Stochastic Spline-Collocation Method for Constrained Optimal Control Problem Governed by Random Elliptic PDE

In this paper, we investigate a stochastic spline-collocation approximation scheme for an optimal control problem governed by an elliptic PDE with random field coefficients. We obtain the necessary and sufficient optimality conditions for the optimal control problem and establish a scheme to approximate the optimality system through the discretization with respect to the spatial space by finite elements method and the probability space by stochastic splinecollocation method. We further investigate Smolyak approximation schemes, which are effective collocation strategies for smooth problems that depend on a moderately large number of random variables. For more general control problems where the state may be non-smooth with respect to the random variables in some areas, we adopt a domain decomposition strategy to partition the random space into smooth and non-smooth parts and then apply Smolyak scheme and spline approximation respectively. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results

A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control

A stochastic Galerkin approximation scheme is proposed for an optimal control problem governed by a parabolic PDE with random perturbation in its coefficients. The objective functional is to minimize the expectation of a cost functional, and the deterministic control is of the obstacle constrained type. We obtain the necessary and sufficient optimality conditions and establish a scheme to approximate the optimality system through the discretization with respect to both the spatial space and the probability space by Galerkin method and with respect to time by the backward Euler scheme. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results

Second Primary Malignancies after Autologous Hematopoietic Cell Transplantation for Multiple Myeloma

AbstractRecent studies demonstrate an increased risk of second primary malignancies (SPMs) in patients with multiple myeloma (MM) receiving maintenance lenalidomide after autologous stem cell transplantation (ASCT). We explored the possibility of other risk factors driving post-ASCT SPMs in patients with MM through analysis of our large transplantation database in conjunction with our Long-Term Follow-Up Program. We conducted a retrospective cohort study of 841 consecutive patients with MM who underwent ASCT at City of Hope between 1989 and 2009, as well as a nested case-control analysis evaluating the role of all therapeutic exposures before, during, and after ASCT. Median duration of follow-up for the entire cohort was 3.4 years (range, 0.3-19.9 years). Sixty cases with a total of 70 SPMs were identified. The overall cumulative incidence of SPMs was 7.4% at 5 years and 15.9% at 10 years when nonmelanoma skin cancers (NMSCs) were included and 5.3% at 5 years and 11.2% at 10 years when NMSCs were excluded. Multivariate analysis of the entire cohort revealed associations of both older age (≥55 years; relative risk, 2.3; P < .004) and race (non-Hispanic white; relative risk, 2.4; P = .01) with an increased risk of SPM. Furthermore, thalidomide exposure demonstrated a trend toward increased risk (odds ratio, 3.5; P = .15); however, an insufficient number of patients were treated with lenalidomide to allow us to accurately assess the risk of this agent. Exclusion of NMSCs retained the association with these variables but was accompanied by loss of statistical significance. This large single-institution analysis identified associations between race and older age and increased risk of developing SPM. The trend toward increased risk with thalidomide exposure suggests a class effect from immunomodulatory drugs that might not be restricted to lenalidomide

Plant immunity regulation by transcription factors SARD1 and CBP60g : downstream, upstream and the amplification loop

