Splicing heterogeneity: separating signal from noise

Separating signal from noise

Suppose that a sequence of numbers xn (a ‘signal’) is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, xn + ξn, where ξn is a sequence of independent standard Gaussian random variables. Suppose further that the signal is known to come from some fixed space X of possible signals. Is it possible to fully recover the transm...

Separating Signal from Noise: Evaluating Emerging Technologies

Separating News from Noise

By treating mouse fibroblasts with varying concentrations of tumor necrosis factor (TNF) and measuring the resulting shifts in the production of transcription factors NFB and ATF-2, the researchers determined that individual cells are essentially capable of a one-bit response to this ligand, where signaling is simply on or ‘off.’ Many intermediate steps lie between TNF and NFB, and the authors ...

Separating microstructure noise from volatility∗

There are two variance components embedded in the returns constructed using high-frequency asset prices: the time-varying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high-frequency return data recorded at different frequencies, we provide a simple and robust...

Separating Speech from Speech Noise

The main work at Columbia this year has been the development of algorithms for extracting and recognizing speech in nonstationary, noisy environments when only a single microphone channel is available. Our particular approach is based on using trained models to distinguish regions of time-frequency containing speech from nonspeech areas [2], and we have pursued this along several directions: On...