ar X iv : 0 70 8 . 13 50 v 1 [ m at h . ST ] 1 0 A ug 2 00 7 The Marginalization Paradox and the Formal Bayes ’ Law

ar X iv : 0 70 8 . 22 12 v 1 [ m at h . C O ] 1 6 A ug 2 00 7 Enumerative properties of NC ( B ) ( p , q )

We determine the rank generating function, the zeta polynomial and the Möbius function for the poset NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers.

ar X iv : 0 70 8 . 37 30 v 1 [ m at h . PR ] 2 8 A ug 2 00 7 DENSITIES FOR ROUGH DIFFERENTIAL EQUATIONS UNDER HÖRMANDER ’ S CONDITION

We consider stochastic differential equations dY = V (Y ) dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Yt admits a density for t ∈ (0, T ] provided (i) the vector fields V = (V1, ..., Vd) satisfy Hörmander’s condition and (ii) the Gaussian driving signal X satisfies certain conditions. Examples of driving signals include fract...

ar X iv : 0 70 8 . 26 18 v 1 [ as tr o - ph ] 2 0 A ug 2 00 7 Using Local Volume data to constrain Dark Matter dynamics

ar X iv : 0 80 3 . 44 39 v 2 [ m at h . D S ] 4 A ug 2 00 8 PERIODIC UNIQUE BETA - EXPANSIONS : THE SHARKOVSKIĬ ORDERING

Let β ∈ (1, 2). Each x ∈ [0, 1 β−1 ] can be represented in the form

ar X iv : 0 70 8 . 02 06 v 1 [ m at h . K T ] 1 A ug 2 00 7 ALGEBRAIC K -

We decompose the K-theory space of a Waldhausen category in terms of its Dwyer-Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria appearing in the literature.