Fluid and Diffusion Limits for Bike Sharing Systems

Bike sharing systems have rapidly developed around the world, and they are served as a promising strategy to improve urban traffic congestion and to decrease polluting gas emissions. So far performance analysis of bike sharing systems always exists many difficulties and challenges under some more general factors. In this paper, a more general large-scale bike sharing system is discussed by means of heavy traffic approximation of multiclass closed queueing networks with non-exponential factors. Based on this, the fluid scaled equations and the diffusion scaled equations are established by means of the numbers of bikes both at the stations and on the roads, respectively. Furthermore, the scaling processes for the numbers of bikes both at the stations and on the roads are proved to converge in distribution to a semimartingale reflecting Brownian motion (SRBM) in a $N^{2}$-dimensional box, and also the fluid and diffusion limit theorems are obtained. Furthermore, performance analysis of the bike sharing system is provided. Thus the results and methodology of this paper provide new highlight in the study of more general large-scale bike sharing systems.Comment: 34 pages, 1 figure

Advection, diffusion and delivery over a network

Many biological, geophysical and technological systems involve the transport of resource over a network. In this paper we present an algorithm for calculating the exact concentration of resource at any point in space or time, given that the resource in the network is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. We consider the implications of advection, diffusion and delivery for simple models of glucose delivery through a vascular network, and conclude that in certain circumstances, increasing the volume of blood and the number of glucose transporters can actually decrease the total rate of glucose delivery. We also consider the case of empirically determined fungal networks, and analyze the distribution of resource that emerges as such networks grow over time. Fungal growth involves the expansion of fluid filled vessels, which necessarily involves the movement of fluid. In three empirically determined fungal networks we found that the minimum currents consistent with the observed growth would effectively transport resource throughout the network over the time-scale of growth. This suggests that in foraging fungi, the active transport mechanisms observed in the growing tips may not be required for long range transport.Comment: 54 pages including appendix, 10 figure

The structural and dynamic responses of Stange Ice Shelf to recent environmental change

Stange Ice Shelf is the most south-westerly ice shelf on the Antarctic Peninsula, a region where positive trends in atmospheric and oceanic temperatures have been recently documented. In this paper, we use a range of remotely sensed datasets to evaluate the structural and dynamic responses of Stange Ice Shelf to these environmental changes. Ice shelf extent and surface structures were examined at regular intervals from optical and radar satellite imagery between 1973 and 2011. Surface speeds were estimated in 1989, 2004 and 2010 by tracking surface features in successive satellite images. Surface elevation change was estimated using radar altimetry data acquired between 1992 and 2008 by the European Remote Sensing Satellite (ERS) -1, -2 and Envisat. The mean number of surface melt days was estimated using the intensity of backscatter from Envisat’s Advanced Synthetic Aperture Radar instrument between 2006 and 2012. These results show significant shear fracturing in the southern portion of the ice shelf linked to enhanced flow speed as a consequence of measured thinning. However, we conclude that, despite the observed changes, Stange Ice Shelf is currently stable

Network traits predict ecological strategies in fungi

Colonization of terrestrial environments by filamentous fungi relies on their ability to form networks that can forage for and connect resource patches. Despite the importance of these networks, ecologists rarely consider network features as functional traits because their measurement and interpretation are conceptually and methodologically difficult. To address these challenges, we have developed a pipeline to translate images of fungal mycelia, from both micro- and macro-scales, to weighted network graphs that capture ecologically relevant fungal behaviour. We focus on four properties that we hypothesize determine how fungi forage for resources, specifically: connectivity; relative construction cost; transport efficiency; and robustness against attack by fungivores. Constrained ordination and Pareto front analysis of these traits revealed that foraging strategies can be distinguished predominantly along a gradient of connectivity for micro- and macro-scale mycelial networks that is reminiscent of the qualitative ‘phalanx’ and ‘guerilla’ descriptors previously proposed in the literature. At one extreme are species with many inter-connections that increase the paths for multidirectional transport and robustness to damage, but with a high construction cost; at the other extreme are species with an opposite phenotype. Thus, we propose this approach represents a significant advance in quantifying ecological strategies for fungi using network information

