Safety cameras and road accidents: effectiveness in local authority areas in England

Safety cameras have been central to strategy for improving road safety in the UK (and other countries) over the past decade and a National Safety Camera (NSC) programme was introduced in the year 2000 to fund and guide the expansion of camera sites. This programme was brought to an end in 2007 and responsibility for decisions on expanding, maintaining or rolling back safety cameras has now been largely devolved to local highway authorities and their partners. To make strategic choices in such areas it is clearly vital to understand the extent to which safety cameras are effective in reducing road accident potential. Although the NSC programme has been evaluated this work has focussed mainly on assessments of impacts at camera sites rather than wider area effects: particularly local highway area effects. The research reported here has explored the rates of personal injury collisions (PIC) over the past decade on the roads of English Local Authority areas and investigated relationships between area characteristics including levels of safety camera introductions and the PIC improvements (or otherwise) reported. To assist in this analysis, an indicator of safety camera intensity has been derived in this research to reflect the relative likelihood in areas of coming into contact with safety camera sites This work shows that area improvement rates differ significantly on an urban/rural dimension and are also very dependent on prior (to camera introductions) levels of PIC risk. Controlling for these factors using a pair comparison approach, analysis shows that safety camera introduction effects are statistically detectable in very highly urbanised, high PIC risk areas and at high risk sites within areas but not elsewhere. Whilst recognising that new high risk sites can emerge in any area, the conclusion is reached that many local areas and especially more rural areas would be unlikely to gain advantage from a further general expansion of fixed point and mobile camera sites and that de-commissioning of current sites should be seriously considered.     

Locating an obnoxious facility within a polygonal region

The purpose of this paper is to review some of the many instances in which a location analyst must make a decision as to where an obnoxious facility should be placed. An obnoxious facility is one that can be defined as a facility which has undesirable interactions with existing facilities. Examples include equipment which emit pollutants such as particulates, noise and radiation or warehouses that contain flammable materials. Other obnoxious facilities include machines that are potential sources of hazards to nearby machines and workers. The interaction between the obnoxious facility and each existing facility is reflected through a weighting factor. The feasible region is considered to be continuous in the form of a convex or nonconvex simple polygon. Since the new facility is to be located away from the existing facilities, an appropriate criterion for optimization is the MAXIMIN or the MAXISUM criterion. Algorithms are reviewed for two common metrics under both criteria, i.e. Euclidean and rectilinear.     

Normal basis for an ideal in a local ring

An effective construction is given for a normal ideal basis (when it exists) in local number field extensions with higher ramification.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 64–68, 1976.     

A framework for predicting gross institutional long-term care cost arising from known commitments at local authority level

As the UK population ages, it is forecasted that there will be an unsustainable increase in the need for, and therefore in the costs of long-term care. Although several studies have been performed to estimate these costs, they do not take into account the impact of survival patterns on costs. Focussing only on residents already in care (known commitments), we have developed, in association with an English local authority, a framework for estimating the future gross cost incurred by this group, built around a survival model. We apply this framework to forecast the cost over a given period of time, of maintaining a group of individuals in residential and nursing care, funded by the local authority. One of the novelties in the model is that it translates survival inputs and unit fees for care into cost in a manner, which was useful and meaningful to decision makers.     

Breakout local search for the Steiner tree problem with revenue,budget and hop constraints

The Steiner tree problem (STP) is one of the most popular combinatorial optimization problems with various practical applications. In this paper, we propose a Breakout Local Search (BLS) algorithm for an important generalization of the STP: the Steiner tree problem with revenue, budget and hop constraints (STPRBH), which consists of determining a subtree of a given undirected graph which maximizes the collected revenues, subject to both budget and hop constraints. Starting from a probabilistically constructed initial solution, BLS uses a Neighborhood Search (NS) procedure based on several specifically designed move operators for local optimization, and employs an adaptive diversification strategy to escape from local optima. The diversification mechanism is implemented by adaptive perturbations, guided by dedicated information of discovered high-quality solutions. Computational results based on 240 benchmarks show that BLS produces competitive results with respect to several previous approaches. For the 56 most challenging instances with unknown optimal results, BLS succeeds in improving 49 and matching one best known results within reasonable time. For the 184 instances which have been solved to optimality, BLS can also match 167 optimal results.     

