Superregular matrices and applications to convolutional codes

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature

Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis

We investigate the properties of hard core Bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body Density Matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the "natural" single particle orbitals and their occupation, including the condensate fraction. At low Boson density, $na^3 < 10^{-5}$, where $n = N/V$ and $a$ is the hard core diameter, the condensate is localized at the center of the trap. As $na^3$ increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At $na^3 \leq 10^{-4}$ the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At $na^3 \approx 10^{-3}$ corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At $na^3 \gtrsim 10^{-2}$, mean field theory fails. At $na^3 \gtrsim 0.1$, the Bosons behave more like a liquid $^4$He droplet than a trapped Boson gas.Comment: 13 pages, 14 figures, submitted Phys. Rev.

The Complexity of the Empire Colouring Problem

We investigate the computational complexity of the empire colouring problem (as defined by Percy Heawood in 1890) for maps containing empires formed by exactly $r > 1$ countries each. We prove that the problem can be solved in polynomial time using $s$ colours on maps whose underlying adjacency graph has no induced subgraph of average degree larger than $s/r$. However, if $s \geq 3$, the problem is NP-hard even if the graph is a forest of paths of arbitrary lengths (for any $r \geq 2$, provided $s < 2r - \sqrt(2r + 1/4+ 3/2)$. Furthermore we obtain a complete characterization of the problem's complexity for the case when the input graph is a tree, whereas our result for arbitrary planar graphs fall just short of a similar dichotomy. Specifically, we prove that the empire colouring problem is NP-hard for trees, for any $r \geq 2$, if $3 \leq s \leq 2r-1$ (and polynomial time solvable otherwise). For arbitrary planar graphs we prove NP-hardness if $s<7$ for $r=2$, and $s < 6r-3$, for $r \geq 3$. The result for planar graphs also proves the NP-hardness of colouring with less than 7 colours graphs of thickness two and less than $6r-3$ colours graphs of thickness $r \geq 3$.Comment: 23 pages, 12 figure

Study Protocol on Defining Core Outcomes and Data Elements in Chronic Subdural Haematoma

Abstract BACKGROUND Core Outcome Sets (COSs) are necessary to standardize reporting in research studies. This is urgently required in the field of chronic subdural hematoma (CSDH), one of the most common disease entities managed in neurosurgery and the topic of several recent trials. To complement the development of a COS, a standardized definition and baseline Data Elements (DEs) to be collected in CSDH patients, would further improve study quality and comparability in this heterogeneous population. OBJECTIVE To, first, define a standardized COS for reporting in all future CSDH studies; and, second, to identify a unified CSDH Definition and set of DEs for reporting in future CSDH studies. METHODS The overall study design includes a Delphi survey process among 150 respondents from 2 main stakeholder groups: healthcare professionals or researchers (HCPRs) and Patients or carers. HCPR, patients and carers will all be invited to complete the survey on the COS, only the HCPR survey will include questions on definition and DE. EXPECTED OUTCOMES It is expected that the COS, definition, and DE will be developed through this Delphi survey and that these can be applied in future CSDH studies. This is necessary to help align future research studies on CSDH and to understand the effects of different treatments on patient function and recovery. DISCUSSION This Delphi survey should result in consensus on a COS and a standardized CSDH Definition and DEs to be used in future CSDH studies. </jats:sec

Exploring leadership in multi-sectoral partnerships

This article explores some critical aspects of leadership in the context of multi-sectoral partnerships. It focuses on leadership in practice and asks the question, `How do managers experience and perceive leadership in such partnerships?' The study contributes to the debate on whether leadership in a multi-sectoral partnership context differs from that within a single organization. It is based on the accounts of practising managers working in complex partnerships. The article highlights a number of leadership challenges faced by those working in multi-sectoral partnerships. Partnership practitioners were clear that leadership in partnerships was more complex than in single organizations. However, it was more difficult for them to agree a consensus on the essential nature of leadership in partnership. We suggest that a first-, second- and third-person approach might be a way of better interpreting leadership in the context of partnerships

'Education, education, education' : legal, moral and clinical

This article brings together Professor Donald Nicolson's intellectual interest in professional legal ethics and his long-standing involvement with law clinics both as an advisor at the University of Cape Town and Director of the University of Bristol Law Clinic and the University of Strathclyde Law Clinic. In this article he looks at how legal education may help start this process of character development, arguing that the best means is through student involvement in voluntary law clinics. And here he builds upon his recent article which argues for voluntary, community service oriented law clinics over those which emphasise the education of students

Neurosurgical randomized trials in low-and middle-income countries

BACKGROUND: The setting of a randomized trial can determine whether its findings are generalizable and can therefore apply to different settings. The contribution of low- and middle-income countries (LMICs) to neurosurgical randomized trials has not been systematically described before.OBJECTIVE: To perform a systematic analysis of design characteristics and methodology, funding source, and interventions studied between trials led by and/or conducted in high-income countries (HICs) vs LMICs.METHODS: From January 2003 to July 2016, English-language trials with >5 patients assessing any one neurosurgical procedure against another procedure, nonsurgical treatment, or no treatment were retrieved from MEDLINE, Scopus, and Cochrane Library. Income classification for each country was assessed using the World Bank Atlas method.RESULTS: A total of 73.3% of the 397 studies that met inclusion criteria were led by HICs, whereas 26.7% were led by LMICs. Of the 106 LMIC-led studies, 71 were led by China. If China is excluded, only 8.8% were led by LMICs. HIC-led trials enrolled a median of 92 patients vs a median of 65 patients in LMIC-led trials. HIC-led trials enrolled from 7.6 sites vs 1.8 sites in LMIC-led studies. Over half of LMIC-led trials were institutionally funded (54.7%). The majority of both HIC- and LMIC-led trials evaluated spinal neurosurgery, 68% and 71.7%, respectively.CONCLUSION: We have established that there is a substantial disparity between HICs and LMICs in the number of published neurosurgical trials. A concerted effort to invest in research capacity building in LMICs is an essential step towards ensuring context- and resource-specific high-quality evidence is generated.Scientific Assessment and Innovation in Neurosurgical Treatment Strategie