Realizability of Point Processes

There are various situations in which it is natural to ask whether a given collection of k functions, ρ j (r 1,…,r j ), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ j ’s for this to be true. Our primary examples are X=ℝ d , X=ℤ d , and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently small densities ρ 1(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example in which a uniform density ρ and translation invariant ρ 2 are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established.

Modelling climate change: the role of unresolved processes

Our understanding of the climate system has been revolutionized recently, by the development of sophisticated computer models. The predictions of such models are used to formulate international protocols, intended to mitigate the severity of global warming and its impacts. Yet, these models are not perfect representations of reality, because they remove from explicit consideration many physical processes which are known to be key aspects of the climate system, but which are too small or fast to be modelled. The purpose of this paper is to give a personal perspective of the current state of knowledge regarding the problem of unresolved scales in climate models. A recent novel solution to the problem is discussed, in which it is proposed, somewhat counter-intuitively, that the performance of models may be improved by adding random noise to represent the unresolved processes.

The impact of moist processes on the African easterly jet-African easterly wave system

The African Easterly Jet-Easterly Wave (AEJ-AEW) system was explored in an idealised model. Prescribed zonally symmetric surface temperature and moisture profiles determine the AEJ which becomes established through meridional contrasts in dry and moist convection.As in previous studies, a realistic AEJ developed with only dry convection. Including moist processes, increased its development rate, but reduced its speed and meridional extent. AEWs grew through barotropic-baroclinic conversions. Negative meridional potential vorticity (PV) gradients arose in the zonally symmetric state through the intrusion of the low-PV Saharan boundary layer. Since moist processes strengthened this significantly through diabatically generated PV in the Intertropical Convergence Zone, moist AEWs were three times stronger. Larger barotropic conversions and faster AEJ development increased the moist wave growth-rate. Jet-level and northerly low-level amplitudes grew, but in the moist case the low-level amplitudes weakened as the AEW interacted with convection, consistent with their absence from observations during the peak monsoon. Striking dependencies between the AEJ, AEW and rainfall existed. Two time-scales governed their evolution, depending on the transfer coefficients: (1) the AEJ's replenishment rate influenced by heat fluxes, and (2) the wave growth-rate, by damping, and the slower jet development rate.Moist AEWs were characterized by intermittent growth/decay, with growth preceded by increased mean rainfall and later, weakening AEJs. These dependencies established an internal 8-10-day variability, consistent with intra-seasonal observations of 9-day rainy sequences. This internal variability offers an alternative explanation to the previously proposed external forcing and a new view of the moist AEW life cycle. Copyright © 2009 Royal Meteorological Society

Mapping the spatial distribution of geomorphological processes in the Okstindan area of northern Norway, using Geomorphic Process Units as derived from remote sensing and ground survey

The delineation of Geomorphic Process Units (GPUs) aims to quantify past, current and future geomorphological processes and the sediment flux associated with them. Five GPUs have been identified for the Okstindan area of northern Norway and these were derived from the combination of Landsat satellite imagery (TM and ETM+) with stereo aerial photographs (used to construct a Digital Elevation Model) and ground survey. The Okstindan study area is sub-arctic and mountainous and is dominated by glacial and periglacial processes. The GPUs exclude the glacial system (some 37% of the study area) and hence they are focussed upon periglacial and colluvial processes. The identified GPUs are: 1. solifluction and rill erosion; 2. talus creep, slope wash and rill erosion; 3. accumulation of debris by rock and boulder fall; 4. rockwalls; and 5. stable ground with dissolved transport. The GPUs have been applied to a ‘test site’ within the study area in order to illustrate their potential for mapping the spatial distribution of geomorphological processes. The test site within the study area is a catchment which is representative of the range of geomorphological processes identified.

