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20
Scalespace Properties of the Multiscale Morphological DilationErosion
 IEEE TRANS. ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1996
"... A multiscale morphological dilationerosion smoothing operation and its associated scalespace expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scalespace monotonic property for signal extrema is demonstrated. Scalespace ..."
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Cited by 53 (2 self)
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A multiscale morphological dilationerosion smoothing operation and its associated scalespace expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scalespace monotonic property for signal extrema is demonstrated. Scalespace fingerprints from this approach have advantages over Gaussian scalespace fingerprints in that they: are defined for negative values of the scale parameter; have
Extending the HOL theorem prover with a Computer Algebra System to Reason about the Reals
 Higher Order Logic Theorem Proving and its Applications (HUG `93
, 1993
"... In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from ..."
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Cited by 33 (4 self)
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In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from their application in computeraided verification, i.e. proving that designs of electronic or computer systems, programs, protocols and cryptosystems satisfy certain properties. Such proofs, as compared with the proofs one finds in mathematics books, usually involve less sophisticated central ideas, but contain far more technical Supported by the Science and Engineering Research Council, UK. y Supported by SERC grant GR/G 33837 and a grant from DSTO Australia. details and therefore tend to be much more difficult for humans to write or check without making mistakes. Hence it is appealing to let computers help. Some fundamental mathematical theories, such as arithmetic, are usually requi...
Convergence Properties of the Likelihood of Computed Dynamic Models
 Econometrica
, 2006
"... This paper studies the econometrics of computed dynamic models. Since these models generally lack a closedform solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function ..."
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Cited by 16 (2 self)
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This paper studies the econometrics of computed dynamic models. Since these models generally lack a closedform solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods.
Morphological Scalespace
 In Proceedings 11th IAPR International Conference on Pattern Recognition
, 1992
"... Scalespace is an important recent concept used in image processing and pattern recognition. Traditional scalespace is generated by a linear smoothing operation. We present here a nonlinear type of smoother related to mathematical morphology which meets (modified) "scalespace axioms " and also gen ..."
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Cited by 15 (9 self)
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Scalespace is an important recent concept used in image processing and pattern recognition. Traditional scalespace is generated by a linear smoothing operation. We present here a nonlinear type of smoother related to mathematical morphology which meets (modified) "scalespace axioms " and also generates a "scalespace." This scalespace is fullplane and preserves the positions of features. 1 Introduction At the 7th IJCAI in 1983, Andrew Witkin introduced the concept of scalespace filtering in a, now classical, four page paper [9]. It had been known for some time that the human visual system processes images via a number of spatialfrequency tuned channels and that a similar multiscale approach is useful in computer vision [7]. However, the question of how to combine signal descriptions at different scales remained a problem. Enter Witkin with the intuitively elegant idea to use a continuous scale parameter for the spatial filter; then the signal features (in this case zerocrossin...
Incipient Fault Diagnosis of Dynamical Systems Using OnLine Approximators
 IEEE Transactions on Automatic Control
, 1998
"... Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this note, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system d ..."
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Cited by 9 (1 self)
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Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this note, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system dynamics due to the fault are modeled as nonlinear functions of the state and input variables, while the time profile of the failure is assumed to be exponentially developing. An automated fault diagnosis architecture using nonlinear online approximators with an adaptation scheme is designed and analyzed. A simulation example of a simple nonlinear massspring system is used to illustrate the results. Keywords Nonlinear Estimator, Failure Detection, OnLine Approximators. I. Introduction Increased productivity requirements and stringent performance specifications lead to more demanding operating conditions of many modern engineering systems. Such conditions increase the possibility of sy...
HOL Light Tutorial (for version 2.20
, 2006
"... The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, ..."
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Cited by 9 (0 self)
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The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, aimed at teaching basic use of the system quickly by means of a graded set of examples. Some readers may find it easier to absorb; those who do not are referred after all to the standard manual. “Shouldn’t we read the instructions?”
Neural Network Based Robust Fault Diagnosis in Robotic Systems
 IEEE Transactions on Neural Networks
, 1997
"... Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have proposed fault diagnosis architectures for robotic manipulators using the modelbased analytical redundancy approach. One of the key issues in the design of such fault diagnosis scheme ..."
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Cited by 2 (0 self)
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Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have proposed fault diagnosis architectures for robotic manipulators using the modelbased analytical redundancy approach. One of the key issues in the design of such fault diagnosis schemes is the effect of modeling uncertainties on their performance. This paper investigates the problem of fault diagnosis in rigidlink robotic manipulators with modeling uncertainties. A learning architecture with sigmoidal neural networks is used to monitor the robotic system for offnominal behavior due to faults. The robustness and stability properties of the fault diagnosis scheme are rigorously established. Simulation examples are presented to illustrate the ability of the neural network based robust fault diagnosis scheme to detect and accommodate faults in a twolink robotic manipulator. 1 1 Introduction Robotic systems are integral components of many complex engineering system...
HOL Light Tutorial (for version 2.20). http://www.cl.cam.ac.uk/ jrh13/hollight/tutorial 220.pdf
"... The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, ..."
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Cited by 1 (0 self)
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The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, aimed at teaching basic use of the system quickly by means of a graded set of examples. Some readers may find it easier to absorb; those who do not are referred after all to the standard manual. “Shouldn’t we read the instructions?”
Monetary Trading: An Optimal Exchange System ∗
, 2002
"... We show that monetary trading is simple, selfenforcing, symmetric, and irreducible in a natural framework. Furthermore, we will show that the utility for each economic agent is at least as big under the monetary system as under any other simple, selfenforcing, symmetric, and irreducible trading sy ..."
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Cited by 1 (1 self)
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We show that monetary trading is simple, selfenforcing, symmetric, and irreducible in a natural framework. Furthermore, we will show that the utility for each economic agent is at least as big under the monetary system as under any other simple, selfenforcing, symmetric, and irreducible trading system of the same complexity. Thus, we rationalize the monetary nature of realworld trade as being an efficient way to achieve those properties. “The search for a means of exchange is almost as old as mankind. ” — The Economist, December 22nd 2001, page 87. 1
On Multipower Equations: Some Iterative Solutions and Applications
, 1996
"... A generalization of McFarland's iterative scheme [12] for solving quadratic equations in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this wider ..."
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Cited by 1 (1 self)
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A generalization of McFarland's iterative scheme [12] for solving quadratic equations in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this wider class of multipower equations. Existence and uniqueness of solutions are addressed within the framework of a uniformly contractive system. To illustrate the use of the new iterative scheme, we employ it when approximating solutions to a Hammerstein equation and a Chandrashekar equation. Due to the nature of the examples, we have found that wavelet/scaling function bases are a natural choice for the implementation of our iterative method. AMS(MOS) Subject Classification (1991 Revision): 47H17,46N20,47N20,65J15. Keywords and Phrases: Multipower equation, klinear equation, uniformly contractive system, Hammerstein equations, Chandrashekar equations, wavelets. 1 Introduction We seek the soluti...