On computational irreducibility and the predictability of complex physical systems

Using elementary cellular automata (CA) as an example, we show how to coarse-grain CA in all classes of Wolfram's classification. We find that computationally irreducible (CIR) physical processes can be predictable and even computationally reducible at a coarse-grained level of description. The resulting coarse-grained CA which we construct emulate the large-scale behavior of the original systems without accounting for small-scale details. At least one of the CA that can be coarse-grained is irreducible and known to be a universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR

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

Ovarian Hyperstimulation Syndrome with pleural effusion: a case report

In corporate governance systems boards perform three functions: the interlocking function (from a resource-dependency and network perspective), a monitoring function (from an agency perspective), and a strategic function (from a strategic choice perspective). In a one-tier board the board of directors incorporates non-executive directors (outsiders, they sometimes represent the interests of key-stakeholders) and executive directors (top management) of the firm. In a two-tier board there is a clear distinction between the directors as members of a supervisory board and the top management team. The board serves in this respect as a supervisory board vis à vis the management board. In the Netherlands a two-tier board is prevalent. Firms who act under the structural regime have boards that are characterized by the co-option principle. This means that board members have to act in the best interest of the firm and ultimately choose each other (and are not chosen by the shareholders or other stakeholders). Co-option has some advantages, but also some clear drawbacks, such as the potentiality of groupthink. The structural regime and other governance regimes, in which the relationship between supervisory board and management board is established, have moderating effects on the hypothesized relationships between the three functions and performance of firms.

Novel continuum modeling of crystal surface evolution

We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual approach where the continuum limit is achieved when typical surface features consist of many steps, our continuum limit is approached when the number of step configurations of the ensemble is very large. The model can handle singular surface structures such as corners and facets. It has a clear computational advantage over discrete models.Comment: 4 pages, 3 postscript figure

Manipulation of the follicular phase: Uterodomes and pregnancy - is there a correlation?

BACKGROUND: Manipulation of the follicular phase uterine epithelium in women undergoing infertility treatment, has not generally shown differing morphological effects on uterine epithelial characteristics using Scanning Electron Microscopy (SEM) and resultant pregnancy rates have remained suboptimal utilising these manipulations. The present study observed manipulation of the proliferative epithelium, with either 7 or 14 days of sequential oestrogen (E) therapy followed by progesterone (P) and assessed the appearance of pinopods (now called uterodomes) for their usefulness as potential implantation markers in seven women who subsequently became pregnant. Three endometrial biopsies per patient were taken during consecutive cycles: day 19 of a natural cycle - (group 1), days 11/12 of a second cycle after 7 days E then P - (group 2), and days 19/22 of a third cycle after 14 days E then P - (group 3). Embryo transfer (ET) was performed in a subsequent long treatment cycle (as per Group 3). RESULTS: Seven pregnancies resulted in seven viable births including one twins and one miscarriage. Analysis of the individual regimes showed 5 days of P treatment to have a higher correlation for uterodomes in all 3 cycles observed individually. It was also observed that all 7 women demonstrated the appearance of uterodomes in at least one of their cycles. CONCLUSIONS: We conclude that manipulation of the follicular phase by shortening the period of E exposure to 7 days, does not compromise uterine epithelial morphology and we add weight to the conclusion that uterodomes indicate a receptive endometrium for implantation

Decay of one dimensional surface modulations

The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the discrete step model into a continuum model for surface dynamics. The model consists of differential equations for the functions alpha(t) and F(x). The solutions of these equations agree with simulation results of the discrete step model. We identify two types of possible scaling solutions. Solutions of the first type have facets at the extremum points, while in solutions of the second type the facets are replaced by cusps. Interactions between steps of opposite signs determine whether a system is of the first or second type. Finally, we relate our model to an actual experiment and find good agreement between a measured AFM snapshot and a solution of our continuum model.Comment: 18 pages, 6 figures in 9 eps file

Fluctuations of elastic interfaces in fluids: Theory and simulation

We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a numerical method, we first discuss the dynamical coupling between the interface and the surrounding fluids. An argument is then presented that generalizes the single-relaxation time lattice-Boltzmann method for the simulation of hydrodynamic interfaces to include the elastic properties of the boundary. The implementation of the new method is outlined and it is tested by simulating the static behavior of spherical bubbles and the dynamics of bending waves. By means of the fluctuation-dissipation theorem we recover analytically the equilibrium frequency power spectrum of thermally fluctuating membranes and the correlation function of the excitations. Also, the non-equilibrium scaling properties of the membrane roughening are deduced, leading us to formulate a scaling law describing the interface growth, W^2(L,T)=L^3 g[t/L^(5/2)], where W, L and T are the width of the interface, the linear size of the system and the temperature respectively, and g is a scaling function. Finally, the phenomenology of thermally fluctuating membranes is simulated and the frequency power spectrum is recovered, confirming the decay of the correlation function of the fluctuations. As a further numerical study of fluctuating elastic interfaces, the non-equilibrium regime is reproduced by initializing the system as an interface immersed in thermally pre-excited fluids.Comment: 15 pages, 11 figure

Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table