A polynomial-time computable curve whose interior has a nonrecursive measure

AbstractA polynomial-time computable simple curve is constructed such that its measure in the two-dimensional plane is positive. This construction is applied to prove the following two results: 1.1) there exists a polynomial-time computable simple closed curve in the two-dimensional plane such that the measure of its interior region is a nonrecursive real number;2.(2) there exists a polynomial-time computable simple curve in the two-dimensional plane such that its length is finite but is a nonrecursive real number

On adaptive versus nonadaptive bounded query machines

AbstractThe polynomial-time adaptive (Turing) and nonadaptive (truth-table) bounded query machines are compared with respect to sparse oracles. A k-query adaptive machine has been found which, relative to a sparse oracle, cannot be simulated by any (2k−2)-query nonadaptive machine, even with a different sparse oracle. Conversely, there is a (3·2k−2)-query nonadaptive machine which, relative to a sparse oracle, cannot be simulated by any k-query adaptive machine, with any sparse oracle

Computational complexity of real functions

AbstractRecursive analysis, the theory of computation of functions on real numbers, has been studied from various aspects. We investigate the computational complexity of real functions using the methods of recursive function theory. Partial recursive real functions are defined and their domains are characterized as the recursively open sets. We define the time complexity of recursive real continuous functions and show that the time complexity and the modulus of uniform continuity of a function are closely related. We study the complexity of the roots and the differentiability of polynomial time computable real functions. In particular, a polynomial time computable real function may have a root of arbitrarily high complexity and may be nowhere differentiable. The concepts of the space complexity and nondeterministic computation are used to study the complexity of the integrals and the maximum values of real functions. These problems are shown to be related to the “P=?NP” and the “P=?PSPACE” questions

Instance Complexity

Peer reviewe

Separating the low and high hierachies by oracles

AbstractThe relativized low and high hierarchies within NP are considered. An oracle A is constructed such that the low and high hierarchies relative to A are infinite, and for each k an oracle Ak is constructed such that the low and high hierarchies relative to Ak have exactly k levels

Making big steps in trajectories

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a similar computation time

An exploratory randomised controlled trial of a premises-level intervention to reduce alcohol-related harm including violence in the United Kingdom

<b>Background</b><p></p> To assess the feasibility of a randomised controlled trial of a licensed premises intervention to reduce severe intoxication and disorder; to establish effect sizes and identify appropriate approaches to the development and maintenance of a rigorous research design and intervention implementation.<p></p> <b>Methods</b><p></p> An exploratory two-armed parallel randomised controlled trial with a nested process evaluation. An audit of risk factors and a tailored action plan for high risk premises, with three month follow up audit and feedback. Thirty-two premises that had experienced at least one assault in the year prior to the intervention were recruited, match paired and randomly allocated to control or intervention group. Police violence data and data from a street survey of study premises’ customers, including measures of breath alcohol concentration and surveyor rated customer intoxication, were used to assess effect sizes for a future definitive trial. A nested process evaluation explored implementation barriers and the fidelity of the intervention with key stakeholders and senior staff in intervention premises using semi-structured interviews.<p></p> <b>Results</b><p></p> The process evaluation indicated implementation barriers and low fidelity, with a reluctance to implement the intervention and to submit to a formal risk audit. Power calculations suggest the intervention effect on violence and subjective intoxication would be raised to significance with a study size of 517 premises.<p></p> <b>Conclusions</b><p></p> It is methodologically feasible to conduct randomised controlled trials where licensed premises are the unit of allocation. However, lack of enthusiasm in senior premises staff indicates the need for intervention enforcement, rather than voluntary agreements, and on-going strategies to promote sustainability

The reduction of intoxication and disorder in premises licensed to serve alcohol: An exploratory randomised controlled trial

Background: Licensed premises offer a valuable point of intervention to reduce alcohol-related harm. Objective: To describe the research design for an exploratory trial examining the feasibility and acceptability of a premises-level intervention designed to reduce severe intoxication and related disorder. The study also aims to assess the feasibility of a potential future large scale effectiveness trial and provide information on key trial design parameters including inclusion criteria, premises recruitment methods, strategies to implement the intervention and trial design, outcome measures, data collection methods and intra-cluster correlations. Design: A randomised controlled trial in licensed premises that had experienced at least one assault in the year preceding the intervention, documented in police or hospital Emergency Department (ED) records. Premises were recruited from four study areas by piloting four recruitment strategies of varying intensity. Thirty two licensed premises were grouped into matched pairs to reduce potential bias and randomly allocated to the control or intervention condition. The study included a nested process evaluation to provide information on intervention acceptability and implementation. Outcome measures included police-recorded violent incidents, assault-related attendances at each premises' local ED and patron Breath Alcohol Concentration assessed on exiting and entering study premises. Results: The most successful recruitment method involved local police licensing officers and yielded a 100% success rate. Police-records of violence provided the most appropriate source of data about disorder at the premises level. Conclusion: The methodology of an exploratory trial is presented and despite challenges presented by the study environment it is argued an exploratory trial is warranted. Initial investigations in recruitment methods suggest that study premises should be recruited with the assistance of police officers. Police data were of sufficient quality to identify disorder and street surveys are a feasible method for measuring intoxication at the individual level