Central limit theorems and diffusion approximations for multiscale Markov chain models

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit theorem provides a method for deriving an appropriate diffusion (Langevin) approximation.Comment: Published in at http://dx.doi.org/10.1214/13-AAP934 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic analysis of multiscale approximations to reaction networks

A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases of biological interest some of the chemical species in the network are present in much greater abundance than others and reaction rate constants can vary over several orders of magnitude. We consider approaches to approximation of such models that take the multiscale nature of the system into account. Our primary example is a model of a cell's viral infection for which we apply a combination of averaging and law of large number arguments to show that the ``slow'' component of the model can be approximated by a deterministic equation and to characterize the asymptotic distribution of the ``fast'' components. The main goal is to illustrate techniques that can be used to reduce the dimensionality of much more complex models.Comment: Published at http://dx.doi.org/10.1214/105051606000000420 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Primary Market Research: Its Role In Feaslblllty Studies

Primary market research and sound marketing analysis based on this research can make a significant contribution to the accuracy and usefulness of feasibility studies in planning for travel, leisure, tourism, recreation/entertainment, and hospitality development. The author contends that changes in the marketplace will increase the need for primary marketing research in the future

OddzOn Products and Derivation of Invention: At Odds with the Purpose of Section 102(f) of the Patent Act of 1952?

Abstract Background Antimicrobial peptides are important components of the host defence with a broad range of functions including direct antimicrobial activity and modulation of inflammation. Lack of cathelin-related antimicrobial peptide (CRAMP) was associated with higher mortality and bacterial burden and impaired neutrophil granulocyte infiltration in a model of pneumococcal meningitis. The present study was designed to characterize the effects of CRAMP deficiency on glial response and phagocytosis after exposure to bacterial stimuli. Methods CRAMP-knock out and wildtype glial cells were exposed to bacterial supernatants from Streptococcus pneumoniae and Neisseria meningitides or the bacterial cell wall components lipopolysaccharide and peptidoglycan. Cell viability, expression of pro- and anti-inflammatory mediators and activation of signal transduction pathways, phagocytosis rate and glial cell phenotype were investigated by means of cell viability assays, immunohistochemistry, real-time RT-PCR and Western blot. Results CRAMP-deficiency was associated with stronger expression of pro-inflammatory and weakened expression of anti-inflammatory cytokines indicating a higher degree of glial cell activation even under resting-state conditions. Furthermore, increased translocation of nuclear factor ‘kappa-light-chain-enhancer’ of activated B-cells was observed and phagocytosis of S. pneumoniae was reduced in CRAMP-deficient microglia indicating impaired antimicrobial activity. Conclusions In conclusion, the present study detected severe alterations of the glial immune response due to lack of CRAMP. The results indicate the importance of CRAMP to maintain and regulate the delicate balance between beneficial and harmful immune response in the brain

Math in Motion

Everything we know about the universe rests on the foundation of mathematics. Somehow, though, the magic of mathematics – the true power of numbers and their beautiful wildness – gets lost in math class. Children, our most magical thinkers, get turned off math in grade school and miss out on a language through which they could learn to read and change the world. VCU Math In Motion will generate a creative, dynamic STEM education initiative within the Richmond community using an innovative curriculum and a customized mobile unit to bring the beauty of math to Richmond region school children in grades 5-9, through partnerships across VCU and within the local school system

Seasonal changes in energy expenditure, body temperature and activity patterns in llamas (Lama glama)

The authors thank Knut Salzmann und Arne Oppermann for technical help and for taking care of the animals and Anna Stölzl for help with the administering of the ruminal unit of the telemetry system. The study was supported by a grant from the German Research Foundation (DFG) to A.R. (RI 1796/3-1).Peer reviewedPublisher PD

Actors that Unify Threads and Events

There is an impedance mismatch between message-passing concurrency and virtual machines, such as the JVM. VMs usually map their threads to heavyweight OS processes. Without a lightweight process abstraction, users are often forced to write parts of concurrent applications in an event-driven style which obscures control flow, and increases the burden on the programmer. In this paper we show how thread-based and event-based programming can be unified under a single actor abstraction. Using advanced abstraction mechanisms of the Scala programming language, we implemented our approach on unmodified JVMs. Our programming model integrates well with the threading model of the underlying VM

Sorting of chromosomes by magnetic separation

Chromosomes were isolated from Chinese hamster x human hybrid cell lines containing four and nine human chromosomes. Human genomic DNA was biotinylated by nick translation and used to label the human chromosomes by in situ hybridization in suspension. Streptavidin was covalently coupled to the surface of magnetic beads and these were incubated with the hybridized chromosomes. The human chromosomes were bound to the magnetic beads through the strong biotin-streptavidin complex and then rapidly separated from nonlabeled Chinese hamster chromosomes by a simple permanent magnet. The hybridization was visualized by additional binding of avidin-FITC (fluorescein) to the unoccupied biotinylated human DNA bound to the human chromosomes. After magnetic separation, up to 98% of the individual chromosomes attached to magnetic beads were classified as human chromosomes by fluorescence microscopy

Towards Space-like Photometric Precision from the Ground with Beam-Shaping Diffusers

We demonstrate a path to hitherto unachievable differential photometric precisions from the ground, both in the optical and near-infrared (NIR), using custom-fabricated beam-shaping diffusers produced using specialized nanofabrication techniques. Such diffusers mold the focal plane image of a star into a broad and stable top-hat shape, minimizing photometric errors due to non-uniform pixel response, atmospheric seeing effects, imperfect guiding, and telescope-induced variable aberrations seen in defocusing. This PSF reshaping significantly increases the achievable dynamic range of our observations, increasing our observing efficiency and thus better averages over scintillation. Diffusers work in both collimated and converging beams. We present diffuser-assisted optical observations demonstrating $62^{+26}_{-16}$ppm precision in 30 minute bins on a nearby bright star 16-Cygni A (V=5.95) using the ARC 3.5m telescope---within a factor of $\sim$2 of Kepler's photometric precision on the same star. We also show a transit of WASP-85-Ab (V=11.2) and TRES-3b (V=12.4), where the residuals bin down to $180^{+66}_{-41}$ppm in 30 minute bins for WASP-85-Ab---a factor of $\sim$4 of the precision achieved by the K2 mission on this target---and to 101ppm for TRES-3b. In the NIR, where diffusers may provide even more significant improvements over the current state of the art, our preliminary tests have demonstrated $137^{+64}_{-36}$ppm precision for a $K_S =10.8$ star on the 200" Hale Telescope. These photometric precisions match or surpass the expected photometric precisions of TESS for the same magnitude range. This technology is inexpensive, scalable, easily adaptable, and can have an important and immediate impact on the observations of transits and secondary eclipses of exoplanets.Comment: Accepted for publication in ApJ. 30 pages, 20 figure