Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm

The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adjacency, which amounts to the inclusion of shifted weight functions in the orthogonality condition. In this paper we extend this mechanism to a new class of two-variable orthogonal polynomials where the variables are related via an elliptic curve. This leads to a `Higher order Analogue of the Discrete-time Toda' (HADT) equation for the associated Hankel determinants, together with its Lax pair, which is derived from the relevant recurrence relations for the orthogonal polynomials. In a similar way as the quotient-difference (QD) algorithm is related to the discrete-time Toda equation, a novel quotient-quotient-difference (QQD) scheme is presented for the HADT equation. We show that for both the HADT equation and the QQD scheme, there exists well-posed $s$-periodic initial value problems, for almost all \s\in\Z^2. From the Lax-pairs we furthermore derive invariants for corresponding reductions to dynamical mappings for some explicit examples.Comment: 38 page

The driving forces of landscape change in Europe: A systematic review of the evidence

Over the past decades, landscapes worldwide have experienced changes (e.g., urbanization, agricultural intensification, expansion of renewable energy uses) at magnitudes that put their sustainability at risk. The understanding of the drivers of these landscape changes remains challenging, partly because landscape research is spread across many domains and disciplines. We here provide a systematic synthesis of 144 studies that identify the proximate and underlying drivers of landscape change across Europe. First, we categorize how driving forces have been addressed and find that most studies consider medium-term time scales and local spatial scales. Most studies assessed only one case study area, one spatial scale, and less than four points in time. Second, we analyze geographical coverage of studies and reveal that countries with a non-European Union/European Free Trade Association membership; low Gross Domestic Product; boreal, steppic, and arctic landscapes; as well as forestland systems are underrepresented in the literature. Third, our review shows that land abandonment/extensification is the most prominent (62% of cases) among multiple proximate drivers of landscape change. Fourthly, we find that distinct combinations of mainly political/institutional, cultural, and natural/spatial underlying drivers are determining landscape change, rather than single key drivers. Our systematic review indicates knowledge gaps that can be filled by: (a) expanding the scope of studies to include underrepresented landscapes; (b) clarifying the identification and role of actors in landscape change; (c) deploying more robust tools and methods to quantitatively assess the causalities of landscape change; (d) setting up long-term studies that go beyond mapping land-cover change only; (e) strengthening cross-site and cross-country comparisons of landscape drivers; (f) designing multi-scale studies that consider teleconnections; (g) considering subtle and novel processes of landscape change

Gene screening of Wharton's jelly derived stem cells.

International audienceStem cells are the most powerful candidate for the treatment of various diseases. Suitable stem cell source should be harvested with minimal invasive procedure, found in great quantity, and transplanted with no risk of immune response and tumor formation. Fetal derived stem cells have been introduced as an excellent alternative to adult and embryonic stem cells use, but unfortunately, their degree of "stemness" and molecular characterization is still unclear. Several studies have been performed deciphering whether fetal stem cells meet the needs of regenerative medicine. We believe that a transcriptomic screening of Wharton's jelly stem cells will bring insights on cell population features