A family of tridiagonal pairs and related symmetric functions

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual eigenbasis are described. The overlap functions between the two dual basis are shown to satisfy a coupled system of recurrence relations and a set of discrete second-order $q-$difference equations which generalize the ones associated with the Askey-Wilson orthogonal polynomials with a discrete argument. Normalizing the fundamental solution to unity, the hierarchy of solutions are rational functions of one discrete argument, explicitly derived in some simplest examples. The weight function which ensures the orthogonality of the system of rational functions defined on a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition corrected compared to published versio

Central extension of the reflection equations and an analog of Miki's formula

Two different types of centrally extended quantum reflection algebras are introduced. Realizations in terms of the elements of the central extension of the Yang-Baxter algebra are exhibited. A coaction map is identified. For the special case of $U_q(\hat{sl_2})$, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's formula - is also proposed, providing a free field realization of $O_q(\hat{sl_2})$ (q-Onsager) currents.Comment: 11 pages; two references added; to appear in J. Phys.

Distribution of miliacin (olean-18-en-3β-ol methyl ether) and related compounds in broomcorn millet (Panicum miliaceum) and other reputed sources: Implications for the use of sedimentary miliacin as a tracer of millet

International audienceUsing sedimentary miliacin (olean-18-en-3β-ol methyl ether) as a molecular tracer of the history of Panicum miliaceum (broomcorn millet) cultivation depends upon broomcorn millet being sedimentary miliacin's dominant source. It also requires knowledge of the variability in miliacin concentration in broomcorn millet. Finally, it is affected by the presence of other pentacyclic triterpene methyl ethers (PTMEs) that may exist in conjunction with miliacin in other sources but not in broomcorn millet. Miliacin biosynthesis has been proposed for other Panicum species, Setaria italica (Italian or foxtail millet), Pennisetum sp., and Chaetomium olivaceum (an olive green mold). We found miliacin concentration in seeds of different varieties of P. miliaceum to be similarly high (with trace amounts of β- and α-amyrin methyl ethers). It was absent from hulls and roots, and nominally present in leaves and stems. The transfer of miliacin from plant to sediments is therefore mostly from seeds. it was abundant (often with larger amounts of β- and α-amyrin methyl ethers) in all other Panicum species studied, but only in some species of the genus Pennisetum and was absent from Setaria italica. Neither C. olivaceum nor its growth medium (rice) showed any trace of miliacin. Our results, with miliacin absent from S. italica and C. olivaceum, its high miliacin in seed of P. miliaceum relative to other PTMEs and to other grasses and, considering the high biomass that cultivated broomcorn millet has relative to other potential plant sources, support the use of sedimentary records of miliacin in some contexts to track past millet agricultural dynamics

A deformed analogue of Onsager's symmetry in the XXZ open spin chain

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected, clarifications in the text; v3: minor changes in references, version to appear in JSTA

Adaptive response and enlargement of dynamic range

Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus, often supported by protein activity-dependent inactivation. Adaptive response is thought to be related to various cellular functions such as homeostasis and enlargement of dynamic range by background compensation. Here we study the quantitative relation between adaptive response and background compensation within a modeling framework. We show that any particular type of adaptive response is neither sufficient nor necessary for adaptive enlargement of dynamic range. In particular a precise adaptive response, where system activity is maintained at a constant level at steady state, does not ensure a large dynamic range neither in input signal nor in system output. A general mechanism for input dynamic range enlargement can come about from the activity-dependent modulation of protein responsiveness by multiple biochemical modification, regardless of the type of adaptive response it induces. Therefore hierarchical biochemical processes such as methylation and phosphorylation are natural candidates to induce this property in signaling systems.Comment: Corrected typos, minor text revision

Environmental changes and the rise and fall of civilizations in the northern Horn of Africa: an approach combining δD analyses of land-plant derived fatty acids with multiple proxies in soil

International audienceThe domains of the ancient polities D'MT and Aksum in the Horn of Africa's highlands are a superior natural system for evaluating roles of environmental change on the rise and fall of civilizations. To compare environmental changes of the times of the two polities, we analyzed stable hydrogen isotopic ratios (δD) of land-plant derived fatty acids (n-C26-30) and other proxies from soil sequences spanning the Holocene from the region. Three results suggest that trends in δD values unambiguously reflect changes in rainfall. First, increases in δD coincide with dry periods inferred from studies of eastern African lakes. Second, changes in δD values were parallel among sections during overlapping time intervals. Third, consideration of vegetation history did not alter directions of trends in δD values over time. By unambiguously recording precipitation, the δD values also enhanced interpretations of proxies that are affected by both climate and land clearing. Both D'MT (ca 2750-2350 cal y BP) and the Aksumite (ca 2100-1250 cal y BP) rose during wetter intervals of the drier part of the Holocene (after ca 6000 cal y BP). Analyses of charred matter indicated that fire had been a common agent of land clearing in all sites. The influence of climate on fire varied, however. Prior to the emergence of D'MT, δD values were correlated with C4:C3 plant ratios estimated from δ13C values. There are no C4 trees and precipitation may have been the main influence on canopy openness. After ca 4300 cal y BP, there was no significant relationship between δD and C4:C3 plant ratios suggesting that factors such as fire influenced canopy openness regardless of climate. Furthermore, the impact of land clearance differed between sites and between D'MT and the Aksumite's times. In one site, the interval from 3550 cal y BP to the decline of D'MT had several anomalies that suggested dramatic increases in thermal severity of fire and human impact. Among these were a large contribution of charred matter to a high% total organic carbon that low hydrogen and oxygen indices suggest was severely altered by other factors than humification. These results support hypotheses about the rise of civilizations being favored by specific climatic conditions but suggest that patterns of land clearing differed during the declines of D'MT and the Aksumite

The Erd\H{o}s-Ko-Rado theorem for twisted Grassmann graphs

We present a "modern" approach to the Erd\H{o}s-Ko-Rado theorem for Q-polynomial distance-regular graphs and apply it to the twisted Grassmann graphs discovered in 2005 by van Dam and Koolen.Comment: 5 page