Stephen Smale

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We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant capturing the rate of decay—which in our model is polynomial—of the influence between birds in the flock as they separate in space. Our main result shows that when 1 2 convergence of the flock to a common velocity is(More)
Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high dimensional spaces. We consider the case where data is drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. We show how to “learn” the homology of the submanifold with high confidence. We discuss an(More)
The events leading to transcription of eukaryotic protein-coding genes culminate in the positioning of RNA polymerase II at the correct initiation site. The core promoter, which can extend ~35 bp upstream and/or downstream of this site, plays a central role in regulating initiation. Specific DNA elements within the core promoter bind the factors that(More)
The generation of cell-mediated immunity against many infectious pathogens involves the production of interleukin-12 (IL-12), a key signal of the innate immune system. Yet, for many pathogens, the molecules that induce IL-12 production by macrophages and the mechanisms by which they do so remain undefined. Here it is shown that microbial lipoproteins are(More)
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whereA is an differential operator and L2 is the Hilbert space of square integrable functions on X with measure ρX on X defined via ρ. This minimization is well-conditioned and solved by straightforward finite dimensional least squares linear algebra to yield fγ,z : X → Y . The problem is posed: How good an approximation is fγ,z to fρ, or measure the error(More)
Ikaros proteins are required for normal T, B, and NK cell development and are postulated to activate lymphocyte-specific gene expression. Here we examined Ikaros distribution in the nucleus of B lymphocytes using confocal microscopy and a novel immunofluorescence in situ hybridization (immuno-FISH) approach. Unexpectedly, Ikaros localized to discrete(More)
We describe a broad mechanistic framework for the transcriptional induction of mammalian primary response genes by Toll-like receptors and other stimuli. One major class of primary response genes is characterized by CpG-island promoters, which facilitate promiscuous induction from constitutively active chromatin without a requirement for SWI/SNF nucleosome(More)