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

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

Non-equivalence of key positively charged residues of the free fatty acid 2 receptor in the recognition and function of agonist versus antagonist ligands

Short chain fatty acids (SCFAs) are produced in the gut by bacterial fermentation of poorly digested carbohydrates. A key mediator of their actions is the G protein-coupled Free Fatty Acid 2 (FFA2) receptor and this has been suggested as a therapeutic target for the treatment of both metabolic and inflammatory diseases. However, a lack of understanding of the molecular determinants dictating how ligands bind to this receptor has hindered development. We have developed a novel radiolabelled FFA2 antagonist in order to probe ligand binding to FFA2 and in combination with mutagenesis and molecular modelling studies define how agonist and antagonist ligands interact with the receptor. Although both agonist and antagonist ligands contain negatively charged carboxylates that interact with two key positively charged arginine residues in transmembrane domains V and VII of FFA2, there are clear differences in how these interactions occur. Specifically, while agonists require interaction with both arginine residues to bind the receptor, antagonists require an interaction with only one of the two. Moreover, different chemical series of antagonist interact preferentially with different arginine residues. A homology model capable of rationalizing these observations was developed and provides a tool that will be invaluable for identifying improved FFA2 agonists and antagonists to further define function and therapeutic opportunities of this receptor

Studying of stowage massifs formation conditions in deep-laying rich KMA iron oxides developing and efficient stowage composition projection

On the example of Yakovlevsky iron-ore field which is characterized by composite hydro-geological and mining development conditions the natural monitoring technique of intense stowage massif strained state, which is formed in the descending layered dredging system of unstable rich iron oxides is proved and approve

On Spin Calogero-Moser system at infinity

We present a construction of a new integrable model as an infinite limit of Calogero models of N particles with spin. It is implemented in the multicomponent Fock space. Explicit formulas for Dunkl operators, the Yangian generators in the multicomponent Fock space are presented. The classical limit of the system is examined

Topsoil pollution forecasting using artificial neural networks on the example of the abnormally distributed heavy metal at Russian subarctic

Forecasting the soil pollution is a considerable field of study in the light of the general concern of environmental protection issues. Due to the variation of content and spatial heterogeneity of pollutants distribution at urban areas, the conventional spatial interpolation models implemented in many GIS packages mostly cannot provide appreciate interpolation accuracy. Moreover, the problem of prediction the distribution of the element with high variability in the concentration at the study site is particularly difficult. The work presents two neural networks models forecasting a spatial content of the abnormally distributed soil pollutant (Cr) at a particular location of the subarctic Novy Urengoy, Russia. A method of generalized regression neural network (GRNN) was compared to a common multilayer perceptron (MLP) model. The proposed techniques have been built, implemented and tested using ArcGIS and MATLAB. To verify the models performances, 150 scattered input data points (pollutant concentrations) have been selected from 8.5 km2 area and then split into independent training data set (105 points) and validation data set (45 points). The training data set was generated for the interpolation using ordinary kriging while the validation data set was used to test their accuracies. The networks structures have been chosen during a computer simulation based on the minimization of the RMSE. The predictive accuracy of both models was confirmed to be significantly higher than those achieved by the geostatistical approach (kriging). It is shown that MLP could achieve better accuracy than both kriging and even GRNN for interpolating surfaces. © 2017 Author(s)