30 Jahre „Geschichte der Gouvernementalität“:: Wir brauchen mehr Geschichte des Wissens

An increasing number of studies have appeared that together come under the label of governmentality. The topics show that an analysis related to practices can integrate a broad spectrum of social phenomena that is out of the range of conventional theories of the state. Less well known is the founding text of governmentality studies. Foucault‘s “history of governmentality” is a genealogy of liberal governments, ending with the rise of the recent so-called neoliberal transformation of the 1970s. The weakness of that text is that it fails to show the connections of the concept of governmentality to epistemology. Also, recent studies mention the power relations of knowledge only globally, leaving science in a sphere of its own. However, originality and strength of the analysis of governmental power depends on its linkage to a history of knowledge

Optimization of mesh hierarchies in Multilevel Monte Carlo samplers

We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and non-geometric sequences of mesh sizes and show that geometric hierarchies, when optimized, are nearly optimal and have the same asymptotic computational complexity as non-geometric optimal hierarchies. We discuss how enforcing constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. These constraints include an upper and a lower bound on the mesh size or enforcing that the number of samples and the number of discretization elements are integers. We also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. To provide numerical grounds for our theoretical results, we apply these optimized hierarchies together with the Continuation MLMC Algorithm. The first example considers a three-dimensional elliptic partial differential equation with random inputs. Its space discretization is based on continuous piecewise trilinear finite elements and the corresponding linear system is solved by either a direct or an iterative solver. The second example considers a one-dimensional It\^o stochastic differential equation discretized by a Milstein scheme

A Continuation Multilevel Monte Carlo algorithm

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding weak and strong errors. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients

Digital Documentation and Reconstruction of an Ancient Maya Temple and Prototype of Internet GIS Database of Maya Architectur

This is a request for Level II Start-Up funding for an international project to develop and test a working prototype for a new platform for an online, searchable database that can bring together GIS maps, 3D models, and virtual environments for teaching and research. (The planning phase was funded by a Level I Start-Up Grant in 2009.) The prototype will employ existing digital collections on Maya architecture at the UNESCO World Heritage Site of Copan, Honduras and a highly-accurate, hybrid 3D model being developed by the project that will test and demonstrate the platform???s capabilities. Art historians and archaeologists from the University of New Mexico (UNM) and the Honduran Institute of Anthropology and History will work with computer experts from ETH Zurich, FBK Trento, and the University of California to design this online tool

Implementation and analysis of an adaptive multilevel Monte Carlo algorithm

We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of solutions to Itô stochastic differential equations (SDE). The work [Oper. Res. 56 (2008), 607-617] proposed and analyzed an MLMC method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a single level Euler-Maruyama Monte Carlo method from ( TOL -3 )${{{\mathcal {O}}({\mathrm {TOL}}^{-3})}}$ to ( TOL -2 log( TOL -1 ) 2 )${{{\mathcal {O}}({\mathrm {TOL}}^{-2}\log ({\mathrm {TOL}}^{-1})^{2})}}$ for a mean square error of ( TOL 2 )${{{\mathcal {O}}({\mathrm {TOL}}^2)}}$ . Later, the work [Lect. Notes Comput. Sci. Eng. 82, Springer-Verlag, Berlin (2012), 217-234] presented an MLMC method using a hierarchy of adaptively refined, non-uniform time discretizations, and, as such, it may be considered a generalization of the uniform time discretization MLMC method. This work improves the adaptive MLMC algorithms presented in [Lect. Notes Comput. Sci. Eng. 82, Springer-Verlag, Berlin (2012), 217-234] and it also provides mathematical analysis of the improved algorithms. In particular, we show that under some assumptions our adaptive MLMC algorithms are asymptotically accurate and essentially have the correct complexity but with improved control of the complexity constant factor in the asymptotic analysis. Numerical tests include one case with singular drift and one with stopped diffusion, where the complexity of a uniform single level method is ( TOL -4 )${{{\mathcal {O}}({\mathrm {TOL}}^{-4})}}$ . For both these cases the results confirm the theory, exhibiting savings in the computational cost for achieving the accuracy ( TOL )${{{\mathcal {O}}({\mathrm {TOL}})}}$ from ( TOL -3 )${{{\mathcal {O}}({\mathrm {TOL}}^{-3})}}$ for the adaptive single level algorithm to essentially ( TOL -2 log( TOL -1 ) 2 )${{{\mathcal {O}}({\mathrm {TOL}}^{-2}\log ({\mathrm {TOL}}^{-1})^2)}}$ for the adaptive MLMC algorith