105 citations · 398 across the 25 of their papers we have counts for
25 papers
Imaging in Reflecting Spheres
Jean-Pierre Eckmann, Gemunu H. Gunaratne, Jason Shulman +1
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reachi…
Anomalous Scaling of Stochastic Processes and the Moses Effect
Lijian Chen, Kevin E. Bassler, Joseph L. McCauley +1
The state of a stochastic process evolving over a time is typically assumed to lie on a normal distribution whose width scales like . However, processes where the prob…
Controlling Networks of Nonlinearly-Coupled Nodes using Response Surfaces
Jason Shulman, Frank Malatino, Alexander Mo +2
Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfor…
Experimental determination of circuit equations
Jason Shulman, Frank Malatino, Matthew Widjaja +1
Kirchhoff's laws offer a general, straightforward approach to circuit analysis. Unfortunately, use of the laws becomes impractical for all but the simplest of circuits. This work p…
Integration I(d) of Nonstationary Time Series: Stationary and nonstationary increments
Joseph L. McCauley, Kevin E. Bassler, Gemunu H. Gunaratne
The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A clas…
Martingales, the Efficient Market Hypothesis, and Spurious Stylized Facts
Joseph L. McCauley, Kevin E. Bassler, Gemunu H. Gunaratne
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts,…