Duality and higher derivative terms in M theory

Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D^6R^4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions this determines the coefficient of the D^6R^4 interaction in eleven-dimensional M-theory. These results are obtained by considering the four-graviton two-loop scattering amplitude in eleven-dimensional supergravity compactified on a circle and on a two-torus -- extending earlier results concerning lower-derivative interactions. The torus compactification leads to an interesting SL(2,Z)-invariant function of the complex structure of the torus (the IIB string coupling) that satisfies a Laplace equation with a source term on the fundamental domain of moduli space. The structure of this equation is in accord with general supersymmetry considerations and immediately determines tree-level and one-loop contributions to D^6R^4 in perturbative IIB string theory that agree with explicit string calculations, and two-loop and three-loop contributions that have yet to be obtained in string theory. The complete solution of the Laplace equation contains infinite series' of single D-instanton and double D-instanton contributions, in addition to the perturbative terms. General considerations of the higher loop diagrams of eleven-dimensional supergravity suggest extensions of these results to interactions of higher order in the low energy expansion.Comment: harvmac. 41 pages. 3 figures. v2 typos corrected and reference list updated. v3. Significant new subsection deriving the non-zero coefficient of the IIB string theory three-loop contributio

Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism.Comment: 10 pages harvmac te

Comparative Fate of Chemically Dispersed and Beached Crude Oil in Subtidal Sediments of the Arctic Nearshore

A three-year investigation was conducted to examine the incorporation of petroleum hydrocarbons (PHC) into subtidal sediments following experimental releases of oil during the Baffin Island Oil Spill (BIOS) Project experiments. The concentrations of PHC were determined by synchronous scanning UV/Fluorescence spectroscopy, while the composition of residual saturated and aromatic hydrocarbons was determined by gas chromatography and gas chromatographic mass spectrometry. ... The eroding oil from the Bay 11 beach was compositionally quite heterogeneous, with weathered, biodegraded oil, as well as relatively unweathered oil, found on the beach and in the offshore sediments. Biodegradation of oil appeared to be restricted to the beached oil, with no significant degradation apparently occurring subtidally. After two years, the offshore oil residues still contained low molecular weight alkanes as well as alkylated naphthalenes. The situation in Bay 9, where chemically dispersed oil was discharged near the bottom, was quite different. In spite of a large water column exposure, the bottom sediments never contained more than 10 micro g/g of oil. Of this amount of oil, a significant fraction (20%) of the PHC was initially associated with the surface flocculent layer. Levels of oil in the Bay 9 sediments were on the order of 1-3 micro g/g one year after the release. Sediment PHC levels in the other less exposed bays (Bays 10 and 7) never exceeded 3 micro g/g.Key words: BIOS, experimental oil spill, petroleum hydrocarbons, arctic sediments, oil pollutionMots clés: BIOS, déversement de pétrole expérimental, hydrocarbures pétroliers, sédiments arctiques, pollution par le pétrol

Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

A semi-parametric model for lactation curves: development and application

We propose a semi-parametric model for lactation curves that, along with stage of lactation, accounts for day of the year at milk recording and stage of gestation. Lactation is described as having 3 different phases defined by 2 change points of which the second is a function of gestation stage. Season of milk recording is modelled using cosine and sine functions. As an application, the model is used to estimate the association between intramammary infections (IMI) dynamics as measured by somatic cell count (SCC) over the dry period and the shape of the lactation curve. Milk recording data collected in 2128 herds from England and Wales between 2004 and 2007 were used in the analysis. From a random sample of 1000 of these herds, smoothed milk production was used to test the behaviour of the model and estimate model parameters. The first change point was set at 60 days in milk. The second change point was set at 100 days of gestation or 200 days in milk when the latter was not available. Using data from the 1128 remaining herds, multilevel models were then used to model individual test-day milk production within lactations within herds. Average milk production at 60 days in milk for cows of parities 1, 2, 3 and greater than 3 were 26.9 kg, 31.6 kg, 34.4 kg and 34.7 kg respectively and, after this stage, decreases in milk production per 100 days milk of lactation were 3.1 kg, 5.1 kg, 6.3 kg and 6.7 kg respectively. Compared to cows that had an SCC below 200,000 cells/mL on both the last milk recording in a lactation and the first milk recording in the following lactation, cows that had an SCC greater than 200,000 cells/mL on their first milk recording after calving had an estimated loss of milk production of between 216 and 518 kg depending on parity. These estimates demonstrate the impact of the dynamics of SCC during the dry period on milk production during the following lactation

