Related papers: Tight Bounds for Averaging Multi-Frequency Differe…

In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…

We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…

Multirate digital signal processing and model reduction applications require computation of the frequency truncated norm of a discrete-time system. This paper explains how to compute the frequency truncated norm of a discrete-time system.…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

Control design for linear, time-invariant mechanical systems typically requires an accurate low-order approximation in the low frequency range. For example a series expansion of the transfer function around zero consisting of a mass,…

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.

We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…

Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…

We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…

Unlike the situation with gain and phase margins in robust stabilization, the problem to determine an exact maximum delay margin is still an open problem, although extensive work has been done to establish upper and lower bounds. The…

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…

Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…

We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…

The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated…

This work is devoted to study the existence of periodic solutions for a family of discontinuous differential systems $Z(x,y;\epsilon)$ with many zones. We show that for $\epsilon$ sufficiently small the averaged functions at any order…

Practical application of H[infinity] robust control relies on system identification of a valid model-set, described by a linear system in feedback with a stable norm-bounded uncertainty, which must explains all possible (or at least all…

A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…

In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…