Segmentation and tracking of cells in long-term time-lapse experiments has emerged as a powerful method to understand how tissue shape changes emerge from the complex choreography of constituent cells. However, methods to store and interrogate the large datasets produced by these experiments are not widely available. Furthermore, recently developed methods for relating tissue shape changes to c...

The first total synthesis of propolisbenzofuran B, a bioactive natural product isolated from honeybee propolis resin, is reported. The convergent synthesis makes use of a silicon-tether controlled oxidative ketone-ketone cross-coupling and a novel benzofuran-generating cascade reaction to deliver the core structure of the natural product from readily prepared precursors.

We prove that the Gelfand-Shilov spaces S α are topological algebras under the Moyal star product if and only if α ≥ β. These spaces of test functions can be used in quantum field theory on noncommutative spacetime. The star product depends continuously in their topology on the noncommutativity parameter. We also prove that the series expansion of the Moyal product is absolutely convergent in S...

T H E present writer has given examples in which an absolutely convergent series is obtained as the result of multiplying two conditionally convergent series together, or of multiplying one conditionally convergent series by a divergent series.* He has also given an example of two divergent series whose product is absolutely convergent.f Pringsheim has treated this subject from a more general p...

Does the $n^{th}$ root of the diagonal Ramsey number converge to a finite limit? The answer is yes. A sequence can be shown to converge if it satifies convergence conditions other than or besides monotonicity. We show such a property holds for which the sequence of $n^{th}$ roots does converge, even if one has no a priori knowledge as to whether the sequence is monotone or not. We show also the...

Geological models of subduction zones impact thinking about many of the central problems in the structure, dynamics, chemistry, and history of the solid earth. Should those models change, the effects will reach across the earth sciences. We are currently in the midst of such a change, brought on by several causes. First, the earth science community recently began an organized, multi-disciplinar...

We define tensor product decompositions of E0-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that such cocycles are convergent.

Kronecker coefficients are tensor product multiplicities for the irreducible representations of the symmetric group. In this paper, we identify directions in the parameter space for tensor products along which these multiplicities are monotone convergent, generalizing a classical result of Murnaghan.

I present and analyze a quadratically convergent algorithm for computing the infinite product ∏∞ n=1(1 − txn) for arbitrary complex t and x satisfying |x| < 1, based on the identity ∞ ∏

A new approach to the medicinally-important natural product triptolide is significantly shorter than previous syntheses, highly convergent and avoids the use of protecting groups; key features include two Diels-Alder reactions and a new deoxygenative aromatisation process.