394 research outputs found
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 -matrices. They yield factorized forms for the
monodromy matrices.Comment: LaTeX, 24 pages. Misprints corrected, comments added in Conclusion on
construction of Hamiltonian
Functional forms of socio-territorial inequities in breast cancer screening – A French cross-sectional study using hierarchical generalised additive models
To reduce the breast cancer burden, the French National Organised Breast Cancer Screening Programme (FNOBCSP) was implemented in 2004. The recommended participation rate has never been achieved and socio-territorial inequities in participation have been reported on several occasions. We investigated the functional forms and consistency of the relationships between neighbourhood deprivation, travel time to the nearest accredited radiology centre and screening uptake. We used two-level hierarchical generalised additive models in 8 types of territories classified by socio-demographic and economic factors. The first level was 368,201 women aged 50–72 invited to the 2013–2014 screening campaign in metropolitan France. They were nested in 41 départements, the level of organisation of the FNOBCSP. The effect of travel time showed two main patterns: it was either linear (with participation decreasing as travel time increased) or participation first increased with increasing travel time to a peak around 5–15 min and decreased afterward. In nearly all types and départements, the probability of participation decreased linearly with increasing deprivation. Territorial inequities in participation were more context-dependent and complex than social inequities. Inequities in participation represent a loss of opportunity for individuals who already have the worst cancer outcomes. Evidence-based public health policies are needed to increase the effectiveness and equity of breast cancer screening
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
The Classical -Matrix for the Relativistic Ruijsenaars-Schneider System
We compute the classical -matrix for the relativistic generalization of
the Calogero-Moser model, or Ruijsenaars-Schneider model, at all values of the
speed-of-light parameter . We connect it with the non-relativistic
Calogero-Moser -matrix and the
sine-Gordon soliton limit.Comment: LaTeX file, no figures, 8 page
Integrable mappings and polynomial growth
We describe birational representations of discrete groups generated by
involutions, having their origin in the theory of exactly solvable
vertex-models in lattice statistical mechanics. These involutions correspond
respectively to two kinds of transformations on matrices: the
inversion of the matrix and an (involutive) permutation of the
entries of the matrix. We concentrate on the case where these permutations are
elementary transpositions of two entries. In this case the birational
transformations fall into six different classes. For each class we analyze the
factorization properties of the iteration of these transformations. These
factorization properties enable to define some canonical homogeneous
polynomials associated with these factorization properties. Some mappings yield
a polynomial growth of the complexity of the iterations. For three classes the
successive iterates, for , actually lie on elliptic curves. This analysis
also provides examples of integrable mappings in arbitrary dimension, even
infinite. Moreover, for two classes, the homogeneous polynomials are shown to
satisfy non trivial non-linear recurrences. The relations between
factorizations of the iterations, the existence of recurrences on one or
several variables, as well as the integrability of the mappings are analyzed.Comment: 45 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
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