Optimal control approach for discontinuous dynamical systems

In this work, we consider a wide class of discontinuous dynamical systems, discontinuity of which is based on the sign (for short sgn) function. We propose a smooth optimal control problem to solve the main discontinuous system. By solving some numerical examples in mechanical engineering, we show the efficiency of our approach with respect to 2 smoothing methods for discontinuous systems.     

Why Does the Molecular Structure of Broadly Neutralizing Monoclonal Antibodies Isolated from Individuals Infected with HIV-1 not Inform the Rational Design of an HIV-1 Vaccine?

It is commonly assumed that neutralizing Mabs that bind to the HIV-1 Env glycoprotein are more specific reagents than anti-HIV-1 polyclonal antisera and that knowledge of the structure of these Mabs facilitates the rational design of effective HIV-1 vaccine immunogens. However, after more than ten years of unsuccessful experimentation using the structure-based reverse vaccinology approach, it is now evident that it is not possible to infer from the structure of neutralizing Mabs which HIV immunogens induced their formation nor which vaccine immunogens will elicit similar Abs in an immunized host. The use of Mabs for developing an HIV-1 vaccine was counterproductive because it overlooked the fact that the apparent specificity of a Mab very much depends on the selection procedure used to obtain it and also did not take into account that an antibody is never monospecific for a single epitope but is always polyspecific for many epitopes. When the rationale of the proponents of the unsuccessful rational design strategy is analyzed, it appears that investigators who claim they are designing a vaccine immunogen are only improving the binding reactivity of a single epitope-paratope pair and are not actually designing an immunogen able to generate protective antibodies. The task of a designer consists in imagining what type of immunogen is likely to elicit a protective immune response but in the absence of knowledge regarding which features of the immune system are responsible for producing a functional neutralizing activity in antibodies, it is not feasible to intentionally optimize a potential immunogen candidate in order to obtain the desired outcome. The only available option is actually to test possible solutions by trial-and-error experiments until the preset goal is perhaps attained. Rational design and empirical approaches in HIV vaccine research should thus not be opposed as alternative options since empirical testing is an integral part of a so-called design strategy.     

Parameter Identification in Uncertain Scalar Conservation Laws Discretized with the Discontinuous Stochastic Galerkin Scheme

We study an identification problem which estimates the parameters of the underlying random distribution for uncertain scalar conservation laws. The hyperbolic equations are discretized with the so-called discontinuous stochastic Galerkin method, i.e., using a spatial discontinuous Galerkin scheme and a Multielement stochastic Galerkin ansatz in the random space. We assume an uncertain flux or uncertain initial conditions and that a data set of an observed solution is given. The uncertainty is assumed to be uniformly distributed on an unknown interval and we focus on identifying the correct endpoints of this interval. The first-order optimality conditions from the discontinuous stochastic Galerkin discretization are computed on the time-continuous level. Then, we solve the resulting semi-discrete forward and backward schemes with the Runge-Kutta method. To illustrate the feasibility of the approach, we apply the method to a stochastic advection and a stochastic equation of Burgers' type. The results show that the method is able to identify the distribution parameters of the random variable in the uncertain differential equation even if discontinuities are present.     

Distributed optimal control of viscous Burgers' equation via a high-order,linearization, integral,nodal discontinuous Gegenbauer-Galerkin method

We developed a novel direct optimization method to solve distributed optimal control of viscous Burgers' equation over a finite-time horizon by minimizing the distance between the state function and a desired target state profile along with the energy of the control. Through a novel linearization strategy, well-conditioned integral reformulations, optimal Gegenbauer barycentric quadratures, and nodal discontinuous Galerkin discretizations, the method reduces such optimal control problems into finite-dimensional, nonlinear programming problems subject to linear algebraic system of equations and discrete mixed path inequality constraints that can be solved easily using standard optimization software. The proposed method produces “an auxiliary control function” that provides a useful model to explicitly define the optimal controller of the state variable. We present an error analysis of the semidiscretization and full discretization of the weak form of the reduced equality constraint system equations to demonstrate the exponential convergence of the method. The accuracy of the proposed method is examined using two numerical examples for various target state functions in the existence/absence of control bounds. The proposed method is exponentially convergent in both space and time, thus producing highly accurate approximations using a significantly small number of collocation points.     

