Papers by Peter Grassberger
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...
Journal of Statistical Mechanics: Theory and Experiment, 2005
We present high statistics simulations of weighted lattice bond animals and lattice trees on the ... more We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees. There is some evidence that the other is subdivided again into two parts with different universality classes. One of these (at the far side from collapsing trees) is bond driven and is represented by the Derrida-Herrmann model of animals having bonds only (no contacts). Between the critical percolation point and this bond driven collapse seems to be an intermediate regime, whose other end point is a multicritical point P * where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. This point P * seems to be attractive (in RG sense) from the side of the intermediate regime, so there are four universality classes on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime.
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, ...
Lettere Al Nuovo Cimento Series 2, 1974
Since the pion-pion scattering lengths are very interesting but extremely difficult to measure, t... more Since the pion-pion scattering lengths are very interesting but extremely difficult to measure, theoretical bounds for them are quite important. While absolute bounds (~) are still rather weak, more restrictive bounds on the 7:~ ~ S-wave scattering length a ~176 have been derived either by assuming the D-wave scattering length a ~176 to be negligible (2), or by using its experimental value (3). The virtue of such bounds may be questioned, as a ~176 in practice is calculated from its Froissart-Gribov representation and thus depends strongly on the experimental S-wave.
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
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
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
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 $X, Y,$ and $Z$ is equal to the sum of the MI between $X$ and $Y$, plus the MI between $Z$ and the combined object
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
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
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...
Physical Review E, 1997
The phase-turbulent (PT) regime for the one dimensional complex Ginzburg-Landau equation (CGLE) i... more The phase-turbulent (PT) regime for the one dimensional complex Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large systems and long integration times, using an efficient new integration scheme. Particular attention is paid to solutions with a non-zero phase gradient. For fixed control parameters, solutions with conserved average phase gradient ν exist only for |ν| less than some upper limit. The transition from phase to defect-turbulence happens when this limit becomes zero. A Lyapunov analysis shows that the system becomes less and less chaotic for increasing values of the phase gradient. For high values of the phase gradient a family of non-chaotic solutions of the CGLE is found. These solutions consist of spatially periodic or aperiodic waves travelling with constant velocity. They typically have incommensurate velocities for phase and amplitude propagation, showing thereby a novel type of quasiperiodic behavior. The main features of these travelling wave solutions can be explained through a modified Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the PT phase. The latter explains also the behavior of the maximal Lyapunov exponents of chaotic solutions.
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.
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.
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.
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...
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. ...
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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Papers by Peter Grassberger