xed large time duration.
We use this result to prove the existence of an open-loop Nash equilibrium point for non-zero sum stochastic
Keywords: Fully coupled Forward-backward stochastic dierential equation, Lévy process, stochastic dier-
MSC 2010: 49K45, 65K10, 91B28, 93E20
Fouzia Baghery, Isabelle Turpin: Université de Valenciennes, LAMAV-ISTV2, Mont Houy, 59313 Valenciennes cedex 9, France,
e-mail: firstname.lastname@example.org, email@example.com
Nabil Khelfallah, Brahim Mezerdi: Université de Biskra
convergence criteria of
these iterative algorithms. The results presented in this paper generalize, unify and improvemany previously
known results for quasi-variational and variational inequality problems.
Keywords: Split general quasi-variational inequality problem, split quasi-variational inequality problem,
split general variational inequality problem, iterative algorithms, convergence analysis
MSC 2010: Primary 47J53, 65K10; secondary 49M37, 90C25
*Corresponding author: Kaleem Raza Kazmi: Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India,
equations to which our analysis can be applied. Moreover, we intro-
duce a certain multilevel preconditioning strategy which in practice promotes the aforementioned spectral
properties for problems where the nonlinearity is a perturbation of a linear operator.
Keywords:Conditional gradientmethod, nonconvexoptimization, sparseminimization, (nonlinear) operator
equations, iterative thresholding, multilevel preconditioning, wavelets
MSC 2010: 65K10, 65J15, 41A25, 65N12, 65T60, 47J06, 47J25
Stephan Dahlke, Ulrich Friedrich: AG Numerik, FB Mathematik und Informatik
The topology of a minimal cluster of four planar regions with equal areas and smallest possible perimeter was found in . Here we describe the computation used to check that the symmetric cluster with the given topology is indeed the unique minimal cluster.
The problem of variational data assimilation for a model of ocean thermodynamics is formulated as an optimal control problem to find the boundary heat flux. The sensitivity of functionals of the optimal solution with respect to observations is studied. Computing the gradient of the functionals is reduced to the solution of a non-standard problem which is a coupled system involving direct and adjoint equations with mutually dependent boundary values. Solvability of the non-standard problem is studied based on the Hessian of the original cost function. An algorithm for computing the gradient of the response function related to the mean surface temperature is developed and justified. Numerical examples are presented for the Baltic Sea thermodynamics model.
The existence of a nonsingular matrix is proved for any space of square symmetric matrices with a trivial quadratic kernel. Some corollaries from this result are obtained for construction of solvers of nonlinear equations and problems of conditional optimization with a Jacobi matrix of incomplete rank based on the theory of p-regularity for p = 2. Some remarks for the case p ⩾ 3 are presented.
The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition. The optimal solution (analysis) error arises due to the errors in the input data (background and observation errors). Under the Gaussian assumption the optimal solution error covariance can be constructed using the Hessian of the auxiliary data assimilation problem. The aim of this paper is to study the evolution of model errors via data assimilation. The optimal solution error covariances are derived in the case of imperfect model and for the weak constraint formulation, when the model euations determine the cost functional.
A problem on pollution risk control related to local sources in region is formulated. Algorithm for solving the problem is proposed. The results of numerical experiment on the solution of the studied problem illustrating the effectiveness of the proposed algorithm are presented.
High-throughput sequencing techniques are increasingly affordable and produce massive amounts of data. Together with other high-throughput technologies, such as microarrays, there are an enormous amount of resources in databases. The collection of these valuable data has been routine for more than a decade. Despite different technologies, many experiments share the same goal. For instance, the aims of RNA-seq studies often coincide with those of differential gene expression experiments based on microarrays. As such, it would be logical to utilize all available data. However, there is a lack of biostatistical tools for the integration of results obtained from different technologies. Although diverse technological platforms produce different raw data, one commonality for experiments with the same goal is that all the outcomes can be transformed into a platform-independent data format – rankings – for the same set of items. Here we present the R package TopKLists, which allows for statistical inference on the lengths of informative (top-k) partial lists, for stochastic aggregation of full or partial lists, and for graphical exploration of the input and consolidated output. A graphical user interface has also been implemented for providing access to the underlying algorithms. To illustrate the applicability and usefulness of the package, we integrated microRNA data of non-small cell lung cancer across different measurement techniques and draw conclusions. The package can be obtained from CRAN under a LGPL-3 license.
We examine the L2-gradient flow of Euler’s elastic energy for closed curves in hyperbolic space and prove convergence to the global minimizer for initial curves with elastic energy bounded by 16. We show the sharpness of this bound by constructing a class of curves whose lengths blow up in infinite time. The convergence results follow from a constrained sharp Reilly-type inequality.