Scaling Properties of Paths on Graphs

Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of places along the way. For each path, sum the weights of its edges, and then list the path weights in increasing order. The asymptotic behaviour of this sequence is described, in terms of the structure and type of strongly connected components on the graph. As a special case, for a Markov chain the asymptotic probability of paths obeys either a power law scaling or a weaker type of scaling, depending on the structure of the transition matrix. This generalizes previous work by Mandelbrot and others, who established asymptotic power law scaling for special classes of Markov chains.Comment: 23 pages, 2 figure

Carbon dioxide flux and net primary production of a boreal treed bog: Responses to warming and water-table-lowering simulations of climate change

Midlatitude treed bogs represent significant carbon (C) stocks and are highly sensitive to global climate change. In a dry continental treed bog, we compared three sites: control, recent (1–3 years; experimental) and older drained (10–13 years), with water levels at 38, 74 and 120 cm below the surface, respectively. At each site we measured carbon dioxide (CO2) fluxes and estimated tree root respiration (Rr; across hummock–hollow microtopography of the forest floor) and net primary production (NPP) of trees during the growing seasons (May to October) of 2011–2013. The CO2–C balance was calculated by adding the net CO2 exchange of the forest floor (NEff-Rr) to the NPP of the trees. From cooler and wetter 2011 to the driest and the warmest 2013, the control site was a CO2–C sink of 92, 70 and 76 g m−2, the experimental site was a CO2–C source of 14, 57 and 135 g m−2, and the drained site was a progressively smaller source of 26, 23 and 13 g CO2–C m−2. The short-term drainage at the experimental site resulted in small changes in vegetation coverage and large net CO2 emissions at the microforms. In contrast, the longer-term drainage and deeper water level at the drained site resulted in the replacement of mosses with vascular plants (shrubs) on the hummocks and lichen in the hollows leading to the highest CO2 uptake at the drained hummocks and significant losses in the hollows. The tree NPP (including above- and below-ground growth and litter fall) in 2011 and 2012 was significantly higher at the drained site (92 and 83 g C m−2) than at the experimental (58 and 55 g C m−2) and control (52 and 46 g C m−2) sites. We also quantified the impact of climatic warming at all water table treatments by equipping additional plots with open-top chambers (OTCs) that caused a passive warming on average of ~ 1 °C and differential air warming of ~ 6 °C at midday full sun over the study years. Warming significantly enhanced shrub growth and the CO2 sink function of the drained hummocks (exceeding the cumulative respiration losses in hollows induced by the lowered water level × warming). There was an interaction of water level with warming across hummocks that resulted in the largest net CO2 uptake at the warmed drained hummocks. Thus in 2013, the warming treatment enhanced the sink function of the control site by 13 g m−2, reduced the source function of the experimental by 10 g m−2 and significantly enhanced the sink function of the drained site by 73 g m−2. Therefore, drying and warming in continental bogs is expected to initially accelerate CO2–C losses via ecosystem respiration, but persistent drought and warming is expected to restore the peatland's original CO2–C sink function as a result of the shifts in vegetation composition and productivity between the microforms and increased NPP of trees over time

1961 Proceedings of the Tenth World Methodist Conference

https://place.asburyseminary.edu/wmcproceedings/1012/thumbnail.jp

1956 Proceedings of the Ninth World Methodist Conference

https://place.asburyseminary.edu/wmcproceedings/1013/thumbnail.jp

Velocity and processivity of helicase unwinding of double-stranded nucleic acids

Helicases are molecular motors which unwind double-stranded nucleic acids (dsNA) in cells. Many helicases move with directional bias on single-stranded (ss) nucleic acids, and couple their directional translocation to strand separation. A model of the coupling between translocation and unwinding uses an interaction potential to represent passive and active helicase mechanisms. A passive helicase must wait for thermal fluctuations to open dsNA base pairs before it can advance and inhibit NA closing. An active helicase directly destabilizes dsNA base pairs, accelerating the opening rate. Here we extend this model to include helicase unbinding from the nucleic-acid strand. The helicase processivity depends on the form of the interaction potential. A passive helicase has a mean attachment time which does not change between ss translocation and ds unwinding, while an active helicase in general shows a decrease in attachment time during unwinding relative to ss translocation. In addition, we describe how helicase unwinding velocity and processivity vary if the base-pair binding free energy is changed.Comment: To appear in special issue on molecular motors, Journal of Physics - Condensed Matte

