Use of Spotted Knapweed/Star Thistle (Asterales: Asteraceae) as the Primary Source of Nectar by Early Migrating Monarch Butterflies (Lepidoptera: Nymphalidae) from Beaver Island, Michigan

Recent observations over the past decade suggest that the invasive star thistle (aka spotted knapweed (Centaurea stoebe L.) provides much of the nectar that supports monarch butterflies (Danaus plexippus) in their pre-migratory and early migratory flight from the Beaver Island archipelago, an isolated chain of islands located in northern Lake Michigan. With the advent and continuation of global climate change, the opportunistic evolutionary changes that may take place between migrating monarchs and their dependence on non-native nectariferous plants, prior to migration, is worth further documentation and examination

Strength in Numbers: State Spending on K-12 Assessment Systems

In the coming years, states will need to make the most significant changes to their assessment systems in a decade as they implement the Common Core State Standards, a common framework for what students are expected to know that will replace existing standards in 45 states and the District of Columbia. The Common Core effort has prompted concerns about the cost of implementing the new standards and assessments, but there is little comprehensive up-to-date information on the costs of assessment systems currently in place throughout the country. This report fills this void by providing the most current, comprehensive evidence on state-level costs of assessment systems, based on new data from state contracts with testing vendors assembled by the Brown Center on Education Policy. These data cover a combined $669 million in annual spending on assessments in 45 states.The report identifies state collaboration on assessments as a clear strategy for achieving cost savings without compromising test quality. For example, a state with 100,000 students that joins a consortium of states containing one million students is predicted to save 37 percent, or$1.4 million per year; a state of 500,000 students saves an estimated 25 percent, or $3.9 million, by joining the same consortium.Collaborating to form assessment consortia is the strategy being pursued by nearly all of the states that have adopted the Common Core standards. But it is not yet clear how these common assessments will be sustained after federal funding for their development ends in 2014, months before the tests are fully implemented. The report identifies a lack of transparency in assessment pricing as a barrier to states making informed decisions regarding their testing systems, and recommends that consortia of states use their market power to encourage test-makers to divulge more details about their pricing models

The Bayesian Formulation of EIT: Analysis and Algorithms

We provide a rigorous Bayesian formulation of the EIT problem in an infinite dimensional setting, leading to well-posedness in the Hellinger metric with respect to the data. We focus particularly on the reconstruction of binary fields where the interface between different media is the primary unknown. We consider three different prior models - log-Gaussian, star-shaped and level set. Numerical simulations based on the implementation of MCMC are performed, illustrating the advantages and disadvantages of each type of prior in the reconstruction, in the case where the true conductivity is a binary field, and exhibiting the properties of the resulting posterior distribution.Comment: 30 pages, 10 figure

MAP Estimators for Piecewise Continuous Inversion

We study the inverse problem of estimating a field $u$ from data comprising a finite set of nonlinear functionals of $u$, subject to additive noise; we denote this observed data by $y$. Our interest is in the reconstruction of piecewise continuous fields in which the discontinuity set is described by a finite number of geometric parameters. Natural applications include groundwater flow and electrical impedance tomography. We take a Bayesian approach, placing a prior distribution on $u$ and determining the conditional distribution on $u$ given the data $y$. It is then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013) it has been shown that MAP estimators can be characterised as minimisers of a generalised Onsager-Machlup functional, in the case where the prior measure is a Gaussian random field. We extend this theory to a more general class of prior distributions which allows for piecewise continuous fields. Specifically, the prior field is assumed to be piecewise Gaussian with random interfaces between the different Gaussians defined by a finite number of parameters. We also make connections with recent work on MAP estimators for linear problems and possibly non-Gaussian priors (Helin, Burger 2015) which employs the notion of Fomin derivative. In showing applicability of our theory we focus on the groundwater flow and EIT models, though the theory holds more generally. Numerical experiments are implemented for the groundwater flow model, demonstrating the feasibility of determining MAP estimators for these piecewise continuous models, but also that the geometric formulation can lead to multiple nearby (local) MAP estimators. We relate these MAP estimators to the behaviour of output from MCMC samples of the posterior, obtained using a state-of-the-art function space Metropolis-Hastings method.Comment: 53 pages, 21 figure