A class of recently introduced multi-states XX models is generalized to include a deformation parameter. This corresponds to an additional nearest-neighbor CC interaction in the defining quadratic hamiltonian. Complete integrability of the one-dimensional models is shown in the context of the quantum inverse scattering method. The new R-matrix is derived. The diagonalization of the XXC models i...

We analyze the folded spinning string in AdS4 × P with spin S in AdS4 and angular momentum J in P. We calculate the one-loop correction to its energy in the scaling limit of both lnS and J large with their ratio kept fixed. This result should correspond to the first subleading strong coupling correction to the anomalous dimension of operators of the type Tr(D(Y †Y )) in the dual N = 6 Chern-Sim...

In this paper we give a simple characterization of the Laplacian spectra of a family of graphs as the eigenvalues of symmetric tridiagonal matrices. In addition, we apply our result to obtain an upper and lower bounds for the Laplacian-energy-like invariant of these graphs. The class of graphs considered are obtained by copies of modified generalized Bethe trees (obtained by joining the vertice...

We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant R-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic...

Classical combinatorial optimization problems can be generalized in a natural way by considering a related problem relative to a given partition of the nodes of the graph into node sets. In the literature one can find generalized problems such as: generalized minimum spanning tree, generalized traveling salesman problem, generalized Steiner tree problem, generalized vehicle routing problem, etc...

A general framework for defining generative models of images is Markov random fields (MRF’s), with shift-invariant (homogeneous) MRF’s being an important special case for modeling textures and generic images. Given a dataset of natural images and a set of filters from which filter histogram statistics are obtained, a shiftinvariant MRF can be defined (as in Zhu [12]) as a distribution of images...

We give two examples of nonmonotonic behavior in symmetric systems, exhibiting more than one critical point at which spontaneous symmetry-breaking appears or disappears. The two systems are the hard-core model and the Widom{Rowlinson model, and both examples take place on a variation of the Cayley tree (Bethe lattice) devised by Schonmann and Tanaka. We obtain similar, though less constructive,...

We consider the hard leptoproduction of a photon off nuclei up to spin-1. As a new result we present here the general azimuthal angular dependence of the differential cross section for a spin-1 target. Its twist-two Fourier coefficients of the interference and squared deeply virtual Compton scattering amplitude are evaluated in leading order approximation of perturbation theory in terms of gene...