Stretching of polymers in a random three-dimensional flow

Behavior of a dilute polymer solution in a random three-dimensional flow with an average shear is studied experimentally. Polymer contribution to the shear stress is found to be more than two orders of magnitude higher than in a laminar shear flow. The results indicate that the polymer molecules get strongly stretched by the random motion of the fluid.Comment: 4 pages, 3 figure

Sequence heterogeneity and the dynamics of molecular motors

The effect of sequence heterogeneity on the dynamics of molecular motors is reviewed and analyzed using a set of recently introduced lattice models. First, we review results for the influence of heterogenous tracks such as a single-strand of DNA or RNA on the dynamics of the motors. We stress how the predicted behavior might be observed experimentally in anomalous drift and diffusion of motors over a wide range of parameters near the stall force and discuss the extreme limit of strongly biased motors with one-way hopping. We then consider the dynamics in an environment containing a variety of different fuels which supply chemical energy for the motor motion, either on a heterogeneous or on a periodic track. The results for motion along a periodic track are relevant to kinesin motors in a solution with a mixture of different nucleotide triphosphate fuel sources.Comment: To appear in a JPhys special issue on molecular motor

New Zealand blackcurrant extract improves high-intensity intermittent running performance.

New Zealand blackcurrant (BC) intake showed reduced blood lactate during low and moderate intensity cycling and improved 16.1 km cycling time trial performance. We examined the effect of BC on high-intensity intermittent treadmill running and post-running lactate clearance. Thirteen active males (age: 25±4 yrs, stature: 1.82±0.07 m, body mass: 81±14 kg, V̇O2max: 56±4 mL∙kg-1∙min-1, velocity at V̇O2max: 17.6±0.8 km∙h-1, mean±SD) visited the laboratory three times. In the 1st visit, a ramp protocol (0.1 km∙h-1 every 5 sec) was completed to establish V̇O2max and velocity at V̇O2max, and subjects were familiarised with the protocols. In visits 2 and 3, subjects completed an high intensity intermittent running capability test which consisted of six 19 s high-intensity running bouts, each interspersed by 15 s of low-intensity running, followed by 1 minute of rest, this was repeated at increasing speeds, until exhaustion. Prior to visits 2 and 3, subjects consumed either New Zealand BC extract (300 mg∙day-1 CurraNZ™; containing 105 mg anthocyanin) or placebo (P) (300 mg∙day-1 microcrystalline cellulose M102) for 7 days in capsules (double blind, randomised, cross-over design, wash-out at least 14 days). Blood lactate was collected for 30 min post-exhaustion. Two-tailed paired t-tests were used and significance accepted at p< .05. BC increased total running distance by 10.6% (BC: 4282±833 m, P: 3871±622 m, p = .023, 10 out of 13 subjects improved), with the distance during the high-intensity running bouts by 10.8% (p= .024). Heart rate, rating of perceived exertion and oxygen uptake were not different between conditions for each stage. At exhaustion, lactate tended to be higher for BC (BC: 6.01±1.07 mmol∙L-1, P: 5.22±1.52 mmol∙L-1, p = .066, 9 out of 13 subjects). There was a trend towards improved lactate clearance following 15 min (BC: -2.89±0.51 mmol∙L-1, P: -2.46±0.39 mmol∙L-1, p = .07) and 30 minutes of passive recovery (BC: -4.12±0.73 mmol∙L-1, P: -3.66±1.01 mmol∙L-1, p = 0.11). It is concluded that New Zealand blackcurrant extract (CurraNZ™) may enhance performance in team sports characterised by high-intensity intermittent exercise as with BC intake greater distances were covered during high-intensity running, there was higher lactate tolerance, and increased lactate clearance after high-intensity exercise

Straightening of Thermal Fluctuations in Semi-Flexible Polymers by Applied Tension

We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.Comment: Latex file; with three postscript figures; .ps available at http://dept.physics.upenn.edu/~nelson/pull.p