Activated plant defense responses consist of PAMP (pathogen associated molecular pattern)-triggered immunity (PTI) and effector-triggered immunity (ETI) at infected sites and a secondary immune response in distal parts of the host plant, termed systemic acquired resistance (SAR). Salicylic acid (SA) plays critical roles in plant immunity and its level increases upon pathogen infection. Pathogen-induced SA biosynthesis predominantly relies on ICS1 (ISOCHORISMATE SYNTHASE 1), whose induction mainly depends on transcription factors SARD1 (SAR DEFICIENT 1) and CBP60g (CALMODULIN BINDING PROTEIN 60 g). Meanwhile, the expression of SARD1 and CBP60g is also highly induced by pathogens. My Ph.D. research focuses on identification of immune regulators that function upstream and downstream of SARD1 and CBP60g. First, we performed chromatin immunoprecipitation-sequencing experiments to identify candidate targets of SARD1. We found that SARD1 and CBP60g directly control the expression of a large number of key regulators involved in PTI, ETI and SAR. Among them, two genes essential for SAR, ALD1 (AGD2-LIKE DEFENSE RESPONSE PROTEIN 1) and SARD4, are involved in the biosynthesis of pipecolic acid (Pip), a plant secondary metabolite required for SAR. Consistently, the sard1cbp60g double mutant accumulates less Pip than wild type, suggesting that SARD1 and CBP60g regulate Pip biosynthesis in addition to SA. Secondly, we showed that transcription factors TGA1 and TGA4 act upstream of SARD1 and CBP60g and thus regulate the biosynthesis of SA and Pip. Lastly, we revealed a novel mechanism of SA perception by its receptors NPR3 (NPR1-LIKE PROTEIN 3) and NPR4. NPR3/NPR4 interact with transcription factors TGA2, TGA5 and TGA6, and act as transcriptional repressors. SA inhibits the transcriptional repression activities of NPR3/NPR4 and promotes the transcriptional activation activity of NPR1 (NONEXPRESSER OF PR GENES 1); both contribute to SA-induced defense gene expression. We also found that SA induces SARD1 expression, revealing a feedback amplification loop between SA and SARD1, where SARD1 promotes SA biosynthesis via directly activating ICS1 expression and SA induces SARD1 expression by regulating the activities of NPR/TGA complexes. Altogether studies in this dissertation provide new insights on the functions of SARD1 and CBP60g in plant immunity and the mechanism of SA perception and signaling.Science, Faculty ofBotany, Department ofGraduat

A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations

A Godunov-mixed finite element method on changing meshes is presented to simulate the nonlinear Sobolev equations. The convection term of the nonlinear Sobolev equations is approximated by a Godunov-type procedure and the diffusion term by an expanded mixed finite element method. The method can simultaneously approximate the scalar unknown and the vector flux effectively, reducing the continuity of the finite element space. Almost optimal error estimates in L2-norm under very general changes in the mesh can be obtained. Finally, a numerical experiment is given to illustrate the efficiency of the method

A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media

An approximation scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by two methods. Under the regularity assumption for the pressure, cubic Hermite finite element method is used for the pressure equation, which ensures the approximation of the velocity smooth enough. A second order characteristic finite element method is presented to handle the material derivative term of the concentration equation. It is of second order accuracy in time increment, symmetric, and unconditionally stable. The optimal L2-norm error estimates are derived for the scalar concentration

A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations

We present a time discontinuous Galerkin finite element scheme for quasi-linear Sobolev equations. The approximate solution is sought as a piecewise polynomial of degree in time variable at most q-1 with coefficients in finite element space. This piecewise polynomial is not necessarily continuous at the nodes of the partition for the time interval. The existence and uniqueness of the approximate solution are proved by use of Brouwer’s fixed point theorem. An optimal L∞(0,T;H1(Ω))-norm error estimate is derived. Just because of a damping term uxxt included in quasi-linear Sobolev equations, which is the distinct character different from parabolic equation, more attentions are paid to this term in the study. This is the significance of this paper

Perception of Salicylic Acid in Physcomitrella patens

Salicylic acid (SA) is a key signaling molecule in plant immunity. Two types of SA receptors, NPR1 and NPR3/NPR4, were reported to be involved in the perception of SA in Arabidopsis. SA is also synthesized in the non-vascular moss Physcomitrella patens following pathogen infection. Sequence analysis revealed that there is only one NPR1/NPR3/NPR4-like protein in P. patens. This agrees with the phylogenetic study that showed the divergence of NPR1 and NPR3/NPR4 from the same ancestor during the evolution of higher plants. Intriguingly, expression of the P. patens NPR1/NPR3/NPR4-like gene in Arabidopsis does not complement the constitutive defense phenotype of the npr3 npr4 double mutant, but can partially rescue the mutant phenotypes of npr1-1, suggesting that it functions as an NPR1-like positive regulator of SA-mediated immunity and P. patens does not have an SA receptor functioning similarly as NPR3/NPR4. Future characterization of the P. patens NPR1-like protein and analysis of its functions through knockout and biochemical approaches will help us better understand how SA is perceived and what its functions are in P. patens