This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinitedimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension g...

We establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation x (t) = L(x t) + g(t,x t) whose linear part y (t) = L(y t) generates a monotone semiflow on the phase space C = C([−r,0],R) with respect to the exponential ordering, and the nonlinearity g has at most linear growth.

Regular expression matching using backtracking can have exponential runtime, leading to an algorithmic complexity attack known as REDoS in the systems security literature. In this paper, we present a static analysis that detects whether a given regular expression can have exponential runtime for some inputs. The analysis works by forming powers and products of transition relations and thereby r...

This paper studies a parabolic equation with exponential nonlinearity, which has several applications, for example the self-trapped beams in plasma. Based on modified concavity method we prove blow-up of solution initial data high energy. We also proposed solution’s lower and upper bound time equation. Our results complement existing results.