A stochastic approximation scheme and convergence theorem for particle interactions with perfectly reflecting boundaries

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and drift of the set of particles. Each particle carries a number of internal coordinates which may evolve continuously in time, determined by what we will refer to as the internal drift, or discretely via the interaction kernels. Perfectly reflecting boundary conditions are imposed on the system and all the processes may be spatially and temporally inhomogeneous. We use a relative compactness argument to construct a sequence of measures that converge weakly to a solution of the governing equation. Since the proof of existence is a constructive one, it provides a stochastic approximation scheme that can be used for the numerical study of molecular dynamics.Comment: 43 page

The Adiabatic Invariance of the Action Variable in Classical Dynamics

We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We present a new proof of the adiabatic invariance of this quantity and illustrate our arguments by means of explicit calculations for the harmonic oscillator. The new proof makes essential use of the Hamiltonian formalism. The key step is the introduction of a slowly-varying quantity closely related to the action variable. This new quantity arises naturally within the Hamiltonian framework as follows: a canonical transformation is first performed to convert the system to action-angle coordinates; then the new quantity is constructed as an action integral (effectively a new action variable) using the new coordinates. The integration required for this construction provides, in a natural way, the averaging procedure introduced in other proofs, though here it is an average in phase space rather than over time.Comment: 8 page

Potential for airborne transmission of infection in the waiting areas of healthcare premises: stochastic analysis using a Monte Carlo model

BACKGROUND: Although many infections that are transmissible from person to person are acquired through direct contact between individuals, a minority, notably pulmonary tuberculosis (TB), measles and influenza are known to be spread by the airborne route. Airborne infections pose a particular threat to susceptible individuals whenever they are placed together with the index case in confined spaces. With this in mind, waiting areas of healthcare facilities present a particular challenge, since large numbers of people, some of whom may have underlying conditions which predispose them to infection, congregate in such spaces and can be exposed to an individual who may be shedding potentially pathogenic microorganisms. It is therefore important to understand the risks posed by infectious individuals in waiting areas, so that interventions can be developed to minimise the spread of airborne infections. METHOD: A stochastic Monte Carlo model was constructed to analyse the transmission of airborne infection in a hypothetical 132 m3 hospital waiting area in which occupancy levels, waiting times and ventilation rate can all be varied. In the model the Gammaitoni-Nucci equation was utilized to predict probability of susceptible individuals becoming infected. The model was used to assess the risk of transmission of three infectious diseases, TB, influenza and measles. In order to allow for stochasticity a random number generator was applied to the variables in the model and a total of 10000 individual simulations were undertaken. The mean quanta production rates used in the study were 12.7, 100 and 570 per hour for TB, influenza and measles, respectively. RESULTS: The results of the study revealed the mean probability of acquiring a TB infection during a 30-minute stay in the waiting area to be negligible (i.e. 0.0034), while that for influenza was an order of magnitude higher at 0.0262. By comparison the mean probability of acquiring a measles infection during the same period was 0.1349. If the duration of the stay was increased to 60 minutes then these values increased to 0.0087, 0.0662 and 0.3094, respectively. CONCLUSION: Under normal circumstances the risk of acquiring a TB infection during a visit to a hospital waiting area is minimal. Likewise the risks associated with the transmission of influenza, although an order of magnitude greater than those for TB, are relatively small. By comparison, the risks associated with measles are high. While the installation of air disinfection may be beneficial, when seeking to prevent the transmission of airborne viral infection it is important to first minimize waiting times and the number of susceptible individuals present before turning to expensive technological solutions

Epidermal Neural Crest Stem Cell (EPI-NCSC)—Mediated Recovery of Sensory Function in a Mouse Model of Spinal Cord Injury

Here we show that epidermal neural crest stem cell (EPI-NCSC) transplants in the contused spinal cord caused a 24% improvement in sensory connectivity and a substantial recovery of touch perception. Furthermore we present a novel method for the ex vivo expansion of EPI-NCSC into millions of stem cells that takes advantage of the migratory ability of neural crest stem cells and is based on a new culture medium and the use of microcarriers. Functional improvement was shown by two independent methods, spinal somatosensory evoked potentials (SpSEP) and the Semmes-Weinstein touch test. Subsets of transplanted cells differentiated into myelinating oligodendrocytes. Unilateral injections of EPI-NCSC into the lesion of midline contused mouse spinal cords elicited bilateral improvements. Intraspinal EPI-NCSC did not migrate laterally in the spinal cord or invade the spinal roots and dorsal root ganglia, thus implicating diffusible factors. EPI-NCSC expressed neurotrophic factors, angiogenic factors, and metalloproteases. The strength of EPI-NCSC thus is that they can exert a combination of pertinent functions in the contused spinal cord, including cell replacement, neuroprotection, angiogenesis and modulation of scar formation. EPI-NCSC are uniquely qualified for cell-based therapy in spinal cord injury, as neural crest cells and neural tube stem cells share a higher order stem cell and are thus ontologically closely related

Complex Reorganization and Predominant Non-Homologous Repair Following Chromosomal Breakage in Karyotypically Balanced Germline Rearrangements and Transgenic Integration

