We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on m...

We apply our general method of duality, introduced in [10], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman’s type, as well as for models with finite population size. Next, using SU(1, 1) raising an...

In the final chain of the countable powerset functor, we show that the set at index ω1, regarded as a transition system, is not strongly extensional because it contains a “ghost” element that has no successor even though its component at index 1 is nonempty. For Jirka Adámek on his 70th birthday, with thanks for his many contributions and his inspiration.

Björner [1] showed how a construction by von Neumann of examples of continuous geometries can be adapted to construct a continuous analogue of finite partition lattices. Björner's construction realizes the continuous partition lattice abstractly, as a completion of a direct limit of finite lattices. Here we give an alternative construction realizing a continuous partition lattice concretely as ...

We note that Fujikawa’s proposal of generalization of the GinspargWilson relation is equivalent to setting R = (aγ5D) 2k in the original Ginsparg-Wilson relation Dγ5 + γ5D = 2aDRγ5D. An explicit realization of D follows from the Overlap construction. The general properties of D are derived. The chiral properties of these higher-order ( k > 0 ) realizations of Overlap Dirac operator are compared...