Universality and programmability of quantum computers

Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum logic circuit model, developed by Feynman and Deutsch, has been more prominent in the research literature than Deutsch's quantum Turing machines. Quantum Turing machines form a class closely related to deterministic and probabilistic Turing machines and one might hope to find a universal machine in this class. A universal machine is the basis of a notion of programmability. The extent to which universality has in fact been established by the pioneers in the field is examined and this key notion in theoretical computer science is scrutinised in quantum computing by distinguishing various connotations and concomitant results and problems.Comment: 17 pages, expands on arXiv:0705.3077v1 [quant-ph

Universal H-colourable graphs

Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: for given m and n with m < n, m is adjacent to n if n has a 1 in the mth position of its binary expansion. It is well known that R is a universal graph in the set Ic of all countable graphs (since every graph in Ic is isomorphic to an induced subgraph of R) and that it is a homogeneous graph (since every isomorphism between two finite induced subgraphs of R extends to an automorphism of R). In this paper we construct a graphU(H) which is H-universal in →Hc, the induced-hereditary hom-property of H-colourable graphs consisting of all (countable) graphs which have a homomorphism into a given (countable) graph H. If H is the (finite) complete graph Kk , then→Hc is the property of k-colourable graphs. The universal graph U(H) is characterised by showing that it is, up to isomorphism, the unique denumerable, H-universal graph in →Hc which is H-homogeneous in →Hc. The graphs H for which U(H) ∼= R are also characterised.With small changes to the definitions, our results translate effortlessly to hold for digraphs too. Another slight adaptation of our work yields related results for (k, l)-split graphs.http://www.springerlink.com/content/0911-011

Universality for and in induced-hereditary graph properties

The well-known Rado graph R is universal in the set of all countable graphs I, since every countable graph is an induced subgraph of R. We study universality in I and, using R, show the existence of 20 pairwise non-isomorphic graphs which are universal in I and denumerably many other universal graphs in I with prescribed attributes. Then we contrast universality for and universality in induced-hereditary properties of graphs and show that the overwhelming majority of induced-hereditary properties contain no universal graphs. This is made precise by showing that there are 2(20 ) properties in the lattice K< of induced-hereditary properties of which only at most 20 contain universal graphs. In a final section we discuss the outlook on future work; in particular the question of characterizing those induced-hereditary properties for which there is a universal graph in the property.http://www.discuss.wmie.uz.zgora.pl/gt/am201

Constructing universal graphs for induced-hereditary graph properties

Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m'th position of its binary expansion. It is well known that R is a universal graph in the set Ic of all countable graphs (since every graph in Ic is isomorphic to an induced subgraph of R). In this paper we construct graphs which are universal in or for P for di erent inducedhereditary properties P of countable graphs. Constructions of universal graphs for the graph properties containing all graphs with colouring-number at most k+1 and k-degenerate graphs are obtained by restricting the edges of R. Results on the properties of these graphs are given and relationships between them are explored. This is followed by a general recursive construction which proves the existence of a countable universal graph for any induced-hereditary property of countable general graphs. A general construction of universal graphs for products of properties of graphs is also presented. The paper is concluded by a comparison between the two types of constructions of universal graphs.Research of the third author was supported by VEGA Grant No. 2/0194/10.http://link.springer.com/journal/12175hb201

Основные положения формирования нового единого сельскохозяйственного налога

Обосновывается введение единого сельскохозяйственного налога как постоянной ставки от стоимости валового дохода предприятий.Обгрунтовується введене єдиного сільськогосподарського податку як постійної ставки до вартості валового доходу підприємств.Introduction of the united agricultural tax is grounded as a permanent size to the cost of gross profit of enterprises

Identification of regulatory variants associated with genetic susceptibility to meningococcal disease.

Non-coding genetic variants play an important role in driving susceptibility to complex diseases but their characterization remains challenging. Here, we employed a novel approach to interrogate the genetic risk of such polymorphisms in a more systematic way by targeting specific regulatory regions relevant for the phenotype studied. We applied this method to meningococcal disease susceptibility, using the DNA binding pattern of RELA - a NF-kB subunit, master regulator of the response to infection - under bacterial stimuli in nasopharyngeal epithelial cells. We designed a custom panel to cover these RELA binding sites and used it for targeted sequencing in cases and controls. Variant calling and association analysis were performed followed by validation of candidate polymorphisms by genotyping in three independent cohorts. We identified two new polymorphisms, rs4823231 and rs11913168, showing signs of association with meningococcal disease susceptibility. In addition, using our genomic data as well as publicly available resources, we found evidences for these SNPs to have potential regulatory effects on ATXN10 and LIF genes respectively. The variants and related candidate genes are relevant for infectious diseases and may have important contribution for meningococcal disease pathology. Finally, we described a novel genetic association approach that could be applied to other phenotypes