On exact solution of a classical 3D integrable model

We investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linear equations for a set of auxiliary linear variables. Dynamical variables for the evolution model are the coefficients of these systems of linear equations. Determinant of any system of linear equations is a polynomial of two numerical quasimomenta of the auxiliary linear variables. For one, this determinant is the generating functions of all integrals of motion for the evolution, and on the other hand it defines a high genus algebraic curve. The dependence of the dynamical variables on the space-time point (exact solution) may be expressed in terms of theta functions on the jacobian of this curve. This is the main result of our paper

Explicit Free Parameterization of the Modified Tetrahedron Equation

The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at N-th root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parameterized in terms of eight free parameters and sixteen discrete phase choices, thus providing a broad starting point for the construction of 3-dimensional integrable lattice models. The Fermat curve points parameterizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail. We also discuss a solution of the MTE in terms of bosonic continuum functions.Comment: 28 pages, 3 figure

Modified Tetrahedron Equations and Related 3D Integrable Models

Using a modified version of the tetrahedron equations we construct a new family of $N$-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particular class of solutions to these equations and parameterize them in terms of elliptic functions. The corresponding models contain one free parameter $k$ -- an elliptic modulus.Comment: 26 pages, LaTeX fil

Effects of synbiotic supplement on human gut microbiota, body composition and weight loss in obesity

Targeting gut microbiota with synbiotics (probiotic supplements containing prebiotic components) is emerging as a promising intervention in the comprehensive nutritional approach to reducing obesity. Weight loss resulting from low-carbohydrate high-protein diets can be significant but has also been linked to potentially negative health effects due to increased bacterial fermentation of undigested protein within the colon and subsequent changes in gut microbiota composition. Correcting obesity-induced disruption of gut microbiota with synbiotics can be more effective than supplementation with probiotics alone because prebiotic components of synbiotics support the growth and survival of positive bacteria therein. The purpose of this placebo-controlled intervention clinical trial was to evaluate the effects of a synbiotic supplement on the composition, richness and diversity of gut microbiota and associations of microbial species with body composition parameters and biomarkers of obesity in human subjects participating in a weight loss program. The probiotic component of the synbiotic used in the study contained Lactobacillus acidophilus, Bifidobacterium lactis, Bifidobacterium longum, and Bifidobacterium bifidum and the prebiotic component was a galactooligosaccharide mixture. The results showed no statistically significant differences in body composition (body mass, BMI, body fat mass, body fat percentage, body lean mass, and bone mineral content) between the placebo and synbiotic groups at the end of the clinical trial (3-month intervention, 20 human subjects participating in weight loss intervention based on a low-carbohydrate, high-protein, reduced energy diet). Synbiotic supplementation increased the abundance of gut bacteria associated with positive health effects, especially Bifidobacterium and Lactobacillus, and it also appeared to increase the gut microbiota richness. A decreasing trend in the gut microbiota diversity in the placebo and synbiotic groups was observed at the end of trial, which may imply the effect of the high-protein low-carbohydrate diet used in the weight loss program. Regression analysis performed to correlate abundance of species following supplementation with body composition parameters and biomarkers of obesity found an association between a decrease over time in blood glucose and an increase in Lactobacillus abundance, particularly in the synbiotic group. However, the decrease over time in body mass, BMI, waist circumstance, and body fat mass was associated with a decrease in Bifidobacterium abundance. The results obtained support the conclusion that synbiotic supplement used in this clinical trial modulates human gut microbiota by increasing abundance of potentially beneficial microbial species

Diagnostic of electromagnetic conditions in space using cosmic rays

The method of spectrographic global survey was used to study the time variations in parameters of cosmic ray (CR) pitch angle anisotropy and their relationship with the variations of some solar wind characteristics under different electromagnetic conditions in interplanetary space. A classification is made of the conditions that are accompanied by the increase in CR anisotropy

PsiPsi - Vectors for Three Dimensional Models

In this paper we apply the method of psi-vectors to three dimensional statistical models. This method gives the correspondence between the Bazhanov -- Baxter model and its vertex formulation. Considering psi-vectors for the Planar model, we obtain its self-duality.Comment: 11 pages, LaTeX, no figure

The modified tetrahedron equation and its solutions

A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator in the space of a triple Weyl algebra. This operator is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for this operator follows without further calculations. If the Weyl parameter is taken to be a root of unity, the mapping operator decomposes into a matrix conjugation and a C-number functional mapping. The operator of the matrix conjugation satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equation. The matrix elements of this operator can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject.Comment: 24 pages, 6 figures using epic/eepic package, Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Spetember 2002, reference adde