Matthew Kennel - Academia.edu (original) (raw)
Papers by Matthew Kennel
Nucleation and Atmospheric Aerosols, 2003
arXiv (Cornell University), Dec 23, 1998
We construct a statistic and null test for examining the stationarity of time-series of discrete ... more We construct a statistic and null test for examining the stationarity of time-series of discrete symbols: whether two data streams appear to originate from the same underlying unknown dynamical system, and if any difference is statistically significant. Using principles and computational techniques from the theory of data compression, the method intelligently accounts for the substantial serial correlation and nonlinearity found in realistic dynamical data, problems which bedevil naive methods. Symbolic methods are computationally efficient and robust to noise. We demonstrate the method on a number of realistic experimental datasets.
arXiv (Cornell University), Dec 21, 1995
SAE Technical Paper Series, Mar 1, 1999
We describe a method for detecting and quantifying time irreversibility in experimental engine da... more We describe a method for detecting and quantifying time irreversibility in experimental engine data. We apply this method to experimental heat-release measurements from four sparkignited engines under leaning fueling conditions. We demonstrate that the observed behavior is inconsistent with a linear Gaussian random process and is more appropriately described as a noisy nonlinear dynamical process.
Given a real-world system with behavior which appears complex, it is difficult to separate the ef... more Given a real-world system with behavior which appears complex, it is difficult to separate the effects of chaos, high dimensionality and noise except in the rare cases where a high-quality model is available. Although great progress has been made in modeling such systems, there is little that is rigorous and most algorithms are slow. To gain understanding it seems necessary to idealize in some way, though not, of course, in the traditional way, which is by linearization. In this paper we simplify the problem by assuming that the system outputs symbols from a finite alphabet, rather than outputting a real number. With this simplification and a reasonable assumption which is the discrete analogue of the standard embedding theorem, it is possible to use known results in data compression theory to produce very fast reconstruction algorithms with guaranteed asymptotic optimality. The models that result can be used to simulate and to predict as well as to calculate all the usual dynamically interesting quantiti...
arXiv (Cornell University), Jul 31, 2007
The scope of this paper is twofold. First, to present to the researchers in combinatorics an inte... more The scope of this paper is twofold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits generated by piecewise monotone maps on one-dimensional intervals have forbidden order patterns, i.e., order patterns that do not occur in any orbit. The allowed patterns are then those patterns avoiding the so-called forbidden root patterns and their shifted patterns. The second scope is to study forbidden patterns in shift systems, which are universal models in information theory, dynamical systems and stochastic processes. Due to its simple structure, shift systems are accessible to a more detailed analysis and, at the same time, exhibit all important properties of low-dimensional chaotic dynamical systems (e.g., sensitivity to initial conditions, strong mixing and a dense set of periodic points), allowing to export the results to other dynamical systems via order-isomorphisms.
Physica D: Nonlinear Phenomena, Jul 1, 2007
Permutation entropy quantifies the diversity of possible orderings of that successively observed ... more Permutation entropy quantifies the diversity of possible orderings of that successively observed values a random or deterministic system can take, just as Shannon entropy quantifies the diversity of values themselves. When the observable or state variable has a natural order relation, making permutation entropy possible to compute, then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source. Herein, extending a previous result on metric entropy rate, we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics. This result is not limited to one-dimensional maps.
AIP Conference Proceedings, 2000
Given a real-world system with behavior which appears complex, it is difficult to separate the ef... more Given a real-world system with behavior which appears complex, it is difficult to separate the effects of chaos, high dimensionality and noise except in the rare cases where a high-quality model is available. Although great progress has been made in modeling such systems, there is little that is rigorous and most algorithms are slow. To gain understanding it seems necessary to idealize in some way, though not, of course, in the traditional way, which is by linearization. In this paper we simplify the problem by assuming that the system outputs symbols from a finite alphabet, rather than outputting a real number. With this simplification and a reasonable assumption which is the discrete analogue of the standard embedding theorem, it is possible to use known results in data compression theory to produce very fast reconstruction algorithms with guaranteed asymptotic optimality. The models that result can be used to simulate and to predict as well as to calculate all the usual dynamically interesting quantiti...
Thesis University of California San Diego 1995 Source Dissertation Abstracts International Volume 56 06 Section B Page 3238, 1995
Physica D: Nonlinear Phenomena, 2007
Permutation entropy quantifies the diversity of possible orderings of that successively observed ... more Permutation entropy quantifies the diversity of possible orderings of that successively observed values a random or deterministic system can take, just as Shannon entropy quantifies the diversity of values themselves. When the observable or state variable has a natural order relation, making permutation entropy possible to compute, then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source. Herein, extending a previous result on metric entropy rate, we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics. This result is not limited to one-dimensional maps.