Mineralised organic remains from cesspits at the Roman town of Silchester: Processes and preservation

Mineralised organic remains (including apple pips and cereal grains) collected during the ongoing excavations of Insula IX at the Roman town of Silchester, Hampshire have been analysed by a combination of SEM-EDX, powder XRD and IR spectroscopy. The experiments included mapping experiments using spatially resolved versions of each technique. IR and powder XRD mapping have been carried out utilising the synchrotron source at The Daresbury Laboratory oil stations 11.1 and 9.6. It is concluded that these samples are preserved by rapid mineralisation in the carbonate-substituted calcium phosphate mineral, dahllite. The rapid mineralisation leads to excellent preservation of the samples and a small crystal size. The value of IR spectroscopy in studying materials like this where the crystal size is small is demonstrated. A comparison is made between the excellent preservation seen in this context and the much poorer preservation of mineralised remains seen in Context 5276 or Cesspit 5251. Comments on the possible mechanism of mineralisation of these samples are made. (C) 2008 Elsevier B.V.. All rights reserved.

The influence of physical processes on extratropical singular vectors

An investigation is made of the impact of a full linearized physical (moist) parameterization package on extratropical singular vectors (SVs) using the ECMWF integrated forecasting system (IFS). Comparison is made for one particular period with a dry physical package including only vertical diffusion and surface drag. The crucial extra ingredient in the full package is found to be the large-scale latent heat release. Consistent with basic theory, its inclusion results in a shift to smaller horizontal scales and enhanced growth for the SVs. Whereas, for the dry SVs, T42 resolution is sufficient, the moist SVs require T63 to resolve their structure and growth. A 24-h optimization time appears to be appropriate for the moist SVs because of the larger growth of moist SVs compared with dry SVs. Like dry SVs, moist SVs tend to occur in regions of high baroclinicity, but their location is also influenced by the availability of moisture. The most rapidly growing SVs appear to enhance or reduce large-scale rain in regions ahead of major cold fronts. The enhancement occurs in and ahead of a cyclonic perturbation and the reduction in and ahead of an anticyclonic perturbation. Most of the moist SVs for this situation are slightly modified versions of the dry SVs. However, some occur in new locations and have particularly confined structures. The most rapidly growing SV is shown to exhibit quite linear behavior in the nonlinear model as it grows from 0.5 to 12 hPa in 1 day. For 5 times this amplitude the structure is similar but the growth is about half as the perturbation damps a potential vorticity (PV) trough or produces a cutoff, depending on its sign.

Bottlenecks in name resolution of migrating processes

Three naming strategies are discussed that allow the processes of a distributed application to continue being addressed by their original logical name, along all the migrations they may be forced to undertake because of performance-improvement goals. A simple centralised solution is firstly discussed which showed a software bottleneck with the increase of the number of processes; other two solutions are considered that entail different communication schemes and different communication overheads for the naming protocol. All these strategies are based on the facility that each process is allowed to survive after migration, even in its original site, only to provide a forwarding service to those communications that used its obsolete address.

Mineralised organic remains from cesspits at the Roman town of Silchester: processes and preservation

Mineralised organic remains (including apple pips and cereal grains) collected during the ongoing excavations of Insula IX at the Roman town of Silchester, Hampshire have been analysed by a combination of SEM-EDX, powder XRD and IR spectroscopy. The experiments included mapping experiments using spatially resolved versions of each technique. IR and powder XRD mapping have been carried out utilising the synchrotron source at The Daresbury Laboratory oil stations 11.1 and 9.6. It is concluded that these samples are preserved by rapid mineralisation in the carbonate-substituted calcium phosphate mineral, dahllite. The rapid mineralisation leads to excellent preservation of the samples and a small crystal size. The value of IR spectroscopy in studying materials like this where the crystal size is small is demonstrated. A comparison is made between the excellent preservation seen in this context and the much poorer preservation of mineralised remains seen in Context 5276 or Cesspit 5251. Comments on the possible mechanism of mineralisation of these samples are made. (C) 2008 Elsevier B.V.. All rights reserved.

