Walter Cai

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Given a finite discrete point set X ⊂ R and distance parameter δ, we may generate the Vietoris-Rips Complex Rδ(X); the simplicial complex where a simplex [xi]i∈I ∈ Rδ(X) if |xi − xj | ≤ δ for all i, j ∈ I. Given arbitrary 1-cycle σ appearing in the Rips Complex, we may define the the birth and death of σ as α = min(δ : σ ∈ C1(Rδ(X))) and γ = min(δ : σ ≡ 0 ∈(More)
We introduce and theoretically study the Gardener's problem that well models many web information monitoring scenarios, where numerous dynamically changing web sources are monitored and local information needs to be periodically updated under communication and computation capacity constraints. Typical such examples include maintenance of inverted indexes(More)
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