Sufficiency in Quantum Statistical Inference

This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways and the non-commutative analogue of the factorization theorem is obtained. As an application we discuss exponential families. Our factorization theorem also implies two further important results, previously known only in finite Hilbert space dimension, but proved here in generality: the Koashi-Imoto theorem on maps leaving a family of states invariant, and the characterization of the general form of states in the equality case of strong subadditivity. Supported by the EU Research Training Network Quantum Probability with Applications to Physics, Information Theory and Biology and Center of Excellence SAS Physics of Information I/2/2005. Supported by the Hungarian grant OTKA T032662     

Some remarks to multivariate regression model

Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model. This work was supported by the Council of Czech Government J14/98:153100011.     

Geometro-stochastic locality in quantum spacetime and quantum diffusions

The issue of the intrinsic nonlocality of quantum mechanics raised by J. S. Bell is examined from the point of view of the recently developed method of geometro-stochastic quantization and its applications to general relativistic quantum theory. This analysis reveals that a distinction should be made between the topological concept of locality used in formulating relativistic causality and a type of geometric locality based on the concept of fiber bundle, which can be used in extending the strong equivalence principle to the quantum domain. Both play an essential role in formulating a notion of geometro-stochastic propagation based on quantum diffusions, which throws new light on the EPR paradox, on the origin of the arrow of time, and on other fundamental issues in quantum cosmology and the theory of measurement.     

Planar Chromatography of Some 1-Arylpiperazines Behaving as Dopaminergic Ligands

JPC – Journal of Planar Chromatography – Modern TLC - The chromatographic behavior of fourteen 1-arylpiperazine derivatives has been studied by thin-layer chromatography on both silica...     

Harnack inequality for some classes of Markov processes

In this paper we establish a Harnack inequality for nonnegative harmonic functions of some classes of Markov processes with jumps. Mathematics Subject Classification (2000): Primary 60J45, 60J75, Secondary 60J25.This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut Oberwolfach. We thank the Institute for the hospitality.The research of this author is supported in part by NSF Grant DMS-9803240.The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia.     

The standard model on non-commutative space-time

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter . No new particles are introduced; the structure group is . We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. Received: 29 November 2001 / Published online: 25 January 2002