Coordinate Bethe Ansatz for Spin s XXX Model

We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model. These results generalize what has been obtained for spin 1/2 and spin 1 chains

Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions

We present a generalization of the coordinate Bethe ansatz that allows us to solve integrable open XXZ and ASEP models with non-diagonal boundary matrices, provided their parameters obey some relations. These relations extend the ones already known in the literature in the context of algebraic or functional Bethe ansatz. The eigenvectors are represented as sums over cosets of the $BC_n$ Weyl group.Comment: typos corrected, references updated, accepted in J. Stat. Mec

Supersymmetric W-algebras

We develop a general theory of $W$-algebras in the context of supersymmetric vertex algebras. We describe the structure of $W$-algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As an application, we produce explicit free generators of the $W$-algebra associated with the odd principal nilpotent element of the Lie superalgebra $\mathfrak{gl}(n+1|n).$Comment: 24page

GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors

We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable models we prove a formula for the Bethe vectors of composite model. We show that this representation is a particular case of general coproduct property of the weight functions (Bethe vectors) found in the theory of the deformed Knizhnik-Zamolodchikov equation.Comment: The title has been changed to make clearer the connexion with the preprint arXiv:1502.0196

GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial monodromy matrices. Assuming that the last ones can be expanded into series with respect to the inverse spectral parameter we calculate matrix elements of the local operators in the basis of the transfer matrix eigenstates. We obtain determinant representations for these matrix elements. Thus, we solve the inverse scattering problem in a weak sense.Comment: The title has been changed to make clearer the connexion with the preprint arXiv:1501.0756

Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric RR-Matrix

We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_3)$ onto intersections of different types of Borel subalgebras, we prove that the set of the nested Bethe vectors is closed under the action of the elements of the monodromy matrix

Rational Calogero-Moser Model: Explicit Form and r-Matrix of the Second Poisson Structure

We compute the full expression of the second Poisson bracket structure for N=2 and N=3 site rational classical Calogero-Moser model. We propose an r-matrix formulation for N=2. It is identified with the classical limit of the second dynamical boundary algebra previously built by the authors

Analytical Bethe ansatz for the open AdS/CFT SU(1|1) spin chain

We prove an inversion identity for the open AdS/CFT SU(1|1) quantum spin chain which is exact for finite size. We use this identity, together with an analytic ansatz, to determine the eigenvalues of the transfer matrix and the corresponding Bethe ansatz equations. We also solve the closed chain by algebraic Bethe ansatz.Comment: 20 pages; new references added; Explanation on crossing-like relation adde

Precursors and Laggards: An Analysis of Semantic Temporal Relationships on a Blog Network

We explore the hypothesis that it is possible to obtain information about the dynamics of a blog network by analysing the temporal relationships between blogs at a semantic level, and that this type of analysis adds to the knowledge that can be extracted by studying the network only at the structural level of URL links. We present an algorithm to automatically detect fine-grained discussion topics, characterized by n-grams and time intervals. We then propose a probabilistic model to estimate the temporal relationships that blogs have with one another. We define the precursor score of blog A in relation to blog B as the probability that A enters a new topic before B, discounting the effect created by asymmetric posting rates. Network-level metrics of precursor and laggard behavior are derived from these dyadic precursor score estimations. This model is used to analyze a network of French political blogs. The scores are compared to traditional link degree metrics. We obtain insights into the dynamics of topic participation on this network, as well as the relationship between precursor/laggard and linking behaviors. We validate and analyze results with the help of an expert on the French blogosphere. Finally, we propose possible applications to the improvement of search engine ranking algorithms