Relevant components in critical random Boolean networks

Random Boolean networks were introduced in 1969 by Kauffman as a model for gene regulation. By combining analytical arguments and efficient numerical simulations, we evaluate the properties of relevant components of critical random Boolean networks independently of update scheme. As known from previous work, the number of relevant components grows logarithmically with network size. We find that in most networks all relevant nodes with more than one relevant input sit in the same component, while all other relevant components are simple loops. As the proportion of nonfrozen nodes with two relevant inputs increases, the number of relevant components decreases and the size and complexity of the largest complex component grows. We evaluate the probability distribution of different types of complex components in an ensemble of networks and confirm that it becomes independent of network size in the limit of large network size. In this limit, we determine analytically the frequencies of occurence of complex components with different topologies.Comment: 9 pages, 6 figure

Two simplified procedures for predicting cyclic material response from a strain history

Simplified inelastic analysis procedures were developed at NASA Lewis and Pratt & Whitney Aircraft for predicting the stress-strain response at the critical location of a thermomechanically cycled structure. These procedures are intended primarily for use as economical structural analysis tools in the early design stages of aircraft engine hot section components where nonlinear finite-element analyses would be prohibitively expensive. Both simplified methods use as input the total strain history calculated from a linear elastic analysis. The elastic results are modified to approximate the characteristics of the inelastic cycle by incremental solution techniques. A von Mises yield criterion is used to determine the onset of active plasticity. The fundamental assumption of these methods is that the inelastic strain is local and constrained from redistribution by the surrounding elastic material

Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems

A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model

From imagery to ecology: Leveraging time series of all available Landsat observations to map and monitor ecosystem state and dynamics

https://zslpublications.onlinelibrary.wiley.com/doi/full/10.1002/rse2.24Published versio

Self-consistent analytic solution for the current and the access resistance in open ion channels.

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the currentvoltage characteristics obtained are in good quantitative agreement with experimental measurements

On the properties of cycles of simple Boolean networks

We study two types of simple Boolean networks, namely two loops with a cross-link and one loop with an additional internal link. Such networks occur as relevant components of critical K=2 Kauffman networks. We determine mostly analytically the numbers and lengths of cycles of these networks and find many of the features that have been observed in Kauffman networks. In particular, the mean number and length of cycles can diverge faster than any power law.Comment: 10 pages, 8 figure

The properties of attractors of canalyzing random Boolean networks

We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory leads to an intuitive understanding of the system's dynamics as it demonstrates the analogy between standard random Boolean networks and networks with canalyzing functions only. It reproduces correctly the scaling of the number of nonfrozen nodes with system size. We then investigate numerically attractor lengths and numbers, and explain the findings in terms of the properties of relevant components. In particular we show that canalyzing networks can contain very long attractors, albeit they occur less often than in standard networks.Comment: 9 pages, 8 figure

Capital Punishment, Proportionality Review, and Claims of Fairness (with Lessons from Washington State)

This Article explores the adequacy of one of the safeguards adopted by many states to ensure that the death penalty is applied fairly, following the reinstatement of capital punishment in 1976. Relying chiefly on evidence drawn from Washington State, this Article asks whether the practice of comparative proportionality review has ensured that there is now a rational basis for distinguishing between those who are sentenced to die and those who are not. An analysis of the trial judge reports employed by the Washington State Supreme Court in reviewing death sentences, as well as the method used by the court in conducting its reviews over the course of the past two decades, indicates that the death penalty remains arbitrary and capricious in its administration. The failure of comparative proportionality review furnishes yet another reason for concluding that capital punishment cannot be conducted in a way that comports with claims of fairness