Providing efficient and accurate parameterizations for model reduction is a key goal in many areas of science technology. Here, we present strong link between data-driven theoretical approaches to achieving this goal. Formal perturbation expansions the Koopman operator allow us derive general stochastic weakly coupled dynamical systems. Such yield set integrodifferential equations with explicit...

We first show how the displacement-traction problem of nonlinear three-dimensional elasticity can be recast either as a boundary value problem or as a minimization problem over a Banach manifold, where the unknown is the Cauchy-Green strain tensor instead of the deformation as is customary. We then consider the pure displacement problem, and we show that, under appropriate smoothness assumption...

Braginskii extended magnetohydrodynamics is used to model transport in collisional astrophysical and high energy density plasmas. We show that commonly approximations the ${\ensuremath{\alpha}}_{\ensuremath{\perp}}$ ${\ensuremath{\beta}}_{\ensuremath{\perp}}$ coefficients [e.g., Epperlein Haines, Phys. Fluids 29, 1029 (1986)] have a subtle inaccuracy causes significant artificial magnetic dissi...

Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The diier-ence involves often only a slight shift of perspective: admitting metavari-ables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program veriication ...

Many population genetic activities, ranging from evolutionary studies to association mapping, to forensic identification, rely on appropriate estimates of population structure or relatedness. All applications require recognition that quantities with an underlying meaning of allelic dependence are not defined in an absolute sense, but instead are made "relative to" some set of alleles other than...

This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderón calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density interpolation methods, the proposed relies on interpolating function around singularity terms solutions underlying homogeneous PDE, so as recast singular nearly inte...