Monotonicity and stability of periodic polling models

Polling Systems;Stability;operations research

Monotonicity and stability of periodic polling models

Projet MEVALThis paper deals with the stability of periodic polling models with mixed service policies. The interarrivals to all queues are independent and exponentially distributed and the service and the switch-over times are independent with general distributions. The necessary and sufficient condition for the stability of such polling systems is established. The proof is based on the stochastic monotonicity of the state process at the polling instants. The stability of only a subset of the queues is also analyzed, and, in case of heavy traffic, the order of explosion of the queues is given

Interplay between function and structure in complex networks

We show that abrupt structural transitions can arise in functionally optimal networks, driven by small changes in the level of transport congestion. Our results offer an explanation as to why so many diverse species of network structure arise in Nature (e.g. fungal systems) under essentially the same environmental conditions. Our findings are based on an exactly solvable model system which mimics a variety of biological and social networks. We then extend our analysis by introducing a novel renormalization scheme involving cost motifs, to describe analytically the average shortest path across multiple-ring-and-hub networks. As a consequence, we uncover a 'skin effect' whereby the structure of the inner multi-ring core can cease to play any role in terms of determining the average shortest path across the network.Comment: Expanded version of physics/0508228 with additional new result

New approaches to investigating the function of mycelial networks

Fungi play a key role in ecosystem nutrient cycles by scavenging, concentrating, translocating and redistributing nitrogen. To quantify and predict fungal nitrogen redistribution, and assess the importance of the integrity of fungal networks in soil for ecosystem function, we need better understanding of the structures and processes involved. Until recently nitrogen translocation has been experimentally intractable owing to the lack of a suitable radioisotope tracer for nitrogen, and the impossibility of observing nitrogen translocation in real time under realistic conditions. We have developed an imaging method for recording the magnitude and direction of amino acid flow through the whole mycelial network as it captures, assimilates and channels its carbon and nitrogen resources, while growing in realistically heterogeneous soil microcosms. Computer analysis and modeling, based on these digitized video records, can reveal patterns in transport that suggest experimentally testable hypotheses. Experimental approaches that we are developing include genomics and stable isotope NMR to investigate where in the system nitrogen compounds are being acquired and stored, and where they are mobilized for transport or broken down. The results are elucidating the interplay between environment, metabolism, and the development and function of transport networks as mycelium forages in soil. The highly adapted and selected foraging networks of fungi may illuminate fundamental principles applicable to other supply networks

Amyloid β induces microglia to phagocytose neurons via activation of protein kinase Cs and NADPH oxidase.

Alzheimer's disease is characterized by brain plaques of amyloid beta and by neuronal loss, but it is unclear how amyloid beta causes neuronal loss and how to prevent this loss. We have previously shown that amyloid beta causes neuronal loss by inducing microglia to phagocytose neurons, and here we investigated whether protein kinase Cs and NADPH oxidase were involved in this. The loss of neurons induced by amyloid beta in co-cultures of primary glia and neurons was completely prevented by inhibiting protein kinase Cs with Gö6976 or Gö6983. Directly activating protein kinase Cs with phorbol myristate acetate stimulated microglial phagocytosis, and induced neuronal loss mediated by MFG-E8/vitronectin receptor pathway of microglial phagocytosis. Blocking phagocytosis by MFG-E8 knockout or receptor inhibition left live neurons, indicating microglial phagocytosis was the cause of neuronal death. Phorbol myristate acetate stimulated the microglial NADPH oxidase, and inhibiting the oxidase prevented neuronal loss. A physiological activator of NADPH oxidase, fMLP, also induced neuronal loss dependent on microglia. Amyloid beta-induced neuronal loss was blocked by NADPH oxidase inhibitors, superoxide dismutase or Toll-like receptor function-blocking antibodies. The results indicate that amyloid beta induces microglial phagocytosis of neurons via activating protein kinase Cs and NADPH oxidase, and that activating the kinases or oxidase is sufficient to induce neuronal loss by microglial phagocytosis. Thus inhibiting protein kinase Cs or NADPH oxidase might be beneficial in Alzheimer's disease or other brain pathologies involving inflammatory neuronal loss mediated by microglia.This work was partially supported by the Medical Research Council UK (MR/L010593). UN was supported by St John’s College (University of Cambridge), Department of Biochemistry (University of Cambridge) and the Cambridge Trust.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.biocel.2016.06.00

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

Radar surveys of the Rutford Ice Stream onset zone, West Antarctica: indications of flow (in)stability?

