Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the pres...

We consider Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Qsuperlinear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear equations due to Powell leads to R-superlinear convergence provided the search directions form a uniformly linearly independent sequence. We...

We propose a new estimation procedure for covariate adjusted nonlinear regression models for situations where both the predictors and response in a nonlinear regression model are not directly observed, however distorted versions of the predictors and response are observed. The distorted versions are assumed to be contaminated with a multiplicative factor that is determined by the value of an un...

We develop an approach to the construction of Lyapunov functions for the forward equation of a nite state nonlinear Markov process. Nonlinear Markov processes can be obtained as a law of large number limit for a system of weakly interacting processes. The approach exploits this connection and the fact that relative entropy de nes a Lyapunov function for the solution of the forward equation for ...

It is shown that the tight-binding approximation of the nonlinear Schrödinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dyn...

We present a new technique for verifying nonlinear and hybrid models with inputs. We observe that once an input signal is fixed, the sensitivity analysis of the model can be computed much more precisely. Based on this result, we propose a new simulation-driven verification algorithm and apply it to a suite of nonlinear and hybrid models of CMOS digital circuits under different input signals. Th...

The nonlinear dynamic response of atomic force microscopy cantilevers tapping on a sample is discussed through theoretical, computational, and experimental analysis. Experimental measurements are presented for the frequency response of a specific microcantilever-sample system to demonstrate the nonlinear features, including multiple jump phenomena leading to reproducible hysteresis. We show tha...

This paper presents a simple methodology for obtaining the entire set of continuous controllers that cause a nonlinear dynamical system to exactly track a given trajectory. The trajectory is provided as a set of algebraic differential equations that may or may not be explicitly dependent on time. The method provided is inspired by results from analytical dynamics and the close connection betwee...

In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymp...

Nonlinear optics is a broad field of research and technology that encompasses subject matter in the fields of physics, chemistry, biology, and engineering. The diversity of nonlinear optics stems, in part, from the need for all-optical and electrooptical devices for applications in telecommunications, optical storage, and all-optical computing. In addition, many nonlinear optical effects have p...