Code loops in dimension at most 8

Code loops are certain Moufang $2$-loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More precisely, code loops are central extensions of the group of order $2$ by an elementary abelian $2$-group $V$ in the variety of loops such that their squaring map, commutator map and associator map are related by combinatorial polarization and the associator map is a trilinear alternating form. Using existing classifications of trilinear alternating forms over the field of $2$ elements, we enumerate code loops of dimension $d=\mathrm{dim}(V)\le 8$ (equivalently, of order $2^{d+1}\le 512$) up to isomorphism. There are $767$ code loops of order $128$, and $80826$ of order $256$, and $937791557$ of order $512$

A note on the estimation of confidence intervals for cost-effectiveness when costs and effects are censored

<i>Background</i>. The relation between methodological advances in estimation of confidence intervals (CIs) for incremental cost-effectiveness ratios (ICER) and estimation of cost effectiveness in the presence of censoring has not been explored. The authors address the joint problem of estimating ICER precision in the presence of censoring. <i>Methods</i>. Using patient-level data (n = 168) on cost and survival from a published placebo-controlled trial, the authors compared 2 methods of measuring uncertainty with censored data: 1)Bootstrap with censor adjustment (BCA); 2) Fieller’s method with censor adjustment (FCA). The authors estimate the FCA over all possible values for the correlation (p) between costs and effects (range= –1 to +1) and also examine the use of the correlation between cases without censoring adjustment (i.e., simple time-on-study) for costs and effects as an approximation for. <i>Results</i>. Using time-on-study, which considers all censored observations as responders (deaths), yields 0.64 life-years gained at an additional cost of 87.9 for a cost per life-year of 137 (95% CI by bootstrap –5.9 to 392). Censoring adjustment corrects for the bias in the time-on-study approach and reduces the cost per life-year estimate to 132 (=72/0.54). Confidence intervals with censor adjustment were approximately 40% wider than the base-case without adjustment. Using the Fieller method with an approximation of based on the uncensored cost and effect correlation provides a 95% CI of (–48 to 529), which is very close to the BCA interval of (–52 to 504). <i>Conclusions</i>. Adjustment for censoring is necessary in cost-effectiveness studies to obtain unbiased estimates of ICER with appropriate uncertainty limits. In this study, BCA and FCA methods, the latter with approximated covariance, are simple to compute and give similar confidence intervals

Surface Free Energies, Interfacial Tensions and Correlation Lengths of the ABF Models

The surface free energies, interfacial tensions and correlation lengths of the Andrews-Baxter-Forrester models in regimes III and IV are calculated with fixed boundary conditions. The interfacial tensions are calculated between arbitrary phases and are shown to be additive. The associated critical exponents are given by $2-\alpha_s=\mu=\nu$ with $\nu=(L+1)/4$ in regime III and $4-2\alpha_s=\mu=\nu$ with $\nu=(L+1)/2$ in regime IV. Our results are obtained using general commuting transfer matrix and inversion relation methods that may be applied to other solvable lattice models.Comment: 21 pages, LaTeX 2e, requires the amsmath packag

Recognition of finite exceptional groups of Lie type

Let $q$ be a prime power and let $G$ be an absolutely irreducible subgroup of $GL_d(F)$, where $F$ is a finite field of the same characteristic as \F_q, the field of $q$ elements. Assume that $G \cong G(q)$, a quasisimple group of exceptional Lie type over \F_q which is neither a Suzuki nor a Ree group. We present a Las Vegas algorithm that constructs an isomorphism from $G$ to the standard copy of $G(q)$. If $G \not\cong {}^3 D_4(q)$ with $q$ even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle

The concept of sexual exploitation in legislation relating to persons with intellectual disability

The focus of this paper is on the use of the concept of sexual exploitation in legislation concerning sexual expression by persons with mental impairment, with particular emphasis on persons with intellectual disability. Two main statutory approaches have been adopted in Australian jurisdictions. The first is prohibition of sexual acts between a person with intellectual disability and others who, by virtue of their employment, are in a position of ascendancy over that person. The second is the prohibition of sexually exploitative acts by any person towards a person with an intellectual disability. The major aim in this article is to critically examine these approaches and evaluate them according to the standards of being non-discriminatory, minimally restrictive of rights, and enforceable. It is argued that comprehensively cataloguing sexually exploitative acts is untenable, with the result that prohibition of all sexual exploitation is unenforceable. The alternative, namely legislation that prohibits sexual relations with any person employed to render any kind of service to the intellectually disabled person, would further restrict an already limited number of potential sexual partners. We suggest that a more useful approach would be to prohibit sexual activity in one-on-one relationships whose scope is commonly understood to exclude such acts, while allowing relations between workers or caregivers and the persons to whom they do not directly render services. This mechanism would have to be narrowly defined to have the desired effect of affording protection to vulnerable persons while preserving their right to sexual expression

Supporting strategy : a survey of UK OR/MS practitioners

This paper reports the results of an on-line survey conducted with practitioner members of the UK Operational Research (OR) Society. The purpose of the survey was to explore the current practice of supporting strategy in terms of activities supported and tools used. The results of the survey are compared to those of previous surveys to explore developments in, inter-alia, the use of management/strategy tools and „soft‟ Operational Research / Management Science (OR/MS) tools. The survey results demonstrate that OR practitioners actively support strategy within their organisations. Whilst a wide variety of tools, drawn from the OR/MS and management / strategy fields are used to support strategy within organisations, the findings suggest that soft OR/MS tools are not regularly used. The findings also demonstrate that tools are combined to support strategy from both within and across the OR/MS and management / strategy fields. The paper ends by identifying a number of areas for further research

Majorana-based fermionic quantum computation

Because Majorana zero modes store quantum information non-locally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majoranas to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majoranas for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, and the simulation of Trotterized Hubbard Hamiltonian in $\mathcal{O}(1)$ time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.Comment: 4 pages + 4 page appendix, 4 figures, 2 table

Resampling adaptive cloth simulations onto fixed-topology meshes

We describe a method for converting an adaptively remeshed simulation of cloth into an animated mesh with fixed topology. The topology of the mesh may be specified by the user or computed automatically. In the latter case, we present a method for computing the optimal output mesh, that is, a mesh with spatially varying resolution which is fine enough to resolve all the detail present in the animation. This technique allows adaptive simulations to be easily used in applications that expect fixed-topology animated meshes