A Bayesian micro-simulation to evaluate the cost-effectiveness of interventions for mastitis control during the dry period in UK dairy herds

Importance of the dry period with respect to mastitis control is now well established although the precise interventions that reduce the risk of acquiring intramammary infections during this time are not clearly understood. There are very few intervention studies that have measured the clinical efficacy of specific mastitis interventions within a cost-effectiveness framework so there remains a large degree of uncertainty about the impact of a specific intervention and its costeffectiveness. The aim of this study was to use a Bayesian framework to investigate the cost-effectiveness of mastitis controls during the dry period. Data were assimilated from 77 UK dairy farms that participated in a British national mastitis control programme during 2009–2012 in which the majority of intramammary infections were acquired during the dry period. The data consisted of clinical mastitis (CM) and somatic cell count (SCC) records, herd management practices and details of interventions that were implemented by the farmer as part of the control plan. The outcomes used to measure the effectiveness of the interventions were i) changes in the incidence rate of clinical mastitis during the first 30 days after calving and ii) the rate at which cows gained new infections during the dry period (measured by SCC changes across the dry period from 200,000 cells/ml). A Bayesian one-step microsimulation model was constructed such that posterior predictions from the model incorporated uncertainty in all parameters. The incremental net benefit was calculated across 10,000 Markov chain Monte Carlo iterations, to estimate the cost-benefit (and associated uncertainty) of each mastitis intervention. Interventions identified as being cost-effective in most circumstances included selecting dry-cow therapy at the cow level, dry-cow rations formulated by a qualified nutritionist, use of individual calving pens, first milking cows within 24 h of calving and spreading bedding evenly in dry-cow yards. The results of this study highlighted the efficacy of specific mastitis interventions in UK conditions which, when incorporated into a costeffectiveness framework, can be used to optimize decision making in mastitis control. This intervention study provides an example of how an intuitive and clinically useful Bayesian approach can be used to form the basis of an on-farm decision support tool

QCD Strings as Constrained Grassmannian Sigma Model:

We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.Comment: 22 pages, Preprint: SFU HEP-116-9

Minimum mass of galaxies from BEC or scalar field dark matter

Many problems of cold dark matter models such as the cusp problem and the missing satellite problem can be alleviated, if galactic halo dark matter particles are ultra-light scalar particles and in Bose-Einstein condensate (BEC), thanks to a characteristic length scale of the particles. We show that this finite length scale of the dark matter can also explain the recently observed common central mass of the Milky Way satellites ($\sim 10^7 M_\odot$) independent of their luminosity, if the mass of the dark matter particle is about $10^{-22} eV$.Comment: 10 pages, 1 figure, accepted in JCA

A probabilistic model for gene content evolution with duplication, loss, and horizontal transfer

We introduce a Markov model for the evolution of a gene family along a phylogeny. The model includes parameters for the rates of horizontal gene transfer, gene duplication, and gene loss, in addition to branch lengths in the phylogeny. The likelihood for the changes in the size of a gene family across different organisms can be calculated in O(N+hM^2) time and O(N+M^2) space, where N is the number of organisms, $h$ is the height of the phylogeny, and M is the sum of family sizes. We apply the model to the evolution of gene content in Preoteobacteria using the gene families in the COG (Clusters of Orthologous Groups) database

Gravitational excitons from extra dimensions

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential have a form of massive scalar fields in the external space-time. Parameters of models which ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20 pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97