Evaluation of the inclusion of a mixture of organic acids or lactulose into the feed of pigs experimentally challenged with Salmonella Typhimurium

A mixture of organic acids and lactulose for preventing or reducing colonization of the gut by Salmonella Typhimurium was evaluated in pigs. A total of 63 4-week-old commercial piglets were randomly distributed into three different experimental dietary groups: a plain diet without additives (PD) and the same diet supplemented with either 0.4% (w/v) formic acid and 0.4% lactic acid (w/v) (AC) or 1% (w/v) lactulose (LC). After 7 days of adaptation, two-thirds of the pigs (14 from each diet) were challenged with a 2-mL oral dose of 10(8) CFU/mL of Salmonella Typhimurium, leaving the remaining animals unchallenged (UC). After 4 and 10 days post-challenge, pigs were euthanized and the ileum and caecum content were aseptically sampled to (a) quantify lactic, formic, and short-chain fatty acids (SCFA), (b) quantify bacterial populations and Salmonella by fluorescence in situ hybridization and (c) qualitatively analyse bacterial populations through denaturing gradient gel electrophoresis (DGGE). Modification of fermentation products and counts of some of the bacterial groups analysed in the challenged pigs receiving the treatments AC and LC were minimal. Treatments only influenced the bacterial diversity after 10 days post-challenge, with AC generating a lower number of DGGE bands than UC(P < 0.05). Neither the inclusion of a mixture of 0.4% (w/v) formic and 0.4% (w/v) lactic acids nor of 1% (w/v) lactulose in the feed influenced numbers of Salmonella in the ileum and caecum of experimentally challenged pigs. (C) 2009 Elsevier B.V. All rights reserved.

A mixture of experts network structure construction algorithm for modelling and control

This paper introduces a new fast, effective and practical model structure construction algorithm for a mixture of experts network system utilising only process data. The algorithm is based on a novel forward constrained regression procedure. Given a full set of the experts as potential model bases, the structure construction algorithm, formed on the forward constrained regression procedure, selects the most significant model base one by one so as to minimise the overall system approximation error at each iteration, while the gate parameters in the mixture of experts network system are accordingly adjusted so as to satisfy the convex constraints required in the derivation of the forward constrained regression procedure. The procedure continues until a proper system model is constructed that utilises some or all of the experts. A pruning algorithm of the consequent mixture of experts network system is also derived to generate an overall parsimonious construction algorithm. Numerical examples are provided to demonstrate the effectiveness of the new algorithms. The mixture of experts network framework can be applied to a wide variety of applications ranging from multiple model controller synthesis to multi-sensor data fusion.

Neurofuzzy mixture of experts network parallel learning and model construction algorithms

A connection between a fuzzy neural network model with the mixture of experts network (MEN) modelling approach is established. Based on this linkage, two new neuro-fuzzy MEN construction algorithms are proposed to overcome the curse of dimensionality that is inherent in the majority of associative memory networks and/or other rule based systems. The first construction algorithm employs a function selection manager module in an MEN system. The second construction algorithm is based on a new parallel learning algorithm in which each model rule is trained independently, for which the parameter convergence property of the new learning method is established. As with the first approach, an expert selection criterion is utilised in this algorithm. These two construction methods are equivalent in their effectiveness in overcoming the curse of dimensionality by reducing the dimensionality of the regression vector, but the latter has the additional computational advantage of parallel processing. The proposed algorithms are analysed for effectiveness followed by numerical examples to illustrate their efficacy for some difficult data based modelling problems.

Necessary and sufficient conditions for realizability of point processes

We give necessary and sufficient conditions for a pair of (generali- zed) functions 1(r1) and 2(r1, r2), ri 2X, to be the density and pair correlations of some point process in a topological space X, for ex- ample, Rd, Zd or a subset of these. This is an infinite-dimensional version of the classical “truncated moment” problem. Standard tech- niques apply in the case in which there can be only a bounded num- ber of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further re- quirement—the existence of a finite third order moment. We general- ize the latter conditions in two distinct ways when X is not compact.