Coarse-graining of cellular automata, emergence, and the predictability of complex systems

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details. Several CA that can be coarse-grained by this construction are known to be universal Turing machines; they can emulate any CA or other computing devices and are therefore undecidable. We thus show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description. The renormalization group flows that we construct induce a hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method. Finally we argue that the large scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of the large scale update rule, and moreover exhibits a novel scaling law. We show that because of this large-scale simplicity, the probability of finding a coarse-grained description of CA approaches unity as one goes to increasingly coarser scales. We interpret this large scale simplicity as a pattern formation mechanism in which large scale patterns are forced upon the system by the simplicity of the rules that govern the large scale dynamics.Comment: 18 pages, 9 figure

Deposition of microparticles by neutrophils onto inflamed epithelium: a new mechanism to disrupt epithelial intercellular adhesions and promote transepithelial migration

Neutrophil [polymorphonuclear leukocyte (PMN)] transepithelial migration (TEM) is a hallmark of inflammatory mucosal disorders. PMN TEM is associated with epithelial injury; however, mechanisms involved in this process are not well defined. The current work describes a new mechanism whereby deposition of PMN membranederived microparticles (PMNâ MPs) onto intestinal epithelial cells (IECs) during TEM leads to loss of epithelial cadherins, thus promoting epithelial injury and increased PMN recruitment. PMNâ MPs secreted by activated PMNs during TEM displayed a high level of enzymatically activematrixmetalloproteinase 9 (MMPâ 9), and were capable of mediating potent effects on IEC integrity. Isolated PMNâ MPs efficiently bound to IEC monolayers and induced cleavage of desmogleinâ 2 (DSGâ 2) but not Eâ cadherin, leading to disruption of IEC intercellular adhesions. Furthermore, PMNâ MP binding to intestinal epithelium in vitro in transwell assays and in vivo in ligated intestinal loop preparations facilitated increases in PMN TEM. These effects were MMPâ 9 dependent and were reversed in the presence of specific pharmacological inhibitors. Finally, we demonstrated that IEC Dsgâ 2 serves as a barrier for migrating PMNs, and its removal by PMNâ MPâ associated MMPâ 9 facilitates PMNtrafficking across epithelial layers. Our findings thus implicate PMNâ MPs in PMNâ mediated inflammation and epithelial damage, as observed in inflammatory disorders ofmucosal surfaces.â Butinâ Israeli, V., Houser, M.C., Feng, M., Thorp, E. B., Nusrat, A., Parkos, C. A, Sumagin, R. Deposition of microparticles by neutrophils onto inflamed epithelium: anewmechanism to disrupt epithelial intercellular adhesions and promote transepithelialmigration. FASEB J. 30, 4007â 4020 (2016). www.fasebj.orgPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154234/1/fsb2fasebj30120734r.pd

Non-invertible transformations and spatiotemporal randomness

We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems can generate random dynamics. For instance, the chaotic Chua's circuit coupled to a circuit with a non-invertible I-V characteristic can generate unpredictable dynamics. In general, a nonperiodic time-series with truncated exponential behavior can be converted into unpredictable dynamics using non-invertible transformations. Using a new theoretical framework for chaos and randomness, we investigate some classes of coupled map lattices. We show that, in some cases, these systems can produce completely unpredictable dynamics. In a similar fashion, we explain why some wellknown spatiotemporal systems have been found to produce very complex dynamics in numerical simulations. We discuss real physical systems that can generate random dynamics.Comment: Accepted in International Journal of Bifurcation and Chao

Slow fluctuations in enhanced Raman scattering and surface roughness relaxation

We propose an explanation for the recently measured slow fluctuations and ``blinking'' in the surface enhanced Raman scattering (SERS) spectrum of single molecules adsorbed on a silver colloidal particle. We suggest that these fluctuations may be related to the dynamic relaxation of the surface roughness on the nanometer scale and show that there are two classes of roughness with qualitatively different dynamics. The predictions agree with measurements of surface roughness relaxation. Using a theoretical model for the kinetics of surface roughness relaxation in the presence of charges and optical electrical fields, we predict that the high-frequency electromagnetic field increases both the effective surface tension and the surface diffusion constant and thus accelerates the surface smoothing kinetics and time scale of the Raman fluctuations in manner that is linear with the laser power intensity, while the addition of salt retards the surface relaxation kinetics and increases the time scale of the fluctuations. These predictions are in qualitative agreement with the Raman experiments

Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Cauchy-perturbative matching and outer boundary conditions: computational studies

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.Comment: 20 pages, RevTe

Local algorithms : Self-stabilization on speed

Non peer reviewe