55 research outputs found
Some notes on feinberg's k-independence problem
AbstractA short proof is given of a recent theorem of M. Feinberg on representable matroids. The result is shown not to hold for nonrepresentable matroids of rank 3
Finding largest small polygons with GloptiPoly
A small polygon is a convex polygon of unit diameter. We are interested in
small polygons which have the largest area for a given number of vertices .
Many instances are already solved in the literature, namely for all odd ,
and for and 8. Thus, for even , instances of this problem
remain open. Finding those largest small polygons can be formulated as
nonconvex quadratic programming problems which can challenge state-of-the-art
global optimization algorithms. We show that a recently developed technique for
global polynomial optimization, based on a semidefinite programming approach to
the generalized problem of moments and implemented in the public-domain Matlab
package GloptiPoly, can successfully find largest small polygons for and
. Therefore this significantly improves existing results in the domain.
When coupled with accurate convex conic solvers, GloptiPoly can provide
numerical guarantees of global optimality, as well as rigorous guarantees
relying on interval arithmetic
Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs
We define 2-decompositions of ribbon graphs, which generalise 2-sums and
tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial
of such a 2-decomposition, and derive the classical Brylawski formula for the
Tutte polynomial of a tensor product as a (very) special case. This study was
initially motivated from knot theory, and we include an application of our
formulae to mutation in knot diagrams.Comment: Version 2 has minor changes. To appear in Annals of Combinatoric
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
We derive some new structural results for the transfer matrix of
square-lattice Potts models with free and cylindrical boundary conditions. In
particular, we obtain explicit closed-form expressions for the dominant (at
large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as
the solution of a special one-dimensional polymer model. We also obtain the
large-q expansion of the bulk and surface (resp. corner) free energies for the
zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47}
(resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <=
m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19
Postscript figures. Also included are Mathematica files data_CYL.m and
data_FREE.m. Many changes from version 1: new material on series expansions
and their analysis, and several proofs of previously conjectured results.
Final version to be published in J. Stat. Phy
The criminal justice voluntary sector: concepts and an agenda for an emerging field
This is the peer reviewed version of the following article: Tomczak, P. & Buck, G. (2019). The criminal justice voluntary sector: concepts and an agenda for an emerging field. Howard Journal of Crime and Justice, 58(3), which has been published in final form at https://doi.org/10.1111/hojo.12326. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.Volunteers and voluntary organisations play significant roles pervading criminal justice. They are key actors, with unrecognised potential to shore up criminal justice and/or collaboratively reshape social justice. Unlike public and for-profit agents, criminal justice volunteers and voluntary organisations (CJVVOs) have been neglected by scholars. We call for analyses of diverse CJVVOs, in national and comparative contexts. We provide three categories to highlight distinctive organising auspices, which hold across criminal justice: statutory volunteers, quasi-statutory volunteers and voluntary organisations. The unknown implications of these different forms of non-state, non-profit justice involvement deserve far greater attention from academics, policymakers and practitioners
Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial
Background:
Many patients with COVID-19 have been treated with plasma containing anti-SARS-CoV-2 antibodies. We aimed to evaluate the safety and efficacy of convalescent plasma therapy in patients admitted to hospital with COVID-19.
Methods:
This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]) is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. The trial is underway at 177 NHS hospitals from across the UK. Eligible and consenting patients were randomly assigned (1:1) to receive either usual care alone (usual care group) or usual care plus high-titre convalescent plasma (convalescent plasma group). The primary outcome was 28-day mortality, analysed on an intention-to-treat basis. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936.
Findings:
Between May 28, 2020, and Jan 15, 2021, 11558 (71%) of 16287 patients enrolled in RECOVERY were eligible to receive convalescent plasma and were assigned to either the convalescent plasma group or the usual care group. There was no significant difference in 28-day mortality between the two groups: 1399 (24%) of 5795 patients in the convalescent plasma group and 1408 (24%) of 5763 patients in the usual care group died within 28 days (rate ratio 1·00, 95% CI 0·93–1·07; p=0·95). The 28-day mortality rate ratio was similar in all prespecified subgroups of patients, including in those patients without detectable SARS-CoV-2 antibodies at randomisation. Allocation to convalescent plasma had no significant effect on the proportion of patients discharged from hospital within 28 days (3832 [66%] patients in the convalescent plasma group vs 3822 [66%] patients in the usual care group; rate ratio 0·99, 95% CI 0·94–1·03; p=0·57). Among those not on invasive mechanical ventilation at randomisation, there was no significant difference in the proportion of patients meeting the composite endpoint of progression to invasive mechanical ventilation or death (1568 [29%] of 5493 patients in the convalescent plasma group vs 1568 [29%] of 5448 patients in the usual care group; rate ratio 0·99, 95% CI 0·93–1·05; p=0·79).
Interpretation:
In patients hospitalised with COVID-19, high-titre convalescent plasma did not improve survival or other prespecified clinical outcomes.
Funding:
UK Research and Innovation (Medical Research Council) and National Institute of Health Research
A proof of McKee's eulerian-bipartite characterization
AbstractA proof is given of the result about binary matroids that implies that a connected graph is Eulerian if and only if every edge lies in an odd number of circuits, and a graph is bipartite if and only if every edge lies in an odd number of cocircuits (minimal cutsets). A proof is also given of the result that the edge set of every graph can be expressed as a disjoint union of circuits and cocircuits. No matroid theory is assumed
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