A Constrained Approach to Multiscale Stochastic Simulation of\ud Chemically Reacting Systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper we introduce a multiscale methodology suitable to address this problem. It is based on the Conditional Stochastic Simulation Algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the Constrained Multiscale Algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems

Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

ENVIROSAT-2000 report: Federal agency satellite requirements

The requirement of Federal agencies, other than NOAA, for the data and services of civil operational environmental satellites (both polar orbiting and geostationary) are summarized. Agency plans for taking advantage of proposed future Earth sensing space systems, domestic and foreign, are cited also. Current data uses and future requirements are addressed as identified by each agency

Comparing placentas from normal and abnormal pregnancies

This report describes work carried out at a Mathematics-in-Medicine Study Group. It is believed that placenta shape villous network characteristics are strongly linked to the placenta’s efficiency, and hence to pregnancy outcome. We were asked to consider mathematical ways to describe the shape and other characteristics of a placenta, as well as forming mathematical models for placenta development. In this report we propose a number of possible measure of placental shape, form, and efficiency, which can be computed from images already obtained. We also consider various models for the early development of placentas and the growth of the villous tree

Relaxed sugar donor selectivity of a Sinorhizobium meliloti ortholog of the Rhizobium leguminosarum mannosyl transferase LpcC: Role of the lipopolysaccharide core in symbiosis of Rhizobiaceae with plants

The lpcC gene of Rhizobium leguminosarum and the lpsB gene of Sinorhizobium meliloti encode protein orthologs that are 58% identical over their entire lengths of about 350 amino acid residues. LpcC and LpsB are required for symbiosis with pea and Medicago plants, respectively. S. meliloti lpsB complements a mutant of R. leguminosarum defective in IpcC, but the converse does not occur. LpcC encodes a highly selective mannosyl transferase that utilizes GDP-mannose to glycosylate the inner 3-deoxy-D-manno-octulosonic acid (Kdo) residue of the lipopolysaccharide precursor Kdo2-lipid IVA. We now demonstrate that LpsB can also efficiently mannosylate the same acceptor substrate as does LpcC. Unexpectedly, however, the sugar nucleotide selectivity of LpsB is greatly relaxed compared with that of LpcC. Membranes of the wild-type S. meliloti strain 2011 catalyze the glycosylation of Kdo2-[4′-32P]lipid IVA at comparable rates using a diverse set of sugar nucleotides, including GDP-mannose, ADP-mannose, UDP-glucose, and ADP-glucose. This complex pattern of glycosylation is due entirely to LpsB, since membranes of the S. meliloti lpsB mutant 6963 do not glycosylate Kdo2-[4′-32P]lipid IVA in the presence of any of these sugar nucleotides. Expression of lpsB in E. coli using a T7lac promoter-driven construct results in the appearance of similar multiple glycosyl transferase activities seen in S. meliloti 2011 membranes. Constructs expressing lpcC display only mannosyl transferase activity. We conclude that LpsB, despite its high degree of similarity to LpcC is a much more versatile glycosyltransferase, probably accounting for the inability of lpcC to complement S. meliloti lpsB mutants. Our findings have important implications for the regulation of core glycosylation in S. meliloti and other bacteria containing LpcC orthologs.Facultad de Ciencias Exacta

Relaxed sugar donor selectivity of a Sinorhizobium meliloti ortholog of the Rhizobium leguminosarum mannosyl transferase LpcC: Role of the lipopolysaccharide core in symbiosis of Rhizobiaceae with plants

The lpcC gene of Rhizobium leguminosarum and the lpsB gene of Sinorhizobium meliloti encode protein orthologs that are 58% identical over their entire lengths of about 350 amino acid residues. LpcC and LpsB are required for symbiosis with pea and Medicago plants, respectively. S. meliloti lpsB complements a mutant of R. leguminosarum defective in IpcC, but the converse does not occur. LpcC encodes a highly selective mannosyl transferase that utilizes GDP-mannose to glycosylate the inner 3-deoxy-D-manno-octulosonic acid (Kdo) residue of the lipopolysaccharide precursor Kdo2-lipid IVA. We now demonstrate that LpsB can also efficiently mannosylate the same acceptor substrate as does LpcC. Unexpectedly, however, the sugar nucleotide selectivity of LpsB is greatly relaxed compared with that of LpcC. Membranes of the wild-type S. meliloti strain 2011 catalyze the glycosylation of Kdo2-[4′-32P]lipid IVA at comparable rates using a diverse set of sugar nucleotides, including GDP-mannose, ADP-mannose, UDP-glucose, and ADP-glucose. This complex pattern of glycosylation is due entirely to LpsB, since membranes of the S. meliloti lpsB mutant 6963 do not glycosylate Kdo2-[4′-32P]lipid IVA in the presence of any of these sugar nucleotides. Expression of lpsB in E. coli using a T7lac promoter-driven construct results in the appearance of similar multiple glycosyl transferase activities seen in S. meliloti 2011 membranes. Constructs expressing lpcC display only mannosyl transferase activity. We conclude that LpsB, despite its high degree of similarity to LpcC is a much more versatile glycosyltransferase, probably accounting for the inability of lpcC to complement S. meliloti lpsB mutants. Our findings have important implications for the regulation of core glycosylation in S. meliloti and other bacteria containing LpcC orthologs.Facultad de Ciencias Exacta

