In this paper we discuss representations of law invariant coherent risk measures in a form of integrals of the average value-at-risk measures. We show that such an integral representation exists iff the dual set of the considered risk measure is generated by one of its elements, and this representation is uniquely defined. On the other hand, representation of risk measures as a maximum of such ...

A doctoral program in computer science with a specialization in information security is described. The focus of the program is constructive security. Key elements of the program are the strong computer science core upon which it builds, coursework on the theory and principles of information assurance, and a unifying research project. The doctoral candidate is a member of the project team, whose...

A polygonisation algorithm is presented which extends an existing skeletal implicit surface technique to include operations based on Constructive Solid Geometry between blended groups of implicit surface objects. The result is a surface definition (to be called Boolean Compound Soft Object, or BCSO for short) which consists of a boolean expression with union, intersection, and set difference op...

A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O( √ n). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In fact, the LovettMeka algorithm finds a half integral point in any “large enough” polytope. However, their algorithm crucially relies on the facet structure and d...

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the mat...

Sheet-metal parts produced by pressing, stamping or similar technology; usually have residual stresses, which tend to deform them. If these parts are intended to be assembled with other elements, it is necessary to perform measurements to check if constructive dimensions are within acceptable tolerance limits. Such measurements require at least four stages: positioning, clamping, measurement, u...

In this paper, we characterize self-dual elements of a free distributive lattice with n generators by means of a median operation on this lattice. Hence, we obtain a constructive characterization of Sperner's families, for which H is equal to Tr H. We construct some infinite sequences of these families. These results generalize those of N. M. Rivi6re (J. Combinatorial Theory 5 (1968), 229-234) ...

This paper introduces two new techniques for solving the Quadratic Assignment Problem. The first is a heuristic technique, defined in accordance to the Ant System metaphor, and includes as a distinctive feature the use of a new lower bound at each constructive step. The second is a branch and bound exact approach, containing some elements introduced in the Ant algorithm. Computational results p...

The Heine-Borel theorem states that any open cover of the closed interval Œa; b contains a nite subcover. We give a new, constructive proof inspired by the concept of a greedy algorithm. In the case when the initial cover consists only of intervals, our proof is optimal in that it constructs a nite subcover with the fewest possible number of elements. Our work leaves open a number of questions...

This paper throws light on the connection between the optimal condition number estimate for the BPX method and constructive approximation theory. We provide a machinery, which allows to understand the optimality as a consequence of an approximation property and an inverse inequality inH , > 0. This machinery constructs so-called approximation spaces, which characterize a certain rate of approxi...