We defined the genetic landscape of balanced chromosomal rearrangements at nucleotide resolution by sequencing 141 breakpoints from cytogenetically-interpreted translocations and inversions. We confirm that the recently described phenomenon of “chromothripsis” (massive chromosomal shattering and reorganization) is not unique to cancer cells but also occurs in the germline where it can resolve to a karyotypically balanced state with frequent inversions. We detected a high incidence of complex rearrangements (19.2%) and substantially less reliance on microhomology (31%) than previously observed in benign CNVs. We compared these results to experimentally-generated DNA breakage-repair by sequencing seven transgenic animals, and revealed extensive rearrangement of the transgene and host genome with similar complexity to human germline alterations. Inversion is the most common rearrangement, suggesting that a combined mechanism involving template switching and non-homologous repair mediates the formation of balanced complex rearrangements that are viable, stably replicated and transmitted unaltered to subsequent generations

A global perspective on the trophic geography of sharks

Sharks are a diverse group of mobile predators that forage across varied spatial scales and have the potential to influence food web dynamics. The ecological consequences of recent declines in shark biomass may extend across broader geographic ranges if shark taxa display common behavioural traits. By tracking the original site of photosynthetic fixation of carbon atoms that were ultimately assimilated into muscle tissues of 5,394 sharks from 114 species, we identify globally consistent biogeographic traits in trophic interactions between sharks found in different habitats. We show that populations of shelf-dwelling sharks derive a substantial proportion of their carbon from regional pelagic sources, but contain individuals that forage within additional isotopically diverse local food webs, such as those supported by terrestrial plant sources, benthic production and macrophytes. In contrast, oceanic sharks seem to use carbon derived from between 30° and 50° of latitude. Global-scale compilations of stable isotope data combined with biogeochemical modelling generate hypotheses regarding animal behaviours that can be tested with other methodological approaches.This research was conducted as part of C.S.B.’s Ph.D dissertation, which was funded by the University of Southampton and NERC (NE/L50161X/1), and through a NERC Grant-in-Kind from the Life Sciences Mass Spectrometry Facility (LSMSF; EK267-03/16). We thank A. Bates, D. Sims, F. Neat, R. McGill and J. Newton for their analytical contributions and comments on the manuscripts.Peer reviewe

Oral abstracts 3: RA Treatment and outcomesO13. Validation of jadas in all subtypes of juvenile idiopathic arthritis in a clinical setting

Background: Juvenile Arthritis Disease Activity Score (JADAS) is a 4 variable composite disease activity (DA) score for JIA (including active 10, 27 or 71 joint count (AJC), physician global (PGA), parent/child global (PGE) and ESR). The validity of JADAS for all ILAR subtypes in the routine clinical setting is unknown. We investigated the construct validity of JADAS in the clinical setting in all subtypes of JIA through application to a prospective inception cohort of UK children presenting with new onset inflammatory arthritis. Methods: JADAS 10, 27 and 71 were determined for all children in the Childhood Arthritis Prospective Study (CAPS) with complete data available at baseline. Correlation of JADAS 10, 27 and 71 with single DA markers was determined for all subtypes. All correlations were calculated using Spearman's rank statistic. Results: 262/1238 visits had sufficient data for calculation of JADAS (1028 (83%) AJC, 744 (60%) PGA, 843 (68%) PGE and 459 (37%) ESR). Median age at disease onset was 6.0 years (IQR 2.6-10.4) and 64% were female. Correlation between JADAS 10, 27 and 71 approached 1 for all subtypes. Median JADAS 71 was 5.3 (IQR 2.2-10.1) with a significant difference between median JADAS scores between subtypes (p < 0.01). Correlation of JADAS 71 with each single marker of DA was moderate to high in the total cohort (see Table 1). Overall, correlation with AJC, PGA and PGE was moderate to high and correlation with ESR, limited JC, parental pain and CHAQ was low to moderate in the individual subtypes. Correlation coefficients in the extended oligoarticular, rheumatoid factor negative and enthesitis related subtypes were interpreted with caution in view of low numbers. Conclusions: This study adds to the body of evidence supporting the construct validity of JADAS. JADAS correlates with other measures of DA in all ILAR subtypes in the routine clinical setting. Given the high frequency of missing ESR data, it would be useful to assess the validity of JADAS without inclusion of the ESR. Disclosure statement: All authors have declared no conflicts of interest. Table 1Spearman's correlation between JADAS 71 and single markers DA by ILAR subtype ILAR Subtype Systemic onset JIA Persistent oligo JIA Extended oligo JIA Rheumatoid factor neg JIA Rheumatoid factor pos JIA Enthesitis related JIA Psoriatic JIA Undifferentiated JIA Unknown subtype Total cohort Number of children 23 111 12 57 7 9 19 7 17 262 AJC 0.54 0.67 0.53 0.75 0.53 0.34 0.59 0.81 0.37 0.59 PGA 0.63 0.69 0.25 0.73 0.14 0.05 0.50 0.83 0.56 0.64 PGE 0.51 0.68 0.83 0.61 0.41 0.69 0.71 0.9 0.48 0.61 ESR 0.28 0.31 0.35 0.4 0.6 0.85 0.43 0.7 0.5 0.53 Limited 71 JC 0.29 0.51 0.23 0.37 0.14 -0.12 0.4 0.81 0.45 0.41 Parental pain 0.23 0.62 0.03 0.57 0.41 0.69 0.7 0.79 0.42 0.53 Childhood health assessment questionnaire 0.25 0.57 -0.07 0.36 -0.47 0.84 0.37 0.8 0.66 0.4