Metrics and spectral triples for Dirichlet and resistance forms

The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance metric, then the intrinsic metric yields a geodesic space. Given a regular Dirichlet form, we consider Dirac operators within the framework of differential 1-forms proposed by Cipriani and Sauvageot, and comment on its spectral properties. If the Dirichlet form admits a carr\'e operator and the generator has discrete spectrum, then we can construct a related spectral triple, and in the compact and strongly local case the associated Connes distance coincides with the intrinsic metric. We finally give a description of the intrinsic metric in terms of vector fields

rcss: R package for optimal convex stochastic switching

© 2018 The R Journal. The R package rcss provides users with a tool to approximate the value functions in the Bellman recursion under certain assumptions that guarantee desirable convergence properties. This R package represents the first software implementation of these methods using matrices and nearest neighbors. This package also employs a pathwise dynamic method to gauge the quality of these value function approximations. Statistical analysis can be performed on the results to obtain other useful practical insights. This paper describes rcss version 1.6

Which Radial Velocity Exoplanets Have Undetected Outer Companions?

(Abridged) The observed radial velocity (RV) eccentricity distribution for extrasolar planets in single-planet systems shows that a significant fraction of planets are eccentric ($e > 0.1$). Here we investigate the effects on an RV planet's eccentricity produced by undetected outer companions. We have carried out Monte Carlo simulations of mock RV data to understand this effect and predict its impact on the observed distribution. We first quantify the statistical effect of undetected outer companions and show that this alone cannot explain the observed distribution. We then modify the simulations to consist of two populations, one of zero-eccentricity planets in double-planet systems and the other of single planets drawn from an eccentric distribution. Our simulations show that a good fit to the observed distribution is obtained with 45% zero-eccentricity double-planets and 55% single eccentric planets. Matching the observed distribution allows us to determine the probability that a known RV planet's orbital eccentricity has been biased by an undetected wide-separation companion. Our simulations show that moderately-eccentric planets, with $0.1 < e < 0.3$ and $0.1 < e < 0.2$, have a $\sim 13$ and $\sim 19$ probability, respectively, of having an undetected outer companion. We encourage both high-contrast direct imaging and RV follow-up surveys of known RV planets with moderate eccentricities to test our predictions and look for previously undetected outer companions.Comment: 23 pages (12 text, 2 tables, 9 figures). Accepted to the Astrophysical Journal 30 June 200

Algorithms for optimal control of stochastic switching systems

© 2016 Society for Industrial and Applied Mathematics. Optimal control problems of switching type with linear state dynamics are ubiquitous in applications of stochastic optimization. For high-dimensional problems of this type, solutions which utilize some convexity related properties are useful. For such problems, we present novel algorithmic solutions which require minimal assumptions while demonstrating remarkable computational efficiency. Furthermore, we devise procedures of the primal-dual kind to assess the distance to optimality of these approximate solutions

Lessons learned: rearing the crown-boring weevil, Ceutorhynchus scrobicollis (Coleoptera: Curculionidae), in containment for biological control of garlic mustard (Alliaria petiolata)

In this paper, we describe lessons learned and protocols developed after a decade of rearing Ceutorhynchus scrobicollis Nerenscheimer and Wagner in a Biosafety Level 2 containment facility. We have developed these protocols in anticipation of approval to release C. scrobicollis in North America for the biocontrol of garlic mustard. The rearing protocol tried to minimize the potential of attack by the adult parasitoid, Perilitus conseutor, which may be present in field collected C. scrobicollis from Europe to prevent inadvertent introduction of parasitoids into North America. All C. scrobicollis used for our quarantine rearing were field collected near Berlin, Germany. We have successfully reared C. scrobicollis on caged garlic mustard plants in a growth chamber by alternating temperatures and photoperiods to simulate those in its native range. In Germany, C. scrobicollis produces one generation per year and F1 adults emerge in late May. In containment, a new generation of adults emerged an average of 108 days after adults were placed on plants. We found the optimal time spent to collect F1 adults was four weeks after the appearance of the first F1 adult, with 95% of potential adults collected. Simulating a three-month summer aestivation period, followed by a week of fall, and three weeks of winter conditions resulted in optimum levels of oviposition in F1 females. Larvae first hatched 8- to-10 days after adults were placed on plants at 15/14 C day/night temperatures with a 9.5 hour photoperiod. We therefore recommend that C. scrobicollis adults are removed from garlic mustard rosettes after 8 days. This will maximize the period of female oviposition while minimizing the time when larvae are available for attack from P. conseutor

