Inversion Sets and Quotient Root Systems

We provide a recursive description of all decompositions of the positive roots $R^+$ of a quotient root system $R$ into disjoint unions of inversion sets. Our description is type-independent and generalizes the analogous result for type $\mathbb A$ root systems in [USRA]. The main tool is the notion of an inflation of a subset of a quotient root system. This new notion allows us to treat all root systems (and their quotients) uniformly. We also obtain some numerical results about the number of special decompositions. The new sequences we obtain may be considered as extensions of Catalan numbers.Comment: Preliminary Versio

Macrophytes as indicators of land-derived wastewater : application of a δ15N method in aquatic systems

Author Posting. © American Geophysical Union, 2005. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Water Resources Research 41 (2005): W01014, doi:10.1029/2004WR003269.We measured δ15N signatures of macrophytes and particulate organic matter (POM) in six estuaries and three freshwater ponds of Massachusetts to assess whether the signatures could be used as indicators of the magnitude of land-derived nitrogen loads, concentration of dissolved inorganic nitrogen in the water column, and percentage of N loads contributed by wastewater disposal. The study focused specifically on sites on Cape Cod and Nantucket Island, in the northeastern United States. There was no evidence of seasonal changes in δ15N values of macrophytes or POM. The δ15N values of macrophytes and POM increased as water column dissolved inorganic nitrogen concentrations increased. We found that δ15N of macrophytes, but not of POM, increased as N load increased. The δ15N values of macrophytes and groundwater NO3 tracked the percent of wastewater contribution linearly. This research confirms that δ15N values of macrophytes and NO3 can be excellent indicators of anthropogenic N in aquatic systems.This work was supported by funds from the Woods Hole Oceanographic Institution Sea Grant Program, from the Cooperative Institute for Coastal and Estuarine Environmental Technology, from a Massachusetts Department of Environmental Protection grant to Applied Science Associates, Narragansett, Rhode Island, and from a National Oceanic and Atmospheric Administration National Estuarine Research Reserve fellowship and Palmer/McCleod fellowship to K.D.K

Nano-scale reservoir computing

This work describes preliminary steps towards nano-scale reservoir computing using quantum dots. Our research has focused on the development of an accumulator-based sensing system that reacts to changes in the environment, as well as the development of a software simulation. The investigated systems generate nonlinear responses to inputs that make them suitable for a physical implementation of a neural network. This development will enable miniaturisation of the neurons to the molecular level, leading to a range of applications including monitoring of changes in materials or structures. The system is based around the optical properties of quantum dots. The paper will report on experimental work on systems using Cadmium Selenide (CdSe) quantum dots and on the various methods to render the systems sensitive to pH, redox potential or specific ion concentration. Once the quantum dot-based systems are rendered sensitive to these triggers they can provide a distributed array that can monitor and transmit information on changes within the material.Comment: 8 pages, 9 figures, accepted for publication in Nano Communication Networks, http://www.journals.elsevier.com/nano-communication-networks/. An earlier version was presented at the 3rd IEEE International Workshop on Molecular and Nanoscale Communications (IEEE MoNaCom 2013

Internet-based cognitive behavioural therapy for subthreshold depression in people over 50 years old:a randomized controlled clinical trial

Background. Subthreshold depression is a highly prevalent condition and a risk factor for developing a major depressive episode. Internet-based cognitive behaviour therapy may be a promising approach for the treatment of subthreshold depression. The current study had two aims: (1) to determine whether an internet-based cognitive behaviour therapy intervention and a group cognitive behaviour therapy intervention are more effective than a waiting-list control group; and (2) to determine whether the effect of the internet-based cognitive behaviour therapy differs from the group cognitive behaviour therapy intervention. Method. A total of 191 women and 110 men with subthreshold depression were randomized into internet-based treatment, group cognitive behaviour therapy (Lewinsohn's Coping With Depression course), or a waiting-list control condition. The main outcome measure was treatment response after 10 weeks, defined as the difference in pre- and post-treatment scores on the Beck Depression Inventory (BDI). Missing data, a major limitation of this study, were imputed using the Multiple Imputation (MI) procedure Data Augmentation. Results. In the waiting-list control group, we found a pre- to post-improvement effect size of 0.45, which was 0.65 in the group cognitive behaviour therapy condition and 1.00 within the internet-based treatment condition. Helmert contrasts showed a significant difference between the waiting-list condition and the two treatment conditions (p=0.04) and no significant difference between both treatment conditions (p=0.62). Conclusions. An internet-based intervention may be at least as effective as a commonly used group cognitive behaviour therapy intervention for subthreshold depression in people over 50 years of age. © 2007 Cambridge University Press

Peridynamics for Predicting Pit-to-Crack Transition

Even though the failure mechanisms in aerospace structures are mainly governed by the incidence of fatigue loading, environmentally assisted fracture related pit-to-crack transition can still occur in many aluminum alloys, stainless steels and high strength low alloy steels. Despite of the relative rarity of this phenomenon, the consequent failures can be extremely destructive and lead to the loss of an aircraft. Prediction of damage evolution starting at corrosion pits acting as precursor to cracking has been hampered by a lack of insight into the process, as well as limitations in visualization and measurement techniques. In this regard, numerical modeling can be beneficial. The current study presents numerical predictions of pit evolution from a flat metal surface to realistic pit morphologies by using a new continuum mechanics formulation, peridynamics. Intergranular/transgranular pit-tocrack transition under different loading conditions and microstructural features are investigated without imposing any limiting assumption on the site of the crack initiation. Based on the numerical results, it can be concluded that microstructure has a significant effect for the prediction of pit-to-crack transition phenomenon

The Power Spectrum of Clusters of Galaxies and the Press-Schechter Approximation

We examine the power spectrum of clusters in the Press-Schechter (PS) theory and in N-body simulations to see how the power spectrum of clusters is related to the power spectrum of matter density fluctuations in the Universe. An analytic model for the power spectrum of clusters for their given number density is presented, both for real space and redshift space. We test this model against results from N-body simulations and find that the agreement between the analytic theory and the numerical results is good for wavelengths $\lambda >60h^{-1}$ Mpc. On smaller scales non-linear processes that are not considered in the linear PS approximation influence the result. We also use our analytic model to study the redshift-space power spectrum of clusters in cold dark matter models with a cosmological constant ($\Lambda$CDM) and with a scale-invariant Harrison-Zel'dovich initial spectrum of density fluctuations. We find that power spectra of clusters in these models are not consistent with the observed power spectra of the APM and Abell-ACO clusters. One possible explanation for the observed power spectra of clusters is an inflationary scenario with a scalar field with the potential that has a localized steplike feature. We use the PS theory to examine the power spectrum of clusters in this model.Comment: 16 pages, 5 figures. Accepted by Ap