693 research outputs found

    Frequency identification of Wiener systems with Backlash operators using separable least squares estimators

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    This paper deals with the identification of Wiener models that involve backlash operators bordered by possibly noninvertible parametric lines. The latter are also allowed to cross each other making possible to account for general-shape static nonlinearities. The linear dynamic subsystem is not-necessarily parametric but is BIBO stable. A frequency identification method is developed that provides estimates of the nonlinear operator parameters as well as estimates of the linear subsystem frequency gain. The method involves standard and separable least squares estimators that all are shown to be consistent. Backlash operators and memoryless nonlinearities are handled within a unified framework.Preprin

    Identification of time-varying systems using multiresolution wavelet models

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    Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm

    Parametric identification of nonlinear fractional Hammerstein models

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    In this paper, a system identification method for continuous fractional-order Hammerstein models is proposed. A block structured nonlinear system constituting a static nonlinear block followed by a fractional-order linear dynamic system is considered. The fractional differential operator is represented through the generalized operational matrix of block pulse functions to reduce computational complexity. A special test signal is developed to isolate the identification of the nonlinear static function from that of the fractional-order linear dynamic system. The merit of the proposed technique is indicated by concurrent identification of the fractional order with linear system coefficients, algebraic representation of the immeasurable nonlinear static function output, and permitting use of non-iterative procedures for identification of the nonlinearity. The efficacy of the proposed method is exhibited through simulation at various signal-to-noise ratios

    Sample Path Analysis of Integrate-and-Fire Neurons

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    Computational neuroscience is concerned with answering two intertwined questions that are based on the assumption that spatio-temporal patterns of spikes form the universal language of the nervous system. First, what function does a specific neural circuitry perform in the elaboration of a behavior? Second, how do neural circuits process behaviorally-relevant information? Non-linear system analysis has proven instrumental in understanding the coding strategies of early neural processing in various sensory modalities. Yet, at higher levels of integration, it fails to help in deciphering the response of assemblies of neurons to complex naturalistic stimuli. If neural activity can be assumed to be primarily driven by the stimulus at early stages of processing, the intrinsic activity of neural circuits interacts with their high-dimensional input to transform it in a stochastic non-linear fashion at the cortical level. As a consequence, any attempt to fully understand the brain through a system analysis approach becomes illusory. However, it is increasingly advocated that neural noise plays a constructive role in neural processing, facilitating information transmission. This prompts to gain insight into the neural code by studying the stochasticity of neuronal activity, which is viewed as biologically relevant. Such an endeavor requires the design of guiding theoretical principles to assess the potential benefits of neural noise. In this context, meeting the requirements of biological relevance and computational tractability, while providing a stochastic description of neural activity, prescribes the adoption of the integrate-and-fire model. In this thesis, founding ourselves on the path-wise description of neuronal activity, we propose to further the stochastic analysis of the integrate-and fire model through a combination of numerical and theoretical techniques. To begin, we expand upon the path-wise construction of linear diffusions, which offers a natural setting to describe leaky integrate-and-fire neurons, as inhomogeneous Markov chains. Based on the theoretical analysis of the first-passage problem, we then explore the interplay between the internal neuronal noise and the statistics of injected perturbations at the single unit level, and examine its implications on the neural coding. At the population level, we also develop an exact event-driven implementation of a Markov network of perfect integrate-and-fire neurons with both time delayed instantaneous interactions and arbitrary topology. We hope our approach will provide new paradigms to understand how sensory inputs perturb neural intrinsic activity and accomplish the goal of developing a new technique for identifying relevant patterns of population activity. From a perturbative perspective, our study shows how injecting frozen noise in different flavors can help characterize internal neuronal noise, which is presumably functionally relevant to information processing. From a simulation perspective, our event-driven framework is amenable to scrutinize the stochastic behavior of simple recurrent motifs as well as temporal dynamics of large scale networks under spike-timing-dependent plasticity

