Integrable variant of the one-dimensional Hubbard model

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the $\eta$-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed

Big data warehouse framework for smart revenue management

Revenue Management’s most cited definitions is probably “to sell the right accommodation to the right customer, at the right time and the right price, with optimal satisfaction for customers and hoteliers”. Smart Revenue Management (SRM) is a project, which aims the development of smart automatic techniques for an efficient optimization of occupancy and rates of hotel accommodations, commonly referred to, as revenue management. One of the objectives of this project is to demonstrate that the collection of Big Data, followed by an appropriate assembly of functionalities, will make possible to generate a Data Warehouse necessary to produce high quality business intelligence and analytics. This will be achieved through the collection of data extracted from a variety of sources, including from the web. This paper proposes a three stage framework to develop the Big Data Warehouse for the SRM. Namely, the compilation of all available information, in the present case, it was focus only the extraction of information from the web by a web crawler – raw data. The storing of that raw data in a primary NoSQL database, and from that data the conception of a set of functionalities, rules, principles and semantics to select, combine and store in a secondary relational database the meaningful information for the Revenue Management (Big Data Warehouse). The last stage will be the principal focus of the paper. In this context, clues will also be giving how to compile information for Business Intelligence. All these functionalities contribute to a holistic framework that, in the future, will make it possible to anticipate customers and competitor’s behavior, fundamental elements to fulfill the Revenue Managemen

A variational approach for the Quantum Inverse Scattering Method

We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability through the existence of a set of conserved operators. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC). The Hamiltonians considered describe systems with interacting Cooper pairs and a bosonic degree of freedom. We obtain general exact solvability requirements which include seven subcases which have previously appeared in the literature.Comment: 18 pages, no eps figure

Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The Lax operator in terms of fermion operators and the quantum R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.Comment: 10 pages, no figur

Coffee acclimation to high temperatures involves lipid composition changes of chloroplast membranes and is strenghtened by elevated air CO2 concentration.

Depending on the greenhouse gas emission scenarios, air [CO2] could rise to between 421 and 936 ?L L-1, accompanied by a global surface warming between 0.3 and 4.8?C along the 2nd half of the present century. It is well known that supra-optimal air temperatures may cause significant disturbances in metabolism and plant growth, since biochemical reactions are accelerated, the chemical bonds are weakened and the lipid matrix of membranes becomes more fluid. Thylakoid membranes are particularly sensitive to supra-optimal temperatures, so that impairments at the photochemical steps of photosynthesis are among the first indicators of sensitivity to heat stress. Plants acclimate to thermal stress by means of a myriad of mechanisms, such as, increased expression and activity of heat shock proteins, reinforcement of antioxidant defense system, and changes in membrane composition regarding lipid classes and fatty acid (FA), as well as their degree of unsaturation. Therefore, the objective of this study was to evaluate whether the increase in [CO2] is involved in the triggering of lipid remodeling of chloroplasts membranes under high temperature conditions, which could contribute to maintain an adequate functional fluidity. Plants were grown for 1 year under controlled conditions (temperature, RH, irradiance, photoperiod), at 380 or 700 µL CO2 L-1 air, without nutrient, water and root space limitations, and then subjected to temperature increase (0.5 ºC/day) from 25/20 ºC (day/night) to 42/34ºC. Lipid classes were separated by thin layer chromatography on G60 silicagel plates and fatty acid methyl esters were analyzed by gas?liquid chromatography. The results suggested that regardless of [CO2], increases in temperature resulted in changes in lipid membranes composition, which could contribute to maintaining the functionality of thylakoid membranes. However, the mitigating effect of increased [CO2] on coffee photosynthetic apparatus at high temperatures observed earlier may be linked to stronger increases in saturation degree and/or with the increasing the weight of galactolipids classes at 37/30 °C (as compared to 380 µL CO2 L-1 plants)

Sparse Continuous Distributions and Fenchel-Young Losses

Exponential families are widely used in machine learning, including many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions in each of these families have fixed support. In contrast, for finite domains, recent work on sparse alternatives to softmax (e.g., sparsemax, $\alpha$-entmax, and fusedmax), has led to distributions with varying support. This paper develops sparse alternatives to continuous distributions, based on several technical contributions: First, we define $\Omega$-regularized prediction maps and Fenchel-Young losses for arbitrary domains (possibly countably infinite or continuous). For linearly parametrized families, we show that minimization of Fenchel-Young losses is equivalent to moment matching of the statistics, generalizing a fundamental property of exponential families. When $\Omega$ is a Tsallis negentropy with parameter $\alpha$, we obtain ``deformed exponential families,'' which include $\alpha$-entmax and sparsemax ($\alpha=2$) as particular cases. For quadratic energy functions, the resulting densities are $\beta$-Gaussians, an instance of elliptical distributions that contain as particular cases the Gaussian, biweight, triweight, and Epanechnikov densities, and for which we derive closed-form expressions for the variance, Tsallis entropy, and Fenchel-Young loss. When $\Omega$ is a total variation or Sobolev regularizer, we obtain a continuous version of the fusedmax. Finally, we introduce continuous-domain attention mechanisms, deriving efficient gradient backpropagation algorithms for $\alpha \in \{1, 4/3, 3/2, 2\}$. Using these algorithms, we demonstrate our sparse continuous distributions for attention-based audio classification and visual question answering, showing that they allow attending to time intervals and compact regions.Comment: JMLR 2022 camera ready version. arXiv admin note: text overlap with arXiv:2006.0721