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Background In 1993, 1000 randomly selected employed Swedish men aged 45–50 years were invited to a nurse-led health examination with a survey on life style, fasting lab tests, and a 12-lead ECG. A repeat examination was offered in 1998. The ECGs were classified according to the Minnesota Code. Upon ethical approval, endpoints in terms of MI and death over 25 years were collected from Swedish national registers with the purpose of analyzing the independent association of ECG abnormalities as risk factors for myocardial infarction and death. Results Seventy-nine of 977 participants had at least one ECG abnormality 1993 or 1998. One hundred participants had a first MI over the 25 years. Odds ratio for having an MI in the group that had one or more ECG abnormality compared with the group with two normal ECGs was estimated to 3.16. 95%CI (1.74; 5.73), p value 0.0001. One hundred fifty-seven participants had died before 2019. For death, similarly no statistically significant difference was shown, OR 1.52, 95%CI (0.83; 2.76). Conclusions Our study suggests that presence of ST- and R-wave changes is associated with an independent 3–4-fold increased risk of MI after 25 years follow-up, but not of death. A 12-lead resting ECG should be included in any MI risk calculation on an individual level.

A class of resource allocation problems is considered where some quality of service measure is set against the agent related costs. Three multiobjective minimization problems are posed, one for a system of Erlang-C queues and two for systems of Erlang-A queues.

A Markovian system model for a contact center chat function is considered and partially validated. A hypothesis test on real chat data shows that it is reasonable to model the arrival process as a ...

International audience; We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue.

An efficient algorithm for determining the unique minimal and stable realization of a window ot Markov parameters and covariances is derived. The main difference compared to the Q-Markov COVER theory is that here we let the variance of the input noise be a variable, thus avoiding a certain data consistency criterion. First, it is shown that maximizing the input variance of the realization over all interpolants yields a minimal degree solution--a result closely related to maximum entropy. Secondly, the state space approach of the Q-Markov COVER theory is used for analyzing the stability and structure of the realization by straightforward application of familiar realization theory concepts, in particular the occurrence of singular spectral measures is characterized.

Methods for determining ARMA(n,m) filters from covariance and cepstral estimates are proposed. In [C. I. Byrnes, P. Enqvist, and A. Lindquist, SIAM J. Control Optim., 41 (2002), pp. 23--59], we have shown that an ARMA(n,m) model determines and is uniquely determined by a window r0,r1,...,rn of covariance lags and c1,c2,...,cn of cepstral lags. This unique model can be determined from a convex optimization problem which was shown to be the dual of a maximum entropy problem. In this paper, generalizations of this problem are analyzed. Problems with covariance lags r0,r1,...,rn and cepstral lags c1,c2,...,cm of different lengths are considered, and by considering different combinations of covariances, cepstral parameters, poles, and zeros, it is shown that only zeros and covariances give a parameterization that is consistent with generic data. However, the main contribution of this paper is a regularization of the optimization problems that is proposed in order to handle generic data. For the covariance and cepstral problem, if the data does not correspond to a system of desired order, solutions with zeros on the boundary occur and the cepstral coefficients are not interpolated exactly. In order to achieve strictly minimum phase filters for estimated covariance and cepstral data, a barrier-like term is introduced to the optimization problem. This term is chosen so that convexity is maintained and so that the unique solution will still interpolate the covariances but only approximate the cepstral lags. Furthermore, the solution will depend analytically on the covariance and cepstral data, which provides robustness, and the barrier term increases the entropy of the solution.

In this paper, we study the well-posedness of the problems of determining shaping filters from combinations of finite windows of cepstral coefficients, covariance lags, or Markov parameters. For example, we determine whether there exists a shaping filter with a prescribed window of Markov parameters and a prescribed window of covariance lags. We show that several such problems are well-posed in the sense of Hadamard; that is, one can prove existence, uniqueness (identifiability), and continuous dependence of the model on the measurements. Our starting point is the global analysis of linear systems, where one studies an entire class of systems or models as a whole, and where one views measurements, such as covariance lags and cepstral coefficients or Markov parameters, from data as functions on the entire class. This enables one to pose such problems in a way that tools from calculus, optimization, geometry, and modern nonlinear analysis can be used to give a rigorous answer to such problems in an algorithm-independent fashion. In this language, we prove that a window of cepstral coefficients and a window of covariance coefficients yield a bona fide coordinate system on the space of shaping filters, thereby establishing existence, uniqueness, and smooth dependence of the model parameters on the measurements from data.

