MDL Convergence Speed for Bernoulli Sequences

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is finitely bounded, implying convergence with probability one, and (b) it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound (comparable to the one for Bayes mixtures) for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models.Comment: 28 page

Circular dichroism of cholesteric polymers and the orbital angular momentum of light

We explore experimentally if the light's orbital angular momentum (OAM) interacts with chiral nematic polymer films. Specifically, we measure the circular dichroism of such a material using light beams with different OAM. We investigate the case of strongly focussed, non-paraxial light beams, where the spatial and polarization degrees of freedom are coupled. Within the experimental accuracy, we cannot find any influence of the OAM on the circular dichroism of the cholesteric polymer.Comment: 3 pages, 4 figure

High titers of transmissible spongiform encephalopathy infectivity associated with extremely low levels of PrP in vivo

Rona Barron - ORCID: 0000-0003-4512-9177 https://orcid.org/0000-0003-4512-9177Diagnosis of transmissible spongiform encephalopathy (TSE) disease in humans and ruminants relies on the detection in post-mortem brain tissue of the protease-resistant form of the host glycoprotein PrP. The presence of this abnormal isoform (PrPSc) in tissues is taken as indicative of the presence of TSE infectivity. Here we demonstrate conclusively that high titers of TSE infectivity can be present in brain tissue of animals that show clinical and vacuolar signs of TSE disease but contain low or undetectable levels of PrPSc. This work questions the correlation between PrPSc level and the titer of infectivity and shows that tissues containing little or no proteinase K-resistant PrP can be infectious and harbor high titers of TSE infectivity. Reliance on protease-resistant PrPSc as a sole measure of infectivity may therefore in some instances significantly underestimate biological properties of diagnostic samples, thereby undermining efforts to contain and eradicate TSEs.https://doi.org/10.1074/jbc.M704329200282pubpub4

Relating Agulhas leakage to the Agulhas Current retroflection location

The relation between the Agulhas Current retroflection location and the magnitude of Agulhas leakage, the transport of water from the Indian to the Atlantic Ocean, is investigated in a high-resolution numerical ocean model. Sudden eastward retreats of the Agulhas Current retroflection loop are linearly related to the shedding of Agulhas rings, where larger retreats generate larger rings. Using numerical Lagrangian floats a 37 year time series of the magnitude of Agulhas leakage in the model is constructed. The time series exhibits large amounts of variability, both on weekly and annual time scales. A linear relation is found between the magnitude of Agulhas leakage and the location of the Agulhas Current retroflection, both binned to three month averages. In the relation, a more westward location of the Agulhas Current retroflection corresponds to an increased transport from the Indian Ocean to the Atlantic Ocean. When this relation is used in a linear regression and applied to almost 20 years of altimetry data, it yields a best estimate of the mean magnitude of Agulhas leakage of 13.2 Sv. The early retroflection of 2000, when Agulhas leakage was probably halved, can be identified using the regression

SUSY vertex algebras and supercurves

This article is a continuation of math.QA/0603633 Given a strongly conformal SUSY vertex algebra V and a supercurve X we construct a vector bundle V_X on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle V_X, corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra.Comment: 50 page

Ab initio parametrised model of strain-dependent solubility of H in alpha-iron

The calculated effects of interstitial hydrogen on the elastic properties of alpha-iron from our earlier work are used to describe the H interactions with homogeneous strain fields using ab initio methods. In particular we calculate the H solublility in Fe subject to hydrostatic, uniaxial, and shear strain. For comparison, these interactions are parametrised successfully using a simple model with parameters entirely derived from ab initio methods. The results are used to predict the solubility of H in spatially-varying elastic strain fields, representative of realistic dislocations outside their core. We find a strong directional dependence of the H-dislocation interaction, leading to strong attraction of H by the axial strain components of edge dislocations and by screw dislocations oriented along the critical slip direction. We further find a H concentration enhancement around dislocation cores, consistent with experimental observations.Comment: part 2/2 from splitting of 1009.3784 (first part was 1102.0187), minor changes from previous version

The Holocene history of the North American Monsoon: 'known knowns' and 'known unknowns' in understanding its spatial and temporal complexity

Evidence for climatic change across the North American Monsoon (NAM) and adjacent areas is reviewed, drawing on continental and marine records and the application of climate models. Patterns of change at 12,000, 9000, 6000 and 4000 cal yr BP are presented to capture the nature of change from the Younger Dryas (YD) and through the mid-Holocene. At the YD, conditions were cooler overall, wetter in the north and drier in the south, while moving into the Holocene wetter conditions became established in the south and then spread north as the NAM strengthened. Until c. 8,000 cal yr BP, the Laurentide Ice Sheet influenced precipitation in the north by pushing the Bermuda High further south. The peak extent of the NAM seems to have occurred around 6000 cal yr BP. 4000 cal yr BP marks the start of important changes across the NAM region, with drying in the north and the establishment of the clear differences between the summer-rain dominated south and central areas and the north, where winter rain is more important. This differentiation between south and north is crucial to understanding many climate responses across the NAM. This increasing variability is coincident with the declining influence of orbital forcing. 4000 cal yr BP also marks the onset of significant anthropogenic activity in many areas. For the last 2000 years, the focus is on higher temporal resolution change, with strong variations across the region. The Medieval Climate Anomaly (MCA) is characterised by centennial scale ‘megadrought’ across the southwest USA, associated with cooler tropical Pacific SSTs and persistent La Niña type conditions. Proxy data from southern Mexico, Central America and the Caribbean reveal generally wetter conditions, whereas records from the highlands of central Mexico and much of the Yucatan are typified by long -term drought. The Little Ice Age (LIA), in the north, was characterised by cooler, wetter winter conditions that have been linked with increased frequency of El Niño’s. Proxy records in the central and southern regions reveal generally dry LIA conditions, consistent with cooler SSTs in the Caribbean and Gulf of Mexico. This synthesis demonstrates that in some periods, one major forcing can dominate across the whole area (e.g. insolation in the early-mid Holocene), but at other times there is strong variability in patterns of change due to the differential impact of forcings such as the Pacific Decadal Oscillation (PDO) and the Atlantic Multidecadal Oscillation (AMO) on precipitation seasonality

On Convergence Properties of Shannon Entropy

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities. Convergence of differential entropy is also characterized in terms of the Kullback-Liebler discriminant for densities with fairly general supports, and it is shown that convergence in variation of probability measures guarantees such convergence under an appropriate boundedness condition on the densities involved. Results for the discrete setting are also provided, allowing for infinitely supported probability measures, by taking advantage of the equivalence between weak convergence and convergence in variation in this setting.Comment: Submitted to IEEE Transactions on Information Theor