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Papers by Peter Grassberger

Research paper thumbnail of Percolation transitions in the survival of interdependent agents on multiplex networks, catastrophic cascades, and solid-on-solid surface growth

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We present an efficient algorithm for simulating percolation transitions of mutually supporting v... more We present an efficient algorithm for simulating percolation transitions of mutually supporting viable clusters on multiplex networks (also known as "catastrophic cascades on interdependent networks"). This algorithm maps the problem onto a solid-on-solid-type model. We use this algorithm to study interdependent agents on duplex Erdös-Rényi (ER) networks and on lattices with dimensions 2, 3, 4, and 5. We obtain surprising results in all these cases, and we correct statements in the literature for ER networks and for two-dimensional lattices. In particular, we find that d=4 is the upper critical dimension and that the percolation transition is continuous for d≤4 but-at least for d≠3-not in the universality class of ordinary percolation. For ER networks we verify that the cluster statistics is exactly described by mean-field theory but find evidence that the cascade process is not. For d=5 we find a first-order transition as for ER networks, but we find also that small clust...

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Research paper thumbnail of Collapsing lattice animals and lattice trees in two dimensions

Journal of Statistical Mechanics: Theory and Experiment, 2005

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Research paper thumbnail of Are there really phase transitions in 1-d heat conduction models?

Arxiv preprint cond-mat/0306173, 2003

Lei Yang and Peter Grassberger John-von-Neumann Institute for Computing, Forschungszentrum Jülich... more Lei Yang and Peter Grassberger John-von-Neumann Institute for Computing, Forschungszentrum Jülich, D-52425 Jülich, Germany (Dated: February 2, 2008) Recently, it has been claimed (OV Gendelman and AV Savin, Phys. Rev. Lett. 84, 2381 (2000); AVSavin and OVGendelman, ...

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Research paper thumbnail of Bounds on the ππS-wave scattering lengths

Lettere Al Nuovo Cimento Series 2, 1974

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Research paper thumbnail of Phase diagram of semi-stiff homopolymers

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Research paper thumbnail of Value of nonlinear time series analysis of the EEG in neocortical epilepsies

Advances in neurology

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Research paper thumbnail of SOC in a population model with global control

We study a plant population model introduced recently by J. Wallinga [OIKOS {\bf 74}, 377 (1995)]... more We study a plant population model introduced recently by J. Wallinga [OIKOS {\bf 74}, 377 (1995)]. It is similar to the contact process (`simple epidemic', `directed percolation'), but instead of using an infection or recovery rate as control parameter, the population size is controlled directly and globally by removing excess plants. We show that the model is very closely related

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Research paper thumbnail of Using Networks to Find Signatures of Causality in Seismicity

Networks to infer causal structure from spatiotemporal data are constructed making minimal a prio... more Networks to infer causal structure from spatiotemporal data are constructed making minimal a priori assumptions about the underlying dynamics. The elementary concept of recurrence for a point process in time is generalized to recurrent events in space and time. An event is defined to be a recurrence of any previous event if it is closer to it in space than

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Research paper thumbnail of Blasting and Zipping: Sequence Alignment and Mutual Information

Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used too... more Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used tools in computational bioscience. While the accomplishments of sequence alignment algorithms are undeniable the fact remains that these algorithms are based upon heuristic scoring schemes. Therefore, these algorithms do not provide model independent and objective measures for how similar two (or more) sequences

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Research paper thumbnail of Hierarchical Clustering Using Mutual Information

Computing Research Repository, 2003

We present a method for hierarchical clustering of data called {\it mutual information clustering... more We present a method for hierarchical clustering of data called {\it mutual information clustering} (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects X,Y,X, Y,X,Y, and ZZZ is equal to the sum of the MI between XXX and YYY, plus the MI between ZZZ and the combined object

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Research paper thumbnail of Hierarchical Clustering Based on Mutual Information

Computing Research Repository, 2003

Motivation: Clustering is a frequently used con- cept in variety of bioinformatical applications.... more Motivation: Clustering is a frequently used con- cept in variety of bioinformatical applications. We present a new method for hierarchical clustering of data called mutual information clustering (MIC) al- gorithm. It uses mutual information (MI) as a sim- ilarity measure and exploits its grouping property: The MI between three objects X,Y, and Z is equal to the sum of the

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Research paper thumbnail of Reliability of ICA Estimates with Mutual Information

Lecture Notes in Computer Science, 2004

Obtaining the most independent components from a mixture (under a chosen model) is only the first... more Obtaining the most independent components from a mixture (under a chosen model) is only the first part of an ICA analysis. After that, it is necessary to measure the actual dependency between the components and the reliability of the decomposition. We have to identify one- and multidimensional components (i.e., clusters of mutually dependent components) or channels which are too close