Effect of a local load on an orthotropic glass-reinforced plastic shell

The deformation of a layered orthotropic cylindrical shell under a local normal load is investigated on the basis of equations that do not depend on the hypothesis of straight normals. The solutions of the analogous classical problems were analyzed in [3]; a solution based on equations that take transverse shear strains approximately into account was proposed in [4]. The high degree of variability of the state of stress created by local loads indicates that it is quite important to take transverse shear strains rigorously into account in problems of this class. An attempt is made to estimate the error introduced by the hypothesis of straight normals and to calculate the load leading to debonding of the shell.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 1, pp. 95–101, January–February, 1970.     

Ideals of an abelian p-extension of a local field as Galois modules

Ideals of the ring of integers of an Abelian p-extension of a local field (a finite extension of the field of p-adic numbers) are studied as modules with operators from the Galois group of the extension. Necessary and sufficient conditions are found for the decomposability of these ideals as Galois modules. When the decomposability conditions are satisfied, the decomposition of the ideal into indecomposable summands is found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 57, pp. 64–84, 1976.     

Efficient, optimal stochastic-action selection when limited by an action budget

The problem that we consider here is a basic operations research problem, but it also a special case of the Stochastic Shortest Path with Recourse Problem and the Canadian Travellers Problem in the probabilistic path planning literature, and it is also a special case of maximizing a submodular set function subject to a matroid constraint. Specifically, suppose an agent has a task and suppose that there is a set of actions, any of which the agent might perform, with respective probabilities of the actions successfully accomplishing the task and respective rewards for the agent if the actions are successful; the agent is to select a sequence of some of these actions that will be performed sequentially, until the task is accomplished or the selected actions are exhausted, but there is a budget on the number of actions that can be performed. We provide an efficient algorithm that chooses a sequence of actions that, under the budget, maximize the agent’s expected reward. An example illustrates how, when conditioning on partial selection of actions, there can be changes to the order of the remaining actions’ adjusted utilities. However, we prove and exploit a nesting result involving solutions.     

The Asymptotic Behaviour of a Curved Line Source Plume within an Enclosure

A line source of heat is situated in an enclosure with inletsand an outlet for the contained fluid. The convection plumeformed must take a curved shape because of the asymmetry ofthe enclosure. We show how boundary-layer theory can be usedto find this shape in the case where the plume's deflectionis small. Two effects govern the shape of the curve; a buoyancyeffect and an inertial effect due to the bounding walls. Bysolving the outer potential flow problem, both effects can beincluded in the model. Finally, a stability analysis is carriedout for steady plumes which shows that any steady solution withan inflection point, as well as several other solutions, isunstable. A comparison is made with previous work which doesnot include all these effects, and with some experimental results.     

Dynamics of a linear beam with an attached local nonlinear energy sink

We provide numerical evidence of passive and broadband targeted energy transfer from a linear flexible beam under shock excitation to a local essentially nonlinear lightweight attachment that acts, in essence, as nonlinear energy sink—NES. It is shown that the NES absorbs shock energy in a one-way, irreversible fashion and dissipates this energy locally, without ‘spreading’ it back to the linear beam. Moreover, we show numerically that an appropriately designed and placed NES can passively absorb and locally dissipate a major portion of the shock energy of the beam, up to an optimal value of 87%. The implementation of the NES concept to the shock isolation of practical engineering structures and to other applications is discussed.     

Deformation of a composite plate on an elastic foundation by local loads

Bending of an elastic annular composite plate with a light filler lying on an elastic foundation is considered. The plate is subjected to local loads. To describe the kinematics of the package, asymmetric across its thickness, the hypotheses of broken normal is accepted. The reaction of foundation is described based on the Winkler model. A system of equilibrium equations is constructed, and its exact solution in displacements is found. Numerical solutions for a metal-polymer sandwich plate are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 109–120, January–February, 2007.     

