Stability in SO(n+3)/SO(3) × SO(n) branching

Le Laboratoire de Lague: Son role et son expansion

Neutral Stability, Rate Propagation, and Critical Branching in Feedforward Networks

Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing patterns. We seek the simplest setting in which these properties emerge, clarifying their origin and relationship in random, feedforward networks of McCulloch...

Cloud SON: A New Member of the SON Family

IRREDUCIBILITY OF COMMUTING VARIETY ASSOCIATED WITH (son+m, son⊕som)

The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra over k and σ an involutory automorphism of g. Then g = g0 ⊕ g1 is the direct sum of σ-eigenspaces. Here g0 is a reductive subalgebra and g1 is a g0-module. Let G be the adjoint group of g and G0 ⊂ G a connected subgroup with LieG0 = g0. The commuting variety of (g, g0) is the follow...

This Stranger, My Son

This is the story of how a conventional middle-class American household?a surgeon, his wife and three normal children?had first to recognise, then to cope with and, finally, to exclude, an abnormal family member. Tony was a beautiful child, the eldest, and apart from long hours of screaming for no apparent reason, he seemed a normal baby. His intellectual and motor development was average, but ...