On the expected uniform error of geometric Brownian motion approximated by the L\'evy-Ciesielski construction

It is known that the Brownian bridge or L\'evy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show for geometric Brownian motion that at level $N$, at which there are $d=2^N$ points evaluated on the Brownian path, the expected uniform error has an upper bound of order $\mathcal{O}(\sqrt{N/2^N})$, or equivalently, $\mathcal{O}(\sqrt{\ln d/d})$. This upper bound matches the known order for the expected uniform error of the standard Brownian motion. We apply the result to an option pricing example

On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction

It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the uniform error. In particular, we show constructively that at level N, at which there are d = 2^N points evaluated on the Brownian path, the uniform error and its square, and the uniform error of geometric Brownian motion, have upper bounds of order O ( (ln d / d)^(1/2) ), matching the known orders. We apply the results to an option pricing example

On the expected uniform error of geometric Brownian motion approximated by the Lévy-Ciesielski construction

It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show for geometric Brownian motion that at level N , at which there are d = 2N points evaluated on the Brownian path, the expected uniform error has an upper bound of order O(√N/2N ), or equivalently, O(√lnd/d). This upper bound matches the known order for the expected uniform error of the standard Brownian motion. We apply the result to an option pricing example

Linking healthcare associated norovirus outbreaks: a molecular epidemiologic method for investigating transmission.

BACKGROUND: Noroviruses are highly infectious pathogens that cause gastroenteritis in the community and in semi-closed institutions such as hospitals. During outbreaks, multiple units within a hospital are often affected, and a major question for control programs is: are the affected units part of the same outbreak or are they unrelated transmission events? In practice, investigators often assume a transmission link based on epidemiological observations, rather than a systematic approach to tracing transmission.Here, we present a combined molecular and statistical method for assessing:1) whether observed clusters provide evidence of local transmission and2) the probability that anecdotally|linked outbreaks truly shared a transmission event. METHODS: 76 healthcare associated outbreaks were observed in an active and prospective surveillance scheme of 15 hospitals in the county of Avon, England from April 2002 to March 2003. Viral RNA from 64 out of 76 specimens from distinct outbreaks was amplified by reverse transcription-PCR and was sequenced in the polymerase (ORF 1) and capsid (ORF 2) regions. The genetic diversity, at the nucleotide level, was analysed in relation to the epidemiological patterns. RESULTS: Two out of four genetic and epidemiological clusters of outbreaks were unlikely to have occurred by chance alone, thus suggesting local transmission. There was anecdotal epidemiological evidence of a transmission link among 5 outbreaks pairs. By combining this epidemiological observation with viral sequence data, the evidence of a link remained convincing in 3 of these pairs. These results are sensitive to prior beliefs of the strength of epidemiological evidence especially when the outbreak strains are common in the background population. CONCLUSION: The evidence suggests that transmission between hospitals units does occur. Using the proposed criteria, certain hypothesized transmission links between outbreaks were supported while others were refuted. The combined molecular/epidemiologic approach presented here could be applied to other viral populations and potentially to other pathogens for a more thorough view of transmission

Quantifying performance of ultrasonic immersion inspection using phased arrays for curvilinear disc forgings

Use of full-matrix capture (FMC), combined with the total focusing method (TFM), has been shown to provide improvements to flaw sensitivity within components of irregular geometry. Ultrasonic immersion inspection of aerospace discs requires strict specifications to ensure full coverage – one of which is that all surfaces should be machined flat. The ability to detect defects through curved surfaces, with an equivalent sensitivity to that obtained through flat surfaces could bring many advantages. In this work, the relationship between surface curvature and sensitivity to standard defects was quantified for various front wall radii. Phased array FMC immersion inspection of curved components was simulated using finite element modelling, then visualized using surface-compensated focusing techniques. This includes the use of BRAIN software developed at the University of Bristol for production of TFM images. Modelling results were compared to experimental data from a series of test blocks with a range of curvatures, containing standard defects. The sensitivity to defects is evaluated by comparing the performance to conventional methods. Results are used to highlight the benefits and limitations of these methods relating to the application area of aerospace engine disc forgings

CCNF mutations in amyotrophic lateral sclerosis and frontotemporal dementia

Amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) are overlapping, fatal neurodegenerative disorders in which the molecular and pathogenic basis remains poorly understood. Ubiquitinated protein aggregates, of which TDP-43 is a major component, are a characteristic pathological feature of most ALS and FTD patients. Here we use genome-wide linkage analysis in a large ALS/FTD kindred to identify a novel disease locus on chromosome 16p13.3. Whole-exome sequencing identified a CCNF missense mutation at this locus. Interrogation of international cohorts identified additional novel CCNF variants in familial and sporadic ALS and FTD. Enrichment of rare protein-altering CCNF variants was evident in a large sporadic ALS replication cohort. CCNF encodes cyclin F, a component of an E3 ubiquitin-protein ligase complex (SCF(Cyclin F)). Expression of mutant CCNF in neuronal cells caused abnormal ubiquitination and accumulation of ubiquitinated proteins, including TDP-43 and a SCF(Cyclin F) substrate. This implicates common mechanisms, linked to protein homeostasis, underlying neuronal degeneration

Hamiltonians for Reduced Gravity

A generalised canonical formulation of gravity is devised for foliations of spacetime with codimension $n\ge1$. The new formalism retains n-dimensional covariance and is especially suited to 2+2 decompositions of spacetime. It is also possible to use the generalised formalism to obtain boundary contributions to the 3+1 Hamiltonian.Comment: 18 pages, revtex, 3 postscript figures include

Selection of variant viruses during replication and transmission of H7N1 viruses in chickens and turkeys

AbstractThe influence of different glycosylation patterns of the haemagglutinin glycoprotein of H7N1 avian influenza viruses on virus replication in vivo was examined. Experimental infection of chickens and turkeys was carried out with H7N1 avian influenza viruses with alternative sites of glycosylation in the haemagglutinin and infected birds were sampled daily by swabbing the buccal and cloacal cavities. cDNAs of the HA1 coding region of the HA gene were prepared from the swabs and cloned into plasmids. Sequencing multiple plasmids made from individual swabs taken over the period of virus shedding showed that viruses with specific patterns of glycosylation near the receptor binding site were stable when birds were infected with a single variant, but when presented with a mixed population of viruses encoding differing patterns of glycosylation a specific variant was rapidly selected in the infected host