Young flattenings, introduced by Landsberg and Ottaviani, give determinantal equations for secant varieties and provide lower bounds for border ranks of tensors. We find special monomial-optimal Young flattenings that provide the best possible lower bound for all monomials up to degree 6. For degree 7 and higher these flattenings no longer suffice for all monomials. To overcome this problem we ...

Article history: Received 22 May 2014 Accepted 8 November 2014 Available online 25 November 2014 Submitted by J.M. Landsberg MSC: 15B99 13P25 20G20

In this note, we show that the examples of non-Berwaldian Landsberg surfaces with vanishing flag curvature, obtained in [5] , are fact Berwaldian. Consequently, Bryant's claim is still unverified.

Tag1 is a transposable element first identified as an insertion in the CHL1 gene of Arabidopsis. The chl1::Tag1 mutant originated from a plant (ecotype Landsberg erecta) that had been transformed with the maize transposon Activator (Ac), which is distantly related to Tag1. Genomic analysis of untransformed Landsberg erecta plants demonstrated that two identical Tag1 elements are present in the ...

We describe a superfamily of Arabidopsis thaliana retrotransposable elements that consists of at least ten related families designated Ta1-Ta10. The Ta1 family has been described previously. Two genomic clones representing the Ta2 and Ta3 elements were isolated from an A. thaliana (race Landsberg erecta) lambda library using sequences derived from the reverse transcriptase region of Ta1 as hybr...

Landsberg’s notion of disorder, entropy normalized to maximum entropy, was originally proposed for the Shannon information-theoretic entropy to overcome deficiencies of entropy as a measure of disorder due to extensivity. We generalize Landsberg’s concept to three classes of extended entropies: Rényi, Tsallis and Landsberg-Vedral. Three examples are treated, including one based on the logistic ...

The complexity measure from Shiner et al. [Physical Review E 59, 1999, 1459–1464] (henceforth abbreviated as SDL-measure) has recently been the subject of a fierce debate. We discuss the properties and shortcomings of this measure, from the point of view of our recently constructed fundamental, statistical mechanics-based measures of complexity Cs (γ, β) [Stoop et al., J. Stat. Phys. 114, 2004,...