AIP Conference Proceedings, 2002
A communication scheme based on the synchronization of two chaotic semiconductor lasers is experi... more A communication scheme based on the synchronization of two chaotic semiconductor lasers is experimentally tested. The Chaos in the single-mode semiconductor lasers is generated by means of an optoelectronic feedback. Synchronization of the chaos is achieved by coupling a fraction of the transmitter's output power into the driving current of the receiver. We present experimental results on the route to chaos and the synchronization of GHz chaotic signals. We then test a proposed communication scheme by successfully transmitting messages.
Springer Series in Synergetics, 2010
SAE Technical Paper Series, 1996
Physical Review E, 1998
We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustio... more We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model's simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. ͓S1063-651X͑98͒08903-X͔
International Journal of Modern Physics B, 1991
We review the idea of Lyapunov exponents for chaotic systems and discuss their evaluation from ob... more We review the idea of Lyapunov exponents for chaotic systems and discuss their evaluation from observed data alone. These exponents govern the growth or decrease of small perturbations to orbits of a dynamical system. They are critical to the predictability of models made from observations as well as known analytic models. The Lyapunov exponents are invariants of the dynamical system and are connected with the dimension of the system attractor and to the idea of information generation by the system dynamics. Lyapunov exponents are among the many ways we can classify observed nonlinear systems, and their appeal to physicists remains their clear interpretation in terms of system stability and predictability. We discuss the familiar global Lyapunov exponents which govern the evolution of perturbations for long times and local Lyapunov exponents which determine the predictability over a finite number of time steps.
![Research paper thumbnail of Publisher’s Note: Context-tree modeling of observed symbolic dynamics [Phys. Rev. E 66 , 056209 (2002)]](https://attachments.academia-assets.com/104495541/thumbnails/1.jpg)
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Nonlinear Dynamics and Statistics, 2001
One of the main themes of this book is the considerable progress that has been made in modeling d... more One of the main themes of this book is the considerable progress that has been made in modeling data from nonlinear systems that may be affected by noise. In this chapter, we describe a modeling method based on an idealization that gives fast algorithms with known properties based on rigorous results from data-compression theory. The idealization is that the system outputs symbols from a finite alphabet, rather than outputting a real number; we also make a reasonable assumption which is the discrete analogue of the standard embedding theorem. The models that result can be used to simulate and to estimate many of the usual dynamically interesting quantities such as topological entropy. They are also well-suited for a specific new application: testing the stationarity of time-series of discrete symbols, whether two data streams appear to originate from the same underlying unknown dynamical system.
Nucleation and Atmospheric Aerosols, 2003
arXiv (Cornell University), Dec 23, 1998
We construct a statistic and null test for examining the stationarity of time-series of discrete ... more We construct a statistic and null test for examining the stationarity of time-series of discrete symbols: whether two data streams appear to originate from the same underlying unknown dynamical system, and if any difference is statistically significant. Using principles and computational techniques from the theory of data compression, the method intelligently accounts for the substantial serial correlation and nonlinearity found in realistic dynamical data, problems which bedevil naive methods. Symbolic methods are computationally efficient and robust to noise. We demonstrate the method on a number of realistic experimental datasets.
arXiv (Cornell University), Dec 21, 1995
SAE Technical Paper Series, Mar 1, 1999
We describe a method for detecting and quantifying time irreversibility in experimental engine da... more We describe a method for detecting and quantifying time irreversibility in experimental engine data. We apply this method to experimental heat-release measurements from four sparkignited engines under leaning fueling conditions. We demonstrate that the observed behavior is inconsistent with a linear Gaussian random process and is more appropriately described as a noisy nonlinear dynamical process.
Given a real-world system with behavior which appears complex, it is difficult to separate the ef... more Given a real-world system with behavior which appears complex, it is difficult to separate the effects of chaos, high dimensionality and noise except in the rare cases where a high-quality model is available. Although great progress has been made in modeling such systems, there is little that is rigorous and most algorithms are slow. To gain understanding it seems necessary to idealize in some way, though not, of course, in the traditional way, which is by linearization. In this paper we simplify the problem by assuming that the system outputs symbols from a finite alphabet, rather than outputting a real number. With this simplification and a reasonable assumption which is the discrete analogue of the standard embedding theorem, it is possible to use known results in data compression theory to produce very fast reconstruction algorithms with guaranteed asymptotic optimality. The models that result can be used to simulate and to predict as well as to calculate all the usual dynamically interesting quantiti...
arXiv (Cornell University), Jul 31, 2007
The scope of this paper is twofold. First, to present to the researchers in combinatorics an inte... more The scope of this paper is twofold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits generated by piecewise monotone maps on one-dimensional intervals have forbidden order patterns, i.e., order patterns that do not occur in any orbit. The allowed patterns are then those patterns avoiding the so-called forbidden root patterns and their shifted patterns. The second scope is to study forbidden patterns in shift systems, which are universal models in information theory, dynamical systems and stochastic processes. Due to its simple structure, shift systems are accessible to a more detailed analysis and, at the same time, exhibit all important properties of low-dimensional chaotic dynamical systems (e.g., sensitivity to initial conditions, strong mixing and a dense set of periodic points), allowing to export the results to other dynamical systems via order-isomorphisms.
