Failed "nonaccelerating" models of prokaryote gene regulatory networks

Much current network analysis is predicated on the assumption that important biological networks will either possess scale free or exponential statistics which are independent of network size allowing unconstrained network growth over time. In this paper, we demonstrate that such network growth models are unable to explain recent comparative genomics results on the growth of prokaryote regulatory gene networks as a function of gene number. This failure largely results as prokaryote regulatory gene networks are "accelerating" and have total link numbers growing faster than linearly with network size and so can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. In the limit, these networks can undergo transitions so marked as to constrain network sizes to be below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are indeed characterized by an accelerating quadratic growth with gene count and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. We develop two "nonaccelerating" network models of prokaryote regulatory gene networks in an endeavor to match observation and demonstrate that these approaches fail to reproduce observed statistics.Comment: Corrected error in biological input parameter: 13 pages, 9 figure

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting "accelerating" growth have total link numbers growing faster than linearly with network size and can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value.Comment: Corrected error in biological input parameter: 15 pages, 10 figure

High effectiveness liquid droplet/gas heat exchanger for space power applications

A high-effectiveness liquid droplet/gas heat exchanger (LDHX) concept for thermal management in space is described. Heat is transferred by direct contact between fine droplets (approx. 100 to 300 micron diameter) of a suitable low vapor pressure liquid and an inert working gas. Complete separation of the droplet and gas media in the zero-g environment is accomplished by configuring the LDHX as a vortex chamber. The large heat transfer area presented by the small droplets permits heat exchanger effectiveness of 0.9 to 0.95 in a compact, lightweight geometry which avoids many of the limitations of conventional plate and fin or tube and shell heat exchangers, such as their tendency toward single point failure. The application of the LDHX in a high temperature Bryaton cycle is discussed to illustrate the performance and operational characteristics of this heat exchanger concept

General Campus Climate from a Conservative Student Perspective

Campus Climate Research studies how students and others in a college community feel about the climate of their institutions, especially how the climate facilitates learning, growth, and expression. Typically, this research has been applied to diversity concerns, especially in the decades after affirmative action became a common practice in higher education admissions. My research adds to this literature, because in the midst of creating a campus community and campus climate that is sensitive and in alliance with the needs of marginalized students, institutions will often find that a struggle occurs between the needs of marginalized students and the perceived neglect towards conservative students (or traditionally privileged students). My study uses the lens of Campus Climate Research to explore the extent to which conservative or conservative-leaning students at Ohio Wesleyan feel that they can comfortably interact with other OWU community members. I utilized Campus Climate Research measures to conduct an anonymous survey that asked a series of questions about the students’ academic and social perceptions regarding fairness and equity. I found that while most students take courses that challenge their personal opinions, it is often the case that conservative students still do not feel comfortable speaking out in class or with their professors due to the negative responses of students and occasionally professors. However, this does not mean that faculty are failing at creating an optimum learning environment. It is often said that, compared to non-academic social interactions students experience, OWU professors are good at making sure that conversations stay civil. Not surprisingly, students are in disagreement over their perceptions on restricted freedom of speech — some believing that we are restricted and others believing that we are not. Conservative students also reported they felt that political views are being left out of discussions about open mindedness and acceptance

Generic Polynomials

In Galois theory one is interested in finding a polynomial over a field that has a given Galois group. A more desirable polynomial is one that parametrizes all such polynomials with that given group as its corresponding Galois group. These are called generic polynomials and we provide detailed proofs of two theorems that give methods for constructing such polynomials. Furthermore, we construct generic polynomials for Sn, C3, V , C4, C6, D3, D4, and D6