Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

Multifractal Behaviour of n-Simplex Lattice

We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an {\em n}-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, $\beta_L$, associated with resistance scaling, for any n. Using current cumulant method we calculate the exact noise exponent for n-simplex lattices.Comment: Latex, 9 pages including one figur

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

A Bethe lattice representation for sandpiles

Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments are reconciled. Critical behavior is here expressed troughout the critical properties of percolation phenomena.Comment: 5 pages, 4 figures, submitted for publicatio

External and Turbomachinery Flow Control Working Group

Broad Flow Control Issues: a) Understanding flow physics. b) Specific control objective(s). c) Actuation. d) Sensors. e) Integrated active flow control system. f) Development of design tools (CFD, reduced order models, controller design, understanding and utilizing instabilities and other mechanisms, e.g., streamwise vorticity)

Systems analyses reveal the resilience of Escherichia coli physiology during accumulation and export of the nonnative organic acid citramalate

© 2019 Webb et al. Productivity of bacterial cell factories is frequently compromised by stresses imposed by recombinant protein synthesis and carbon-to-product conversion, but little is known about these bioprocesses at a systems level. Production of the unnatural metabolite citramalate in Escherichia coli requires the expression of a single gene coding for citramalate synthase. Multiomic analyses of a fermentation producing 25 g liter1 citramalate were undertaken to uncover the reasons for its productivity. Metabolite, transcript, protein, and lipid profiles of high-cell-density, fed-batch fermentations of E. coli expressing either citramalate synthase or an inactivated enzyme were similar. Both fermentations showed downregulation of flagellar genes and upregulation of chaperones IbpA and IbpB, indicating that these responses were due to recombinant protein synthesis and not citramalate production. Citramalate production did not perturb metabolite pools, except for an increased intracellular pyruvate pool. Gene expression changes in response to citramalate were limited; none of the general stress response regulons were activated. Modeling of transcription factor activities suggested that citramalate invoked a GadW-mediated acid response, and changes in GadY and RprA regulatory small RNA (sRNA) expression supported this. Although changes in membrane lipid composition were observed, none were unique to citramalate production. This systems analysis of the citramalate fermentation shows that E. coli has capacity to readily adjust to the redirection of resources toward recombinant protein and citramalate production, suggesting that it is an excellent chassis choice for manufacturing organic acids. IMPORTANCE Citramalate is an attractive biotechnology target because it is a precursor of methylmethacrylate, which is used to manufacture Perspex and other high-value products. Engineered E. coli strains are able to produce high titers of citramalate, despite having to express a foreign enzyme and tolerate the presence of a nonnative biochemical. A systems analysis of the citramalate fermentation was undertaken to uncover the reasons underpinning its productivity. This showed that E. coli readily adjusts to the redirection of metabolic resources toward recombinant protein and citramalate production and suggests that E. coli is an excellent chassis for manufacturing similar small, polar, foreign molecules.We thank the Biotechnology and Biological Sciences Research Council UK and InnovateUK for funding (Industrial Biotechnology Catalyst BB/N01040X/1) and the Centre of Excellence in Mass Spectrometry funded by Science City York (Yorkshire Forward, EP/K039660/1, EP/M028127/1)

On species delimitation: Yet another lemur species or just genetic variation?

<p>Abstract</p> <p>Background</p> <p>Although most taxonomists agree that species are independently evolving metapopulation lineages that should be delimited with several kinds of data, the taxonomic practice in Malagasy primates (Lemuriformes) looks quite different. Several recently described lemur species are based solely on evidence of genetic distance and diagnostic characters of mitochondrial DNA sequences sampled from a few individuals per location. Here we explore the validity of this procedure for species delimitation in lemurs using published sequence data.</p> <p>Results</p> <p>We show that genetic distance estimates and <it>Population Aggregation Analysis </it>(PAA) are inappropriate for species delimitation in this group of primates. Intra- and interspecific genetic distances overlapped in 14 of 17 cases independent of the genetic marker used. A simulation of a fictive taxonomic study indicated that for the mitochondrial D-loop the minimum required number of individuals sampled per location is 10 in order to avoid false positives via PAA.</p> <p>Conclusions</p> <p>Genetic distances estimates and PAA alone should not be used for species delimitation in lemurs. Instead, several nuclear and sex-specific loci should be considered and combined with other data sets from morphology, ecology or behavior. Independent of the data source, sampling should be done in a way to ensure a quantitative comparison of intra- and interspecific variation of the taxa in question. The results of our study also indicate that several of the recently described lemur species should be reevaluated with additional data and that the number of good species among the currently known taxa is probably lower than currently assumed.</p