We introduce a class of incremental network design problems focused on investigating the optimal choice and timing of network expansions. We concentrate on an incremental network design problem with shortest paths. We investigate structural properties of optimal solutions, we show that the simplest variant is NP-hard, we analyze the worst-case performance of natural greedy heuristics, and we derive a 4-approximation algorithm.

IntroductionWhile Cumulus – a semi-automated method for measuring breast density – is utilised extensively in research, it is labour-intensive and unsuitable for screening programmes that require an efficient and valid measure on which to base screening recommendations. We develop an automated method to measure breast density (AutoDensity) and compare it to Cumulus in terms of association with breast cancer risk and breast cancer screening outcomes.MethodsAutoDensity automatically identifies the breast area in the mammogram and classifies breast density in a similar way to Cumulus, through a fast, stand-alone Windows or Linux program. Our sample comprised 985 women with screen-detected cancers, 367 women with interval cancers and 4,975 controls (women who did not have cancer), sampled from first and subsequent screening rounds of a film mammography screening programme. To test the validity of AutoDensity, we compared the effect estimates using AutoDensity with those using Cumulus from logistic regression models that tested the association between breast density and breast cancer risk, risk of small and large screen-detected cancers and interval cancers, and screening programme sensitivity (the proportion of cancers that are screen-detected). As a secondary analysis, we report on correlation between AutoDensity and Cumulus measures.ResultsAutoDensity performed similarly to Cumulus in all associations tested. For example, using AutoDensity, the odds ratios for women in the highest decile of breast density compared to women in the lowest quintile for invasive breast cancer, interval cancers, large and small screen-detected cancers were 3.2 (95% CI 2.5 to 4.1), 4.7 (95% CI 3.0 to 7.4), 6.4 (95% CI 3.7 to 11.1) and 2.2 (95% CI 1.6 to 3.0) respectively. For Cumulus the corresponding odds ratios were: 2.4 (95% CI 1.9 to 3.1), 4.1 (95% CI 2.6 to 6.3), 6.6 (95% CI 3.7 to 11.7) and 1.3 (95% CI 0.9 to 1.8). Correlation between Cumulus and AutoDensity measures was 0.63 (P < 0.001).ConclusionsBased on the similarity of the effect estimates for AutoDensity and Cumulus in models of breast density and breast cancer risk and screening outcomes, we conclude that AutoDensity is a valid automated method for measuring breast density from digitised film mammograms.

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Wired and wireless communications both play an important role in the blend of communications technologies necessary to enable future smart grid communications. Hybrid networks exploit independent mediums to extend network coverage and improve performance. However, whereas individual technologies have been applied in simulation networks, as far as we know there is only limited attention that has been paid to the development of a suite of hybrid communication simulation models for the communications system design. Hybrid simulation models are needed to capture the mixed communication technologies and IP address mechanisms in one simulation. To close this gap, we have developed a suite of hybrid communication system simulation models to validate the critical system design criteria for a distributed solar Photovoltaic (PV) communications system, including a single trip latency of 300 ms, throughput of 9.6 Kbps, and packet loss rate of 1%. The results show that three low-power wireless personal area network (LoWPAN)-based hybrid architectures can satisfy three performance metrics that are critical for distributed energy resource communications.