Mutual information in random Boolean models of regulatory networks

The amount of mutual information contained in time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating show that as the number of network nodes N approaches infinity, the quantity N exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.Comment: 11 pages, 6 figures; Minor revisions for clarity and figure format, one reference adde

Critical Networks Exhibit Maximal Information Diversity in Structure-Dynamics Relationships

Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic, separated by a critical phase transition. Numerous studies have shown that the most complex dynamics arise near the critical regime. Here we use an information theoretic approach to study structure-dynamics relationships within a unified framework and how that these relationships are most diverse in the critical regime

Diffusion measurements to understand dynamics and structuring in solutions involving a homologous series of ionic liquids

The self-diffusion coefficients of each of the components in mixtures containing pyridine and each of the homologous series 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imides in acetonitrile were determined using NMR diffusometry (i. e., Pulsed Gradient Spin Echo). The nature of solvation was found to change significantly with the proportion of salt in the mixtures. Increased diffusion coefficients (when corrected for viscosity) for the molecular components were observed with increasing proportion of ionic liquid and with increasing alkyl chain length on the cation. Comparison of the molecular solvents suggests increased interactions in solution of the pyridine with other components of the mixture, consistent with the proposed interactions shown previously to drive changes in reaction kinetics. Discontinuities were seen in the diffusion data for each species in solution across different ionic liquids between the hexyl and octyl derivatives, suggesting a change in the structuring in solution as the alkyl chain on the cation changes and demonstrating the importance of such when considering homologous series

Collaboration between academics and teachers : a complex relationship

Collaboration between academics and teachers has become increasingly prevalent over recent years. Whether its aim is joint research or continuing professional development for teachers, collaboration seems to offer a realistic opportunity for reducing the perceived gap between theory and practice. However, collaboration is not merely academics and teachers working together on a common project. It is complex in nature and involves a range of requirements that must be satisfied in order to maximise the potential of the relationship. In this paper we will theorise on the nature of academics and teachers working together and suggest that a working relationship between academic researchers and teachers can be one of three models: client–supplier, a coercive relationship or a collaborative relationship. We identify and unpack specific factors that underpin collaboration and suggest a number of concrete actions to establish collaboration between academics and teachers. We draw heavily from existing literature and our own reflections on two collaborative projects with which we have recently been involved. We use data from these projects to provide a number of anecdotes from the teachers who participated to support our own reflections. Finally, we suggest that further research should investigate the different ways attempts to collaborate fail, to build a more complete sense of the problems and potential of this special relationship. Keywords: collaboration; continuing professional development; action research; science teacher

Relativistic Models for Binary Neutron Stars with Arbitrary Spins

We introduce a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled Einstein field equations and equations of relativistic hydrodynamics are solved in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences of circular-orbit binaries of varying separation, keeping the rest mass and circulation constant along each sequence. Solutions are presented for configurations obeying an n=1 polytropic equation of state and spinning parallel and antiparallel to the orbital angular momentum. We treat stars with moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all but the highest circulation sequences, the spins of the neutron stars increase as the binary separation decreases. Our zero-circulation cases approximate irrotational sequences, for which the spin angular frequencies of the stars increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19) by the time the innermost circular orbit is reached. In addition to leaving an imprint on the inspiral gravitational waveform, this spin effect is measurable in the electromagnetic signal if one of the stars is a pulsar visible from Earth.Comment: 21 pages, 14 figures. A few explanatory sentences added and some typos corrected. Accepted for publication in Phys. Rev.

