The size sz(Γ) of an l1-graph Γ = (V,E) is the minimum of nf/tf over all the possible l1-embeddings f into nf -dimensional hypercube with scale tf . The sum of distances between all the pairs of vertices of Γ is at most sz(Γ)⌈v/2⌉⌊v/2⌋ (v = |V |). The latter is an equality if and only if Γ is equicut graph, that is, Γ admits an l1-embedding f that for any 1 ≤ i ≤ nf satisfies ∑ x∈X f(x)i ∈ {⌈v/...

Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence matrix of a symmetric design and the all-ones matrix. Amorphous pseudocyclic association schemes are examples of such association schemes whose associated sym...

Spoken term detection (STD) is the task of looking up a spoken term in a large volume of speech segments. In order to provide fast search, speech segments are first indexed into an intermediate representation using speech recognition engines which provide multiple hypotheses for each speech segment. Approximate matching techniques are usually applied at the search stage to compensate the poor p...

We present a Prym construction which associates abelian varieties to vertex-transitive strongly regular graphs. As an application we construct Prym-Tyurin varieties of arbitrary exponent ≥ 3, generalizing a result by Lange, Recillas and Rochas.

The chromatic number of a Latin square is the least number of partial transversals which cover its cells. This is just the chromatic number of its associated Latin square graph. Although Latin square graphs have been widely studied as strongly regular graphs, their chromatic numbers appear to be unexplored. We determine the chromatic number of a circulant Latin square, and find bounds for some ...

We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weak converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the ...

A graph monoid is a commutative monoid for which there is a particularly simple presentation, given in terms of a quiver. Such monoids are known to satisfy various nonstable K-theoretical representability properties for either von Neumann regular rings or C*-algebras. We give a characterization of graph monoids within finitely generated antisymmetric refinement monoids. This characterization is...

A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra a...

Abstract. We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical approximation of infinite models with suitable sequences of finite models which in turn allow (relatively) easy computations. Let X be an infinite set a...

We investigate a connection between distance-regular graphs and Uq (sl(2)), the quantum universal enveloping algebra of the Lie algebra sl(2). Let 0 be a distance-regular graph with diameter d ≥ 3 and valency k ≥ 3, and assume0 is not isomorphic to the d-cube. Fix a vertex x of0, and let T = T (x) denote the Terwilliger algebra of 0 with respect to x . Fix any complex number q 6∈ {0, 1,−1}. The...