André Klein

The peroxisomal membrane protein Pex13p shows a novel mode of SH3 interaction

Src homology 3 (SH3) domains are small non‐catalytic protein modules capable of mediating protein–protein interactions by binding to proline‐X‐X‐proline (P‐X‐X‐P) motifs. Here we demonstrate that the SH3 domain of the integral peroxisomal membrane protein Pex13p is able to bind two proteins, one of which, Pex5p, represents a novel non‐P‐X‐X‐P ligand. Using alanine scanning, two‐hybrid and in vitro interaction analysis, we show that an α‐helical element in Pex5p is necessary and sufficient for SH3 interaction. Sup pressor analysis using Pex5p mutants located in this α‐helical element allowed the identification of a unique site of interaction for Pex5p on the Pex13p‐SH3 domain that is distinct from the classical P‐X‐X‐P binding pocket. On the basis of a structural model of the Pex13p‐SH3 domain we show that this interaction probably takes place between the RT‐ and distal loops. Thus, the Pex13p‐SH3–Pex5p interaction establishes a novel mode of SH3 interaction.

Topography for Independent Binding of α-Helical and PPII-Helical Ligands to a Peroxisomal SH3 Domain.

While the function of most small signaling domains is confined to binary ligand interactions, the peroxisomal Pex13p SH3 domain has the unique capacity of binding to two different ligands, Pex5p and Pex14p. We have used this domain as a model to decipher its structurally independent ligand binding sites. By the combined use of X-ray crystallography, NMR spectroscopy, and circular dichroism, we show that the two ligands bind in unrelated conformations to patches located at opposite surfaces of this SH3 domain. Mutations in the Pex13p SH3 domain that abolish interactions within the Pex13p-Pex5p interface specifically impair PTS1-dependent protein import into yeast peroxisomes.

On Fisher's information matrix of an ARMAX process and Sylvester's resultant matrices

We establish a relation between Fishers information matrix of a stationary autoregressive moving average process, with an exogenous component, and two Sylvesters resultant matrices.

The information matrix of multiple-input single-output time series models

Expressions are given for the information matrix of the parameters of the multiple-input single-output time series model for correlated and uncorrelated inputs, allowing lags between inputs. The model under consideration is a generalization of the multiple-regression model with autocorrelated errors, the transfer function model and the autoregressive moving average exogenous (ARMAX) model. The elements of the Fisher matrix are evaluated using algorithms developed for the univariate ARMA model.

On a fast algorithm for the exact information matrix of a Gaussian ARMA time series

The paper is devoted to a new algorithm for the computation of the exact Fisher information matrix of a Gaussian autoregressive-moving average time series. The number of operations is an order of magnitude smaller than the fastest existing procedure. The algorithm is based on a set of new recursions for the covariance matrix of the derivatives of the state vector with respect to the parameters, combined with the Chandrasekhar recursions used in the evaluation of the likelihood function. >

On Stein's equation, Vandermonde matrices and Fisher's information matrix of time series processes. I. The autoregressive moving average process

Abstract This paper introduces several forms of relationships between Fishers information matrix of an autoregressive-moving average or ARMA process and the solution of a corresponding Stein equation. Fishers information matrix consists of blocks associated with the autoregressive and moving average parameters. An interconnection with a solution of Steins equation is set forth for the block case as well as for Fishers information matrix as a global matrix involving all parameter blocks. Both cases have their importance for the interpretation of the estimated parameters. The cases of distinct and multiple eigenvalues are addressed. The obtained links involve equations with left and right inverses, these can be expressed in terms of the inverse of appropriate Vandermonde matrices. A condition is set forth for establishing an equality between Fishers information matrix and a solution to Steins equation. Two examples are presented for illustrating some of the results obtained. The global and off-diagonal block case with distinct and multiple roots, respectively, are considered.

A generalization of Whittle's formula for the information matrix of vector-mixed time series

Abstract In a pioneering paper Whittle developed a formula for expressing Fishers information matrix of multivariate time series models (cf. P. Whittle, J. Royal Statist Soc. B 15 (1953) 125–139). It is described as a function of the spectral density of the time series process. The existing relationship is extended to the whole matrix instead of one element and is related with a time domain alternative expression. The latter derives Fishers information matrix from the log Gaussian likelihood function. The equivalence of both approaches, frequency and time domain, which is summarized in a theorem, shows that a considerable reduction in matrix integrals is taking place when moving from the former to the latter. The Hermitian property of the matrices under study contributes to construct the link between the two approaches, and the theorem is further illustrated by an example.

On Fisher's information matrix of an ARMA process.

In this paper we study the Fisher information matrix for a stationary ARMA process with the aid of Sylvester’s resultant matrix. Some properties are explained via realizations in state space form of the derivates of the white noise process with respect to the parameters.

Forecasting the Antwerp maritime traffic flows using transformations and intervention models

This article uses univariate time-series models with data transformations and intervention models to forecast the volumes of twenty-two maritime traffic flows in the port of Antwerp which are expressed in tonnes. The models obtained produce forecasts that are a substantial improvement over those obtained with unadjusted data. The models also provide useful insight into the behaviour of maritime traffic flows during the period 1971–82.

On the cumulated multi-step-ahead predictions of vector autoregressive moving average processes

When a time series model is used for making predictions, then it is often meaningful to evaluate its performance on the basis of cumulated multi-step-ahead prediction errors. In this paper some theoretical properties of cumulated multi-step-ahead predictors and cumulated multi-step-ahead prediction errors for vector autoregressive moving average processes are considered. A general expression for the optimal cumulated multi-step-ahead predictor is derived. The predictors are based on the Kalman filter algorithm. To determine the maximum prediction horizon of cumulated multi-step-ahead predictions, two information measures are introduced. For univariate ARMA(p, q) processes with p < 3 and q < 3, these measures are evaluated analytically as well as numerically. It is shown that the information content of cumulated multi-step-ahead predictions depends on the prediction horizon and the location of the roots of the AR and MA polynomials.