Collapse to Black Holes in Brans-Dicke Theory: II. Comparison with General Relativity

We discuss a number of long-standing theoretical questions about collapse to black holes in the Brans-Dicke theory of gravitation. Using a new numerical code, we show that Oppenheimer-Snyder collapse in this theory produces black holes that are identical to those of general relativity in final equilibrium, but are quite different from those of general relativity during dynamical evolution. We find that there are epochs during which the apparent horizon of such a black hole passes {\it outside\/} the event horizon, and that the surface area of the event horizon {\it decreases\/} with time. This behavior is possible because theorems which prove otherwise assume $R_{ab}l^al^b \ge 0$ for all null vectors $l^a$. We show that dynamical spacetimes in Brans-Dicke theory can violate this inequality, even in vacuum, for any value of $\omega$.Comment: 24 pages including figures, uuencoded gz-compressed postscript, Submitted to Phys Rev

The geography of recent genetic ancestry across Europe

The recent genealogical history of human populations is a complex mosaic formed by individual migration, large-scale population movements, and other demographic events. Population genomics datasets can provide a window into this recent history, as rare traces of recent shared genetic ancestry are detectable due to long segments of shared genomic material. We make use of genomic data for 2,257 Europeans (the POPRES dataset) to conduct one of the first surveys of recent genealogical ancestry over the past three thousand years at a continental scale. We detected 1.9 million shared genomic segments, and used the lengths of these to infer the distribution of shared ancestors across time and geography. We find that a pair of modern Europeans living in neighboring populations share around 10-50 genetic common ancestors from the last 1500 years, and upwards of 500 genetic ancestors from the previous 1000 years. These numbers drop off exponentially with geographic distance, but since genetic ancestry is rare, individuals from opposite ends of Europe are still expected to share millions of common genealogical ancestors over the last 1000 years. There is substantial regional variation in the number of shared genetic ancestors: especially high numbers of common ancestors between many eastern populations likely date to the Slavic and/or Hunnic expansions, while much lower levels of common ancestry in the Italian and Iberian peninsulas may indicate weaker demographic effects of Germanic expansions into these areas and/or more stably structured populations. Recent shared ancestry in modern Europeans is ubiquitous, and clearly shows the impact of both small-scale migration and large historical events. Population genomic datasets have considerable power to uncover recent demographic history, and will allow a much fuller picture of the close genealogical kinship of individuals across the world.Comment: Full size figures available from http://www.eve.ucdavis.edu/~plralph/research.html; or html version at http://ralphlab.usc.edu/ibd/ibd-paper/ibd-writeup.xhtm

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

A preliminary modelling investigation into the safe correction zone for high tibial osteotomy

Purpose: High tibial osteotomy (HTO) re-aligns the weight-bearing axis (WBA) of the lower limb. The surgery reduces medial load (reducing pain and slowing progression of cartilage damage) while avoiding overloading the lateral compartment. The optimal correction has not been established. This study investigated how different WBA re-alignments affected load distribu- tion in the knee, to consider the optimal post-surgery re-alignment. Methods: We collected motion analysis and 7T MRI data from 3 healthy sub- jects, and combined this data to create sets of subject-specific finite element models (total=45 models). Each set of models simulated a range of potential post-HTO knee re-alignments. We shifted the WBA from its native align- ment to between 40% and 80% medial-lateral tibial width (corresponding to 2.8◦-3.1◦ varus and 8.5◦-9.3◦ valgus), in 3% increments. We then compared stress/pressure distributions in the models. Results/Discussion: Correcting the WBA to 50% tibial width (0◦ varus- valgus) approximately halved medial compartment stresses, with minimal changes to lateral stress levels, but provided little margin for error in under- correction. Correcting the WBA to a more commonly-used 62%-65% tibial width (3.4◦-4.6◦ valgus) further reduced medial stresses but introduced the danger of damaging lateral compartment tissues. To balance optimal loading environment with that of the historical risk of under-correction, we propose a new target: WBA correction to 55% tibial width (1.7◦-1.9◦ valgus), which anatomically represented the apex of the lateral tibial spine. Conclusions: Finite element models can successfully simulate a variety of HTO re-alignments. Correcting the WBA to 55% tibial width (1.7◦-1.9◦ valgus) optimally distributes medial and lateral stresses/pressures