16,421 research outputs found
M-partitions: Optimal partitions of weight for one scale pan
An M-partition of a positive integer m is a partition with as few parts as
possible such that any positive integer less than m has a partition made up of
parts taken from that partition of m. This is equivalent to partitioning a
weight m so as to be able to weigh any integer weight l < m with as few weights
as possible and only one scale pan.
We show that the number of parts of an M-partition is a log-linear function
of m and the M-partitions of m correspond to lattice points in a polytope. We
exhibit a recurrence relation for counting the number of M-partitions of m and,
for ``half'' of the positive integers, this recurrence relation will have a
generating function. The generating function will be, in some sense, the same
as the generating function for counting the number of distinct binary
partitions for a given integer.Comment: 11 page
A Civic Republican Analysis of Mental Capacity Law
This article draws upon the civic republican tradition to offer new conceptual resources for the normative assessment of mental capacity law. The republican conception of liberty as non-domination is used to identify ways in which such laws generate arbitrary power that can underpin relationships of servility and insecurity. It also shows how non-domination provides a basis for critiquing legal tests of decision-making that rely upon ‘diagnostic’ rather than ‘functional’ criteria. In response, two main civic republican strategies are recommended for securing freedom in the context of the legal regulation of psychological disability: self-authorisation techniques and participatory shaping of power. The result is a series of proposals for the reform of decisional capacity law, including a transition towards purely functional assessment of decisional capacity, surer legal footing for advanced care planning, and greater control over the design and administration of decision-making capacity laws by those with psychological disabilities
Multiples of Pfister forms
The isotropy of multiples of Pfister forms is studied. In particular, an
improved lower bound on the values of their first Witt indices is obtained. A
number of corollaries of this result are outlined. An investigation of generic
Pfister multiples is also undertaken. These results are applied to distinguish
between properties preserved by Pfister products.Comment: 14 page
Group and round quadratic forms
We offer some elementary characterisations of group and round quadratic
forms. These characterisations are applied to establish new (and recover
existing) characterisations of Pfister forms. We establish "going-up" results
for group and anisotropic round forms with respect to iterated Laurent series
fields, which contrast with the established results with respect to rational
function field extensions. For forms of two-power dimension, we determine when
there exists a field extension over which the form becomes an anisotropic group
form that is not round.Comment: 12 page
Semi-Supervised Radio Signal Identification
Radio emitter recognition in dense multi-user environments is an important
tool for optimizing spectrum utilization, identifying and minimizing
interference, and enforcing spectrum policy. Radio data is readily available
and easy to obtain from an antenna, but labeled and curated data is often
scarce making supervised learning strategies difficult and time consuming in
practice. We demonstrate that semi-supervised learning techniques can be used
to scale learning beyond supervised datasets, allowing for discerning and
recalling new radio signals by using sparse signal representations based on
both unsupervised and supervised methods for nonlinear feature learning and
clustering methods
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