Strong coupling expansion for the Bose-Hubbard and the Jaynes-Cummings lattice model

A strong coupling expansion, based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131] and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The approach, which allows to generate numerically all diagrams up to a desired order in the interaction strength is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the Jaynes-Cummings lattice model will be presented and compared with results from VCA and DMRG. Our focus will be on the Mott insulator to superfluid transition.Comment: 29 pages, 21 figure

Local Binary Patterns as a Feature Descriptor in Alignment-free Visualisation of Metagenomic Data

Shotgun sequencing has facilitated the analysis of complex microbial communities. However, clustering and visualising these communities without prior taxonomic information is a major challenge. Feature descriptor methods can be utilised to extract these taxonomic relations from the data. Here, we present a novel approach consisting of local binary patterns (LBP) coupled with randomised singular value decomposition (RSVD) and Barnes-Hut t-stochastic neighbor embedding (BH-tSNE) to highlight the underlying taxonomic structure of the metagenomic data. The effectiveness of our approach is demonstrated using several simulated and a real metagenomic datasets

Signatures for Black Hole production from hadronic observables at the Large Hadron Collider

The concept of Large Extra Dimensions (LED) provides a way of solving the Hierarchy Problem which concerns the weakness of gravity compared with the strong and electro-weak forces. A consequence of LED is that miniature Black Holes (mini-BHs) may be produced at the Large Hadron Collider in p+p collisions. The present work uses the CHARYBDIS mini-BH generator code to simulate the hadronic signal which might be expected in a mid-rapidity particle tracking detector from the decay of these exotic objects if indeed they are produced. An estimate is also given for Pb+Pb collisions.Comment: 11 pages, 9 figures, ISHIP 2006 conference proceedin

Code Construction and Decoding Algorithms for Semi-Quantitative Group Testing with Nonuniform Thresholds

We analyze a new group testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the most general semi-quantitative group testing model, we define three new families of sequences capturing the constraints on the code design imposed by the choice of the thresholds. The sequences represent extensions and generalizations of Bh and certain types of super-increasing and lexicographically ordered sequences, and they lead to code structures amenable for efficient recursive decoding. We describe the decoding methods and provide an accompanying computational complexity and performance analysis

The topological Atiyah-Segal map

Associated to each finite dimensional linear representation of a group $G$, there is a vector bundle over the classifying space $BG$. We introduce a framework for studying this construction in the context of infinite discrete groups, taking into account the topology of representation spaces. This involves studying the homotopy group completion of the topological monoid formed by all unitary (or general linear) representations of $G$, under the monoid operation given by block sum. In order to work effectively with this object, we prove a general result showing that for certain homotopy commutative topological monoids $M$, the homotopy groups of $\Omega BM$ can be described explicitly in terms of unbased homotopy classes of maps from spheres into $M$. Several applications are developed. We relate our constructions to the Novikov conjecture; we show that the space of flat unitary connections over the 3-dimensional Heisenberg manifold has extremely large homotopy groups; and for groups that satisfy Kazhdan's property (T) and admit a finite classifying space, we show that the reduced $K$-theory class associated to a spherical family of finite dimensional unitary representations is always torsion.Comment: 57 pages. Comments welcome

Construction of Bh[g] sets in product of groups

A subset A of an abelian group G is a Bh[g] set on G if every element of G can be written at most g ways as sum of h elements in A. In this work we present three constructions of Bh[g] sets on product of groups.Comment: 10 page

Renormalization Group and Black Hole Production in Large Extra Dimensions

It has been suggested that the existence of a non-Gaussian fixed point in general relativity might cure the ultraviolet problems of this theory. Such a fixed point is connected to an effective running of the gravitational coupling. We calculate the effect of the running gravitational coupling on the black hole production cross section in models with large extra dimensions.Comment: 4 pages, 3 figures, corrected typos, shorten titl