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Research paper thumbnail of Sequence alignment and mutual information

Background: Alignment of biological sequences such as DNA, RNA or proteins is one of the most wid... more Background: Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used tools in computational bioscience. All existing alignment algorithms rely on heuristic scoring schemes based on biological expertise. Therefore, these algorithms do not provide model independent and objective measures for how similar two (or more) sequences actually are. Although information theory provides such a similarity measure -- the mutual information (MI) -- previous attempts to connect sequence alignment and information theory have not produced realistic estimates for the MI from a given alignment. Results: Here we describe a simple and flexible approach to get robust estimates of MI from {\it global} alignments. For mammalian mitochondrial DNA, our approach gives pairwise MI estimates for commonly used global alignment algorithms that are strikingly close to estimates obtained by an entirely unrelated approach -- concatenating and zipping the sequences. Conclusions: Th...

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Research paper thumbnail of Studies of phase turbulence in the one-dimensional complex Ginzburg-Landau equation

Physical Review E, 1997

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Research paper thumbnail of Characterization of experimental (noisy) strange attractors

Physical Review A, 1984

In experiments involving deterministic chaotic signals, contamination by random noise is unavoida... more In experiments involving deterministic chaotic signals, contamination by random noise is unavoidable. A practical method that disentangles the deterministic chaos from the random part is discussed. The method yields a characterization of the strange attractors together with an estimate of the size of random noise.

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Research paper thumbnail of Event synchronization: a simple and fast method to measure synchronicity and time delay patterns

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

We propose a simple method to measure synchronization and time-delay patterns between signals. It... more We propose a simple method to measure synchronization and time-delay patterns between signals. It is based on the relative timings of events in the time series, defined, e.g., as local maxima. The degree of synchronization is obtained from the number of quasisimultaneous appearances of events, and the delay is calculated from the precedence of events in one signal with respect to the other. Moreover, we can easily visualize the time evolution of the delay and synchronization level with an excellent resolution. We apply the algorithm to short rat electroencephalogram (EEG) signals, some of them containing spikes. We also apply it to an intracranial human EEG recording containing an epileptic seizure, and we propose that the method might be useful for the detection of epileptic foci. It can be easily extended to other types of data and it is very simple and fast, thus being suitable for on-line implementations.

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Research paper thumbnail of Kulback-Leibler and renormalized entropies: applications to electroencephalograms of epilepsy patients

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

Recently, "renormalized entropy" was proposed as a novel measure of relative entropy [P... more Recently, "renormalized entropy" was proposed as a novel measure of relative entropy [P. Saparin et al., Chaos, Solitons and Fractals 4, 1907 (1994)] and applied to several physiological time sequences, including electroencephalograms (EEGs) of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (KL) relative entropy, and it gives similar numerical results to the standard KL entropy. The latter better distinguishes frequency contents of, e.g., seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing, we also make some critical remarks about the implementation of these methods.

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Research paper thumbnail of Learning driver-response relationships from synchronization patterns

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

We test recent claims that causal (driver-response) relationships can be deduced from interdepend... more We test recent claims that causal (driver-response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures that should give results similar to cross predictabilities used by previous authors. The systems that we study are asymmetrically coupled simple models (Lorenz, Roessler, and Hénon models), the couplings being such that they lead to generalized synchronization. If the data were perfect (noise-free, infinitely long), we should be able to detect, at least in some cases, which of the coupled systems is the driver and which the response. This might no longer be true if the time series has finite length. Instead, estimated interdependencies depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them, and causal relationships are more difficult to detect. We also show that slightly different variants of the interdepende...

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Research paper thumbnail of Efficient large-scale simulations of a uniformly driven system

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1994

... It was found that the scaling function 0(x) is monotonic and that D > 2 for all values of ... more ... It was found that the scaling function 0(x) is monotonic and that D > 2 for all values of a ... sizes are large enough to refute also another claim of [21], namely that P(s) shows ordinary finite-size scal-ing. ... While the distribution of the stress difference between neighbors (shown in Fig. ...

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Research paper thumbnail of Four-pomeron couplings in cut reggeon field theory

ABSTRACT Four-pomeron cutting rules are studied in cut reggeon field theory (CRFT). Without any m... more ABSTRACT Four-pomeron cutting rules are studied in cut reggeon field theory (CRFT). Without any microscopic model, CRFT allows for three different 4-pomeron couplings. Demanding that CRFT is interpretable as a Markov process, only one of these couplings remains. The cutting rules for the 4-pomeron vertex thus become unique, disagreeing with those found in weak coupling phi3 theory.