From non-symmetric particle systems to non-linear PDEs on fractals

We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging to a non-linear heat equation. We discuss a joint density-current law of large numbers and a corresponding large deviations principle.Comment: v2: 10 pages, 1 figure. To appear in the proceedings for the 2016 conference "Stochastic Partial Differential Equations & Related Fields" in honor of Michael R\"ockner's 60th birthday, Bielefel

Sensitivity of point scale runoff predictions to rainfall resolution

International audienceThis paper investigates the effects of using non-linear, high resolution rainfall, compared to time averaged rainfall on the triggering of hydrologic thresholds and therefore model predictions of infiltration excess and saturation excess runoff. The bounded random cascade model, parameterized to south western Australian rainfall, was used to scale rainfall intensities at various time resolutions ranging from 1.875 min to 2 h. A one dimensional, conceptual rainfall partitioning model was used that instantaneously partitions water into infiltration excess, infiltration, storage, deep drainage, saturation excess and surface runoff, where the fluxes into and out of the soil store are controlled by thresholds. For example, saturation excess is triggered when the soil water content reaches the storage capacity threshold. The results of the numerical modelling were scaled by relating soil infiltration properties to soil draining properties, and inturn, relating these to average storm intensities. By relating maximum soil infiltration capacities to saturated drainage rates (f*), we were able to split soils into two groups; those where all runoff is a result of infiltration excess alone (f*?0.2) and those susceptible to both infiltration excess and saturation excess runoff (f*>0.2). For all soil types, we related maximum infiltration capacities to average storm intensities (k*) and were able to show where model predictions of infiltration excess were most sensitive to rainfall resolution (ln k=0.4) and where using time averaged rainfall data can lead to an under prediction of infiltration excess and an over prediction of the amount of water entering the soil (ln k*>2). For soils susceptible to both infiltration excess and saturation excess, total runoff sensitivity was scaled by relating saturated drainage rates to average storm intensities (g*) and parameter ranges where predicted runoff was dominated by infiltration excess or saturation excess depending on the resolution of rainfall data was determined (ln g*<2). Infiltration excess predicted from high resolution rainfall is short and intense, whereas saturation excess produced from low resolution rainfall is more constant and less intense. This has important implications for the accuracy of current hydrological models that use time averaged rainfall under these soil and rainfall conditions and predictions of further thresholds such as erosion. It offers insight into areas where the understanding of the dynamics of high resolution rainfall is required and a means by which we can improve our understanding of the way variations in rainfall intensities within a storm relate to hydrological thresholds and model predictions

Dynamical Masses in Luminous Infrared Galaxies

We have studied the dynamics and masses of a sample of ten nearby luminous and ultraluminous infrared galaxies (LIRGS and ULIRGs), using 2.3 micron CO absorption line spectroscopy and near-infrared H- and Ks-band imaging. By combining velocity dispersions derived from the spectroscopy, disk scale-lengths obtained from the imaging, and a set of likely model density profiles, we calculate dynamical masses for each LIRG. For the majority of the sample, it is difficult to reconcile our mass estimates with the large amounts of gas derived from millimeter observations and from a standard conversion between CO emission and H_2 mass. Our results imply that LIRGs do not have huge amounts of molecular gas (10^10-10^11 Msolar) at their centers, and support previous indications that the standard conversion of CO to H_2 probably overestimates the gas masses and cannot be used in these environments. This in turn suggests much more modest levels of extinction in the near-infrared for LIRGs than previously predicted (A_V~10-20 versus A_V~100-1000). The lower gas mass estimates indicated by our observations imply that the star formation efficiency in these systems is very high and is triggered by cloud-cloud collisions, shocks, and winds rather than by gravitational instabilities in circumnuclear gas disks.Comment: 14 pages, 2 figures, accepted to Ap