Repetition-free longest common subsequence of random sequences

A repetition free Longest Common Subsequence (LCS) of two sequences x and y is an LCS of x and y where each symbol may appear at most once. Let R denote the length of a repetition free LCS of two sequences of n symbols each one chosen randomly, uniformly, and independently over a k-ary alphabet. We study the asymptotic, in n and k, behavior of R and establish that there are three distinct regimes, depending on the relative speed of growth of n and k. For each regime we establish the limiting behavior of R. In fact, we do more, since we actually establish tail bounds for large deviations of R from its limiting behavior. Our study is motivated by the so called exemplar model proposed by Sankoff (1999) and the related similarity measure introduced by Adi et al. (2007). A natural question that arises in this context, which as we show is related to long standing open problems in the area of probabilistic combinatorics, is to understand the asymptotic, in n and k, behavior of parameter R.Comment: 15 pages, 1 figur

Classification of Southern Ocean krill and icefish echoes using random forests

Acknowledgements The authors thank the crews, fishers, and scientists who conducted the various surveys from which data were obtained. This work was supported by the Government of South Georgia and South Sandwich Islands. Additional logistical support provided by The South Atlantic Environmental Research Institute, with thanks to Paul Brickle. PF receives funding from the MASTS pooling initiative (TheMarine Alliance for Science and Technology for Scotland), and their support is gratefully acknowledged. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions. SF is funded by the Natural Environment Research Council, and data were provided from the British Antarctic Survey Ecosystems Long-term Monitoring and Surveys programme as part of the BAS Polar Science for Planet Earth Programme. The authors also thank the anonymous referees for their helpful suggestions on an earlier version of this manuscript.Peer reviewedPostprin

The Private Cost of Long-Term Care in Canada: Where You Live Matters

Canadians expect the same access to health care whether they are rich or poor, and wherever they live, often without direct charge at the point of service. However, we find that the private cost of long-term care differs greatly across the country, and within provinces, we find substantial variation, depending on income level, marital status, and, in Quebec alone, on assets owned. A non-married person with average income would pay more than twice as much in the Atlantic provinces as in Quebec, while a couple with one in care would pay almost four times as much in Newfoundland as in Alberta.long-term care, private cost

The Private Cost of Long-Term Care in Canada: Where You Live Matters

Canadians expect the same access to health care whether they are rich or poor, and wherever they live, often without direct charge at the point of service. However, we find that the private cost of long-term care differs greatly across the country, and within provinces, we find substantial variation, depending on income level, marital status, and, in Quebec alone, on assets owned. A non-married person with average income would pay more than twice as much in the Atlantic provinces as in Quebec, while a couple with one in care would pay almost four times as much in Newfoundland as in Alberta.long-term care , private cost