A Common Market Measure for Libor and Pricing Caps, Floors and Swaps in a Field Theory of Forward Interest Rates

The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally for such models. To elaborate how the martingale for the Libor belongs to the general class of numeraire for the forward interest rates, two other numeraire's are considered, namely the money market measure that makes the evolution of the zero coupon bonds a martingale, and the forward measure for which the forward bond price is a martingale. The price of an interest rate cap is computed for all three numeraires, and is shown to be numeraire invariant. Put-call parity is discussed in some detail and shown to emerge due to some non-trivial properties of the numeraires. Some properties of swaps, and their relation to caps and floors, are briefly discussed.Comment: 28 pages, 4 figure

Time-Changed Fast Mean-Reverting Stochastic Volatility Models

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales

Multiple indices of diffusion identifies white matter damage in mild cognitive impairment and Alzheimer's disease

The study of multiple indices of diffusion, including axial (DA), radial (DR) and mean diffusion (MD), as well as fractional anisotropy (FA), enables WM damage in Alzheimer's disease (AD) to be assessed in detail. Here, tract-based spatial statistics (TBSS) were performed on scans of 40 healthy elders, 19 non-amnestic MCI (MCIna) subjects, 14 amnestic MCI (MCIa) subjects and 9 AD patients. Significantly higher DA was found in MCIna subjects compared to healthy elders in the right posterior cingulum/precuneus. Significantly higher DA was also found in MCIa subjects compared to healthy elders in the left prefrontal cortex, particularly in the forceps minor and uncinate fasciculus. In the MCIa versus MCIna comparison, significantly higher DA was found in large areas of the left prefrontal cortex. For AD patients, the overlap of FA and DR changes and the overlap of FA and MD changes were seen in temporal, parietal and frontal lobes, as well as the corpus callosum and fornix. Analysis of differences between the AD versus MCIna, and AD versus MCIa contrasts, highlighted regions that are increasingly compromised in more severe disease stages. Microstructural damage independent of gross tissue loss was widespread in later disease stages. Our findings suggest a scheme where WM damage begins in the core memory network of the temporal lobe, cingulum and prefrontal regions, and spreads beyond these regions in later stages. DA and MD indices were most sensitive at detecting early changes in MCIa

Local regularity for fractional heat equations

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0756

Sensitivity and Specificity of Multiple Kato-Katz Thick Smears and a Circulating Cathodic Antigen Test for Schistosoma mansoni Diagnosis Pre- and Post-repeated-Praziquantel Treatment

Two Kato-Katz thick smears (Kato-Katzs) from a single stool are currently recommended for diagnosing Schistosoma mansoni infections to map areas for intervention. This ‘gold standard’ has low sensitivity at low infection intensities. The urine point-of-care circulating cathodic antigen test (POC-CCA) is potentially more sensitive but how accurately they detect S. mansoni after repeated praziquantel treatments, their suitability for measuring drug efficacy and their correlation with egg counts remain to be fully understood. We compared the accuracies of one to six Kato-Katzs and one POC-CCA for the diagnosis of S. mansoni in primary-school children who have received zero to ten praziquantel treatments. We determined the impact each diagnostic approach may have on monitoring and evaluation (M&E) and drug-efficacy findings

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Using Support Vector Machines with Multiple Indices of Diffusion for Automated Classification of Mild Cognitive Impairment

Few studies have looked at the potential of using diffusion tensor imaging (DTI) in conjunction with machine learning algorithms in order to automate the classification of healthy older subjects and subjects with mild cognitive impairment (MCI). Here we apply DTI to 40 healthy older subjects and 33 MCI subjects in order to derive values for multiple indices of diffusion within the white matter voxels of each subject. DTI measures were then used together with support vector machines (SVMs) to classify control and MCI subjects. Greater than 90% sensitivity and specificity was achieved using this method, demonstrating the potential of a joint DTI and SVM pipeline for fast, objective classification of healthy older and MCI subjects. Such tools may be useful for large scale drug trials in Alzheimer's disease where the early identification of subjects with MCI is critical

The genomic architecture of novel Simulium damnosum Wolbachia prophage sequence elements and implications for onchocerciasis epidemiology

