Related papers: Smoothing Strange Attractors Using Splines
Smoothing and filtering two-dimensional sequences are fundamental tasks in fields such as computer vision. Conventional filtering algorithms often rely on the selection of the filtering window, limiting their applicability in certain…
We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by L\'evy white noises. A recent paper showed that these processes are limits in law of…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…
Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…
We present a static analysis for discovering differentiable or more generally smooth parts of a given probabilistic program, and show how the analysis can be used to improve the pathwise gradient estimator, one of the most popular methods…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
I describe a new method for smoothing a one-dimensional curve in Euclidian space with an arbitrary number of dimensions. The basic idea is borrowed from renormalization group theory which previously was applied to biological macromolecules.…
3D animations are an effective method to learn about complex dynamic phenomena, such as mesoscale biological processes. The animators' goals are to convey a sense of the scene's overall complexity while, at the same time, visually guiding…
This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…
In this paper, new methods for smoothing gamma-ray spectra measured by NaI detector are derived. Least squares fitting method with B-spline basis functions is used to reduce the influence of statistical fluctuations. The derived procedures…
We present an efficient B-spline finite element method (FEM) for cloth simulation. While higher-order FEM has long promised higher accuracy, its adoption in cloth simulators has been limited by its larger computational costs while…
The task of reconstructing smooth signals from streamed data in the form of signal samples arises in various applications. This work addresses such a task subject to a zero-delay response; that is, the smooth signal must be reconstructed…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
Fine stratification survey is useful in many applications as its point estimator is unbiased, but the variance estimator under the design cannot be easily obtained, particularly when the sample size per stratum is as small as one unit. One…
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…
Noise is a part of data whether the data is from measurement, experiment or ... A few techniques are suggested for noise reduction to improve the data quality in recent years some of which are based on wavelet, orthogonalization and neural…
We study the effect of noise for a physically realizable flow system with a hyperbolic chaotic attractor of the Smale - Williams type in the Poincare cross-section [S.P. Kuznetsov, Phys. Rev. Lett. 95, 2005, 144101]. It is shown numerically…