Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

Fractal spaces in planning and governance

This paper discusses concepts of space within the planning literature, the issues they give rise to and the gaps they reveal. It then introduces the notion of 'fractals' borrowed from complexity theory and illustrates how it unconsciously appears in planning practice. It then moves on to abstract the core dynamics through which fractals can be consciously applied and illustrates their working through a reinterpretation of the People's Planning Campaign of Kerala, India. Finally it highlights the key contribution of the fractal concept and the advantages that this conceptualisation brings to planning.

Do smart grids offer a new incentive for SME carbon reduction?

Collectively small and medium sized enterprises (SMEs) are significant energy users although many are unregulated by existing policies due to their low carbon emissions. Carbon reduction is often not a priority but smart grids may create a new opportunity. A smart grid will give electricity suppliers a picture of real-time energy flows and the opportunity for consumers to receive financial incentives for engaging in demand side management. As well as creating incentives for local carbon reduction, engaging SMEs with smart grids has potential for contributing to wider grid decarbonisation. Modelling of buildings, business activities and technology solutions is needed to identify opportunities for carbon reduction. The diversity of the SME sector complicates strategy development. SMEs are active in almost every business area and occupy the full range of property types. This paper reviews previous modelling work, exposing valuable data on floor space and energy consumption associated with different business activities. Limitations are seen with the age of this data and an inability to distinguish SME energy use. By modelling SME energy use, electrical loads are identified which could be shifted on demand, in a smart network. Initial analysis of consumption, not constrained by existing policies, identifies heating and cooling in retail and commercial offices as having potential for demand response. Hot water in hotel and catering and retail sectors may also be significant because of the energy storage potential. Areas to consider for energy efficiency schemes are also indicated.

Changes in gene expression in Arabidopsis shoots during phosphate starvation and the potential for developing smart plants

Our aim was to generate and prove the concept of "smart" plants to monitor plant phosphorus (P) status in Arabidopsis. Smart plants can be genetically engineered by transformation with a construct containing the promoter of a gene up-regulated specifically by P starvation in an accessible tissue upstream of a marker gene such as beta-glucuronidase (GUS). First, using microarrays, we identified genes whose expression changed more than 2.5-fold in shoots of plants growing hydroponically when P, but not N or K, was withheld from the nutrient solution. The transient changes in gene expression occurring immediately (4 h) after P withdrawal were highly variable, and many nonspecific, shock-induced genes were up-regulated during this period. However, two common putative cis-regulatory elements (a PHO-like element and a TATA box-like element) were present significantly more often in the promoters of genes whose expression increased 4 h after the withdrawal of P compared with their general occurrence in the promoters of all genes represented on the microarray. Surprisingly, the expression of only four genes differed between shoots of P-starved and -replete plants 28 h after P was withdrawn. This lull in differential gene expression preceded the differential expression of a new group of 61 genes 100 h after withdrawing P. A literature survey indicated that the expression of many of these "late" genes responded specifically to P starvation. Shoots had reduced P after 100 h, but growth was unaffected. The expression of SQD1, a gene involved in the synthesis of sulfolipids, responded specifically to P starvation and was increased 100 h after withdrawing P. Leaves of Arabidopsis bearing a SQD1::GUS construct showed increased GUS activity after P withdrawal, which was detectable before P starvation limited growth. Hence, smart plants can monitor plant P status. Transferring this technology to crops would allow precision management of P fertilization, thereby maintaining yields while reducing costs, conserving natural resources, and preventing pollution.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

CASCADE: An Agent Based Framework For Modeling The Dynamics Of Smart Electricity Systems

