Anti-Pasch optimal packings with triples

It is shown that for v ≠ 6, 7, 10, 11, 12, 13, there exists an optimal packing with triples on v points that contains no Pasch configurations. Furthermore, for all v ≡ 5 (mod 6), there exists a pairwise balanced design of order v, whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples

Fast Discovery of Reliable k-terminal Subgraphs

Peer reviewe

Partial Covering Arrays: Algorithms and Asymptotics

A covering array $\mathsf{CA}(N;t,k,v)$ is an $N\times k$ array with entries in $\{1, 2, \ldots , v\}$, for which every $N\times t$ subarray contains each $t$-tuple of $\{1, 2, \ldots , v\}^t$ among its rows. Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems. A central question is to determine or bound $\mathsf{CAN}(t,k,v)$, the minimum number $N$ of rows of a $\mathsf{CA}(N;t,k,v)$. The well known bound $\mathsf{CAN}(t,k,v)=O((t-1)v^t\log k)$ is not too far from being asymptotically optimal. Sensible relaxations of the covering requirement arise when (1) the set $\{1, 2, \ldots , v\}^t$ need only be contained among the rows of at least $(1-\epsilon)\binom{k}{t}$ of the $N\times t$ subarrays and (2) the rows of every $N\times t$ subarray need only contain a (large) subset of $\{1, 2, \ldots , v\}^t$. In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two. In each case, a randomized algorithm constructs such arrays in expected polynomial time

Orthogonal Arrays of Strength Three from Regular 3-Wise Balanced Designs

The construction given in Kreher, J Combin Des 4 (1996) 67 is extended to obtain new infinite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction

Minimal Obstructions for Partial Representations of Interval Graphs

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. Two linear-time algorithms are known for solving this problem. In this paper, we characterize the minimal obstructions which make partial representations non-extendible. This generalizes Lekkerkerker and Boland's characterization of the minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible if and only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to a linear-time certifying algorithm for partial representation extension

Community-linked maternal death review (CLMDR) to measure and prevent maternal mortality: a pilot study in rural Malawi.

In Malawi, maternal mortality remains high. Existing maternal death reviews fail to adequately review most deaths, or capture those that occur outside the health system. We assessed the value of community involvement to improve capture and response to community maternal deaths

A critical analysis of the drivers of human migration patterns in the presence of climate change: A new conceptual model

Both climate change and migration present key concerns for global health progress. Despite this, a transparent method for identifying and understanding the relationship between climate change, migration and other contextual factors remains a knowledge gap. Existing conceptual models are useful in understanding the complexities of climate migration, but provide varying degrees of applicability to quantitative studies, resulting in non-homogenous transferability of knowledge in this important area. This paper attempts to provide a critical review of climate migration literature, as well as presenting a new conceptual model for the identification of the drivers of migration in the context of climate change. It focuses on the interactions and the dynamics of drivers over time, space and society. Through systematic, pan-disciplinary and homogenous application of theory to different geographical contexts, we aim to improve understanding of the impacts of climate change on migration. A brief case study of Malawi is provided to demonstrate how this global conceptual model can be applied into local contextual scenarios. In doing so, we hope to provide insights that help in the more homogenous applications of conceptual frameworks for this area and more generally

Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels

The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d=6 or d=10. In contrast to their result, we show that the King's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.Comment: REVTeX4, 4 page

Entanglement-assisted quantum low-density parity-check codes

This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error correction performance, high rates, and low decoding complexity. The proposed method produces infinitely many new codes with a wide variety of parameters and entanglement requirements. Our framework encompasses various codes including the previously known entanglement-assisted quantum LDPC codes having the best error correction performance and many new codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.Comment: 20 pages, 5 figures. Final version appearing in Physical Review

Factors associated with healthcare seeking behaviour for children in Malawi: 2016

Objective: To characterise health seeking behaviour (HSB) and determine its predictors amongst children in Malawi in 2016. Methods: We used the 2016 Malawi Integrated Household Survey data set. The outcome of interest was HSB, defined as seeking care at a health facility amongst people who reported one or more of a list of possible symptoms given on the questionnaire in the past two weeks. We fitted a multivariate logistic regression model of HSB using a forward step-wise selection method, with age, sex and symptoms entered as a priori variables. Results: Of 5350 children, 1666 (32%) had symptoms in the past two weeks. Of the 1666, 1008 (61%) sought care at health facility. The children aged 5–14 years were less likely to be taken to health facilities for health care than those aged 0–4 years. Having fever vs. not having fever and having a skin problem vs. not having skin problem were associated with increased likelihood of HSB. Having a headache vs. not having a headache was associated with lower likelihood of accessing care at health facilities (AOR = 0.50, 95% CI: 0.26–0.96, P = 0.04). Children from urban areas were more likely to be taken to health facilities for health care (AOR = 1.81, 95% CI: 1.17–2.85, P = 0.008), as were children from households with a high wealth status (AOR = 1.86, 95% CI: 1.25–2.78, P = 0.02). Conclusion: There is a need to understand and address individual, socio-economic and geographical barriers to health seeking to increase access and use of health care and fast-track progress towards Universal Health Coverage