A static cost analysis for a higher-order language

We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the expression's evaluation derivation in a standard big-step operational semantics. The latter is a measure of the "future" cost of using the value of that expression. A translation function tr maps target expressions to complexities. Our main result is the following Soundness Theorem: If t is a term in the target language, then the cost component of tr(t) is an upper bound on the cost of evaluating t. The proof of the Soundness Theorem is formalized in Coq, providing certified upper bounds on the cost of any expression in the target language.Comment: Final versio

Broadband spin-controlled focusing via logarithmic-spiral nanoslits of varying width

This work presents analytical, numerical and experimental demonstrations of light diffracted through a logarithmic spiral (LS) nanoslit, which forms a type of switchable and focus-tunable structure. Owing to a strong dependence on the incident photon spin, the proposed LS-nanoslit converges incoming light of opposite handedness (to that of the LS-nanoslit) into a confined subwavelength spot, while it shapes light with similar chirality into a donut-like intensity profile. Benefitting from the varying width of the LS-nanoslit, different incident wavelengths interfere constructively at different positions, i.e., the focal length shifts from 7.5 μm (at λ = 632.8 nm) to 10 μm (at λ = 488 nm), which opens up new opportunities for tuning and spatially separating broadband light at the micrometer scale

The Twenty-First Century Law Library

On November 6, 2008, the J. Michael Goodson Law Library at the Duke University School of Law held a number of events in celebration of its newly renovated and expanded space. This is an edited version of the program, "The 21st Century Law Library: A Conversation," that was held as part of that celebration. The conversation explores the role of the academic law library in legal education in an increasingly digital environment

Liquid Crystal-Solid Interface Structure at the Antiferroelectric-Ferroelectric Phase Transition

Total Internal Reflection (TIR) is used to probe the molecular organization at the surface of a tilted chiral smectic liquid crystal at temperatures in the vicinity of the bulk antiferroelectric-ferroelectric phase transition. Data are interpreted using an exact analytical solution of a real model for ferroelectric order at the surface. In the mixture T3, ferroelectric surface order is expelled with the bulk ferroelectric-antiferroelectric transition. The conditions for ferroelectric order at the surface of an antiferroelectric bulk are presented

City Energy Demand Simulation (CEDS) Feasibility Study

CEDS - The City Energy Demand Simulation - provides cities and local authorities with the means to visualise future energy demand (including gas and electricity) for any geographic area ranging from a street, to a district, to the city itself, including both residential and industrial/commercial energy demand.CEDS allows planners and decision makers to easily visualise the impacts of alternative demand and supply side energy investment strategies on overall energy costs, emissions, and fuel poverty levels. This will be important for cities and planners because the innovative features of CEDS will enable planners to understand the impacts of new energy technology deployments on the energy demand of buildings. - CEDS can demonstrate the relative economic and environmental attractiveness of local energy supply schemes such as district heating combined with power versus importing electricity from the grid; - CEDS can illuminate the impacts of technology deployment by social geography within the city boundaries Therefore, CEDS will allow cities and local authorities to clearly identify how to deploy limited capital budgets to greatest effect when developing low carbon, cost effective local energy infrastructure. By modelling future demand, supply and cost scenarios, cities will be able to prioritise the development of local energy assets, such as district heating networks, energy from waste, retrofit and new build locations. CEDS will enable cities to understand how they can deliver on their priorities for ensuring there are cost effective locations for business and industry, with a secure supply, whilst also helping tackle fuel poverty and reducing carbon emissions and energy costs