Physica D: Nonlinear Phenomena, Jul 1, 2007
Permutation entropy quantifies the diversity of possible orderings of that successively observed ... more Permutation entropy quantifies the diversity of possible orderings of that successively observed values a random or deterministic system can take, just as Shannon entropy quantifies the diversity of values themselves. When the observable or state variable has a natural order relation, making permutation entropy possible to compute, then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source. Herein, extending a previous result on metric entropy rate, we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics. This result is not limited to one-dimensional maps.
AIP Conference Proceedings, 2000
Given a real-world system with behavior which appears complex, it is difficult to separate the ef... more Given a real-world system with behavior which appears complex, it is difficult to separate the effects of chaos, high dimensionality and noise except in the rare cases where a high-quality model is available. Although great progress has been made in modeling such systems, there is little that is rigorous and most algorithms are slow. To gain understanding it seems necessary to idealize in some way, though not, of course, in the traditional way, which is by linearization. In this paper we simplify the problem by assuming that the system outputs symbols from a finite alphabet, rather than outputting a real number. With this simplification and a reasonable assumption which is the discrete analogue of the standard embedding theorem, it is possible to use known results in data compression theory to produce very fast reconstruction algorithms with guaranteed asymptotic optimality. The models that result can be used to simulate and to predict as well as to calculate all the usual dynamically interesting quantiti...
Thesis University of California San Diego 1995 Source Dissertation Abstracts International Volume 56 06 Section B Page 3238, 1995
Physica D: Nonlinear Phenomena, 2007
Permutation entropy quantifies the diversity of possible orderings of that successively observed ... more Permutation entropy quantifies the diversity of possible orderings of that successively observed values a random or deterministic system can take, just as Shannon entropy quantifies the diversity of values themselves. When the observable or state variable has a natural order relation, making permutation entropy possible to compute, then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source. Herein, extending a previous result on metric entropy rate, we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics. This result is not limited to one-dimensional maps.
AIP Conference Proceedings, 2002
A communication scheme based on the synchronization of two chaotic semiconductor lasers is experi... more A communication scheme based on the synchronization of two chaotic semiconductor lasers is experimentally tested. The Chaos in the single-mode semiconductor lasers is generated by means of an optoelectronic feedback. Synchronization of the chaos is achieved by coupling a fraction of the transmitter's output power into the driving current of the receiver. We present experimental results on the route to chaos and the synchronization of GHz chaotic signals. We then test a proposed communication scheme by successfully transmitting messages.
Springer Series in Synergetics, 2010
SAE Technical Paper Series, 1996
Physical Review E, 1998
We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustio... more We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model's simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. ͓S1063-651X͑98͒08903-X͔
International Journal of Modern Physics B, 1991
We review the idea of Lyapunov exponents for chaotic systems and discuss their evaluation from ob... more We review the idea of Lyapunov exponents for chaotic systems and discuss their evaluation from observed data alone. These exponents govern the growth or decrease of small perturbations to orbits of a dynamical system. They are critical to the predictability of models made from observations as well as known analytic models. The Lyapunov exponents are invariants of the dynamical system and are connected with the dimension of the system attractor and to the idea of information generation by the system dynamics. Lyapunov exponents are among the many ways we can classify observed nonlinear systems, and their appeal to physicists remains their clear interpretation in terms of system stability and predictability. We discuss the familiar global Lyapunov exponents which govern the evolution of perturbations for long times and local Lyapunov exponents which determine the predictability over a finite number of time steps.
Nonlinear Dynamics and Statistics, 2001
One of the main themes of this book is the considerable progress that has been made in modeling d... more One of the main themes of this book is the considerable progress that has been made in modeling data from nonlinear systems that may be affected by noise. In this chapter, we describe a modeling method based on an idealization that gives fast algorithms with known properties based on rigorous results from data-compression theory. The idealization is that the system outputs symbols from a finite alphabet, rather than outputting a real number; we also make a reasonable assumption which is the discrete analogue of the standard embedding theorem. The models that result can be used to simulate and to estimate many of the usual dynamically interesting quantities such as topological entropy. They are also well-suited for a specific new application: testing the stationarity of time-series of discrete symbols, whether two data streams appear to originate from the same underlying unknown dynamical system.