15,301 research outputs found
Code loops in dimension at most 8
Code loops are certain Moufang -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 by an elementary abelian -group 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 elements, we enumerate code loops of dimension
(equivalently, of order ) up to isomorphism. There are
code loops of order , and of order , and of order
Cost-effectiveness acceptability curves - facts, fallacies and frequently asked questions
Cost-effectiveness acceptability curves (CEACs) have been widely adopted as a method to quantify and graphically represent uncertainty in economic evaluation studies of health-care technologies. However, there remain some common fallacies regarding the nature and shape of CEACs that largely result from the textbook illustration of the CEAC. This textbook CEAC shows a smooth curve starting at probability 0, with an asymptote to 1 for higher money values of the health outcome (). But this familiar ogive shape which makes the textbook CEAC look like a cumulative distribution function is just one special case of the CEAC. The reality is that the CEAC can take many shapes and turns because it is a graphic transformation from the cost-effectiveness plane, where the joint density of incremental costs and effects may straddle quadrants with attendant discontinuities and asymptotes. In fact CEACs: (i) do not have to cut the y-axis at 0; (ii) do not have to asymptote to 1; (iii) are not always monotonically increasing in ; and (iv) do not represent cumulative distribution functions (cdfs). Within this paper we present a gallery of CEACs in order to identify the fallacies and illustrate the facts surrounding the CEAC. The aim of the paper is to serve as a reference tool to accompany the increased use of CEACs within major medical journals
Recognition of finite exceptional groups of Lie type
Let be a prime power and let be an absolutely irreducible subgroup of
, where is a finite field of the same characteristic as \F_q,
the field of elements. Assume that , 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 to the
standard copy of . If with even, then the
algorithm runs in polynomial time, subject to the existence of a discrete log
oracle
Reliability and reproducibility of Atlas information
We discuss the reliability and reproducibility of much of the information
contained in the Atlas of Finite Groups
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