Related papers: Asymptotic compatibility of parametrized optimal d…
State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to…
We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter $\delta$, which…
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in…
This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through…
In this paper, we study optimal control problems on the internal energy for a system governed by a class of elliptic boundary hemivariational inequalities with a parameter. The system has been originated by a steady-state heat conduction…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function.…
In this paper we design and analyze an explicit partitioned procedure for a 2D dynamic local-to-nonlocal (LtN) coupling problem, based on a new nonlocal Robin-type transmission condition. The nonlocal subproblem is modeled by the nonlocal…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
We derived an asymptotic bound the accuracy of the estimation when we use the quantum correlation in the measuring apparatus. It is also proved that this bound can be achieved in any model in the quantum two-level system. Moreover, we show…
We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter {\epsilon}. We study the asymptotic, as {\epsilon} goes to 0, of the corresponding value functions, and show convergence, in…
Given an optimal control problem on a heterogeneous body with a periodical structure of particles depending on a small parameter e, we study the asymptotic behavior, as e converges to zero, of the optimal control functional and the optimal…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…