On the volumetric path

We consider the logarithmic and the volumetric barrier functions used in interior point methods. In the case of the logarithmic barrier function, the analytic center of a level set is the point at which the central path intersects that level set. We prove that this also holds for the volumetric path. For the central path, it is also true that the analytic center of the optimal level set is the limit point of the central path. The only known case where this last property for the logarithmic barrier function fails occurs in case of semidefinite optimization in the absence of strict complementarity. For the volumetric path, we show with an example that this property does not hold even for a linear optimization problem in canonical form.     

Hypergraphs as a mean of discovering the dependence structure of a discrete multivariate probability distribution

Most everyday reasoning and decision making is based on uncertain premises. The premises or attributes, which we must take into consideration, are random variables, therefore we often have to deal with a high dimensional multivariate random vector. A multivariate random vector can be represented graphically as a Markov network. Usually the structure of the Markov network is unknown. In this paper we construct special type of junction trees, in order to obtain good approximations of the real probability distribution. These junction trees are capable of revealing some of the conditional independences of the network. We have already introduced the concept of the t-cherry junction tree (E. Kovács and T. Szántai in Proceedings of the IFIP/IIASA//GAMM Workshop on Coping with Uncertainty, 2010), based on the t-cherry tree graph structure. This approximation uses only two and three dimensional marginal probability distributions. Now we use k-th order t-cherry trees, also called simplex multitrees to introduce the concept of the k-th order t-cherry junction tree. We prove that the k-th order t-cherry junction tree gives the best approximation among the family of k-width junction trees. Then we give a method which starting from a k-th order t-cherry junction tree constructs a (k+1)-th order t-cherry junction tree which gives at least as good approximation. In the last part we present some numerical results and some possible applications.     

Minor Posets of Functions as Quotients of Partition Lattices

Order - We study the structure of the partially ordered set of minors of an arbitrary function of several variables. We give an abstract characterization of such “minor posets” in terms...     

The arity gap of order-preserving functions and extensions of pseudo-Boolean functions

The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are the so-called aggregation functions. We first explicitly classify the Lovász extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a similar explicit classification for this function class.     

Opportunities for measurements of astrophysical-relevant alpha-capture reaction rates at CRYRING@ESR

The heavy-ion storage ring CRYRING@ESR has recently been installed and commissioned at GSI as one of the first installations of the upcoming Facility for Antiproton and Ion Research (FAIR). It is designed to store highly charged ions in the energy range between 300 keV/u and about 10 MeV/u. It will incorporate a gas-jet target providing high-density jets of, among other gases, hydrogen and helium. This will allow to study alpha-capture reaction rates of astrophysical interest in the energy range of the Gamow window for core-collapse supernovae. Special interest comes from the long-lived radio-isotope ⁴⁴Ti (t_1/2 = 58.9 years), which is supposed to be produced in the alpha-rich freeze-out during such an event. The nucleosynthesis of this isotope is of great interest, as the amount of material produced can be estimated by direct observation in remnants of recent supernovae. The disagreements between the observations and the estimations from astrophysical models show the need of more experimental data for the production and consumption reactions in the energy range of a core-collapse supernova. In this article, we will describe the proposed method of injecting beams of ⁴⁴Ti into CRYRING@ESR and performing the actual reaction rate measurements.     

On Cyclic Caps in Projective Spaces

Let H be a subgroup of a cyclic Singer group of PG (n,q). In this paper we study the following problem: When is a point orbit of H a cap? A necessary and sufficient condition for this is derived and used to give a short proof of some results by Ebert [6] and to show that small orbits are typically caps.     

Symmetry classes of tensors associated with certain groups

We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with certain subgroups of the full symmetric group The dimensions of these symmetry classes of tensors are also given     

Sectional curvatures in nonlinear optimization

The aim of the paper is to show how to explicitly express the function of sectional curvature with the first and second derivatives of the problem’s functions in the case of submanifolds determined by equality constraints in the n-dimensional Euclidean space endowed with the induced Riemannian metric, which is followed by the formulation of the minimization problem of sectional curvature at an arbitrary point of the given submanifold as a global minimization one on a Stiefel manifold. Based on the results, the sectional curvatures of Stiefel manifolds are analysed and the maximal and minimal sectional curvatures on an ellipsoid are determined. This research was supported in part by the Hungarian Scientific Research Fund, Grant No. OTKA-T043276 and OTKA-K60480.