In this paper we investigate certain properties of the curves sk generated by a non-uniform variational refinement scheme defined over a k-window of some bi-infinite sequence of points. In particular, we show that error between sn and sk for k ≪ n over some fixed interval decays exponentially as k ↑ n, showing that sn can be well-approximated by sk for k much smaller than n. We use this result ...

We introduce an interpolation framework for H∞ model reduction founded on ideas originating in optimal-H2 interpolatory model reduction, realization theory, and complex Chebyshev approximation. By employing a Loewner “data-driven” framework within each optimization cycle, large-scale H∞ norm calculations can be completely avoided. Thus, we are able to formulate a method that remains effective i...

Given a triangular array of points on [−1, 1] satisfying certain minimal separation conditions, a classical theorem of Szabados asserts the existence of polynomial operators that provide interpolation at these points as well as a near-optimal degree of approximation for arbitrary continuous functions on the interval. This paper provides a simple, functional-analytic proof of this fact. This abs...

There is a long tradition in both philosophy and psychology to separate process accounts from dependency accounts of causation. In this paper, we motivate a unifying account that explains people’s causal attributions in terms of counterfactuals defined over probabilistic generative models. In our experiments, participants see two billiard balls colliding and indicate to what extent ball A cause...

A new method for calculating the stress field in bounded ice shelves is used to compare strain rate and deviatoric stress on the Ross Ice Shelf, Antarctica. The analysis shows that strain rate (per second) increases as the third power of deviatoric stress (in newtons per square meter), with a constant of proportionality equal to 2.3 x 10(-25).

We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.

This paper is devoted to prove the unbounded divergence on superdense sets, with respect to product quadrature formulas of interpolatory type on Jacobi nodes. Mathematics Subject Classification (2010): 41A10, 41A55, 65D32.