The Origin of Non-chaotic Behavior in Identically Driven Systems

Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show that the origin of the non-chaotic behavior lies in the structural instability of the attractor of these systems which changes to a stable fixed point for strong enough drive. We see this to be true in all the systems studied in literature. Thus we affirm that in chaotic systems, synchronization can not occur only by addition of noise unless the noise destroys the strange attractor and the system is no longer chaotic.Comment: Figures could be obtained from [email protected]. The document below is a latex fil

Phase separation in coupled chaotic maps on fractal networks

The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the phases. The persistence saturates and phase domains freeze for all values of the coupling parameter as a consequence of the fractal structure of the networks, in contrast to the phase transition behavior previously observed in regular Euclidean lattices. Several discontinuities and other features found in the saturation persistence curve as a function of the coupling are explained in terms of changes of stability of local phase configurations on the fractals.Comment: (4 pages, 4 Figs, Submitted to PRE

Delay-induced Synchronization Phenomena in an Array of Globally Coupled Logistic Maps

We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized states in which the elements of the array evolve along a periodic orbit of the uncoupled map, while the spatial correlation along the array is such that an individual map sees all other maps in his present, current, state. For values of the nonlinear parameter such that the uncoupled maps are chaotic, time-delayed mutual coupling suppress the chaotic behavior by stabilizing a periodic orbit which is unstable for the uncoupled maps. The stability analysis of the synchronized state allows us to calculate the range of the coupling strength in which global synchronization can be obtained.Comment: 8 pages, 7 figures, changed content, added reference

Analytical results for coupled map lattices with long-range interactions

We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-\alpha}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements are piecewise linear maps, we get an algebraic expression for the Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the Lyapunov spectrum for a completely synchronized state is analytically obtained. The critical lines characterizing the synchronization transition are determined from the expression for the largest transversal Lyapunov exponent. In particular, it is shown that in the thermodynamical limit, such transition is only possible for sufficiently long-range interactions, namely, for $\alpha\le alpha_c<d$, where $d$ is the lattice dimension.Comment: 4 pages, 2 figures, corrections included. Phys. Rev. E 68, 045202(R) (2003); correction in pres

Effect of Chaotic Noise on Multistable Systems

In a recent letter [Phys.Rev.Lett. {\bf 30}, 3269 (1995), chao-dyn/9510011], we reported that a macroscopic chaotic determinism emerges in a multistable system: the unidirectional motion of a dissipative particle subject to an apparently symmetric chaotic noise occurs even if the particle is in a spatially symmetric potential. In this paper, we study the global dynamics of a dissipative particle by investigating the barrier crossing probability of the particle between two basins of the multistable potential. We derive analytically an expression of the barrier crossing probability of the particle subject to a chaotic noise generated by a general piecewise linear map. We also show that the obtained analytical barrier crossing probability is applicable to a chaotic noise generated not only by a piecewise linear map with a uniform invariant density but also by a non-piecewise linear map with non-uniform invariant density. We claim, from the viewpoint of the noise induced motion in a multistable system, that chaotic noise is a first realization of the effect of {\em dynamical asymmetry} of general noise which induces the symmetry breaking dynamics.Comment: 14 pages, 9 figures, to appear in Phys.Rev.

Topology and Computational Performance of Attractor Neural Networks

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most efficient for storage and retrieval of patterns by the entire network. However, in the scale-free case retrieval errors are not distributed uniformly: the portion of a pattern encoded by the subset of highly connected nodes is more robust and efficiently recognized than the rest of the pattern. The scale-free network thus achieves a very strong partial recognition. Implications for brain function and social dynamics are suggestive.Comment: 2 figures included. Submitted to Phys. Rev. Letter

Improving Genetic Prediction by Leveraging Genetic Correlations Among Human Diseases and Traits

