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In the framework of transport theory, we are interested in the following optimization problem: given the distributions of working people and of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of from with respect to a metric which depends on the transportation network....
In the framework of transport theory, we are interested in the following optimization problem: given the distributions µ+ of working people and µ- of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of µ+ from µ- with respect to a metric which depends on the transportation...
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....
We consider the wave and Schrödinger equations on a bounded open connected subset of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset of during a time interval with . It is well known that, if the pair satisfies the Geometric Control Condition ( being an open set), then an observability inequality holds guaranteeing that the total energy of solutions can be...
We prove partial regularity with optimal Hölder exponent of
vector-valued minimizers u of the quasiconvex variational integral under polynomial growth. We employ the indirect
method of the bilinear form.
In this paper, we investigate the optimal location of secondary sources (controls) to enhance the reduction of the noise field in a one-dimensional acoustic cavity. We first formulate the active control strategy as a linear quadratic tracking (LQT) problem in a Hilbert space, and then formulate the optimization problem as minimizing an appropriate performance criterion based on the LQT cost function with respect to the location of the controls. A numerical scheme based on the Legendre–tau method...
We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate...
We consider the Schrödinger operator on , where is a given domain of . Our goal is to study some optimization problems where an optimal potential has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.
In the paper there is discussed a problem of the resource allocation in a large scale system in the presence of the resource shortages. The control task is devided into two levels, with the coordinator on the upper level and local controllers on the lower one. It is assumed that they have different information. The coordinator has an information on mean values of users demands, an inflow forecast and an estimation of the resource amount in a storage reservoir. On the basis on this information it...
We present a model for describing the spread of an infectious disease with public
screening measures to control the spread. We want to address the problem of determining an
optimal screening strategy for a disease characterized by appreciable duration of the
infectiveness period and by variability of the transmission risk. The specific disease we
have in mind is the HIV infection. However the model will apply to a disease for which
class-age structure...
We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example...
The construction of reduced order models for dynamical systems using
proper orthogonal decomposition (POD) is based on the information
contained in so-called snapshots. These provide the spatial
distribution of the dynamical system at discrete time instances.
This work is devoted to optimizing the choice of these time
instances in such a manner that the error between the POD-solution
and the trajectory of the dynamical system is minimized. First and
second order optimality systems are given. Numerical...
The scheduling of angiogenic inhibitors to control a vascularized tumor is analyzed as an optimal control problem for a mathematical model that was developed and biologically validated by Hahnfeldt et al. [Cancer Res. 59 (1999)]. Two formulations of the problem are considered. In the first one the primary tumor volume is minimized for a given amount of angiogenic inhibitors to be administered, while a balance between tumor reduction and the total amount of angiogenic inhibitors given is minimized...
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