Noise measurement. Series of 2 lectures. 1.

LECTURES 1-27

Lectures 1 and 2 of “ Model

These notes are for the first two lectures of the lecture series ”Model Theory and Diophantine Geometry” by Thomas Scanlon and myself. The full series of lectures will be on the Manin-Mumford conjecture and variants. As is well-known, model-theoretic ideas, specifically definability theory in difference fields of characteristic zero, were used by Hrushovski [2] to give another proof of the Mani...

Lectures on (2+1)-Dimensional Gravity

These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of the classical theory and three approaches to quantization are discussed in some detail, and a number of other approaches are summarized. An extensive, althoug...

lectures 1-27

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Estimating measurement noise in a time series by exploiting nonstationarity

A measured time series is always corrupted by noise to some degree. Even a rough estimation of the level of noise contained in an experimental time series is valuable. This is so, for example, when one wishes to apply techniques from nonlinear dynamics theory to analyze a time series. However, this is a very difficult problem. It becomes even harder when the measured signal is nonstationary, wh...