For a large class of second order Lagrangian dynamics, one may reformulate the problem of finding periodic solutions as a problem in solving second-order recurrence relations satisfying a twist condition. We project periodic solutions of such discretized Lagrangian systems onto the space of closed braids and apply topological techniques. Under this reformulation, one obtains a gradient flow on ...

Blind Source Separation (BSS) arises in a variety of fields in speech processing such as speech enhancement, speakers diarization and identification. Generally, methods for BSS consider several observations of the same recording. Single microphone analysis is the worst underdetermined case, but, it is also the more realistic one. In this article, the autoregressive structure (short term predict...

This paper describes the design of an identification, prediction and estimation algorithm of a two-dimensional (2-D) autoregressive moving average (ARMA) model using a 2-D innovation process using raw data. This model has been applied to a finite size of electronic healthcare image of human white blood cell chromosomes. An optimum smoothing approach based on this model has been implemented. The...

We consider nonparametric estimation of the parameter functions a i () , i = 1; : : : ; p , of a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions a i , the empirical wavelet coeecients are derived from the time series data as the solution of a least squares minimization problem. In order to allow the a i to be functions of inhomogeneous ...

• This paper aims to analyze the extremal properties of periodic integer-valued sequences with marginal distribution belonging to a particular class defined by Anderson [1970. J. Appl. Probab. 7, 99–113] where the tail decays exponentially. An expression for calculating the extremal index of sequences satisfying certain local conditions, similar to those introduced by Chernick et al. [1991. Adv...

We propose a new strategy to analyse the periodicity of gene expression profiles using Singular Spectrum Analysis (SSA) and Autoregressive (AR) model based spectral estimation. By combining the advantages of SSA and AR modelling, more periodic genes are extracted in the Plasmodium falciparum data set, compared with the classical Fourier analysis technique. We are able to identify more gene targ...

We consider nonparametric estimation of the parameter functions a i () , i = 1; : : : ; p , of a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions a i , the empirical wavelet coeecients are derived from the time series data as the solution of a least squares minimization problem. In order to allow the a i to be functions of inhomogeneous ...

This paper suggests a robust estimation procedure for the parameters of the periodic AR (PAR) models when the data contains additive outliers. The proposed robust methodology is an extension of the robust scale and covariance functions given in, respectively, Rousseeuw and Croux [29] and Ma and Genton [24], to accommodate periodicity. These periodic robust functions are used in the Yule-Walker ...