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We show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic…

The recent success in implementing supervised learning to classify modulation types suggests that other problems akin to modulation classification would eventually benefit from that implementation. One of these problems is classifying the…

This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…

In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

A beam splitter is a simple, readily available device which can act to entangle the output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states…

The goal of this article is twofold. Firstly, nonlinear system identification is introduced to a wide audience, guiding practicing engineers and newcomers in the field to a sound solution of their data driven modeling problems for nonlinear…

Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…

In this report, we lay the foundation for amplitude noise and phase noise analysis in nonlinear devices. We build a theoretical framework that helps us to analyze extremely difficult problems which include both nonlinearity and noise of…

The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce…

In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Li\'enard type oscillators exhibit this interesting property. We show that a…

Myopotential pattern recognition to decode the intent of the user is the most advanced approach to controlling a powered bioprosthesis. Unfortunately, many factors make this a difficult problem and achieving acceptable recognition quality…

In this paper, we show an approach to build deep learning algorithms for recognizing signals in distributed fiber optic monitoring and security systems for long perimeters. Synthesizing such detection algorithms poses a non-trivial research…

Understanding the sleep quality and architecture is essential to human being's health, which is usually represented using multiple sleep stages. A standard sleep stage determination requires Electroencephalography (EEG) signals during the…

We will consider two special families of polynomial perturbations of the linear center. For the resulting perturbed systems, which are generalized Li\'enard systems, we provide the exact upper bound for the number of limit cycles that…

An ensemble of classifiers combines several single classifiers to deliver a final prediction or classification decision. An increasingly provoking question is whether such systems can outperform the single best classifier. If so, what form…

Composite pulses are essential for universal manipulation of singlet-triplet spin qubits. In the absence of noise, they are required to perform arbitrary single-qubit operations due to the special control constraint of a singlet-triplet…

This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…