Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?

We demonstrate that in a certain gauge the Lax matrices of the rational and hyperbolic Ruijsenaars--Schneider models have a quadratic $r$-matrix Poisson bracket which is an exact quadratization of the linear $r$--matrix Poisson bracket of the Calogero--Moser models. This phenomenon is explained by a geometric derivation of Lax equations for arbitrary flows of both hierarchies, which turn out to be governed by the same dynamical $R$--operator.Comment: LaTeX, 18pp, a revised versio

On the r-matrix structure of the hyperbolic BC(n) Sutherland model

Working in a symplectic reduction framework, we construct a dynamical r-matrix for the classical hyperbolic BC(n) Sutherland model with three independent coupling constants. We also examine the Lax representation of the dynamics and its equivalence with the Hamiltonian equation of motion.Comment: 20 page

Structures in BC_N Ruijsenaars-Schneider models

We construct the classical r-matrix structure for the Lax formulation of BC_N Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the A_N Ruijsenaars-Schneider Poisson bracket behavior, although the dynamical dependence is more complicated. Commuting Hamiltonians stemming from the BC_N Ruijsenaars-Schneider Lax matrix are shown to be linear combinations of particular Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings. Uniqueness of such commuting Hamiltonians is established once the first of them and the general analytic structure are given.Comment: 18 pages, gzip latex fil

On the scattering theory of the classical hyperbolic C(n) Sutherland model

In this paper we study the scattering theory of the classical hyperbolic Sutherland model associated with the C(n) root system. We prove that for any values of the coupling constants the scattering map has a factorized form. As a byproduct of our analysis, we propose a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model with two independent coupling constants, thereby setting the stage to establish the duality between the hyperbolic C(n) Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.Comment: 15 page

Data-Informed Platform for Health. Structured district decision-making using local data. Prototype Phase, West Bengal, India

This report presents findings and recommendations from an evaluation of the Data Informed Platform for Health (DIPH), a structured decision-support strategy to promote the use of local data for health decision-making. The DIPH was developed and pilot-tested in India by the IDEAS project of the London School of Hygiene & Tropical Medicine (LSHTM) from December 2015 to March 2017

Spin chains from dynamical quadratic algebras

We present a construction of integrable quantum spin chains where local spin-spin interactions are weighted by ``position''-dependent potential containing abelian non-local spin dependance. This construction applies to the previously defined three general quadratic reflection-type algebras: respectively non-dynamical, semidynamical, fully dynamical.Comment: 12 pages, no figures; v2: corrected formulas of the last sectio

R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model

It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions. It is governed by two dynamical r and $\bar{r}$-matrices satisfying a closed system of equations. The corresponding quantum R and $\overline{R}$-matrices are found as solutions to quantum analogs of these equations. We present the quantum L-operator algebra and show that the system of equations on R and $\overline{R}$ arises as the compatibility condition for this algebra. It turns out that the R-matrix is twist-equivalent to the Felder elliptic R^F-matrix with $\overline{R}$ playing the role of the twist. The simplest representation of the quantum L-operator algebra corresponding to the elliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum L-operator algebra to the fundamental relation RLL=LLR with Belavin's elliptic R matrix is established. As a byproduct of our construction, we find a new N-parameter elliptic solution to the classical Yang-Baxter equation.Comment: latex, 29 pages, some misprints are corrected and the meromorphic version of the quantum L-operator algebra is discusse

Parametrization of semi-dynamical quantum reflection algebra

We construct sets of structure matrices for the semi-dynamical reflection algebra, solving the Yang-Baxter type consistency equations extended by the action of an automorphism of the auxiliary space. These solutions are parametrized by dynamical conjugation matrices, Drinfel'd twist representations and quantum non-dynamical $R$-matrices. They yield factorized forms for the monodromy matrices.Comment: LaTeX, 24 pages. Misprints corrected, comments added in Conclusion on construction of Hamiltonian

Statistical Modeling of EMG Signal

The aim of this research is to measure and build a statistical model of EMG signals . A linear regression method was applied as a statistical modeling method ,the common types of linear regression models was explored. The electromyography (EMG) was measured from the two hands of a person as a way to perform noise reduction with the use of XOR logical operation facilities . To measure EMG signals, the research used six OLIMEXnbsp EMG shield , controllednbsp by Arduino 328 control board , a new classification and modeling of EMG signals of 5 movements of an arm are presented. One of the six channelsnbsp used for the EMGnbsp measurements was used as anbsp reference channel , while the remaining as a measuring channels . The resultantnbsp EMG of each channel was considered as an independent variable (emg)nbsp for the linear regression model and the movement angle (degree) as a dependent variable for the model

Diffusion coulombienne multiple a haute énergie dans l'emulsion nucléaire

L'étude de la diffusion coulombienne multiple à haute énergie et à grandes longueurs de cellule pose le problème de la validité du facteur de diffusion K introduit de manière théorique par Voyvodic et Pickup. Les émulsions nucléaires K 5, exposées à des faisceaux de muons de haute énergie (6 GeV et 12 GeV) constituent un matériel de choix pour une telle étude. Nous avons ainsi pu déterminer expérimentalement la valeur de K pour des cellules de 1 mm à 15 mm et compléter des résultats encore parcellaires. Dans ce travail, nous étudions également plusieurs méthodes de mesure par diffusion coulombienne multiple