One of the most widely used methods of spectral estimation in signal and speech processing is linear predictive coding (LPC), LPC has some attractive features, which account for its popularity, including the properties that the resulting modeling filter (i) matches a finite window of n+1 covariance lags, (ii) is rational of degree at most n, and (iii) has stable zeros and poles. The only limiting factor of this methodology is that the modeling filter is "all-pole," i.e., an autoregressive (AR) model. In this paper, we present a systematic description of all autoregressive moving-average (ARMA) models of processes that have properties (i)-(iii) in the context of cepstral analysis and homomorphic filtering. We show that each such an ARMA model determines and is completely determined by its finite windows of cepstral coefficients and covariance lags. We show that these nth-order windows form local coordinates for all ARMA models of degree n and that the pole-zero model can be determined from the windows as the unique minimum of a convex objective function. We refine this optimization method by first noting that the maximum entropy design of an LPC filter is obtained by maximizing the zeroth cepstral coefficient, subject to the constraint (i). More generally, we modify this scheme to a more well-posed optimization problem where the covariance data enter as a constraint and the linear weights of the cepstral coefficients are "positive"-in a sense that a certain pseudo-polynomial is positive-rather succinctly generalizing the maximum entropy method. This new problem is a homomorphic filter generalization of the maximum entropy method. providing a procedure for the design of any stable, minimum-phase modeling filter of degree less or equal to n that interpolates the given covariance window. We present an algorithm for realizing these filters in a lattice-ladder form, given the covariance window and the moving average part of the model, While we also show how to determine the moving average part using cepstral smoothing, one can make use of any good a priori estimate for the system zeros to initialize the algorithm. We conclude the paper with an example of this method, incorporating an example from the literature on ARMA modeling.

In the Markov and covariance interpolation problem a transfer function $W$ is sought that match the first coefficients in the expansion of $W$ around zero and the first coefficients of the Laurent expansion of the corresponding spectral density $WW^\star$. Here we solve an interpolation problem where the matched parameters are the coefficients of expansions of $W$ and $WW^\star$ around various points in the disc. The solution is derived using input-to-state filters and is determined by simple calculations such as solving Lyapunov equations and generalized eigenvalue problems., Comment: CDC 2007 paper

Identification of power spectral densities rely on measured second order statistics such as, e.g. covariance estimates. In the family of power spectra consistent with such an estimate a representative spectra is singled out; examples of such choices are the Maximum entropy spectrum and the Correlogram. Here, we choose a prior spectral density to represent a priori information, and the spectrum closest to the prior in the Itakura-Saito distance is selected. It is known that this can be seen as the limit case when the cross-entropy principle is applied to a gaussian process. This work provides a quantitative measure of how close a finite covariance sequence is to a spectral density in the Itakura-Saito distance. It is given by a convex optimization problem and by considering its dual the structure of the optimal spectrum is obtained. Furthermore, it is shown that strong duality holds and that a covariance matching coercive spectral density always exists. The methods presented here provides tools for discrimination between power spectrum, identification of power spectrum, and for incorporating given data in this process.

Given a p×p Schur function S, we consider the problem of constructing a symmetric Darlington synthesis of minimal size. This amounts essentially to finding a stable all-pass square extension of S of minimal size. The characterization is done in terms of the multiplicities of the zeros. As a special case we obtain conditions for symmetric Darlington synthesis to be possible without increasing the McMillan degree for a symmetric rational contractive matrix which is strictly contractive in the right half-plane. This technique immediately extends to the case where, allowing for a higher dimension of the extension, we require no increase in the McMillan degree. Also in this case we obtain sharper results than those existing in the literature (see [1]).

Given the pole-zero configuration of a stable and rational transfer function it is trivial to determine the normalized covariances and Markov parameters. It is nontrivial and was recently shown that for finite windows of these parameters there corresponds a unique minimal and stable rational transfer function. Furthermore, small changes in the parameters corresponds to small changes of the transfer function, which makes the method robust. However, the proof was non-constructive and no algorithm for determining the inverse map was known. An efficient algorithm for determining the pole-zero configuration of the interpolating transfer function is the main contribution of this paper. As a corollary a novel and simplified approach to the minimal stochastic realization problem is obtained. Using an example from speech processing it is shown how this realization theory result can be used for identification of time series.

We study the well-posedness of the problems of determining shaping filters from combinations of finite windows of cepstral coefficients, covariance lags, or Markov parameters. For example, we determine whether there exists a shaping filter with prescribed window of Markov parameters and a prescribed window of covariance lags. We show that several such problems are well-posed in the sense of Hadamard; that is, one can prove existence, uniqueness (identifiability) and continuous dependence of the model on the measurements. Our starting point is the global analysis of linear systems, where one studies an entire class of systems or models as a whole, and where one views measurements, such as covariance lags and cepstral coefficients or Markov parameters, from data as functions on the entire class. This enables one to pose such problems in a way that tools from calculus, optimization, geometry and modern nonlinear analysis can be used to give a rigorous answer to such problems in an algorithm-independent fashion.

Spline functions are well known and are widely used for practical approximation of functions or more commonly for fitting smooth curves through preassigned points. Spline techniques have the advantage over most approximation and interpolation techniques in that they are computationally feasible. Most of the published spline algorithms are for polynomial splines and the vast preponderance are for cubic splines. There is a small but excellent literature on the so called exponential splines and there is an even smaller literature on splines with more or less arbitrary nodal functions,[9, 3].