Krešimir Fresl

Graph approach to quantum systems

Using a graph approach to quantum systems, we show that descriptions of 3-dim Kochen–Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie diagrams (a kind of lattice) that we find in the literature are wrong. Correct lattices generated by McKay-Megill-Pavicic (MMP) hypergraphs and Hilbert subspace equations are given. To enable future exhaustive generation of 3-dim KS setups by means of our recently found stripping technique, bipartite graph generation is used to provide us with lattices with equal numbers of elements and blocks (orthogonal triples of elements)—up to 41 of them. We obtain several new results on such lattices and hypergraphs, in particular, on properties such as superposition and orthoraguesian equations.

Probabilistic Generation of Quantum Contextual Sets

We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these sets, and it gives all sets while the parity proof method gives only sets with an odd number of edges in their hypergraph representation. Thus we obtain 35 new kinds of critical KS sets with an even number of edges. Using a random sample of the sets generated with our method, we give a statistical estimate of the number of sets that might be obtained in an eventual exhaustive enumeration.

C++ Bindings to External Software Libraries with Examples from BLAS, LAPACK, UMFPACK, and MUMPS

FORTRAN and C software packages are often used in generic C++ software. Calling nongeneric functions in generic code is not straightforward. The bindings in this article help the C++ programmer using external software with a small effort. The bindings provide a mechanism to keep external software interfaces and specific vector and matrix containers orthogonal. We show examples using BLAS, LAPACK, UMFPACK, and MUMPS functions and subroutines.

Reconstruction of Rector’ s Palace atrium in Dubrovnik: a key role of column connections

Rector’ s Palace is one of the most valuable heritage buildings in the historic Old town of Dubrovnik and the world famous setting for concerts and exhibitions. The Palace Atrium is surrounded by two stories structure comprising quadripartite masonry vaults supported by masonry walls and stone columns. Historically, this structure has suffered numerous collapses and damages and restorations were frequently made. Despite this, many distinct fractures are concentrated around the traditionally made column connections with capitals and bases. Carefully smoothed stone contact areas are joined with iron dowel, which is centrally placed in a slightly larger hole, with a lead infill. These contacts do not have sufficient rotational stiffness and the ability to transmit eccentric loads. Therefore, high edge stresses and fractures at connections are unavoidable. With time, the small rotational stiffness of joints becomes even smaller and the behaviour is approaching one of the hinge joint. This effect may endanger the global stability of this structure, as only three aligned hinges are sufficient to render the system unstable, i.e. the system is “ almost” statically determinate and has only a small reserve in bearing capacity. Various retrofit strategies for column connections can cause considerably different stress distribution and by ignoring or underrating these effects, the safety factor can be seriously overestimated. This paper confirms the above assertions using a range of computational models: from simple frame and shell models to complex 3D solid models. This work also points out the significance of connections in historical buildings and attempts to investigate possible retrofit concepts. Numerous retrofit solutions were considered and results show a significant influence of this small detail of the bearing system on the global behaviour and stability of structure.