In this paper we combine the theory of probability aggregation with results of machine learning theory concerning the optimality of predictions under expert advice. In probability aggregation theory several characterisation results for linear aggregation exist. However, in linear aggregation weights are not fixed, but free parameters. We show how fixing such weights by successbased scores allow...

In this work an acoustic application is studied. The goal is to estimate the complex-valued admittance from given point measurements of the sound pressure. This parameter identification problem is formulated in terms of an infinite-dimensional optimization problem. First-and second-order optimality conditions are discussed. For the numerical realization a reduced-order model based on proper ort...

In this study, we investigate three well-known problems, the longest path problem on directed acyclic graphs, the minimum spanning tree problem and the single machine scheduling problem with total flow time criterion, where the input data for all problems are given as interval numbers. Since optimal solutions depend on the realization of the data, we define new optimality concepts to aid decisi...

We consider the problem of estimating the state of a diffusion process, based on discrete time observations in singular noise. We reduce the problem to a static problem, and we show that the solution is provided by the area or co–area formula of ge~ metric measure theory, provided the observed value is a regular value of the observation function. In order to address the case of singular values,...

We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete E 6-singlet sector, which has been recently evaluated using techniques of spectral and exact sequences. We use the discrete symmetries of the models to find flat directions of symmetry breaking that leave unbroken a low energy matter parity and make all...

In the classical decision theory framework, the loss is a function of the decision taken and the state of nature as represented by a parameter 0. Information about 0 can be obtained via observation of a random variable X. In some situations however the loss will depend not directly on 0 but on the observed value of another random variable Y whose distribution depends on 0. This adds an extra la...

An integer-valued sequence π = (d1, . . . , dn) is graphic if there is a simple graph G with degree sequence of π . We say the π has a realization G. Let Z3 be a cyclic group of order three. A graph G is Z3-connected if for every mapping b : V (G) → Z3 such that  v∈V (G) b(v) = 0, there is an orientation of G and amapping f : E(G) → Z3−{0} such that for each vertex v ∈ V (G), the sum of the va...

Option pricing and hedging in a complete market are well-studied with nice results using martingale theories. However, they remain as open questions in incomplete markets. In particular, when the underlying processes involve jumps, there could be infinitely many martingale measures which give an interval of no-arbitrage prices instead of a unique one. Consequently, there is no martingale repres...

In this paper we develop a stochastic realization theory for multiscale autoregressive (MAR) processes that leads to computationally ecient realization algorithms. The utility of MAR processes has been limited by the fact that the previously known general purpose realization algorithm, based on canonical correlations, leads to model inconsistencies and has complexity quartic in problem size. O...

The paper deals with new interpretation of LQG optimality. Known description of LQG optimality is abstract and that is why it is not popular for usage in applications. Presented interpretation is based on familiar terms of the control theory and it is shown that LQG optimality can be interpreted in deterministic point of view.