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Research paper thumbnail of Percolation transitions in the survival of interdependent agents on multiplex networks, catastrophic cascades, and solid-on-solid surface growth

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We present an efficient algorithm for simulating percolation transitions of mutually supporting v... more We present an efficient algorithm for simulating percolation transitions of mutually supporting viable clusters on multiplex networks (also known as "catastrophic cascades on interdependent networks"). This algorithm maps the problem onto a solid-on-solid-type model. We use this algorithm to study interdependent agents on duplex Erdös-Rényi (ER) networks and on lattices with dimensions 2, 3, 4, and 5. We obtain surprising results in all these cases, and we correct statements in the literature for ER networks and for two-dimensional lattices. In particular, we find that d=4 is the upper critical dimension and that the percolation transition is continuous for d≤4 but-at least for d≠3-not in the universality class of ordinary percolation. For ER networks we verify that the cluster statistics is exactly described by mean-field theory but find evidence that the cascade process is not. For d=5 we find a first-order transition as for ER networks, but we find also that small clust...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Collapsing lattice animals and lattice trees in two dimensions

Journal of Statistical Mechanics: Theory and Experiment, 2005

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Are there really phase transitions in 1-d heat conduction models?

Arxiv preprint cond-mat/0306173, 2003

Lei Yang and Peter Grassberger John-von-Neumann Institute for Computing, Forschungszentrum Jülich... more Lei Yang and Peter Grassberger John-von-Neumann Institute for Computing, Forschungszentrum Jülich, D-52425 Jülich, Germany (Dated: February 2, 2008) Recently, it has been claimed (OV Gendelman and AV Savin, Phys. Rev. Lett. 84, 2381 (2000); AVSavin and OVGendelman, ...

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Research paper thumbnail of Bounds on the ππS-wave scattering lengths

Lettere Al Nuovo Cimento Series 2, 1974

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Phase diagram of semi-stiff homopolymers

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Value of nonlinear time series analysis of the EEG in neocortical epilepsies

Advances in neurology

Bookmarks Related papers MentionsView impact

Research paper thumbnail of SOC in a population model with global control

We study a plant population model introduced recently by J. Wallinga [OIKOS {\bf 74}, 377 (1995)]... more We study a plant population model introduced recently by J. Wallinga [OIKOS {\bf 74}, 377 (1995)]. It is similar to the contact process (`simple epidemic', `directed percolation'), but instead of using an infection or recovery rate as control parameter, the population size is controlled directly and globally by removing excess plants. We show that the model is very closely related

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Using Networks to Find Signatures of Causality in Seismicity

Networks to infer causal structure from spatiotemporal data are constructed making minimal a prio... more Networks to infer causal structure from spatiotemporal data are constructed making minimal a priori assumptions about the underlying dynamics. The elementary concept of recurrence for a point process in time is generalized to recurrent events in space and time. An event is defined to be a recurrence of any previous event if it is closer to it in space than

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Blasting and Zipping: Sequence Alignment and Mutual Information

Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used too... more Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used tools in computational bioscience. While the accomplishments of sequence alignment algorithms are undeniable the fact remains that these algorithms are based upon heuristic scoring schemes. Therefore, these algorithms do not provide model independent and objective measures for how similar two (or more) sequences

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Hierarchical Clustering Using Mutual Information

Computing Research Repository, 2003

We present a method for hierarchical clustering of data called {\it mutual information clustering... more We present a method for hierarchical clustering of data called {\it mutual information clustering} (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects X,Y,X, Y,X,Y, and ZZZ is equal to the sum of the MI between XXX and YYY, plus the MI between ZZZ and the combined object

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Hierarchical Clustering Based on Mutual Information

Computing Research Repository, 2003

Motivation: Clustering is a frequently used con- cept in variety of bioinformatical applications.... more Motivation: Clustering is a frequently used con- cept in variety of bioinformatical applications. We present a new method for hierarchical clustering of data called mutual information clustering (MIC) al- gorithm. It uses mutual information (MI) as a sim- ilarity measure and exploits its grouping property: The MI between three objects X,Y, and Z is equal to the sum of the

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Reliability of ICA Estimates with Mutual Information

Lecture Notes in Computer Science, 2004

Obtaining the most independent components from a mixture (under a chosen model) is only the first... more Obtaining the most independent components from a mixture (under a chosen model) is only the first part of an ICA analysis. After that, it is necessary to measure the actual dependency between the components and the reliability of the decomposition. We have to identify one- and multidimensional components (i.e., clusters of mutually dependent components) or channels which are too close

