Universal Bethe ansatz solution for the Temperley-Lieb spin chain

We consider the Temperley-Lieb (TL) open quantum spin chain with "free" boundary conditions associated with the spin-$s$ representation of quantum-deformed $sl(2)$. We construct the transfer matrix, and determine its eigenvalues and the corresponding Bethe equations using analytical Bethe ansatz. We show that the transfer matrix has quantum group symmetry, and we propose explicit formulas for the number of solutions of the Bethe equations and the degeneracies of the transfer-matrix eigenvalues. We propose an algebraic Bethe ansatz construction of the off-shell Bethe states, and we conjecture that the on-shell Bethe states are highest-weight states of the quantum group. We also propose a determinant formula for the scalar product between an off-shell Bethe state and its on-shell dual, as well as for the square of the norm. We find that all of these results, except for the degeneracies and a constant factor in the scalar product, are universal in the sense that they do not depend on the value of the spin. In an appendix, we briefly consider the closed TL spin chain with periodic boundary conditions, and show how a previously-proposed solution can be improved so as to obtain the complete (albeit non-universal) spectrum.Comment: v2: 21 pages; minor revisions, references added, publishe

Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell equation satisfied by the Bethe vectors.Comment: v2: 28 pages; minor revisions, publishe

Multivariate Survival Mixed Models for Genetic Analysis of Longevity Traits

A class of multivariate mixed survival models for continuous and discrete time with a complex covariance structure is introduced in a context of quantitative genetic applications. The methods introduced can be used in many applications in quantitative genetics although the discussion presented concentrates on longevity studies. The framework presented allows to combine models based on continuous time with models based on discrete time in a joint analysis. The continuous time models are approximations of the frailty model in which the hazard function will be assumed to be piece-wise constant. The discrete time models used are multivariate variants of the discrete relative risk models. These models allow for regular parametric likelihood-based inference by exploring a coincidence of their likelihood functions and the likelihood functions of suitably defined multivariate generalized linear mixed models. The models include a dispersion parameter, which is essential for obtaining a decomposition of the variance of the trait of interest as a sum of parcels representing the additive genetic effects, environmental effects and unspecified sources of variability; as required in quantitative genetic applications. The methods presented are implemented in such a way that large and complex quantitative genetic data can be analyzed.Comment: 36 pages, 2 figures, 3 table

“LAS ADQUISICIONES VÍA LICITACIÓN PÚBLICA, UNA PERSPECTIVA DESDE LA ADMINISTRACIÓN PÚBLICA; ESTUDIO DE CASO MUNICIPIO DE TENANCINGO, ESTADO DE MÉXICO”

Con ello, el principal objetivo de la presente investigación será, conocer y describir cómo realiza las adquisiciones de recursos materiales el gobierno Municipal de Tenancingo, por medio del proceso de licitación pública a fin de verificar las desviaciones que marca la misma administración pública del marco lega

The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains

A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A_{2n-1}^(2) integrable open spin chains with U_q(D_n) symmetry, and two families of D_{n+1}^(2) integrable open spin chains with U_q(B_n) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider D_{n+1}^(2) chains with other integrable boundary conditions, which do not have quantum group symmetry.Comment: 47 pages; v2: two references added and minor change

A tale of two Bethe ans\"atze

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov's construction. A simple explicit relation between the eigenvectors from the two Bethe ans\"atze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov-Bethe vectors.Comment: 28 pages; v2: 30 pages, added proof of (4.40) and (5.39), minor changes to match the published versio

Monitoring water-soil dynamics and tree survival using soil sensors under a big data approach

ArticleThe high importance of green urban planning to ensure access to green areas requires modern and multi-source decision-support tools. The integration of remote sensing data and sensor developments can contribute to the improvement of decision-making in urban forestry. This study proposes a novel big data-based methodology that combines real-time information from soil sensors and climate data to monitor the establishment of a new urban forest in semi-arid conditions. Water-soil dynamics and their implication in tree survival were analyzed considering the application of di erent treatment restoration techniques oriented to facilitate the recovery of tree and shrub vegetation in the degraded area. The synchronized data-capturing scheme made it possible to evaluate hourly, daily, and seasonal changes in soil-water dynamics. The spatial variation of soil-water dynamics was captured by the sensors and it highly contributed to the explanation of the observed ground measurements on tree survival. The methodology showed how the e ciency of treatments varied depending on species selection and across the experimental design. The use of retainers for improving soil moisture content and adjusting tree-watering needs was, on average, the most successful restoration technique. The results and the applied calibration of the sensor technology highlighted the random behavior of water-soil dynamics despite the small-scale scope of the experiment. The results showed the potential of this methodology to assess watering needs and adjust watering resources to the vegetation status using real-time atmospheric and soil datainfo:eu-repo/semantics/publishedVersio

Nonlocality in sequential correlation scenarios

As first shown by Popescu [S. Popescu, Phys. Rev. Lett. 74, 2619 (1995)], some quantum states only reveal their nonlocality when subjected to a sequence of measurements while giving rise to local correlations in standard Bell tests. Motivated by this manifestation of "hidden nonlocality" we set out to develop a general framework for the study of nonlocality when sequences of measurements are performed. Similar to [R. Gallego et al., Phys. Rev. Lett. 109, 070401 (2013)] our approach is operational, i.e. the task is to identify the set of allowed operations in sequential correlation scenarios and define nonlocality as the resource that cannot be created by these operations. This leads to a characterisation of sequential nonlocality that contains as particular cases standard nonlocality and hidden nonlocality.Comment: 13 pages, 3 figure