Search results for "Linear model"
showing 10 items of 598 documents
Information Dynamics Analysis: A new approach based on Sparse Identification of Linear Parametric Models*
2020
The framework of information dynamics allows to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of a complex network. The information transfer from one process to another can be quantified through Transfer Entropy, and under the assumption of joint Gaussian variables it is strictly related to the concept of Granger Causality (GC). According to the most recent developments in the field, the computation of GC entails representing the processes through a Vector Autoregressive (VAR) model and a state space (SS) model typically identified by means of the Ordinary Least Squares (OLS). In this work, we propose a new identification …
Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis
2011
This tutorial paper introduces a common framework for the evaluation of widely used frequency-domain measures of coupling (coherence, partial coherence) and causality (directed coherence, partial directed coherence) from the parametric representation of linear multivariate (MV) processes. After providing a comprehensive time-domain definition of the various forms of connectivity observed in MV processes, we particularize them to MV autoregressive (MVAR) processes and derive the corresponding frequency-domain measures. Then, we discuss the theoretical interpretation of these MVAR-based connectivity measures, showing that each of them reflects a specific time-domain connectivity definition an…
So Many Variables: Joint Modeling in Community Ecology
2015
Technological advances have enabled a new class of multivariate models for ecology, with the potential now to specify a statistical model for abundances jointly across many taxa, to simultaneously explore interactions across taxa and the response of abundance to environmental variables. Joint models can be used for several purposes of interest to ecologists, including estimating patterns of residual correlation across taxa, ordination, multivariate inference about environmental effects and environment-by-trait interactions, accounting for missing predictors, and improving predictions in situations where one can leverage knowledge of some species to predict others. We demonstrate this by exa…
Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions.
2010
The Partial Directed Coherence (PDC) and its generalized formulation (gPDC) are popular tools for investigating, in the frequency domain, the concept of Granger causality among multivariate (MV) time series. PDC and gPDC are formalized in terms of the coefficients of an MV autoregressive (MVAR) model which describes only the lagged effects among the time series and forsakes instantaneous effects. However, instantaneous effects are known to affect linear parametric modeling, and are likely to occur in experimental time series. In this study, we investigate the impact on the assessment of frequency domain causality of excluding instantaneous effects from the model underlying PDC evaluation. M…
Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series
2011
A common way of obtaining information about a physiological system is to measure one or more signals from the system, consider their temporal evolution in the form of numerical time series, and obtain quantitative indexes through the application of time series analysis techniques. While historical approaches to time series analysis were addressed to the study of single signals, recent advances have made it possible to study collectively the behavior of several signals measured simultaneously from the considered system. In fact, multivariate (MV) time series analysis is nowadays extensively used to characterize interdependencies among multiple signals collected from dynamical physiological s…
The Pursuit of Happiness in Music: Retrieving Valence with Contextual Music Descriptors
2009
In the study of music emotions, Valence is usually referred to as one of the dimensions of the circumplex model of emotions that describes music appraisal of happiness, whose scale goes from sad to happy. Nevertheless, related literature shows that Valence is known as being particularly difficult to be predicted by a computational model. As Valence is a contextual music feature, it is assumed here that its prediction should also require contextual music descriptors in its predicting model. This work describes the usage of eight contextual (also known as higher-level) descriptors, previously developed by us, to calculate happiness in music. Each of these descriptors was independently tested …
Combining poly(dimethyldiphenylsiloxane) and nitrile phases for improving the separation and quantitation of benzalkonium chloride homologues: In-tub…
2013
The retention and separation of four homologues of benzalkonium chloride (alkyl (C12, C14, C16, C18) dimethylbenzylammonium chloride) have been studied in poly(dimethyldiphenylsiloxane) (TRB) and nitrile capillary phases, respectively. Under the optimized conditions (50% acetonitrile in processed samples, 35% of diphenyl content of the TRB, capillary length 43 cm and water:methanol 60:40 as replacing solvent), the extraction efficiency was similar for all the homologues with satisfactory reproducibility and independently of the amount and proportion of homologues. Industrial samples with high viscosity or with complex composition and washes waters have been analyzed without previous treatme…
Calculation of nonlinear stationary magnetic field
1996
Currently, linear models of various physical fields can successfully be implemented numerically. Efficient numerical methods have been developed during last two or three decades and sufficiently capable computers are available. The situation is different with nonlinear models. There is no general numerical method for solving all nonlinear problems, and consequently every class of problems has to be investigated individually. The specific features of the class are taken into account in this process [Berger].
Identification of Nonlinear Systems Described by Hammerstein Models
2004
This paper deals with a method for identification of nonlinear systems suitable to be described by Hammerstein models consisting of a static nonlinearity followed by an ARX linear model. The estimation of the static nonlinearity is carried out supplying the system with a sequence of step signals of various amplitude and determining the corresponding steady-state responses. The estimation of the parameters of the ARX linear system is carried out by means of a least square estimator using data generated supplying the system with a Pseudorandom Binary Sequence (PRBS). The method in question is able to identify static nonlinearities of general type, also with hysteresis and/or discontinuities. …
A taxonomy for wavelet neural networks applied to nonlinear modelling
2008
This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.