3,426 research outputs found
A cost function for similarity-based hierarchical clustering
The development of algorithms for hierarchical clustering has been hampered
by a shortage of precise objective functions. To help address this situation,
we introduce a simple cost function on hierarchies over a set of points, given
pairwise similarities between those points. We show that this criterion behaves
sensibly in canonical instances and that it admits a top-down construction
procedure with a provably good approximation ratio
Homotopy classification of gerbes
Gerbes are locally connected presheaves of groupoids on a small Grothendieck site C. They are classified up to local weak equivalence by path components of a cocycle category taking values in the big 2-groupoid Iso(Gr(C)) consisting of all sheaves of groups on C, their isomorphisms and homotopies. If F is a full sub- presheaf of Iso(Gr(C)) then the set [*,BF] of morphisms in the homotopy category of simplicial presheaves classifies gerbes locally weakly equivalent to objects of F. Id St(пF)is the stack completion of the fundamental groupoid(пF)of F if L is a global section of St(пF) and if FL is the homotopy fibre over L of the canonical map BF --> B St(пF), then [*FL] is in bijective correspondence with Giraud's non-abelian cohomology object H2 (C, L) of equivalence classes of gerbes with band L
The Power of the Bankruptcy Court to Enjoin Creditor Claims Against Nondebtor Parties in Light of 11 U.S.C. § 524( e): In re Dow Corning Corp.
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