529 research outputs found
Stability, Causality, and Passivity in Electrical Interconnect Models
Modern packaging design requires extensive signal integrity simulations in order to assess the electrical performance of the system. The feasibility of such simulations is granted only when accurate and efficient models are available for all system parts and components having a significant influence on the signals. Unfortunately, model derivation is still a challenging task, despite the extensive research that has been devoted to this topic. In fact, it is a common experience that modeling or simulation tasks sometimes fail, often without a clear understanding of the main reason. This paper presents the fundamental properties of causality, stability, and passivity that electrical interconnect models must satisfy in order to be physically consistent. All basic definitions are reviewed in time domain, Laplace domain, and frequency domain, and all significant interrelations between these properties are outlined. This background material is used to interpret several common situations where either model derivation or model use in a computer-aided design environment fails dramatically.We show that the root cause for these difficulties can always be traced back to the lack of stability, causality, or passivity in the data providing the structure characterization and/or in the model itsel
Rank-based estimation for all-pass time series models
An autoregressive-moving average model in which all roots of the
autoregressive polynomial are reciprocals of roots of the moving average
polynomial and vice versa is called an all-pass time series model. All-pass
models are useful for identifying and modeling noncausal and noninvertible
autoregressive-moving average processes. We establish asymptotic normality and
consistency for rank-based estimators of all-pass model parameters. The
estimators are obtained by minimizing the rank-based residual dispersion
function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These
estimators can have the same asymptotic efficiency as maximum likelihood
estimators and are robust. The behavior of the estimators for finite samples is
studied via simulation and rank estimation is used in the deconvolution of a
simulated water gun seismogram.Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Quantifying information transfer and mediation along causal pathways in complex systems
Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer aimed at decompositions of predictive information about a target variable, while excluding effects of common drivers and indirect influences. While common drivers clearly constitute a spurious causality, the aim of the present article is to develop measures quantifying different notions of the strength of information transfer along indirect causal paths, based on first reconstructing the multivariate causal network. Another class of novel measures quantifies to what extent different intermediate processes on causal paths contribute to an interaction mechanism to determine pathways of causal information transfer. The proposed framework complements predictive decomposition schemes by focusing more on the interaction mechanism between multiple processes. A rigorous mathematical framework allows for a clear information-theoretic interpretation that can also be related to the underlying dynamics as proven for certain classes of processes. Generally, however, estimates of information transfer remain hard to interpret for nonlinearly intertwined complex systems. But if experiments or mathematical models are not available, then measuring pathways of information transfer within the causal dependency structure allows at least for an abstraction of the dynamics. The measures are illustrated on a climatological example to disentangle pathways of atmospheric flow over Europe
Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields
We present \emph{telescoping} recursive representations for both continuous
and discrete indexed noncausal Gauss-Markov random fields. Our recursions start
at the boundary (a hypersurface in , ) and telescope inwards.
For example, for images, the telescoping representation reduce recursions from
to , i.e., to recursions on a single dimension. Under
appropriate conditions, the recursions for the random field are linear
stochastic differential/difference equations driven by white noise, for which
we derive recursive estimation algorithms, that extend standard algorithms,
like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal
Markov random fields.Comment: To appear in the Transactions on Information Theor
Linear estimation of boundary value processes
Bibliography: leaf [4].Caption title. "August 1983."Supported by the National Science Foundation under Grant ECS-8012668by Milton B. Adams, Bernard C. Levy, Alan S. Willsky
Linear estimation for 2-D nearest-neighbor models
Cover title.Includes bibliographical references.Supported in part by the National Science Foundation. ECS-8700903 Supported in part by the Army Research Office. DAAL03-86-K-0171Milton B. Adams, Bernard C. Levy and Alan S. Willsky
- âŠ