Discontinuous unilateral involvement of 12 part core biopsies by adenocarcinoma predicts bilateral involvement of subsequent radical prostatectomy

At our institution, percent tumor burden in prostate core biopsies is quantified using variations of one of two methods. Measurement by the Aggregate method reports only adenocarcinoma and omits intervening stroma and benign prostatic glands while the Discontinuous method includes the intervening stroma and benign glands between distinct foci of adenocarcinoma. In this study, we selected cases with 12‐part core biopsies that were followed by a radical prostatectomy within two years. Interestingly, we found that when adenocarcinoma involved prostate 12‐part core biopsies and subsequent resection unilaterally, there is no significant difference in absolute percentage of tumor using either measuring method (P = 0.4). In contrast, when adenocarcinoma involved the biopsies unilaterally and subsequent prostatectomy bilaterally, the two measurement methods had a statistically significant difference in percentage scores (P = 0.002). In the study cohort, other factors including Gleason score (P = 0.88) and total number of adenocarcinoma‐involved cores (P = 0.27) did not introduce any significant correlation with bilateral involvement. In this study, we found that biopsies that discontinuously and unilaterally involve half of a prostate are much more likely to involve both lobes than those that are unilateral and present in nodular aggregates.     

血细胞的Percoll不连续密度梯度分离法

以Percoll作为分离介质,采用60%SIP、50%SIP2种浓度,经2次离心,成功地分离了12名健康供血者周周血的单核、淋巴和粒细胞,纯度分别为83%、85%和98%;得率分别为48%、49%和47%。常规涂片、瑞氏染色后形态学观察示细胞形态完整,台盼蓝拒染实验示细胞活力良好(拒染率>95%).     

一层缝合术在消化道手术中的临床应用

目的:探讨消化道肿瘤切除术后吻合口采用一层缝合法的应用价值.方法:回顾性分析295例消化道肿瘤切除后,采用一层缝合法行消化道重建的效果,对术后吻合口并发症进行随访.结果:296例均治愈,无手术死亡病例,无吻合口出血及吻合口瘘.术后随访1～12个月,未发现吻合口狭窄.结论:消化道肿瘤切除术后一层缝合术操作简便,安全性高,费用低廉,可广泛应用于全消化道的重建.     

Scoring of nonmetric cranial traits: a population study

The aims of the present study were: (1) to supply further knowledge about variations in nonmetric cranial traits in relation to sex, age and laterality and (2) to evaluate biological distance between samples from a recent population. The incidence of 18 nonmetric variants of the cranium were determined in 3 adult samples of 394 skulls of known sex from North Sardinia (Sassari, Alghero and Ozieri); for the Sassari sample (n = 200) age at death was also known. Some significant sex differences were observed. Age did not appear to influence the frequency of the discontinuous traits but did for legibility. Side differences may provide important information about environmental influences. The interpopulation analysis indicates a stronger relationship between samples that are geographically closer (Sassari and Alghero), in accordance with other studies, strengthening the hypothesis of the validity of the use of nonmetric traits in the study of the peopling of a territory.     

Prognostic significance of laminin in adenocarcinoma of the lung

The distribution of laminin in tumor-associated basement membrane was immunohistochemically investigated in 115 cases of adenocarcinoma of the lung. The distribution of laminin was classified into continuous and discontinuous staining patterns. The incidence of the discontinuous pattern was less in early-stage disease than that in advanced stages (P less than 0.01). In patients with stage I, the incidence of discontinuous patterns was greater in short-term survivors than in long-term survivors (P less than 0.05). By contrast, in patients with stage III, the discontinuous pattern of laminin was frequently seen in both long-term survivors and short-term survivors, with no difference between the two groups. These data suggest that the discontinuous pattern of laminin in tumor-associated basement membrane reflects the spread and dissemination of tumor, hence a close relationship to the prognosis.