On NP-Hardness of the Paired de Bruijn Sound Cycle Problem

The paired de Bruijn graph is an extension of de Bruijn graph incorporating mate pair information for genome assembly proposed by Mevdedev et al. However, unlike in an ordinary de Bruijn graph, not every path or cycle in a paired de Bruijn graph will spell a string, because there is an additional soundness constraint on the path. In this paper we show that the problem of checking if there is a sound cycle in a paired de Bruijn graph is NP-hard in general case. We also explore some of its special cases, as well as a modified version where the cycle must also pass through every edge.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Lichenometric dating (lichenometry) and the biology of the lichen genus rhizocarpon:challenges and future directions

Lichenometric dating (lichenometry) involves the use of lichen measurements to estimate the age of exposure of various substrata. Because of low radial growth rates and considerable longevity, species of the crustose lichen genus Rhizocarpon have been the most useful in lichenometry. The primary assumption of lichenometry is that colonization, growth and mortality of Rhizocarpon are similar on surfaces of known and unknown age so that the largest thalli present on the respective faces are of comparable age. This review describes the current state of knowledge regarding the biology of Rhizocarpon and considers two main questions: (1) to what extent does existing knowledge support this assumption; and (2) what further biological observations would be useful both to test its validity and to improve the accuracy of lichenometric dates? A review of the Rhizocarpon literature identified gaps in knowledge regarding early development, the growth rate/size curve, mortality, regeneration, competitive effects, colonization, and succession on rock surfaces. The data suggest that these processes may not be comparable on different rock surfaces, especially in regions where growth rates and thallus turnover are high. In addition, several variables could differ between rock surfaces and influence maximum thallus size, including rate and timing of colonization, radial growth rates, environmental differences, thallus fusion, allelopathy, thallus mortality, colonization and competition. Comparative measurements of these variables on surfaces of known and unknown age may help to determine whether the basic assumptions of lichenometry are valid. Ultimately, it may be possible to take these differences into account when interpreting estimated dates

Online Learning and Resource-Bounded Dimension: Winnow Yields New Lower Bounds for Hard Sets

We establish a relationship between the online mistake-bound model of learning and resource-bounded dimension. This connection is combined with the Winnow algorithm to obtain new results about the density of hard sets under adaptive reductions. This improves previous work of Fu (1995) and Lutz and Zhao (2000), and solves one of Lutz and Mayordomo's "Twelve Problems in Resource-Bounded Measure" (1999)