The Complex Adaptive Systems, Cognitive Agents and Distributed Energy (CASCADE) project is developing a framework based on Agent Based Modelling (ABM). The CASCADE Framework can be used both to gain policy and industry relevant insights into the smart grid concept itself and as a platform to design and test distributed ICT solutions for smart grid based business entities. ABM is used to capture the behaviors of diff erent social, economic and technical actors, which may be defi ned at various levels of abstraction. It is applied to understanding their interactions and can be adapted to include learning processes and emergent patterns. CASCADE models ‘prosumer’ agents (i.e., producers and/or consumers of energy) and ‘aggregator’ agents (e.g., traders of energy in both wholesale and retail markets) at various scales, from large generators and Energy Service Companies down to individual people and devices. The CASCADE Framework is formed of three main subdivisions that link models of electricity supply and demand, the electricity market and power fl ow. It can also model the variability of renewable energy generation caused by the weather, which is an important issue for grid balancing and the profi tability of energy suppliers. The development of CASCADE has already yielded some interesting early fi ndings, demonstrating that it is possible for a mediating agent (aggregator) to achieve stable demandfl attening across groups of domestic households fi tted with smart energy control and communication devices, where direct wholesale price signals had previously been found to produce characteristic complex system instability. In another example, it has demonstrated how large changes in supply mix can be caused even by small changes in demand profi le. Ongoing and planned refi nements to the Framework will support investigation of demand response at various scales, the integration of the power sector with transport and heat sectors, novel technology adoption and diffusion work, evolution of new smart grid business models, and complex power grid engineering and market interactions.

Parameter spaces of environmental fields responsible for cyclone development from tropics to extratropics

Objective cyclone tracking applied to a 30-yr reanalysis dataset shows that cyclone development in the summer and autumn seasons is active in the tropics and extratropics and inactive in the subtropics. To understand this geographically bimodal distribution of cyclone development associated with tropical and extratropical cyclones quantitatively, the direct relationship between cyclone types and their environments are assessed by using a parameter space of environmental variables [environmental parameter space (EPS)]. The number of cyclones is analyzed in terms of two different factors: the environmental conditions favorable for cyclone development and the area size that satisfies the favorable condition. The EPS analysis is mainly conducted for two representative environmental parameters that are commonly used for cyclone analysis: potential intensity for tropical cyclones and baroclinicity for extratropical cyclones. The geographically bimodal distribution is attributed to the high sensitivity of the cyclone development to the change in the environmental fields from tropics to extratropics. In addition, the bimodal distribution is partly attributed to the rapid change in the environmental fields from tropics to extratropics. The EPS analysis also shows that other environmental parameters, including relative humidity and vertical velocity, may enhance the contrast between the tropics (extratropics) and subtropics, whereas they are not essential for determining cyclone types. The relationship between cyclones and their environments is found to be similar between the hemispheres in the EPS, although the geographical distribution, particularly the longitudinal uniformity, is markedly different between the hemispheres.

Pragmatic oriented data interoperability for smart healthcare information systems

Smart healthcare is a complex domain for systems integration due to human and technical factors and heterogeneous data sources involved. As a part of smart city, it is such a complex area where clinical functions require smartness of multi-systems collaborations for effective communications among departments, and radiology is one of the areas highly relies on intelligent information integration and communication. Therefore, it faces many challenges regarding integration and its interoperability such as information collision, heterogeneous data sources, policy obstacles, and procedure mismanagement. The purpose of this study is to conduct an analysis of data, semantic, and pragmatic interoperability of systems integration in radiology department, and to develop a pragmatic interoperability framework for guiding the integration. We select an on-going project at a local hospital for undertaking our case study. The project is to achieve data sharing and interoperability among Radiology Information Systems (RIS), Electronic Patient Record (EPR), and Picture Archiving and Communication Systems (PACS). Qualitative data collection and analysis methods are used. The data sources consisted of documentation including publications and internal working papers, one year of non-participant observations and 37 interviews with radiologists, clinicians, directors of IT services, referring clinicians, radiographers, receptionists and secretary. We identified four primary phases of data analysis process for the case study: requirements and barriers identification, integration approach, interoperability measurements, and knowledge foundations. Each phase is discussed and supported by qualitative data. Through the analysis we also develop a pragmatic interoperability framework that summaries the empirical findings and proposes recommendations for guiding the integration in the radiology context.

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.