We present 1 and 100 MHz ground-based radar data from the onset region of Rutford Ice Stream, West Antarctica, which indicate the form and internal structure of isochrones. In the flow-parallel lines, modelled isochrone patterns reproduce the gross pattern of the imaged near-surface layers, assuming steady-state flow velocity from GPS records and the current accumulation rate for the last 200 years. We interpret this as indicating overall stability in flow in the onset region of Rutford Ice Stream throughout this period. However, in the cross-flow lines some local variability in accumulation is seen in areas close to the ice-stream margin where a number of tributaries converge towards the ice-stream onset zone. Episodic surface lowering events are observed followed by rapid fill episodes. The fill events indicate deposition towards the northwest, most likely generated by storm winds, which blow at an oblique angle to ice flow. More problematic is explaining the generation of episodic surface lowering in this area. We speculate this may be due 10: changing ice-flow direction in the complex tributary area of the onset zone; a change in basal sediments or sedimentary landforms; a change in basal melt rates or water supply; or episodic lake drainage events in the fjord systems of the Ellsworth Subglacial Highlands. The study highlights the difficulty of assessing flow stability in the complex onset regions of West Antarctic ice streams

Primary phagocytosis of viable neurons by microglia activated with LPS or Aβ is dependent on calreticulin/LRP phagocytic signalling.

BACKGROUND: Microglia are resident brain macrophages that can phagocytose dead, dying or viable neurons, which may be beneficial or detrimental in inflammatory, ischaemic and neurodegenerative brain pathologies. Cell death caused by phagocytosis of an otherwise viable cell is called 'primary phagocytosis' or 'phagoptosis'. Calreticulin (CRT) exposure on the surface of cancer cells can promote their phagocytosis via LRP (low-density lipoprotein receptor-related protein) on macrophages, but it is not known whether this occurs with neurons and microglia. METHODS: We used primary cultures of cerebellar neurons, astrocytes and microglia to investigate the potential role of CRT/LRP phagocytic signalling in the phagocytosis of viable neurons by microglia stimulated with lipopolysaccharide (LPS) or nanomolar concentrations of amyloid-β peptide1-42 (Aβ). Exposure of CRT on the neuronal surface was investigated using surface biotinylation and western blotting. A phagocytosis assay was also developed using BV2 and PC12 cell lines to investigate CRT/LRP signalling in microglial phagocytosis of apoptotic cells. RESULTS: We found that BV2 microglia readily phagocytosed apoptotic PC12 cells, but this was inhibited by a CRT-blocking antibody or LRP-blocking protein (receptor-associated protein: RAP). Activation of primary rat microglia with LPS or Aβ resulted in loss of co-cultured cerebellar granule neurons, and this was blocked by RAP or antibodies against CRT or against LRP, preventing all neuronal loss and death. CRT was present on the surface of viable neurons, and this exposure did not change in inflammatory conditions. CRT antibodies prevented microglia-induced neuronal loss when added to neurons, while LRP antibodies prevented neuronal loss when added to the microglia. Pre-binding of CRT to neurons promoted neuronal loss if activated microglia were added, but pre-binding of CRT to microglia or both cell types prevented microglia-induced neuronal loss. CONCLUSIONS: CRT exposure on the surface of viable or apoptotic neurons appears to be required for their phagocytosis via LRP receptors on activated microglia, but free CRT can block microglial phagocytosis of neurons by acting on microglia. Phagocytosis of CRT-exposing neurons by microglia can be a direct cause of neuronal death during inflammation, and might therefore contribute to neurodegeneration and be prevented by blocking the CRT/LRP pathway.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are