Forecasting using relative entropy

The paper describes a relative entropy procedure for imposing moment restrictions on simulated forecast distributions from a variety of models. Starting from an empirical forecast distribution for some variables of interest, the technique generates a new empirical distribution that satisfies a set of moment restrictions. The new distribution is chosen to be as close as possible to the original in the sense of minimizing the associated Kullback-Leibler Information Criterion, or relative entropy. The authors illustrate the technique by using several examples that show how restrictions from other forecasts and from economic theory may be introduced into a model's forecasts.Forecasting

Search for Large Rapidity Gap Events in e^+ e^- Annihilation

We investigate the cross-section for the production of a low-mass colour-singlet cluster in $e^+e^-$ annihilation with a large rapidity gap between the colour-singlet cluster and the other jets. It is argued that such events are the cross-channel analogue of large-rapidity-gap events in deep-inelastic scattering, and therefore could in principle be used to investigate the analytic continuation of the BFKL pomeron to the positive-$t$ kinematic regime, where one would expect the trajectory to pass through glueball states. The cross section can be calculated in perturbative QCD, so that the infrared scale arising from non-perturbative effects, which prevents an exponential fall-off with rapidity gap in the case of deep-inelastic scattering, is absent in $e^+ e^-$ annihilation. Correspondingly, the cross section for such events decreases rapidly with increasing rapidity gap.Comment: LATEX file - 21 pages + 15 figure

Stylolites in the Burlington Limestone near Kinderhook, Illinois

Weil developed stylolites showing a peculiar relationship to chert occur in the Burlington limestone north of Kinderhook, Illinois. Specimens were studied by the preparation of insoluble residues of the limestone and clay cap, and by making thin sections of the chert nodules. Stockdale\u27s conclusion of origin by solution in an indurated rock is ascribed to for the stylolites in question because, (1) crinoid stems are fluted along the sides of prongs the same as the mass of the rock, (2) the suite of minerals occurring in the clay cap\u27\u27 represents nearly a true average of the suites of minerals from the residues above and below the stylolite, (3) the chert in every case examined was prior to the stylolite formation as shown by fluting along the sides and pitting of upper and lower surfaces, and (4) the presence of systems of subsidiary stylolites which crosscut the prongs of the earlier and larger system. The thickness of the clay cap has little relation to the amount of material removed, as it varied up to 75 per cent soluble

Fast Sorting of Weyl Sequences Using Comparisons

An algorithm is given which makes only $O(\log n)$ comparisons, and which will determine the ordering of the uniformly distributed (pseudo random) Weyl sequences given by $\{ (k\alpha )\bmod 1:1 \leqq k \leqq n\}$, where $\alpha$ is an unspecified irrational number. This result is shown to be best possible in the sense that no algorithm can perform the same task with fewer than $\Omega (\log n)$ comparisons

Astrophysical Probes of the Constancy of the Velocity of Light

We discuss possible tests of the constancy of the velocity of light using distant astrophysical sources such as gamma-ray bursters (GRBs), Active Galactic Nuclei (AGNs) and pulsars. This speculative quest may be motivated by some models of quantum fluctuations in the space-time background, and we discuss explicitly how an energy-dependent variation in photon velocity \delta c/ c \sim - E / M arises in one particular quantum-gravitational model. We then discuss how data on GRBs may be used to set limits on variations in the velocity of light, which we illustrate using BATSE and OSSE observations of the GRBs that have recently been identified optically and for which precise redshifts are available. We show how a regression analysis can be performed to look for an energy-dependent effect that should correlate with redshift. The present data yield a limit M \gsim 10^{15} GeV for the quantum gravity scale. We discuss the prospects for improving this analysis using future data, and how one might hope to distinguish any positive signal from astrophysical effects associated with the sources.Comment: 37 pages LaTeX, 9 eps figures included, uses aasms4.st

M Theory from World-Sheet Defects in Liouville String

We have argued previously that black holes may be represented in a D-brane approach by monopole and vortex defects in a sine-Gordon field theory model of Liouville dynamics on the world sheet. Supersymmetrizing this sine-Gordon system, we find critical behaviour in 11 dimensions, due to defect condensation that is the world-sheet analogue of D-brane condensation around an extra space-time dimension in M theory. This supersymmetric description of Liouville dynamics has a natural embedding within a 12-dimensional framework suggestive of F theory.Comment: 17 pages LATEX, 1 epsf figure include

Investigating the effects of inter-annual weather variation (1968- 2016) on the functional response of cereal grain yield to applied nitrogen, using data from the Rothamsted Long-Term experiments

