93,699 research outputs found
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 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 from data comprising a
finite set of nonlinear functionals of , subject to additive noise; we
denote this observed data by . 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 and determining the conditional distribution on
given the data . 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
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