Genomic prediction has the potential to contribute to precision medicine. However, to date, the utility of such predictors is limited due to low accuracy for most traits. Here theory and simulation study are used to demonstrate that widespread pleiotropy among phenotypes can be utilised to improve genomic risk prediction. We show how a genetic predictor can be created as a weighted index that combines published genome-wide association study (GWAS) summary statistics across many different traits. We apply this framework to predict risk of schizophrenia and bipolar disorder in the Psychiatric Genomics consortium data, finding substantial heterogeneity in prediction accuracy increases across cohorts. For six additional phenotypes in the UK Biobank data, we find increases in prediction accuracy ranging from 0.7 for height to 47 for type 2 diabetes, when using a multi-trait predictor that combines published summary statistics from multiple traits, as compared to a predictor based only on one trait. © 2018 The Author(s)

Genome-wide association study identifies 30 Loci Associated with Bipolar Disorder

This paper is dedicated to the memory of Psychiatric Genomics Consortium (PGC) founding member and Bipolar disorder working group co-chair Pamela Sklar. We thank the participants who donated their time, experiences and DNA to this research, and to the clinical and scientific teams that worked with them. We are deeply indebted to the investigators who comprise the PGC. The views expressed are those of the authors and not necessarily those of any funding or regulatory body. Analyses were carried out on the NL Genetic Cluster Computer (http://www.geneticcluster.org ) hosted by SURFsara, and the Mount Sinai high performance computing cluster (http://hpc.mssm.edu).Bipolar disorder is a highly heritable psychiatric disorder. We performed a genome-wide association study including 20,352 cases and 31,358 controls of European descent, with follow-up analysis of 822 variants with P<1x10-4 in an additional 9,412 cases and 137,760 controls. Eight of the 19 variants that were genome-wide significant (GWS, p < 5x10-8) in the discovery GWAS were not GWS in the combined analysis, consistent with small effect sizes and limited power but also with genetic heterogeneity. In the combined analysis 30 loci were GWS including 20 novel loci. The significant loci contain genes encoding ion channels, neurotransmitter transporters and synaptic components. Pathway analysis revealed nine significantly enriched gene-sets including regulation of insulin secretion and endocannabinoid signaling. BDI is strongly genetically correlated with schizophrenia, driven by psychosis, whereas BDII is more strongly correlated with major depressive disorder. These findings address key clinical questions and provide potential new biological mechanisms for BD.This work was funded in part by the Brain and Behavior Research Foundation, Stanley Medical Research Institute, University of Michigan, Pritzker Neuropsychiatric Disorders Research Fund L.L.C., Marriot Foundation and the Mayo Clinic Center for Individualized Medicine, the NIMH Intramural Research Program; Canadian Institutes of Health Research; the UK Maudsley NHS Foundation Trust, NIHR, NRS, MRC, Wellcome Trust; European Research Council; German Ministry for Education and Research, German Research Foundation IZKF of Münster, Deutsche Forschungsgemeinschaft, ImmunoSensation, the Dr. Lisa-Oehler Foundation, University of Bonn; the Swiss National Science Foundation; French Foundation FondaMental and ANR; Spanish Ministerio de Economía, CIBERSAM, Industria y Competitividad, European Regional Development Fund (ERDF), Generalitat de Catalunya, EU Horizon 2020 Research and Innovation Programme; BBMRI-NL; South-East Norway Regional Health Authority and Mrs. Throne-Holst; Swedish Research Council, Stockholm County Council, Söderström Foundation; Lundbeck Foundation, Aarhus University; Australia NHMRC, NSW Ministry of Health, Janette M O'Neil and Betty C Lynch

Dynamic transitions in Domany-Kinzel cellular automata on small-world network

We study Domany-Kinzel cellular automata on small-world network. Every link on a one dimensional chain is rewired and coupled with any node with probability p. We observe that, the introduction of long-range interactions does not remove the critical character of the model and the system still exhibits a well-defined phase transition to absorbing state. In case of directed percolation (DP), we observe a very anomalous behavior as a function of size. The system shows long lived metastable states and a jump in order parameter. This jump vanishes in thermodynamic limit and we recover second-order transition. The critical exponents are not equal to the mean-field values even for large p. However, for compact directed percolation(CDP), the critical exponents reach their mean-field values even for small p