Cisternal Organization of the Endoplasmic Reticulum during Mitosis

The endoplasmic reticulum (ER) of animal cells is a single, dynamic, and continuous membrane network of interconnected cisternae and tubules spread out throughout the cytosol in direct contact with the nuclear envelope. During mitosis, the nuclear envelope undergoes a major rearrangement, as it rapidly partitions its membrane-bound contents into the ER. It is therefore of great interest to determine whether any major transformation in the architecture of the ER also occurs during cell division. We present structural evidence, from rapid, live-cell, three-dimensional imaging with confirmation from high-resolution electron microscopy tomography of samples preserved by high-pressure freezing and freeze substitution, unambiguously showing that from prometaphase to telophase of mammalian cells, most of the ER is organized as extended cisternae, with a very small fraction remaining organized as tubules. In contrast, during interphase, the ER displays the familiar reticular network of convolved cisternae linked to tubules

On the error term in Weyl's law for the Heisenberg manifolds (II)

In this paper we study the mean square of the error term in the Weyl's law of an irrational $(2l+1)$-dimensional Heisenberg manifold . An asymptotic formula is established

Dynamic calcium-mediated stress response and recovery signatures in the fungal pathogen, Candida albicans

Acknowledgements AB conceived the project and wrote the manuscript. CVG conceived the experimental design. SW designed the GCaMP reporter. AM, KL, LV-M, SC and TB constructed strains and optimised imaging. MF developed the image analysis software. CVG and CP carried out the microfluidics experiments and imaging analysis. NG assisted with preparation of the manuscript. PS, SN and DMR developed and undertook the theoretical data analysis and contributed to the interpretation of the results. Funding AB, CG and TB were funded by the Wellcome Trust [Grant number 206412/A/17/Z]. AB and DR were supported by a Wellcome Trust Institutional Strategic Support Award (WT204909/Z/16/Z). CP was funded by a University of Exeter studentship (113516). This work was also supported by a Royal Society URF (UF080611), an MRC NIRG (G0900211/90671) and the MRC-Centre for Medical Mycology at the University of Exeter (MR/N006364/2). DR was funded by the Medical Research Council (MR/P022405/1). SN was supported by the Medical Research Council via the GW4 BioMed2 DTP (MR/W006308/1). MCA was supported by a European Commission ITN ‘FungiBrain’ studentship (607963). LL and SC were funded by a Wellcome Trust Institutional Strategic Support Award to the University of Aberdeen. NG acknowledges support of Wellcome Trust Investigator, Collaborative, Equipment, Strategic and Biomedical Resource awards (101873, 200208, 215599, 224323). NG and AB thank the MRC (MR/M026663/2) for support. This study/research is funded by the National Institute for Health and Care Research (NIHR) Exeter Biomedical Research Centre (BRC). The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care. For the purpose of open access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.Peer reviewedPublisher PD

Ocean forced variability of Totten Glacier mass loss

This is the author accepted manuscript. The final version is available from the Geological Society of London via the DOI in this record.A large volume of the East Antarctic Ice Sheet drains through the Totten Glacier (TG) and is thought to be a potential source of substantial global sea level rise over the coming centuries. We show the surface velocity and heightof the floating part of TG, which buttresses the grounded component, have varied substantially over two decades (1989–2011), with variations in surface height strongly anti-correlated with simulated basal melt rates (r=0.70, p<0.05). Coupled glacier/ice-shelf simulations confirm ice flow and thickness respond to both basal melting of the ice shelf and grounding on bed obstacles. We conclude the observed variability of TG is primarily ocean-driven. Ocean warming in this region will lead to enhanced ice-sheet dynamism and loss of upstream grounded ice.This work was supported by, Australian Antarctic Division projects 3103, 4077, 4287 and 4346, National Computing Infrastructure grant m68, NSF grant ANT-0733025, NASA grant NNX09AR52G (Operation Ice Bridge), NERC grant NE/F016646/1, NERC fellowship NE/G012733/2, the Jackson School of Geoscience, the Jet Propulsion Laboratory and the G. Unger Vetlesen Foundation. This research was also supported by the Australian Government’s Cooperative Research Centres Programme through the Antarctic Climate & Ecosystems Cooperative Research Centre. The work is also supported under the Australian Research Councils Special Research Initiative for Antarctic Gateway Partnership SR140300001. Landsat 4 and 7 images courtesy of the U.S. Geological Survey. This is UTIG contribution 2486. Thanks to Benoit Legresy for useful discussions

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks