior to all analyses. For every Monday during the in-season periods, session availability (%) in the prior 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, and 84 days was determined as the number of training sessions/matches fully completed (injury free) relative to the number of training sessions/matches possible in each window. Each variable was modeled using logistic regression to determine its impact on subsequent injury risk. Throughout the study period, 173 non-contact lower limb injuries that resulted in at least one missed/modified training session or match during the in-season periods occurred. Greater availability in the prior 7 days increased injury probabilities by up to 4.4%. The impact of session availability on subsequent injury risk diminished with expanding windows (i.e., availability in the prior 14 days through to the prior 84 days). Lesser availability in the prior 84 days increased injury probabilities by up to 14.1%, only when coupled with greater availability in the prior 7 days. Session availability may provide an informative marker of the impact of prior injury on subsequent injury risk and can be used by coaches and clinicians to guide the progression of training, particularly for athletes that are returning from long periods of injury

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Blinatumomab vs historical standard therapy of adult relapsed/refractory acute lymphoblastic leukemia

We compared outcomes from a single-arm study of blinatumomab in adult patients with B-precursor Ph-negative relapsed/refractory acute lymphoblastic leukemia (R/R ALL) with a historical data set from Europe and the United States. Estimates of complete remission (CR) and overall survival (OS) were weighted by the frequency distribution of prognostic factors in the blinatumomab trial. Outcomes were also compared between the trial and historical data using propensity score methods. The historical cohort included 694 patients with CR data and 1112 patients with OS data compared with 189 patients with CR and survival data in the blinatumomab trial. The weighted analysis revealed a CR rate of 24% (95% CI: 20-27%) and a median OS of 3.3 months (95% CI: 2.8-3.6) in the historical cohort compared with a CR/CRh rate of 43% (95% CI: 36-50%) and a median OS of 6.1 months (95% CI: 4.2-7.5) in the blinatumomab trial. Propensity score analysis estimated increased odds of CR/CRh (OR=2.68, 95% CI: 1.67-4.31) and improved OS (HR=0.536, 95% CI: 0.394-0.730) with blinatumomab. The analysis demonstrates the application of different study designs and statistical methods to compare novel therapies for R/R ALL with historical data

Less Anterior Knee Pain with a Mobile-bearing Prosthesis Compared with a Fixed-bearing Prosthesis

Anterior knee pain is one of the major short-term complaints after TKA. Since the introduction of the mobile-bearing TKA, numerous studies have attempted to confirm the theoretical advantages of a mobile-bearing TKA over a fixed-bearing TKA but most show little or no actual benefits. The concept of self-alignment for the mobile bearing suggests the posterior-stabilized mobile-bearing TKA would provide a lower incidence of anterior knee pain compared with a fixed-bearing TKA. We therefore asked whether the posterior-stabilized mobile-bearing knee would in fact reduce anterior knee pain. We randomized 103 patients scheduled for cemented three-component TKA for osteoarthrosis in a prospective, double-blind clinical trial. With a 1-year followup, more patients experienced persistent anterior knee pain in the posterior-stabilized fixed-bearing group (10 of 53, 18.9%) than in the posterior-stabilized mobile-bearing group (two of 47, 4.3%). No differences were observed for range of motion, visual analog scale for pain, Oxford 12-item questionnaire, SF-36, or the American Knee Society score. The posterior-stabilized mobile-bearing knee therefore seems to provide a short-term advantage compared with the posterior-stabilized fixed-bearing knee

Green Pathways for the Enzymatic Synthesis of Furan-Based Polyesters and Polyamides

The attention towards the utilization of sustainable feedstocks for polymer synthesis has grown exponentially in recent years. One of the spotlighted monomers derived from renewable resources is 2,5-furandicarboxylic acid (FDCA), one of the most promising bio-based monomers, due to its resemblance to petroleum-based terephthalic acid. Very interesting synthetic routes using this monomer have been reported in the last two decades. Combining the use of bio-based monomers and non-toxic chemicals via enzymatic polymerizations can lead to a robust and favorable approach towards a greener technology of bio-based polymer production. In this chapter, a brief introduction to FDCA-based monomers and enzymatic polymerizations is given, particularly focusing on furan-based polymers and their polymerization. In addition, an outline of the recent developments in the field of enzymatic polymerizations is discussed. </p

In vivo assembly of the axon initial segment in motor neurons

International audienceThe axon initial segment (AIS) is responsible for both the modulation of action potentials and the maintenance of neuronal polarity. Yet, the molecular mechanisms controlling its assembly are incompletely understood. Our study in single electroporated motor neurons in mouse embryos revealed that AnkyrinG (AnkG), the AIS master organizer, is undetectable in bipolar migrating motor neurons, but is already expressed at the beginning of axonogenesis at E9.5 and initially distributed homogeneously along the entire growing axon. Then, from E11.5, a stage when AnkG is already apposed to the membrane, as observed by electron microscopy, the protein progressively becomes restricted to the proximal axon. Analysis on the global motor neurons population indicated that Neurofascin follows an identical spatio-temporal distribution, whereas sodium channels and beta 4-spectrin only appear along AnkG(+) segments at E11.5. Early patch-clamp recordings of individual motor neurons indicated that at E12.5 these nascent AISs are already able to generate spikes. Using knock-out mice, we demonstrated that neither beta 4-spectrin nor Neurofascin control the distal-to-proximal restriction of AnkG