We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use measurement scale as a type of information constraint. We argue that a very common measurement scale is linear at small magnitudes grading into logarithmic at large m...

As a method to establish the Lyapunov stability of differential/difference equations systems, the LaSalle invariance principle was originally proposed in the 1950’s and has become a fundamental mathematical tool in the area of dynamical systems and control. In both theoretical research and engineering practice, discrete-time dynamical systems have been at least as extensively studied as continu...

We consider one-dimensional biased voter models, where 1’s replace 0’s at a faster rate than the other way round, started in Heaviside initial state describing interface between two infinite populations of and 1’s. In limit weak bias, for diffusively rescaled process, we measure-valued process local fraction type 1 sites as function time. Under finite second moment condition on rates, show that...