We describe the application of data mining algorithms to research problems in astronomy. We posit that data mining has always been fundamental to astronomical research, since data mining is the basis of evidencebased discovery, including classification, clustering, and novelty discovery. These algorithms represent a major set of computational tools for discovery in large databases, which will b...

The L4.verified project has produced a formal, machinechecked Isabelle/HOL proof that the C code of the seL4 OS microkernel correctly implements its abstract implementation. This paper briefly summarises the proof, its main implications and assumptions, reports on the experience in conducting such a large-scale verification, and finally lays out a vision how this formally verified kernel may be...

For scattering on the modular surface and on the hyperbolic cylinder, we show that the solutions of the wave equations can be expanded in terms of resonances, despite the presence of trapping. Expansions of this type are expected to hold in greater generality but have been understood only in non-trapping situations. 1. Introduction In this note we give two examples for which we can obtain, on c...

The purpose of this paper is to present two examples of an economy possessing an optimum but no competitive equilibrium. Their essential features are having production and preferences over an infinite horizon; in fact, it seems similar examples may not occur in overlapping generations and/or pure exchange models. There is a growing literature of equilibrium existence theorems in this field. We ...

Idiographic methods focus on time-dependent variation within a single individual (intra-subject variability) in contrast to group-level relationships (inter-subject variability) that may yield different results. Equivalent results occur only if two, probably unrealistic, conditions specified by Ergodic Theorems are met: (1) Each trajectory follows the same dynamic laws, and (2) Each trajectory ...

We consider the differential game associated with robust control of a system in a compact state domain, using Skorokhod dynamics on the boundary. A specific class of problems motivated by queueing network control is considered. A constructive approach to the Hamilton-Jacobi-Isaacs equation is developed which is based on an appropriate family of extremals, including boundary extremals for which ...

The computation of large problems in scientifical and industrial fields needs for efficient computer systems. A rising number parallel computers are used to deliver necessary computation resources. The physical restrictions of circuit integration limit the speed of single processor solutions. The use of consumer components is a cost–effective way to built a parallel computer. The deployment of ...

We define the notions of finite-state and functionally recursive matrices and their growth. We also introduce two rings generated by functionally recursive matrices. The first is isomorphic to the 2-generated free ring. The second is a 2-generated monomial ring such that the multiplicative semigroup of monomials in the generators is nil of degree 5 and the ring has Gelfand Kirillov dimension 1 ...