The integration of an interior-point cutting plane method within a branch-and-price algorithm

This paper presents a novel integration of interior point cutting plane methods within branch-and-price algorithms. Unlike the classical method, columns are generated at a central dual solution by applying the analytic centre cutting plane method (ACCPM) on the dual of the full master problem. First, we introduce some modifications to ACCPM. We propose a new procedure to recover primal feasibility after adding cuts and use, for the first time, a dual Newtons method to calculate the new analytic centre after branching. Second, we discuss the integration of ACCPM within the branch-and-price algorithm. We detail the use of ACCPM as the search goes deep in the branch and bound tree, making full utilization of past information as a warm start. We exploit dual information from ACCPM to generate incumbent feasible solutions and to guide branching. Finally, the overall approach is implemented and tested for the bin-packing problem and the capacitated facility location problem with single sourcing. We compare against Cplex-MIP 7.5 as well as a classical branch-and-price algorithm.Mathematics Subject Classification (1991): 20E28, 20G40, 20C20     

Cut problems in graphs with a budget constraint

We study budgeted variants of classical cut problems: the Multiway Cut problem, the Multicut problem, and the k-Cut problem, and provide approximation algorithms for these problems. Specifically, for the budgeted multiway cut and the k-cut problems we provide constant factor approximation algorithms. We show that the budgeted multicut problem is at least as hard to approximate as the sparsest cut problem, and we provide a bi-criteria approximation algorithm for it.     

The dynamics of pyramidal bodies within the framework of the local interaction model

Two-dimensional inertial motion of pyramidal bodies in a medium is investigated, on the assumption that the force exerted by the medium on their surface is described by the local interaction model. Assuming unseparated flow around the bodies and small perturbations applied at the initial time to the parameters of rectilinear motion, an analytical solution is constructed of the problem of the two-dimensional motion of slender bodies with bases whose contour is a rhombus or a star consisting of four symmetrical cycles. It is shown that the solution provides the basis for a complete parameterc analysis of the dynamics of the body and for evaluating the forces and torques experienced by the body along its trajectory. A criterion for the stability of the body is found, using which, knowing the velocity, mass and position of the body's centre of gravity, one can determine the form of the perturbed motion of the pyramidal body. It is shown that the body shape is one of the most important factors affecting the stability of motion, and that, of all bodies with the same shape and position of the centre of mass, those with the least mass have the largest reserve of stability. The analytical results are confirmed by numerical solution of the Cauchy problem for the system of equations of motion obtained without the simplifying assumptions.     

Bending of a multilayer cylindrical shell with an elastic core under a local radial load

The problem of the state of stress and strain of a multilayer cylindrical shell with a soft elastic core subjected to an external, locally distributed radial load is solved under the simplifying assumption that all the layers satisfy the generalized Hooke's law and work together without slip. A numerical example is given.     

A hybrid optimization technique coupling an evolutionary and a local search algorithm

Evolutionary algorithms are robust and powerful global optimization techniques for solving large-scale problems that have many local optima. However, they require high CPU times, and they are very poor in terms of convergence performance. On the other hand, local search algorithms can converge in a few iterations but lack a global perspective. The combination of global and local search procedures should offer the advantages of both optimization methods while offsetting their disadvantages. This paper proposes a new hybrid optimization technique that merges a genetic algorithm with a local search strategy based on the interior point method. The efficiency of this hybrid approach is demonstrated by solving a constrained multi-objective mathematical test-case.     

A local saddle point theorem and an application to a nonlocal PDE

We prove a local saddle point theorem that can be viewed as a generalization of the saddle point theorem of Rabinowitz. A difficulty to overcome is that there isn’t any linking. We then apply the theorem to show the existence of solutions of a nonlocal partial differential equations.     

The local linking theorem with an application to a class of second-order systems

In the present paper, some existence theorems are obtained concerning periodic and homoclinic solutions for a class of second-order systems by means of a local linking theorem.