Fast Update of Conditional Simulation Ensembles

Gaussian random field (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. This work studies settings where conditioning observations are assimilated batch sequentially, with one point or a batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, the goal is to take advantage of already available sample paths and by-products to produce updated conditional simulations at mini- mal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on n ≥ 0 observations to an ensemble conditioned on n + q observations, for arbitrary q ≥ 1. Compared to direct approaches, the proposed formulae proveto substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the q new observations are updating the old sample paths. Detailed complexity calculations highlighting the benefits of this approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.

Designing new cereal cultivars as an adaptation measure using crop model ensembles

To date, crop models have been little used for characterising the types of cultivars suited to a changed climate, though simulations of altered management (e.g. sowing) are often reported. However, in neither case are model uncertainties evaluated at the same time.

Description of microcolumnar ensembles in association cortex and their disruption in Alzheimer and Lewy body dementias

The cortex of the brain is organized into clear horizontal layers, laminae, which subserve much of the connectional anatomy of the brain. We hypothesize that there is also a vertical anatomical organization that might subserve local interactions of neuronal functional units, in accord with longstanding electrophysiological observations. We develop and apply a general quantitative method, inspired by analogous methods in condensed matter physics, to examine the anatomical organization of the cortex in human brain. We find, in addition to obvious laminae, anatomical evidence for tightly packed microcolumnar ensembles containing approximately 11 neurons, with a periodicity of about 80 μm. We examine the structural integrity of this new architectural feature in two common dementing illnesses, Alzheimer disease and dementia with Lewy bodies. In Alzheimer disease, there is a dramatic, nearly complete loss of microcolumnar ensemble organization. The relative degree of loss of microcolumnar ensembles is directly proportional to the number of neurofibrillary tangles, but not related to the amount of amyloid-β deposition. In dementia with Lewy bodies, a similar disruption of microcolumnar ensemble architecture occurs despite minimal neuronal loss. These observations show that quantitative analysis of complex cortical architecture can be applied to analyze the anatomical basis of brain disorders.