Asymptotic growth and least common multiples in groups

In this article we relate word and subgroup growth to certain functions that arise in the quantification of residual finiteness. One consequence of this endeavor is a pair of results that equate the nilpotency of a finitely generated group with the asymptotic behavior of these functions. The second half of this article investigates the asymptotic behavior of two of these functions. Our main result in this arena resolves a question of Bogopolski from the Kourovka notebook concerning lower bounds of one of these functions for nonabelian free groups.Comment: 13 page

Bertrand's postulate and subgroup growth

In this article we investigate the L^1-norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on profinite groups, we define the residual average of a finitely generated group. One of the main results in this article is the finiteness of residual averages on finitely generated linear groups. Whether or not the residual average is finite depends on growth rates of indices of finite index subgroups. Our results on index growth rates are analogous to results on gaps between primes, and provide a variant of the subgroup growth function, which may be of independent interest.Comment: 33 page

Inverse Cascade Evidenced by Information Entropy of Passive Scalars in Submerged Canopy Flows

Turbulent mixing of scalars within canopies is investigated using a flume experiment with canopy-like rods of height h mounted to the channel bed. The data comprised a time sequence of high-resolution images of a dye recorded in a plane parallel to the bed at z/h= 0.2. Image processing shows that von Kármán wakes shed by canopy drag and downward turbulent transport from upper canopy layers impose distinct scaling regimes on the scalar spectrum. Measures from information theory are then used to explore the dominant directionality of the interaction between small and large scales underlying these two spectral regimes, showing that the arrival of sweeps from aloft establishes an inertial-range spectrum with forward “information” cascade. In contrast, wake growth with downstream distance leads to persistent upscale transfer (inverse cascade) of scalar variance, which hints at their nondiffusive character and the significance of the stem diameter as an active length scale in canopy turbulence

The Functionality of the three-sited Ferroxidase center of E. coli Bacterial Ferritin (EcFtnA)

At least three ferritins are found in the bacterium Escherichia coli, the heme-containing bacterioferritin (EcBFR) and two non-heme bacterial ferritins (EcFtnA and EcFtnB). In addition to the conserved A- and B-sites of the diiron ferroxidase center, EcFtnA has a third iron-binding site (the C-site) of unknown function that is nearby the diiron site. In the present work, the complex chemistry of iron oxidation and deposition in EcFtnA has been further defined through a combination of oximetry, pH stat, stopped-flow and conventional kinetics, UV-visible, fluorescence and EPR spectroscopic measurements on the wildtype protein and site-directed variants of the A-, B- and C-sites. The data reveal that, while H2O2 is a product of dioxygen reduction in EcFtnA and oxidation occurs with a stoichiometry of Fe(II)/O2 ~ 3:1, most of the H2O2 produced is consumed in subsequent reactions with a 2:1 Fe(II)/H2O2 stoichiometry, thus suppressing hydroxyl radical formation. While the A- and B-sites are essential for rapid iron oxidation, the C-site slows oxidation and suppresses iron turnover at the ferroxidase center. A tyrosyl radical, assigned to Tyr24 near the ferroxidase center, is formed during iron oxidation and its possible significance to the function of the protein is discussed. Taken as a whole, the data indicate that there are multiple iron-oxidation pathways in EcFtnA with O2 and H2O2 as oxidants. Furthermore, the data are inconsistent with the C-site being a transit site, providing iron to the A- and B-sites, and does not support a universal mechanism for iron oxidation in all ferritins as recently proposed

Residual Finiteness Growths of Virtually Special Groups

Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $\text{SL}_k(\mathbb{Z})$, for $k > 2$, has residual finiteness growth $n^{k-1}$.Comment: Updated version contains minor changes incorporating referee comments/suggestions and a simplified proof of Lemma 4.

Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

Data on CUX1 isoforms in idiopathic pulmonary fibrosis lung and systemic sclerosis skin tissue sections

This data article contains complementary figures related to the research article entitled, “Transforming growth factor-β-induced CUX1 isoforms are associated with fibrosis in systemic sclerosis lung fibroblasts” (Ikeda et al. (2016) [2], http://dx.doi.org/10.1016/j. bbrep.2016.06.022), which presents that TGF-β increased CUX1 binding in the proximal promoter and enhancer of the COL1A2 and regulated COL1. Further, in the scleroderma (SSc) lung and diffuse alveolar damage lung sections, CUX1 localized within the α- smooth muscle actin (α-SMA) positive cells (Fragiadaki et al., 2011) [1], “High doses of TGF-beta potently suppress type I collagen via the transcription factor CUX1” (Ikeda et al., 2016) [2]. Here we show that CUX1 isoforms are localized within α-smooth muscle actin-positive cells in SSc skin and idiopathic pulmonary fibrosis (IPF) lung tissue sections. In particular, at the granular and prickle cell layers in the SSc skin sections, CUX1 and α-SMA are colocalized. In addition, at the fibrotic loci in the IPF lung tissue sections, CUX1 localized within the α-smooth muscle actin (α- SMA) positive cells

Vortex Collisions: Crossing or Recombination?

We investigate the collision of two vortex lines moving with viscous dynamics and driven towards each other by an applied current. Using London theory in the approach phase we observe a non-trivial vortex conformation producing anti-parallel segments; their attractive interaction triggers a violent collision. The collision region is analyzed using the time-dependent Ginzburg-Landau equation. While we find vortices will always recombine through exchange of segments, a crossing channel appears naturally through a double collision process.Comment: 4 pages, 3 figure

Omega-3 canola oil effectively replaces fish oil as a new safe dietary source of docosahexaenoic acid (DHA) in feed for juvenile Atlantic salmon

Limited availability of fish oils (FO), rich in n-3 long-chain (≥C20) PUFA, is a major constraint for further growth of the aquaculture industry. Long-chain n-3 rich oils from crops GM with algal genes are promising new sources for the industry. This project studied the use of a newly developed n-3 canola oil (DHA-CA) in diets of Atlantic salmon fingerlings in freshwater. The DHA-CA oil has high proportions of the n-3 fatty acids (FA) 18 : 3n-3 and DHA and lower proportions of n-6 FA than conventional plant oils. Levels of phytosterols, vitamin E and minerals in the DHA-CA were within the natural variation of commercial canola oils. Pesticides, mycotoxins, polyaromatic hydrocarbons and heavy metals were below lowest qualifiable concentration. Two feeding trials were conducted to evaluate effects of two dietary levels of DHA-CA compared with two dietary levels of FO at two water temperatures. Fish increased their weight approximately 20-fold at 16°C and 12-fold at 12°C during the experimental periods, with equal growth in salmon fed the FO diets compared with DHA-CA diets. Salmon fed DHA-CA diets had approximately the same EPA+DHA content in whole body as salmon fed FO diets. Gene expression, lipid composition and oxidative stress-related enzyme activities showed only minor differences between the dietary groups, and the effects were mostly a result of dietary oil level, rather than the oil source. The results demonstrated that DHA-CA is a safe and effective replacement for FO in diets of Atlantic salmon during the sensitive fingerling life-stage.acceptedVersio

Challenges and opportunities in transdisciplinary science: The experience of next generation scientists in an agriculture and climate research collaboration

Agriculture in the twenty-first century faces unprecedented challenges from increasing climate variability to growing demands on natural resources to globalizing economic markets. These emerging agricultural issues, spanning both human and natural dimensions, are uniquely formulated, exceedingly complex, and difficult to address within existing disciplinary domains (Eigenbrode et al. 2007; Reganold et al. 2011; Foley et al. 2005; Hansen et al. 2013). Therefore, the next generation of scientists working on these issues must not only be highly trained within a disciplinary context but must also have the capacity to collaborate with others to solve systems-level problems