Set-theoretical reflection equation: Classification of reflection maps

The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for constructing reflection maps and we obtain a classification of solutions associated to all the families of quadrirational Yang-Baxter maps that have been classified recently

Integrable boundary conditions for multi-species ASEP

The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species. All the solutions we have obtained can be seen as representations of a new algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is not sufficient to build these solutions. This is the second result of our paper.Comment: 20 page

Integrable boundary for quad-graph systems: Three-dimensional boundary consistency

We propose the notion of integrable boundary in the context of discrete integrable systems on quad-graphs. The equation characterizing the boundary must satisfy a compatibility equation with the one characterizing the bulk that we called the three-dimensional (3D) boundary consistency. In comparison to the usual 3D consistency condition which is linked to a cube, our 3D boundary consistency condition lives on a half of a rhombic dodecahedron. The We provide a list of integrable boundaries associated to each quad-graph equation of the classification obtained by Adler, Bobenko and Suris. Then, the use of the term "integrable boundary" is justified by the facts that there are Bäcklund transformations and a zero curvature representation for systems with boundary satisfying our condition. We discuss the three-leg form of boundary equations, obtain associated discrete Toda-type models with boundary and recover previous results as particular cases. Finally, the connection between the 3D boundary consistency and the set-theoretical reflection equation is established

Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which we use to propose the Bethe-ansatz-type expressions for the eigenvalues of the transfer matrix. At most two of the boundary parameters are set to be arbitrary and the bulk anisotropy parameter has values \eta = i\pi/2, i\pi/4,... We also provide numerical evidence for the completeness of the Bethe-ansatz-type solutions derived, using s = 1 case as an example.Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:0901.3558; v2: published versio

Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models

We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This "matrix coordinate Bethe Ansatz" can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing inComment: 18 pages; Version to appear in J Phys

Renyi entropy of the totally asymmetric exclusion process

The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate explicitly an entropy whereby the squares of configuration probabilities are summed, using the matrix product formalism to map the problem to one involving a six direction lattice walk in the upper quarter plane. We derive the generating function across the whole phase diagram, using an obstinate kernel method. This gives the leading behaviour of the Renyi entropy and corrections in all phases of the TASEP. The leading behaviour is given by the result for a Bernoulli measure and we conjecture that this holds for all Renyi entropies. Within the maximal current phase the correction to the leading behaviour is logarithmic in the system size. Finally, we remark upon a special property of equilibrium systems whereby discontinuities in the Renyi entropy arise away from phase transitions, which we refer to as secondary transitions. We find no such secondary transition for this nonequilibrium system, supporting the notion that these are specific to equilibrium cases

Toward an Identification of Resources Influencing Habitat Use in a Multi-Specific Context

Interactions between animal behaviour and the environment are both shaping observed habitat use. Despite the importance of inter-specific interactions on the habitat use performed by individuals, most previous analyses have focused on case studies of single species. By focusing on two sympatric populations of large herbivores with contrasting body size, we went one step beyond by studying variation in home range size and identifying the factors involved in such variation, to define how habitat features such as resource heterogeneity, resource quality, and openness created by hurricane or forest managers, and constraints may influence habitat use at the individual level. We found a large variability among individual's home range size in both species, particularly in summer. Season appeared as the most important factor accounting for observed variation in home range size. Regarding habitat features, we found that (i) the proportion of area damaged by the hurricane was the only habitat component that inversely influenced roe deer home range size, (ii) this habitat type also influenced both diurnal and nocturnal red deer home range sizes, (iii) home range size of red deer during the day was inversely influenced by the biomass of their preferred plants, as were both diurnal and nocturnal core areas of the red deer home range, and (iv) we do not find any effect of resource heterogeneity on home range size in any case. Our results suggest that a particular habitat type (i.e. areas damaged by hurricane) can be used by individuals of sympatric species because it brings both protected and dietary resources. Thus, it is necessary to maintain the openness of these areas and to keep animal density quite low as observed in these hunted populations to limit competition between these sympatric populations of herbivores

Distribution, status and conservation problems of the Spanish Ibex, Capra pyrenaica (Mammalia: Artiodactyla)

In this paper, the distribution and status of the Spanish Ibex, Capra pyrenaica (Mammalia: Artiodactyla), are revised. The whole Iberian population numbers nearly 50 000, distributed in more than 50 nuclei, and has generally increased during the last decades. Nevertheless, within this wider context, different conditions apply to different populations, including recent extinction (the Pyrenean population), recovery from recent severe epizooty of sarcoptic mange (e.g. the Sierras de Cazorla and Segura y Las Villas range population) and populations at high densities (e.g. Gredos mountain range and Sierra de Grazalema Natural Park, among others). The main factors affecting the conservation of this species are also reported and discussed. On the basis of current information we propose the status of 'vulnerable' for the Spanish Ibex.Peer Reviewe

Molecular Monitoring in Adult Philadelphia Chromosome-Positive Acute Lymphoblastic Leukemia with the Variant e13a3 BCR-ABL1 Fusion

Monitoring BCR-ABL1 transcript levels in patients with Philadelphia chromosome-positive acute lymphoblastic leukemia (Ph+ ALL) is a widely adopted method to assess response to therapy. However, a small minority of Ph+ ALL patients express variant BCR-ABL1 transcript types, usually due to splicing of alternative BCR or ABL1 exons. Whether patients expressing these rare, variant BCR-ABL1 transcripts have a distinct phenotype or response to therapy is not known due to the limited number of reported cases. Here, we report the presenting features of Ph+ ALL in a young adult with a variant e13a3 BCR-ABL1 fusion. Molecular monitoring reflected the disease response from diagnosis through allogeneic stem cell transplantation which resulted in undetectable e13a3 BCR-ABL1 transcripts. This case highlights the value of molecular monitoring in Ph+ ALL patients with variant BCR-ABL1 transcripts and the requirement for standardization of such assays