Exact Results for Spatio-Temporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium

We introduce a self-organized critical model of punctuated equilibrium with many internal degrees of freedom ($M$) per site. We find exact solutions for $M\rightarrow \infty$ of cascade equations describing avalanche dynamics in the steady state. This proves the existence of simple power laws with critical exponents that verify general scaling relations for nonequilibrium phenomena. Punctuated equilibrium is described by a Devil's staircase with a characteristic exponent, $\tau_{FIRST}=2-d/4$ where $d$ is the spatial dimension.Comment: 4 pages, postscript, uuencoded, (two ps-figures included) Final Version, to appear in PR

Boolean Models of Bistable Biological Systems

This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex differential equations models. The motivation for this work comes from mathematical systems biology. While Boolean mechanisms do not provide information about exact concentration rates or time scales, they are often sufficient to capture steady states and other key dynamics. Due to their intuitive nature, such models are very appealing to researchers in the life sciences. This paper is focused on dynamical systems that exhibit bistability and are desc ribedby delay equations. It is shown that if a certain motif including a feedback loop is present in the wiring diagram of the system, the Boolean model captures the bistability of molecular switches. The method is appl ied to two examples from biology, the lac operon and the phage lambda lysis/lysogeny switch

Ultrametricity and Memory in a Solvable Model of Self-Organized Criticality

Slowly driven dissipative systems may evolve to a critical state where long periods of apparent equilibrium are punctuated by intermittent avalanches of activity. We present a self-organized critical model of punctuated equilibrium behavior in the context of biological evolution, and solve it in the limit that the number of independent traits for each species diverges. We derive an exact equation of motion for the avalanche dynamics from the microscopic rules. In the continuum limit, avalanches propagate via a diffusion equation with a nonlocal, history-dependent potential representing memory. This nonlocal potential gives rise to a non-Gaussian (fat) tail for the subdiffusive spreading of activity. The probability for the activity to spread beyond a distance $r$ in time $s$ decays as $\sqrt{24\over\pi}s^{-3/2}x^{1/3} \exp{[-{3\over 4}x^{1/3}]}$ for $x={r^4\over s} \gg 1$. The potential represents a hierarchy of time scales that is dynamically generated by the ultrametric structure of avalanches, which can be quantified in terms of ``backward'' avalanches. In addition, a number of other correlation functions characterizing the punctuated equilibrium dynamics are determined exactly.Comment: 44 pages, Revtex, (12 ps-figures included

Constructing the extended Haagerup planar algebra

We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the `extended Haagerup' principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range $(4,3+\sqrt{3})$, which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram.Comment: 45 pages (final version; improved introduction

The Roots of Bioinformatics in Theoretical Biology

From the late 1980s onward, the term “bioinformatics” mostly has been used to refer to computational methods for comparative analysis of genome data. However, the term was originally more widely defined as the study of informatic processes in biotic systems. In this essay, I will trace this early history (from a personal point of view) and I will argue that the original meaning of the term is re-emerging

Specialization Can Drive the Evolution of Modularity

Organismal development and many cell biological processes are organized in a modular fashion, where regulatory molecules form groups with many interactions within a group and few interactions between groups. Thus, the activity of elements within a module depends little on elements outside of it. Modularity facilitates the production of heritable variation and of evolutionary innovations. There is no consensus on how modularity might evolve, especially for modules in development. We show that modularity can increase in gene regulatory networks as a byproduct of specialization in gene activity. Such specialization occurs after gene regulatory networks are selected to produce new gene activity patterns that appear in a specific body structure or under a specific environmental condition. Modules that arise after specialization in gene activity comprise genes that show concerted changes in gene activities. This and other observations suggest that modularity evolves because it decreases interference between different groups of genes. Our work can explain the appearance and maintenance of modularity through a mechanism that is not contingent on environmental change. We also show how modularity can facilitate co-option, the utilization of existing gene activity to build new gene activity patterns, a frequent feature of evolutionary innovations

An implementation study of neonatal hearing screening in the Netherlands

The objective of this study was to investigate whether universal neonatal hearing screening could be integrated in the youth health care program. The screening was performed by nurses of the well baby clinics. A three stage transient evoked otoacoustic emission screening was performed in three different screening settings in order to study the most effective set up regarding participation, refer rates, and costs. In one setting parents visited the well baby clinic, and in two settings babies were screened at home (either in combination with the screening for metabolic diseases or during an intake visit). Screening was performed on 3114 healthy newborns. The setting where universal neonatal hearing screening is integrated with the screening for metabolic diseases, proved to be most efficient and effective. The participation rate of 88.9% was highest in this setting and the overall refer rate (1.4%) was the lowest. The implementation of universal neonatal hearing screening by the well baby clinic nurses was judged to be possible. The results of this study formed the basis for nationwide implementation. © 2009 British Society of Audiology, International Society of Audiology, and Nordic Audiological Society