scholarly journals Emergence of disconnected clusters in heterogeneous complex systems

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
István A. Kovács ◽  
Róbert Juhász
Keyword(s):  
Complex Systems ◽  
Percolation Theory ◽  
Contact Process ◽  
Heterogeneous Systems ◽  
Critical Dynamics ◽  
Magnetic Domains ◽  
3 Dimensional ◽  
Quantum Ising Model ◽  
Highly Correlated ◽  
Exact Renormalization Group

AbstractPercolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated sites in complex systems can be inherently disconnected. This finding indicates a counter-intuitive organization of dynamical correlations, where functional similarity decouples from physical connectivity. We illustrate the phenomenon on the example of the disordered contact process (DCP) of infection spreading in heterogeneous systems. We apply numerical simulations and an asymptotically exact renormalization group technique (SDRG) in 1, 2 and 3 dimensional systems as well as in two-dimensional lattices with long-ranged interactions. We conclude that the critical dynamics is well captured by mostly one, highly correlated, but spatially disconnected cluster. Our findings indicate that at criticality the relevant, simultaneously infected sites typically do not directly interact with each other. Due to the similarity of the SDRG equations, our results hold also for the critical behavior of the disordered quantum Ising model, leading to quantum correlated, yet spatially disconnected, magnetic domains.

scholarly journals Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1202
Author(s):  
Luca Spolladore ◽  
Michela Gelfusa ◽  
Riccardo Rossi ◽  
Andrea Murari
Keyword(s):  
Model Selection ◽  
Complex Systems ◽  
Selection Criteria ◽  
A Priori ◽  
Synthetic Data ◽  
Information Criterion ◽  
Model Selection Criteria ◽  
Dependent Variables ◽  
Chi Squared ◽  
Highly Correlated

Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better understood. In the derivation of these indicators, it was assumed that the model’s dependent variables have already been properly identified and that the entries are not affected by significant uncertainties. These are issues that can become quite serious when investigating complex systems, especially when variables are highly correlated and the measurement uncertainties associated with them are not negligible. More sophisticated versions of this criteria, capable of better detecting spurious relations between variables when non-negligible noise is present, are proposed in this paper. Their derivation is obtained starting from a Bayesian statistics framework and adding an a priori Chi-squared probability distribution function of the model, dependent on a specifically defined information theoretic quantity that takes into account the redundancy between the dependent variables. The performances of the proposed versions of these criteria are assessed through a series of systematic simulations, using synthetic data for various classes of functions and noise levels. The results show that the upgraded formulation of the criteria clearly outperforms the traditional ones in most of the cases reported.

Beyond empiricism: Quantitative models for the permeability of heterogeneous magmas

2020 ◽  
Author(s):  
Jérémie Vasseur ◽  
Fabian Wadsworth ◽  
Donald Dingwell
Keyword(s):  
Percolation Theory ◽  
Volcanic Rocks ◽  
Large Database ◽  
3 Dimensional ◽  
Wide Range ◽  
Universality Classes ◽  
Flow Through ◽  
Overlapping Spheres ◽  
Fitting Parameters ◽  
Good Agreement

<p>Measurements abound for the permeability of volcanic rocks, high temperature magmas, synthetic analogues for magma and rock, and 3-dimensional domains of porous media simulated numerically. Despite a wealth of data, the dominant approach to parameterisation has been empirical, and scarcely goes beyond the power-law models for percolating systems. Here we propose a suite of methods to bring the data for these complex systems in line with theoretically grounded percolation models. To do this we create numerical samples using variations on theme of overlapping spheres filling volumes. In order to create a wide range of possible geometries, we can either define the spheres as the pore phase, or the inter-sphere volume as the pore phase, such that one option is the inverse of the other. In either case, we simulate fluid flow through the pore phase until steady state, to determine the Darcian and inertial permeability tensors. We compare these results with derived, fully theoretical percolation theory and find good agreement without fitting parameters. In order to render this useful for understanding permeability in volcanic scenarios, we compare these validated models to a large database of compiled published permeability data. This approach allows us to group the permeability of magmas into three universality classes, which each have just one dimensionless solution: (1) initially granular magmas, such as variably welded ignimbrites or tuffisites, and (2) bubbly magmas, such as pumice.</p>

scholarly journals Critical dynamics of the contact process with quenched disorder

1996 ◽  
Vol 54 (4) ◽  
pp. R3090-R3093 ◽  
Author(s):  
Adriana G. Moreira ◽  
Ronald Dickman
Keyword(s):  
Contact Process ◽  
Quenched Disorder ◽  
Critical Dynamics

Placental Morphologic Features and Chorionic Surface Vasculature at Term Are Highly Correlated With 3-Dimensional Sonographic Measurements at 11 to 14 Weeks

2011 ◽  
Vol 30 (9) ◽  
pp. 1171-1178 ◽  
Author(s):  
Nadav Schwartz ◽  
Danielle Mandel ◽  
Oleksandr Shlakhter ◽  
Jaclyn Coletta ◽  
Cara Pessel ◽  
...  
Keyword(s):  
3 Dimensional ◽  
Highly Correlated

Right Ventricular Volumes Measured by 3-Dimensional Echocardiography Are Highly Correlated to Cardiac MRI

2006 ◽  
Vol 12 (6) ◽  
pp. S27-S28
Author(s):  
Jigar D. Patel ◽  
Michael Smith ◽  
Robert Russo ◽  
David Rubenson ◽  
James T. Heywood
Keyword(s):  
Right Ventricular ◽  
Cardiac Mri ◽  
Ventricular Volumes ◽  
3 Dimensional ◽  
Dimensional Echocardiography ◽  
Highly Correlated

scholarly journals Suv39h-catalysed H3K9me3 is critical for euchromatic genome organisation and the maintenance of gene transcription

2020 ◽  
Author(s):  
Christine R. Keenan ◽  
Hannah D. Coughlan ◽  
Nadia Iannarella ◽  
Timothy M. Johanson ◽  
Wing Fuk Chan ◽  
...  
Keyword(s):  
Gene Transcription ◽  
Genome Organization ◽  
Dimensional Space ◽  
Nuclear Periphery ◽  
Nuclear Lamina ◽  
Genome Organisation ◽  
Protein Coding ◽  
3 Dimensional ◽  
Protein Coding Genes ◽  
Highly Correlated

SummaryH3K9me3-dependent heterochromatin is critical for the silencing of repeat-rich pericentromeric regions and also has key roles in repressing lineage-inappropriate protein-coding genes in differentiation and development. Here, we investigate the molecular consequences of heterochromatin loss in cells deficient in both Suv39h1 and Suv39h2 (Suv39DKO), the major mammalian histone methyltransferase enzymes that catalyse heterochromatic H3K9me3 deposition. Unexpectedly, we reveal a predominant repression of protein-coding genes in Suv39DKO cells, with these differentially expressed genes principally in euchromatic (DNaseI-accessible, H3K27ac-marked) rather than heterochromatic (H3K9me3-marked) regions. Examination of the 3D nucleome reveals that transcriptomic dysregulation occurs in euchromatic regions close to the nuclear periphery in 3-dimensional space. Moreover, this transcriptomic dysregulation is highly correlated with altered 3-dimensional genome organization in Suv39DKO cells. Together, our results suggest that the nuclear lamina-tethering of Suv39-dependent H3K9me3 domains provides an essential scaffold to support euchromatic genome organisation and the maintenance of gene transcription for healthy cellular function.

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