In this paper we consider the optimization of a functional F defined as the convolution of a function f with a Gaussian kernel. This type of objective function is of interest in the optimization of the expensive output of complex computational simulations, which often present some form of deterministic noise and need to be smoothed for the results to be meaningful. We introduce a derivative-fre...

We investigate the core mass distribution (CMD) resulting from numerical models of turbulent fragmentation of molecular clouds. In particular we study its dependence on the sonic rms Mach numberMs. We analyze simulations withMs ranging from 1 to 15 to show that, asMs increases, the number of cores increases as well, while their average mass decreases. This stems from the fact that high Mach num...

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and Avg-P, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the in...

Importance weighting is a convenient general way to adjust for draws from the wrong distribution, but the resulting ratio estimate can be noisy when the importance weights have a heavy right tail, as routinely occurs when there are aspects of the target distribution not well captured by the approximating distribution. More stable estimates can be obtained by truncating the importance ratios. He...

Let X be a semi-stable arithmetic surface over the spectrum S of the ring of integers in a number field K. We assume that the generic fiber XK is geometrically irreducible and has positive genus. Consider a line bundle L on X , which is non-negative on every vertical fiber and equipped with an admissible metric (in the sense of Arakelov [A]) of positive curvature. In [S] we have shown that any ...