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Sequence alignment and mutual information

Background: Alignment of biological sequences such as DNA, RNA or proteins is one of the most wid... more Background: Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used tools in computational bioscience. All existing alignment algorithms rely on heuristic scoring schemes based on biological expertise. Therefore, these algorithms do not provide model independent and objective measures for how similar two (or more) sequences actually are. Although information theory provides such a similarity measure -- the mutual information (MI) -- previous attempts to connect sequence alignment and information theory have not produced realistic estimates for the MI from a given alignment. Results: Here we describe a simple and flexible approach to get robust estimates of MI from {\it global} alignments. For mammalian mitochondrial DNA, our approach gives pairwise MI estimates for commonly used global alignment algorithms that are strikingly close to estimates obtained by an entirely unrelated approach -- concatenating and zipping the sequences. Conclusions: Th...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Studies of phase turbulence in the one-dimensional complex Ginzburg-Landau equation

Physical Review E, 1997

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Characterization of experimental (noisy) strange attractors

Physical Review A, 1984

In experiments involving deterministic chaotic signals, contamination by random noise is unavoida... more In experiments involving deterministic chaotic signals, contamination by random noise is unavoidable. A practical method that disentangles the deterministic chaos from the random part is discussed. The method yields a characterization of the strange attractors together with an estimate of the size of random noise.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Event synchronization: a simple and fast method to measure synchronicity and time delay patterns

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

We propose a simple method to measure synchronization and time-delay patterns between signals. It... more We propose a simple method to measure synchronization and time-delay patterns between signals. It is based on the relative timings of events in the time series, defined, e.g., as local maxima. The degree of synchronization is obtained from the number of quasisimultaneous appearances of events, and the delay is calculated from the precedence of events in one signal with respect to the other. Moreover, we can easily visualize the time evolution of the delay and synchronization level with an excellent resolution. We apply the algorithm to short rat electroencephalogram (EEG) signals, some of them containing spikes. We also apply it to an intracranial human EEG recording containing an epileptic seizure, and we propose that the method might be useful for the detection of epileptic foci. It can be easily extended to other types of data and it is very simple and fast, thus being suitable for on-line implementations.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Kulback-Leibler and renormalized entropies: applications to electroencephalograms of epilepsy patients

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

Recently, "renormalized entropy" was proposed as a novel measure of relative entropy [P... more Recently, "renormalized entropy" was proposed as a novel measure of relative entropy [P. Saparin et al., Chaos, Solitons and Fractals 4, 1907 (1994)] and applied to several physiological time sequences, including electroencephalograms (EEGs) of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (KL) relative entropy, and it gives similar numerical results to the standard KL entropy. The latter better distinguishes frequency contents of, e.g., seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing, we also make some critical remarks about the implementation of these methods.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Learning driver-response relationships from synchronization patterns

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

We test recent claims that causal (driver-response) relationships can be deduced from interdepend... more We test recent claims that causal (driver-response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures that should give results similar to cross predictabilities used by previous authors. The systems that we study are asymmetrically coupled simple models (Lorenz, Roessler, and Hénon models), the couplings being such that they lead to generalized synchronization. If the data were perfect (noise-free, infinitely long), we should be able to detect, at least in some cases, which of the coupled systems is the driver and which the response. This might no longer be true if the time series has finite length. Instead, estimated interdependencies depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them, and causal relationships are more difficult to detect. We also show that slightly different variants of the interdepende...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Efficient large-scale simulations of a uniformly driven system

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1994

... It was found that the scaling function 0(x) is monotonic and that D > 2 for all values of ... more ... It was found that the scaling function 0(x) is monotonic and that D > 2 for all values of a ... sizes are large enough to refute also another claim of [21], namely that P(s) shows ordinary finite-size scal-ing. ... While the distribution of the stress difference between neighbors (shown in Fig. ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Four-pomeron couplings in cut reggeon field theory

ABSTRACT Four-pomeron cutting rules are studied in cut reggeon field theory (CRFT). Without any m... more ABSTRACT Four-pomeron cutting rules are studied in cut reggeon field theory (CRFT). Without any microscopic model, CRFT allows for three different 4-pomeron couplings. Demanding that CRFT is interpretable as a Markov process, only one of these couplings remains. The cutting rules for the 4-pomeron vertex thus become unique, disagreeing with those found in weak coupling phi3 theory.

Bookmarks Related papers MentionsView impact