We study the dispersive character for waves on the one-dimensional free surface of an infinitely deep perfect fluid under the influence of surface tension. The main result state that, on average in time, the solution of the water-wave problem gains locally 1/4 derivative of smoothness in the spatial variable, compared to the initial state. The regularizing effect is a direct consequence of disp...

This paper presents a method for calculating the smoothed state distribution Jump Markov Linear Systems. More specifically, details novel two-filter smoother that provides closed-form expressions hybrid distribution. can be expressed as Gaussian mixture with known, but exponentially increasing, number of components time index increases. is accompanied by exponential growth in memory and computa...

In this study, a hybrid synergy model integrating exponential smoothing and neural network is proposed for financial time series prediction. The proposed model attempts to incorporate the linear characteristics of an exponential smoothing model and nonlinear patterns of neural network to create a “synergetic” model via the linear programming technique. For verification, two real-world financial...

Quadratic elements place stringent requirements on a surface mesh smoother. One of the biggest challenges is that a good linear element may become invalid when mid-side nodes are introduced. To help alleviate this problem, a new objective function for optimization-based smoothing is proposed for triangular and quadrilateral elements, linear or quadratic. Unlike the current popular approaches, t...

The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first chapters we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp...

The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first sections we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp...

Local regularization methods for ill-posed linear Volterra equations have been shown to be efficient regularization procedures preserving the causal structure of the Volterra problem and allowing for sequential solution methods. However questions posed recently in Ring and Prix (2000 Inverse Problems 16 619–34) raise doubts as to whether such methods are convergent for problems which are more t...

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. The...