The effect of weather on inter-annual variation in the crop yield response to nitrogen (N) fertilizer for winter wheat (Triticum aestivvum L.) and spring barley (Hordeum vulgare L.) was investigated using yield data from the Broadbalk Wheat and Hoosfield Spring Barley long-term experiments at Rothamsted Research. Grain yields of crops from 1968 to 2016 were modelled as a function of N rates using a linear-plus-exponential (LEXP) function. The extent to which inter-annual variation in the parameters of these responses was explained by variations in weather (monthly summarized temperatures and rainfall), and by changes in the cultivar grown, was assessed. The inter-annual variability in rainfall and underlying temperature influenced the crop N response and hence grain yields in both crops. Asymptotic yields in wheat were particularly sensitive to mean temperature in November, April and May, and to total rainfall in October, February and June. In spring barley asymptotic yields were sensitive to mean temperature in February and June, and to total rainfall in April to July inclusive and September. The method presented here explores the separation of agronomic and environmental (weather) influences on crop yield over time. Fitting N response curves across multiple treatments can support an informative analysis of the influence of weather variation on the yield variability. Whilst there are issues of the confounding and collinearity of explanatory variables within such models, and that other factors also influence yields over time, our study confirms the considerable impact of weather variables at certain times of the year. This emphasizes the importance of including weather temporal variation when evaluating the impacts of climate change on crops

Metastable Charged Sparticles and the Cosmological Li7 Problem

We consider the effects of metastable charged sparticles on Big-Bang Nucleosynthesis (BBN), including bound-state reaction rates and chemical effects. We make a new analysis of the bound states of negatively-charged massive particles with the light nuclei most prominent in BBN, and present a new code to track their abundances, paying particular attention to that of Li7. Assuming, as an example, that the gravitino is the lightest supersymmetric particle (LSP), and that the lighter stau slepton, stau_1, is the metastable next-to-lightest sparticle within the constrained minimal supersymmetric extension of the Standard Model (CMSSM), we analyze the possible effects on the standard BBN abundances of stau_1 bound states and decays for representative values of the gravitino mass. Taking into account the constraint on the CMSSM parameter space imposed by the discovery of the Higgs boson at the LHC, we delineate regions in which the fit to the measured light-element abundances is as good as in standard BBN. We also identify regions of the CMSSM parameter space in which the bound state properties, chemistry and decays of metastable charged sparticles can solve the cosmological Li7 problem.Comment: 49 pages, 29 eps figure

Small Business Enterprise and Development: Consultation Modes

By  means  of four   illustrative  case studies,  consultation  interventions  in small  and  medium sized  (SMEs)  enterprises  are  explored     Recognized  consultation  intervention  modes  of 'expert ',  'doctor-patient' and  'process  consultation'  are found  to fluctuate  rapidly  within each case st11dy, making apparent the need for  consultants to be flexible  and adopt an appropriate stance for  client and contingencies of the situation.  The permeability  of the boundaries between content and process issues, with diagnosis and intervention inter-woven, is also apparent. The article concludes with a consideration of the conditions for success for different consultation modes with small businesses and implications for small businesses and enterprise development in their use of consultants

Nuclear Reaction Uncertainties, Massive Gravitino Decays and the Cosmological Lithium Problem

We consider the effects of uncertainties in nuclear reaction rates on the cosmological constraints on the decays of unstable particles during or after Big-Bang nucleosynthesis (BBN). We identify the nuclear reactions due to non-thermal hadrons that are the most important in perturbing standard BBN, then quantify the uncertainties in these reactions and in the resulting light-element abundances. These results also indicate the key nuclear processes for which improved cross section data would allow different light-element abundances to be determined more accurately, thereby making possible more precise probes of BBN and evaluations of the cosmological constraints on unstable particles. Applying this analysis to models with unstable gravitinos decaying into neutralinos, we calculate the likelihood function for the light-element abundances measured currently, taking into account the current experimental errors in the determinations of the relevant nuclear reaction rates. We find a region of the gravitino mass and abundance in which the abundances of deuterium, He4 and Li7 may be fit with chi^2 = 5.5, compared with chi^2 = 31.7 if the effects of gravitino decays are unimportant. The best-fit solution is improved to chi^2 ~ 2.0 when the lithium abundance is taken from globular cluster data. Some such re-evaluation of the observed light-element abundances and/or nuclear reaction rates would be needed if this region of gravitino parameters is to provide a complete solution to the cosmological Li7 problem.Comment: 24 pages, 10 figure