We study confluence and the Church-Rosser property in term rewriting and λ-calculus with explicit bounds on term sizes and reduction lengths. Given a system R, we are interested in the lengths of the reductions in the smallest valleys t→∗ s′ ∗← t′ expressed as a function: — for confluence a function vsR(m,n) where the valleys are for peaks t ∗← s→∗ t′ with s of size at most m and the reductions...

This paper gives a detailed analysis of the error surfaces of certain recurrent networks and explains some difficulties encountered in training recurrent networks. We show that these error surfaces contain many spurious valleys, and we analyze the mechanisms that cause the valleys to appear. We demonstrate that the principle mechanism can be understood through the analysis of the roots of rando...

Waddington's epigenetic landscape is probably the most famous and most powerful metaphor in developmental biology. Cells, represented by balls, roll downhill through a landscape of bifurcating valleys. Each new valley represents a possible cell fate and the ridges between the valleys maintain the cell fate once it has been chosen. Here I examine models of two important developmental processes -...

Soil moisture is a spatially heterogeneous quantity in the McMurdo Dry Valleys of Antarctica that exerts a large influence on the biological community and on the thermal state of Dry Valleys permafrost. The goal of this project was to determine whether hyperspectral remote sensing techniques could be used to determine soil moisture conditions in the Dry Valleys. We measured the spectral reflect...

276 (eds M.C.S. Wopereis et al.) regimes ranging from 1100 mm to 1400 mm per year, while convex inland valleys (Fig. 22.3c) are formed under the high-rainfall regimes of 1400 mm and above, typical of the equatorial forest zone. With an estimated land area of 190 Mha,1 inland valleys are common landscapes serving a multitude of ecosystem functions in many parts of Africa. In general, wetland env...