We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because best existing algorithm becomes numerically unstable sample sizes over n=500, there has been much attention alternative approaches like approximate (Gibbs sampling, variational Bayes, etc.), shrinkage (e.g. Horseshoe prior and Spike-and-S...

We establish a long exact sequence for Legendrian submanifolds L ⊂ P × R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L to P off of itself. In this sequence, the singular homology H∗ maps to linearized contact cohomology CH, which maps to linearized contact homology CH∗, which maps to singular homology. In particular, the sequence ...

If V is a vector space over some field F, then we have the well known exact sequence 0 → Λ2(V ) T2(V S2(V 0, where first map given by x∧y x⊗y−y⊗x and second x⊗y 7→ xy. The obvious generalization, an sequence, Λk(V T