    Change-point Problem and Regression: An Annotated Bibliography

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    The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

    Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

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    Issued as Progress report, and Final report, Project no. E-21-67

    Model based estimation of image depth and displacement

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    Passive depth and displacement map determinations have become an important part of computer vision processing. Applications that make use of this type of information include autonomous navigation, robotic assembly, image sequence compression, structure identification, and 3-D motion estimation. With the reliance of such systems on visual image characteristics, a need to overcome image degradations, such as random image-capture noise, motion, and quantization effects, is clearly necessary. Many depth and displacement estimation algorithms also introduce additional distortions due to the gradient operations performed on the noisy intensity images. These degradations can limit the accuracy and reliability of the displacement or depth information extracted from such sequences. Recognizing the previously stated conditions, a new method to model and estimate a restored depth or displacement field is presented. Once a model has been established, the field can be filtered using currently established multidimensional algorithms. In particular, the reduced order model Kalman filter (ROMKF), which has been shown to be an effective tool in the reduction of image intensity distortions, was applied to the computed displacement fields. Results of the application of this model show significant improvements on the restored field. Previous attempts at restoring the depth or displacement fields assumed homogeneous characteristics which resulted in the smoothing of discontinuities. In these situations, edges were lost. An adaptive model parameter selection method is provided that maintains sharp edge boundaries in the restored field. This has been successfully applied to images representative of robotic scenarios. In order to accommodate image sequences, the standard 2-D ROMKF model is extended into 3-D by the incorporation of a deterministic component based on previously restored fields. The inclusion of past depth and displacement fields allows a means of incorporating the temporal information into the restoration process. A summary on the conditions that indicate which type of filtering should be applied to a field is provided

    The herd moves? Emergence and self-organization in collective actors?

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    The puzzle about collective actors is in the focus of this contribution. The first section enters into the question of the adequateness and inadequateness of reductionist explanations for the description of entities. The considerations in this part do not draw on systems and hence not on principles of self-organisation, because this concept necessitates a systemic view. In other words, the first section discusses reductionism and holism on a very general level. The scope of these arguments goes far beyond self-organising systems. Pragmatically, these arguments will be discussed within the domain of corporative actors. Emergence is a concept embedded in system theory. Therefore, in the second part the previous general considerations about holism are integrated with respect to the concept “emergence”. In order to close the argument by exactly characterising self-organising systems and giving the conceptual link between self-organisation and emergence – which is done in the section four – the third section generally conceptualises systems. This conceptualisation is independent of whether these systems are self-organising or not. Feedback loops are specified as an essential component of systems. They establish the essential precondition of system-theoretic models where causes may also be effects and vice versa. System-theory is essential for dynamic models like ecological models and network thinking. In the fourth part mathematical chaos-theory bridges the gap between the presentation of systems in general and the constricted consideration of self-organising systems. The capability to behave or react chaotically is a necessary precondition of self-organisation. Nevertheless, there are striking differences in the answers given from theories of self-organisation in biology, economics or sociology on the question “What makes the whole more than the sum of its parts?” The fracture seems particularly salient at the borderline between formal-mathematical sciences like natural sciences including economy and other social sciences like sociology, for instance in the understanding and conceptualisation of “chaos” or “complexity”. Sometimes it creates the impression that originally well defined concepts from mathematics and natural science are metaphorically used in social sciences. This is a further reason why this paper concentrates on conceptualisations of self-organisation from natural sciences. The fifth part integrates the arguments from a system-theoretic point of view given in the three previous sections with respect to collective and corporative actors. Due to his prominence all five sections sometimes deal with the sociological system theory by Niklas Luhmann, especially in those parts with rigorous and important differences between his conception and the view given in this text. Despite Luhmann’s undoubted prominence in sociology, the present text strives for a more analytical and formal understanding of social systems and tries to find a base for another methodological approach.
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