Uniform Distribution, Discrepancy, and Reproducing Kernel Hilbert Spaces

AbstractIn this paper we define a notion of uniform distribution and discrepancy of sequences in an abstract set E through reproducing kernel Hilbert spaces of functions on E. In the case of the finite-dimensional unit cube these discrepancies are very closely related to the worst case error obtained for numerical integration of functions in a reproducing kernel Hilbert space. In the compact case we show that the discrepancy tends to zero if and only if the sequence is uniformly distributed in our sense. Next we prove an existence theorem for such uniformly distributed sequences and investigate the relation to the classical notion of uniform distribution. Some examples conclude this paper

Performance Analysis, PVM and MPI Implementation of a DSCF Hartree Fock Program

A new Direct SCF-Hartree Fock program (DSCF) has been improved by the method of DIIS. (17), (18) General performance measurement tools, as provided on the SGIPower Challenge/R10000 (194 MHz) running IRIX 6.2, which are the shell-commands perfex -a a.out and ssrun -(pcsampl, ideal, usertime) a.out, have been used for profiling the code. The main cpu-time-consuming subroutine was detected and parallel versions for PVM 3.3 as well as MPI have been deduced. An additional module for the purpose of achieving load-balancewas introduced and obtained speed-up parameters are presented and compared

Towards Confidential Computing: A Secure Cloud Architecture for Big Data Analytics and AI

Cloud computing provisions computer resources at a cost-effective way based on demand. Therefore it has become a viable solution for big data analytics and artificial intelligence which have been widely adopted in various domain science. Data security in certain fields such as biomedical research remains a major concern when moving their workflows to cloud, because cloud environments are generally outsourced which are more exposed to risks. We present a secure cloud architecture and describes how it enables workflow packaging and scheduling while keeping its data, logic and computation secure in transit, in use and at rest.Comment: 2023 IEEE 16th International Conference on Cloud Computing (IEEE CLOUD), Chicago, Illinois, USA, July 2-8, 202

Konstruktion von schlichten Funktionen mit unendlich vielen Fixpunkten

Si costruiscono funzioni convesse univalenti $f(z)=z+a_{2}z^{2}+\ldots$ che hanno i punti $0,z_{1},z_{2},\ldots z_{n},\ldots$del disco unitario aperto come punti fissi.Convex univalent functions $f(z)=z+a_{2}z^{2}+\ldots$fixing exactly the points $0,z_{1},z_{2},\ldots z_{n},\ldots$of the open unit disc are explicitly constructed

Parallel Number Theoretical Numerics for Solving s-dimensional Integral Equations of the Convolution Type

2 1 Number Theoretical Methods 4 1.1 Equidistributed Sequences modulo 1 : : : : : : : : : : : : : : : : : : : : : 4 1.2 Lattices : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.2.1 Orthogonal Lattices : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2.2 k\Theta--Sequences : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2.3 Lattices According to A. Weil : : : : : : : : : : : : : : : : : : : : : 7 1.2.4 Parallelepipedic Lattices : : : : : : : : : : : : : : : : : : : : : : : : 7 1.2.5 Examples for s = 2 : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2 Integral Equation and Laplace Transform 10 3 Numerical Computation of the Solution \Phi(T ) 14 3.1 A Mapping : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 3.2 Periodization and Mapping onto G s : : : : : : : : : : : : : : : : : : : : : : 15 3.3 Error Estimations for the Numerical Solution of \Phi(T ) : : : : : : : : : : : : 17 4 Numerical Experiments..