Breeding Biology of Atlantic Population Canada Geese in Nunavik, Northern Québec

The Atlantic population of Canada Geese (Branta canadensis interior) experienced a sharp decline in numbers in the late 1980s. Management agencies in Canada and the United States responded by implementing several measures, notably closing sport hunting seasons for a number of years in most Atlantic Flyway states and provinces and funding a research project to study the nesting ecology and the factors affecting productivity of this goose population. In this paper we present the nesting phenology and breeding biology of Atlantic population Canada Geese on their tundra nesting grounds in Nunavik, Québec, specifically on a primary study area (32.8 km2) along Hudson Bay (1997–2003) and on several secondary sites (most smaller than 1 km2) distributed along the coastal lowlands of Hudson Bay and Ungava Bay (1996–2005). In the late 1990s the population rebounded, with strong increases in the population of breeding pairs and the density of nests between 1996 and 2001, followed by stabilization of both variables from 2001 to 2005. As a result, there was a near doubling in productivity index (the number of goslings produced per km2) on the primary study area, from 17.9 in 1997 to 32.0 in 2003. Geese start laying eggs soon after snow disappears from their nesting grounds. On the primary study area, for all years pooled, mean clutch initiation date, clutch size, hatching date, and Mayfield nesting success were 27 May, 4.54 eggs, 26 June, and 67.3%, respectively. Among secondary sites along both Hudson Bay and Ungava Bay, we found a correlation between the annual average daily temperature for 4–24 May (the period leading up to egg-laying) and the annual mean clutch initiation date: higher temperatures were correlated with earlier initiation. Similarly, an earlier annual mean clutch initiation date was correlated with large mean clutch size.La population de l’Atlantique de la bernache du Canada (Branta canadensis interior) a subi un déclin prononcé à la fin des années 1980. Les organismes chargés de la gestion de la faune au Canada et aux États-Unis ont réagi en mettant en place plusieurs mesures. Ils ont notamment fermé la saison de chasse sportive dans la plupart des États et provinces de la voie migratoire de la population de l’Atlantique pendant un certain nombre d’années et financé un projet de recherche sur l’écologie de la nidification et sur les facteurs limitant la productivité de cette population. Dans le présent article, nous décrivons la phénologie de la nidification et la biologie de la reproduction de la population de l’Atlantique de la bernache du Canada dans son aire de nidification de la toundra du Nunavik (Québec), plus précisément dans une aire d’étude principale (32,8 km2) établie en bordure de la baie d’Hudson (1997 – 2003) et dans plusieurs sites secondaires de superficie plus modeste (dans la plupart des cas, inférieure à 1 km2) disséminés dans les basses-terres côtières de la baie d’Hudson et de la baie d’Ungava (1996 – 2005). À la fin des années 1990, la population a rebondi, le nombre de couples nicheurs et la densité des nids augmentant fortement entre 1996 et 2001 pour ensuite se stabiliser de 2001 à 2005. Par suite de ce redressement, le nombre d’oisons produits par kilomètre carré a presque doublé (indice de productivité) dans l’aire d’étude principale, passant de 17,9 en 1997 à 32,0 en 2003. La ponte débute peu après la disparition de la neige dans les sites de nidification. Dans l’aire d’étude principale, nous avons enregistré les valeurs moyennes suivantes (années regroupées) : début de la période de ponte : 27 mai; taille des couvées : 4,54 oeufs; premières éclosions : 26 juin; succès de la nidification en mai : 67,3 %. Aux sites secondaires, en bordure de la baie d’Hudson et de la baie d’Ungava, nous avons relevé une corrélation entre la température journalière moyenne annuelle pour la période du 4 au 24 mai (période précédant le début de la période de ponte) et la date annuelle moyenne du début de la ponte: les températures plus élevées donnaient une corrélation avec un début de période de ponte plus hâtif. De même, une date annuelle moyenne plus hâtive du début de la ponte a été corrélée avec une grande taille moyenne des couvées

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides

All-optical signal processing is envisioned as an approach to dramatically decrease power consumption and speed up performance of next-generation optical telecommunications networks. Nonlinear optical effects, such as four-wave mixing (FWM) and parametric gain, have long been explored to realize all-optical functions in glass fibers. An alternative approach is to employ nanoscale engineering of silicon waveguides to enhance the optical nonlinearities by up to five orders of magnitude, enabling integrated chip-scale all-optical signal processing. Previously, strong two-photon absorption (TPA) of the telecom-band pump has been a fundamental and unavoidable obstacle, limiting parametric gain to values on the order of a few dB. Here we demonstrate a silicon nanophotonic optical parametric amplifier exhibiting gain as large as 25.4 dB, by operating the pump in the mid-IR near one-half the band-gap energy (E~0.55eV, lambda~2200nm), at which parasitic TPA-related absorption vanishes. This gain is high enough to compensate all insertion losses, resulting in 13 dB net off-chip amplification. Furthermore, dispersion engineering dramatically increases the gain bandwidth to more than 220 nm, all realized using an ultra-compact 4 mm silicon chip. Beyond its significant relevance to all-optical signal processing, the broadband parametric gain also facilitates the simultaneous generation of multiple on-chip mid-IR sources through cascaded FWM, covering a 500 nm spectral range. Together, these results provide a foundation for the construction of silicon-based room-temperature mid-IR light sources including tunable chip-scale parametric oscillators, optical frequency combs, and supercontinuum generators