Research interest in Wolbachia is growing as new discoveries and technical advancements reveal the public health importance of both naturally occurring and artificial infections. Improved understanding of the Wolbachia bacteriophages (WOs) WOcauB2 and WOcauB3 [belonging to a sub-group of four WOs encoding serine recombinases group 1 (sr1WOs)], has enhanced the prospect of novel tools for the genetic manipulation of Wolbachia. The basic biology of sr1WOs, including host range and mode of genomic integration is, however, still poorly understood. Very few sr1WOs have been described, with two such elements putatively resulting from integrations at the same Wolbachia genome loci, about 2 kb downstream from the FtsZ cell-division gene. Here, we characterize the DNA sequence flanking the FtsZ gene of wDam, a genetically distinct line of Wolbachia isolated from the West African onchocerciasis vector Simulium squamosum E. Using Roche 454 shot-gun and Sanger sequencing, we have resolved >32 kb of WO prophage sequence into three contigs representing three distinct prophage elements. Spanning ≥36 distinct WO open reading frame gene sequences, these prophage elements correspond roughly to three different WO modules: a serine recombinase and replication module (sr1RRM), a head and base-plate module and a tail module. The sr1RRM module contains replication genes and a Holliday junction recombinase and is unique to the sr1 group WOs. In the extreme terminal of the tail module there is a SpvB protein homolog—believed to have insecticidal properties and proposed to have a role in how Wolbachia parasitize their insect hosts. We propose that these wDam prophage modules all derive from a single WO genome, which we have named here sr1WOdamA1. The best-match database sequence for all of our sr1WOdamA1-predicted gene sequences was annotated as of Wolbachia or Wolbachia phage sourced from an arthropod. Clear evidence of exchange between sr1WOdamA1 and other Wolbachia WO phage sequences was also detected. These findings provide insights into how Wolbachia could affect a medically important vector of onchocerciasis, with potential implications for future control methods, as well as supporting the hypothesis that Wolbachia phages do not follow the standard model of phage evolution

Multi-parallel qPCR provides increased sensitivity and diagnostic breadth for gastrointestinal parasites of humans: field-based inferences on the impact of mass deworming

BACKGROUND: Although chronic morbidity in humans from soil transmitted helminth (STH) infections can be reduced by anthelmintic treatment, inconsistent diagnostic tools make it difficult to reliably measure the impact of deworming programs and often miss light helminth infections. METHODS: Cryopreserved stool samples from 796 people (aged 2-81 years) in four villages in Bungoma County, western Kenya, were assessed using multi-parallel qPCR for 8 parasites and compared to point-of-contact assessments of the same stools by the 2-stool 2-slide Kato-Katz (KK) method. All subjects were treated with albendazole and all Ascaris lumbricoides expelled post-treatment were collected. Three months later, samples from 633 of these people were re-assessed by both qPCR and KK, re-treated with albendazole and the expelled worms collected. RESULTS: Baseline prevalence by qPCR (n = 796) was 17 % for A. lumbricoides, 18 % for Necator americanus, 41 % for Giardia lamblia and 15% for Entamoeba histolytica. The prevalence was <1% for Trichuris trichiura, Ancylostoma duodenale, Strongyloides stercoralis and Cryptosporidium parvum. The sensitivity of qPCR was 98% for A. lumbricoides and N. americanus, whereas KK sensitivity was 70% and 32%, respectively. Furthermore, qPCR detected infections with T. trichiura and S. stercoralis that were missed by KK, and infections with G. lamblia and E. histolytica that cannot be detected by KK. Infection intensities measured by qPCR and by KK were correlated for A. lumbricoides (r = 0.83, p < 0.0001) and N. americanus (r = 0.55, p < 0.0001). The number of A. lumbricoides worms expelled was correlated (p < 0.0001) with both the KK (r = 0.63) and qPCR intensity measurements (r = 0.60). CONCLUSIONS: KK may be an inadequate tool for stool-based surveillance in areas where hookworm or Strongyloides are common or where intensity of helminth infection is low after repeated rounds of chemotherapy. Because deworming programs need to distinguish between populations where parasitic infection is controlled and those where further treatment is required, multi-parallel qPCR (or similar high throughput molecular diagnostics) may provide new and important diagnostic information