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...

Male pufferfish (Torquigener albomaculosus) construct “mystery circles”, geometric circular structures with radially aligned peaks and valleys, on sandy seabeds for reproduction. We discovered an earliest-stage mystery circle composed of dozens of irregular depressions. The structure changed to a primitive circular form with radially aligned valleys and a circular depression in the central area...

The McMurdo Dry Valleys of Antarctica are considered to be one of the most physically and chemically extreme terrestrial environments on the Earth. However, little is known about the organisms involved in nitrogen transformations in these environments. In this study, we investigated the diversity and abundance of ammonia-oxidizing archaea (AOA) and bacteria (AOB) in four McMurdo Dry Valleys wit...

Quantum theory of self-organization based on the idea that quantum jump serves as the basic step of self-organization, is represented. The notion of self and the identification of self as the fundamental statistical ensemble gives totally new meaning for the concept of selforganization as a generation of hierarchies of selves. Zero modes of the configuration space geometry, whose existence deri...

Introduction: Most of the cratered uplands of Mars are dissected by networks of branching valleys, whose evolutionary history is still controversial [e.g. 1, 2]. The valleys show branching patterns closely analogous to terrestrial fluvial valleys, which may indicate that the valleys were cut primarily by surface runoff after precipitation [2]. However, short, stubby tributaries and amphitheater...