Commutativity, comeasurability, and contextuality in the Kochen-Specker arguments

If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting (ii) associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality.Comment: 27 pages, 1 figur

On diagonal quasi-free automorphisms of simple Cuntz-Krieger algebras

We show that an outer action of a finite abelian group on a simple Cuntz-Krieger algebra is strongly approximately inner in the sense of Izumi if the action is given by diagonal quasi-free automorphisms and the associated matrix is aperiodic. This is achieved by an approximate cohomology vanishing-type argument for the canonical shift restricted to the relative commutant of the set of domain projections of the canonical generating isometries in the fixed point algebra.Comment: v3 17 pages; this version has been accepted for publication in Mathematica Scandinavic

Bell inequality and common causal explanation in algebraic quantum field theory

Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not known for Bell inequalities in algebraic quantum field theories establishing constraints for the expectation of specific linear combinations of projections in a quantum state. In the paper we address the question as to whether a 'common causal justification' of these non-classical Bell inequalities is possible. We will show that although the classical notion of common causal explanation can readily be generalized for the non-classical case, the Bell inequalities used in quantum theories cannot be derived from these non-classical common causes. Just the opposite is true: for a set of correlations there can be given a non-classical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the non-classical case is wider than that restricted by the Bell inequalities

Theoretical Aspects of Molecular Recognition

Molecular recognition is a key process in non-covalent interactions, which determines, among others, host-guest complexation, drug action and protein-protein interaction. A simple and attractive formulation is the lock-and-key analogy defining the host as a lock accommodating the guest as a key. We stress three major aspects of molecular recognition, determining both complementarity between host and guest and similarity within a group of guest molecules. These aspects are: steric, i.e. maximization of close contacts, electrostatic, i.e. maximization of electrostatic attraction between host and guest, as well as hydrophobic, i.e. avoiding hydrophobic hydration, which can be reached by the maximization of apolar contacts between interacting molecules. Some examples are presented from our laboratory: the complexes of acylaminoacyl peptidase with small peptides, the effect of heparin binding on inhibitory potency of C1- inhibitor as well as small-molecule ligand binding to prolyl oligopeptidase and calmodulin

Generating spherical multiquadrangulations by restricted vertex splittings and the reducibility of equilibrium classes

A quadrangulation is a graph embedded on the sphere such that each face is bounded by a walk of length 4, parallel edges allowed. All quadrangulations can be generated by a sequence of graph operations called vertex splitting, starting from the path P_2 of length 2. We define the degree D of a splitting S and consider restricted splittings S_{i,j} with i <= D <= j. It is known that S_{2,3} generate all simple quadrangulations. Here we investigate the cases S_{1,2}, S_{1,3}, S_{1,1}, S_{2,2}, S_{3,3}. First we show that the splittings S_{1,2} are exactly the monotone ones in the sense that the resulting graph contains the original as a subgraph. Then we show that they define a set of nontrivial ancestors beyond P_2 and each quadrangulation has a unique ancestor. Our results have a direct geometric interpretation in the context of mechanical equilibria of convex bodies. The topology of the equilibria corresponds to a 2-coloured quadrangulation with independent set sizes s, u. The numbers s, u identify the primary equilibrium class associated with the body by V\'arkonyi and Domokos. We show that both S_{1,1} and S_{2,2} generate all primary classes from a finite set of ancestors which is closely related to their geometric results. If, beyond s and u, the full topology of the quadrangulation is considered, we arrive at the more refined secondary equilibrium classes. As Domokos, L\'angi and Szab\'o showed recently, one can create the geometric counterparts of unrestricted splittings to generate all secondary classes. Our results show that S_{1,2} can only generate a limited range of secondary classes from the same ancestor. The geometric interpretation of the additional ancestors defined by monotone splittings shows that minimal polyhedra play a key role in this process. We also present computational results on the number of secondary classes and multiquadrangulations.Comment: 21 pages, 11 figures and 3 table

Véges rugalmas-képlékeny alakváltozás elméleti és numerikus vizsgálata = Theoretical and numerical investigation of finite elasto-plastic deformation

Az OTKA kutatási téma keretében az alábbi kutatási eredmények születtek: -A mikropoláris testek rugalmas-képlékeny alakváltozásának számítására végelemes eljárás dolgoztunk ki háromdimenziós testek és és kis alakváltozások esetén. -A Mises-féle képlékenységi feltételt kiterjesztettük a mikropoláris anyagokra, a rugalmas torzítási energia alapján. -A kétdimenziós rugalmasságtani feladatok és a peridynamikus modell számítására meshless eljáráson alapuló program kidolgására került sor. -A Prandtl-Reuss modell anyagegyenleteinek integrálására egzakt eljárásokat dolgoztunk ki lineárisan keményedő modellek esetén. -Egykristályok véges rugalmas-képlékeny alakváltozára javasolt modellekben a rugalmas alakváltozás leírására vonatkozó anyagegyenleteket elemeztük különböző csúszási rendszerek esetén | The research work within in the present OTKA can be summarized as follows: -A 3D finite elment program was developed for micropolar elastoplasticity at small deformations. -The classical Mises yield function has been extended to micropolar solids based on elastic distorsional energy. -The nonlocal peridynamic material model was analysed by the meshless method. and a two dimesional computer code was developed -A new exact integration method for Prandtl-Reuss model with linear isotropic-kinematic hardening has been presented. -The constitutive relations of single crystal elastoplasticity was investigated, and its elastic model was analysed by different test examples (one and two slips system