Nonlinear Rayleigh functionals

Renormalizing Experiments for Nonlinear Functionals

Let f = f(t), t 2 R be an unknown \object" (real-valued function), and suppose we are interested in recovering the nonlinear functional T (f). We know a priori that f 2 F , a certain convex class of functions (e.g. a class of smooth functions). For various types of measurements Yn = (y1; y2; : : : ; yn), problems of this form arise in statistical settings, such as nonparametric density estimati...

1Renormalizing Experiments for Nonlinear Functionals

Let f = f(t), t 2 R d be an unknown \object" (real-valued function), and suppose we are interested in recovering the nonlinear functional T(f). We know a priori that f 2 F, a certain convex class of functions (e.g. a class of smooth functions). For various types of measurements problems of this form arise in statistical settings, such as nonparamet-ric density estimation and nonparametric regre...

Wick Calculus For Nonlinear Gaussian Functionals

This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevan...

Nonlinear square patterns in Rayleigh-Bénard convection

Rayleigh–Taylor instability in nonlinear Schrödinger flow

The Rayleigh–Taylor instability (RTI) is a fundamental fluid instability that occurs when a light fluid is accelerated into a heavier one. While techniques for observing the RTI in classical fluids continue to improve, the instability has not been demonstrated in quantum fluids. Here, we exploit the formal equivalence between condensed matter and coherent nonlinear optics to observe the superfl...