Stability and triviality of the transverse invariant from Khovanov homology

We explore properties of braids such as their fractional Dehn twist coefficients, right-veeringness, and quasipositivity, in relation to the transverse invariant from Khovanov homology defined by Plamenevskaya for their closures, which are naturally transverse links in the standard contact $3$-sphere. For any $3$-braid $\beta$, we show that the transverse invariant of its closure does not vanish whenever the fractional Dehn twist coefficient of $\beta$ is strictly greater than one. We show that Plamenevskaya's transverse invariant is stable under adding full twists on $n$ or fewer strands to any $n$-braid, and use this to detect families of braids that are not quasipositive. Motivated by the question of understanding the relationship between the smooth isotopy class of a knot and its transverse isotopy class, we also exhibit an infinite family of pretzel knots for which the transverse invariant vanishes for every transverse representative, and conclude that these knots are not quasipositive.Comment: 23 pages, 8 figures. Updated to most recent versio

Reviews Matter: How Distributed Mentoring Predicts Lexical Diversity on Fanfiction.net

Fanfiction.net provides an informal learning space for young writers through distributed mentoring, networked giving and receiving of feedback. In this paper, we quantify the cumulative effect of feedback on lexical diversity for 1.5 million authors.Comment: Connected Learning Summit 201

Effect of Substrate Support on Dynamic Graphene/Metal Electrical Contacts.

Recent advances in graphene and other two-dimensional (2D) material synthesis and characterization have led to their use in emerging technologies, including flexible electronics. However, a major challenge is electrical contact stability, especially under mechanical straining or dynamic loading, which can be important for 2D material use in microelectromechanical systems. In this letter, we investigate the stability of dynamic electrical contacts at a graphene/metal interface using atomic force microscopy (AFM), under static conditions with variable normal loads and under sliding conditions with variable speeds. Our results demonstrate that contact resistance depends on the nature of the graphene support, specifically whether the graphene is free-standing or supported by a substrate, as well as on the contact load and sliding velocity. The results of the dynamic AFM experiments are corroborated by simulations, which show that the presence of a stiff substrate, increased load, and reduced sliding velocity lead to a more stable low-resistance contact

Production and Nitrogen Dynamics of a Vallisneria Americana Grass Bed in Lake Pontchartrain, Louisiana (Nitrogen Cycle, Modeling, Seagrasses, Decomposition Phenology, Vallisneria-Celery Grass-Eelgrass, Environmental Factors).

Vallisneria americana grass beds of Lake Pontchartrain contribute approximately 200 g dry weight/m(\u272)/yr primary production, a continuous release of detrital material, and rapid nutrient recycling. A harvest method was used to estimate production. The addition of litterfall to harvest production raised annual production estimates by up to 28%. When litterfall was corrected for decomposition, the production estimates were raised by up to 85% over harvest estimates alone. Litterfall and decomposition increased toward shore and occurred throughout the year providing a continuous supply of energy and nutrients. Grass bed production varied along the coastline and was greatest at mid-depths. Values of the environmental factors were most extreme near and far from shore. Severe environmental conditions are related to the patterns of biomass and production. The bell-shaped depth distribution pattern is perpetuated annually by survival of grass and by dormancy of fruit during the winter at mid-depths. The majority of fruit are produced at mid-depths where biomass and production are greatest. The surviving plants or new shoots start growing first at mid-depths, and later radiate out via the rhizome system to revegetate the entire grass bed. Although depth distribution patterns are similar along the coastline, the grass bed extends almost twice as far from shore at the control area as at the nitrogen enriched area. Water clarity was significantly greater at the control area than at the nitrogen enriched area. Light penetration may determine the compensation depth of the grass bed. Seasonal fluctuations of leaf and root and rhizome nitrogen simulated by GROW are very similar to field experimental values. GROW was most sensitive to the forcing functions light, temperature, and sediment nitrogen. GROW was validated using initial conditions from the nitrogen enriched grass bed and had correlations better than 80% between simulated and measured leaf and root and rhizome nitrogen. Once validated, GROW was run under normal and reduced light conditions. When light reaching the sediment surface was reduced by 50%, the Vallisneria leaf and root and rhizome nitrogen declined to zero within a year. This suggests that conditions that reduce water clarity could cause the loss of the grass beds