Grey-box radial basis function modelling: the art of incorporating prior knowledge

A basic principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: the underlying data generating mechanism exhibits known symmetric property and the underlying process obeys a set of given boundary value constraints. The class of orthogonal least squares regression algorithms can readily be applied to construct parsimonious grey-box RBF models with enhanced generalisation capability.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

NOx and O3 above a tropical rainforest: an analysis with a global and box model

A cross-platform field campaign, OP3, was conducted in the state of Sabah in Malaysian Borneo between April and July of 2008. Among the suite of observations recorded, the campaign included measurements of NOx and O3 – crucial outputs of any model chemistry mechanism. We describe the measurements of these species made from both the ground site and aircraft. We then use the output from two resolutions of the chemistry transport model p-TOMCAT to illustrate the ability of a global model chemical mechanism to capture the chemistry at the rainforest site. The basic model performance is good for NOx and poor for ozone. A box model containing the same chemical mechanism is used to explore the results of the global model in more depth and make comparisons between the two. Without some parameterization of the nighttime boundary layer – free troposphere mixing (i.e. the use of a dilution parameter), the box model does not reproduce the observations, pointing to the importance of adequately representing physical processes for comparisons with surface measurements. We conclude with a discussion of box model budget calculations of chemical reaction fluxes, deposition and mixing, and compare these results to output from p-TOMCAT. These show the same chemical mechanism behaves similarly in both models, but that emissions and advection play particularly strong roles in influencing the comparison to surface measurements.

Ontology supported comparison in vague domains

It is problematic to use standard ontology tools when describing vague domains. Standard ontologies are designed to formally define one view of a domain, and although it is possible to define disagreeing statements, it is not advisable, as the resulting inferences could be incorrect. Two different solutions to the above problem in two different vague domains have been developed and are presented. The first domain is the knowledge base of conversational agents (chatbots). An ontological scripting language has been designed to access ontology data from within chatbot code. The solution developed is based on reifications of user statements. It enables a new layer of logics based on the different views of the users, enabling the body of knowledge to grow automatically. The second domain is competencies and competency frameworks. An ontological framework has been developed to model different competencies using the emergent standards. It enables comparison of competencies using a mix of linguistic logics and descriptive logics. The comparison results are non-binary, therefore not simple yes and no answers, highlighting the vague nature of the comparisons. The solution has been developed with small ontologies which can be added to and modified in order for the competency user to build a total picture that fits the user’s purpose. Finally these two approaches are viewed in the light of how they could aid future work in vague domains, further work in both domains is described and also in other domains such as the semantic web. This demonstrates two different approaches to achieve inferences using standard ontology tools in vague domains.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Evaluation of a Lagrangian box model using field measurements from EASE (Eastern Atlantic Summer Experiment) 1996

The Cambridge Tropospheric Trajectory model of Chemistry and Transport (CiTTyCAT), a Lagrangian chemistry model, has been evaluated using atmospheric chemical measurements collected during the East Atlantic Summer Experiment 1996 (EASE '96). This field campaign was part of the UK Natural Environment Research Council's (NERC) Atmospheric Chemistry Studies in the Oceanic Environment (ACSOE) programme, conducted at Mace Head, Republic of Ireland, during July and August 1996. The model includes a description of gas-phase tropospheric chemistry, and simple parameterisations for surface deposition, mixing from the free troposphere and emissions. The model generally compares well with the measurements and is used to study the production and loss of O3 under a variety of conditions. The mean difference between the hourly O3 concentrations calculated by the model and those measured is 0.6 ppbv with a standard deviation of 8.7 ppbv. Three specific air-flow regimes were identified during the campaign – westerly, anticyclonic (easterly) and south westerly. The westerly flow is typical of background conditions for Mace Head. However, on some occasions there was evidence of long-range transport of pollutants from North America. In periods of anticyclonic flow, air parcels had collected emissions of NOx and VOCs immediately before arriving at Mace Head, leading to O3 production. The level of calculated O3 depends critically on the precise details of the trajectory, and hence on the emissions into the air parcel. In several periods of south westerly flow, low concentrations of O3 were measured which were consistent with deposition and photochemical destruction inside the tropical marine boundary layer.

A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary-value problems for many trial values of the spectral parameter. We present numerical results both for eigenvalues and for resonances, comparing with results reported by Aslanyan, Parnovski and Vassiliev.

Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

Grey-box radial basis function modelling

A fundamental principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: (i) the underlying data generating mechanism exhibits known symmetric property, and (ii) the underlying process obeys a set of given boundary value constraints. The class of efficient orthogonal least squares regression algorithms can readily be applied without any modification to construct parsimonious grey-box RBF models with enhanced generalisation capability.

Mapping of domains on HIV envelope protein mediating association with calnexin and protein-disulfide isomerase.

The cell catalysts calnexin (CNX) and protein-disulfide isomerase (PDI) cooperate in establishing the disulfide bonding of the HIV envelope (Env) glycoprotein. Following HIV binding to lymphocytes, cell-surface PDI also reduces Env to induce the fusogenic conformation. We sought to define the contact points between Env and these catalysts to illustrate their potential as therapeutic targets. In lysates of Env-expressing cells, 15% of the gp160 precursor, but not gp120, coprecipitated with CNX, whereas only 0.25% of gp160 and gp120 coprecipitated with PDI. Under in vitro conditions, which mimic the Env/PDI interaction during virus/cell contact, PDI readily associated with Env. The domains of Env interacting in cellulo with CNX or in vitro with PDI were then determined using anti-Env antibodies whose binding site was occluded by CNX or PDI. Antibodies against domains V1/V2, C2, and the C terminus of V3 did not bind CNX-associated Env, whereas those against C1, V1/V2, and the CD4-binding domain did not react with PDI-associated Env. In addition, a mixture of the latter antibodies interfered with PDI-mediated Env reduction. Thus, Env interacts with intracellular CNX and extracellular PDI via discrete, largely nonoverlapping, regions. The sites of interaction explain the mode of action of compounds that target these two catalysts and may enable the design of further new competitive agents.