Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Social Meets Molecular: Combining Phylogenetic and Latent Class Analyses to Understand HIV-1 Transmission in Switzerland

Switzerland has a complex human immunodeficiency virus (HIV) epidemic involving several populations. We examined transmission of HIV type 1 (HIV-1) in a national cohort study. Latent class analysis was used to identify socioeconomic and behavioral groups among 6,027 patients enrolled in the Swiss HIV Cohort Study between 2000 and 2011. Phylogenetic analysis of sequence data, available for 4,013 patients, was used to identify transmission clusters. Concordance between sociobehavioral groups and transmission clusters was assessed in correlation and multiple correspondence analyses. A total of 2,696 patients were infected with subtype B, 203 with subtype C, 196 with subtype A, and 733 with recombinant subtypes (mainly CRF02_AG and CRF01_AE). Latent class analysis identified 8 patient groups. Most transmission clusters of subtype B were shared between groups of gay men (groups 1-3) or between the heterosexual groups "heterosexual people of lower socioeconomic position" (group 4) and "injection drug users" (group 8). Clusters linking homosexual and heterosexual groups were associated with "older heterosexual and gay people on welfare" (group 5). "Migrant women in heterosexual partnerships" (group 6) and "heterosexual migrants on welfare" (group 7) shared non-B clusters with groups 4 and 5. Combining approaches from social and molecular epidemiology can provide insights into HIV-1 transmission and inform the design of prevention strategies.

The Social Geography of Education: Neighborhood, Class Composition, and the Educational Achievement of Elementary School Students in Zurich, Switzerland

Despite an impressive amount of research and policy intervention no robust pattern of neighborhood effects on educational attainment has previously been identified. Adequate theoretical modeling and the sensitivity of the results to the method of the study are the major challenges in this area of research. This paper elaborates the social mechanisms of neighborhood effects and applies various methodological approaches to test them. Using data from Switzerland, the research reported here has detected heterogeneous effects of neighborhood on elementary school students’ educational achievement in Zurich. Although modest in comparison with the effects of classroom composition, these effects appear to be mediated primarily through social integration into a local peer network and are differentiated according to students’ gender and their social origin.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.