Mod/Resc Parsimony Inference

We address in this paper a new computational biology problem that aims at understanding a mechanism that could potentially be used to genetically manipulate natural insect populations infected by inherited, intra-cellular parasitic bacteria. In this problem, that we denote by \textsc{Mod/Resc Parsimony Inference}, we are given a boolean matrix and the goal is to find two other boolean matrices with a minimum number of columns such that an appropriately defined operation on these matrices gives back the input. We show that this is formally equivalent to the \textsc{Bipartite Biclique Edge Cover} problem and derive some complexity results for our problem using this equivalence. We provide a new, fixed-parameter tractability approach for solving both that slightly improves upon a previously published algorithm for the \textsc{Bipartite Biclique Edge Cover}. Finally, we present experimental results where we applied some of our techniques to a real-life data set.Comment: 11 pages, 3 figure

Reducing Livestock Effects on Public Lands in the Western United States as the Climate Changes: A Reply to Svejcar et al.

Beschta et al. (2013) synthesized the ecological effects 41 of climate change and ungulate grazing on western public lands, grounding their recommendations in ecological considerations and federal agency legal authority and obligations. Svejcar et al. (2014) suggest that Beschta et al. (2013) neither “present a balanced synthesis of the scientific literature” nor “reflect the complexities associated with herbivore grazing.” Svejcar et al. (2014) “dispute the notion that eliminating [livestock] grazing will provide a solution to problems created by climate change,” although we made no such claim. Instead, Beschta et al. (2013: p. 474) indicate that removal or reduction of livestock across large areas of public land will reduce a pervasive ecological stress, diminishing cumulative impacts on these ecosystems under climate change. We respond to three livestock grazing issues raised by Svejcar et al. (2014): (1) legacy vs. contemporary effects, (2) fuels reduction and fire effects, and (3) grazing complexity and restoration.Keywords: Climate change, Public lands, Restoration, Ungulates, Livestock grazing, Biodiversit

Arboreality increases reptile community resistance to disturbance from livestock grazing

1. Domestic livestock grazing directly alters ground-level habitat but its effects on arboreal habitat are poorly known. Similarly, the response to grazing of ground-dwelling fauna has been examined, but there are few studies of arboreal fauna. Globally, grazing has been implicated in the decline of vertebrate fauna species, but some species appear resistant to the effects of grazing, either benefiting from the structural changes at ground level or avoiding them, as may be the case with arboreal species. Here we examine arboreal and terrestrial habitat responses and reptile community responses to grazing, to determine whether arboreal reptile species are more resistant than terrestrial reptile species. 2. We conducted arboreal and terrestrial reptile surveys on four different grazing treatments, at a 19-year experimental grazing trial in northern Australia. To compare the grazing response of arboreal and terrestrial reptile assemblages, we used community, functional group and individual species-level analyses. Species responses were modelled in relation to landscape-scale and microhabitat variables. 3. Arboreal reptile species were resistant to the impact of grazing, whereas terrestrial reptiles were negatively affected by heavy grazing. Terrestrial reptiles were positively associated with complex ground structures, which were greatly reduced in heavily grazed areas. Arboreal lizards responded positively to microhabitat features such as tree hollows. 4. Synthesis and applications. Arboreal and terrestrial reptiles have different responses to the impact of livestock grazing. This has implications for rangeland management, particularly if management objectives include goals relating to conserving certain species or functional groups. Arboreal reptiles showed resistance in a landscape that is grazed, but where trees have not been cleared. We highlight the importance of retaining trees in rangelands for both terrestrial and arboreal microhabitats

A model for finding transition-minors

The well known cycle double cover conjecture in graph theory is strongly related to the compatible circuit decomposition problem. A recent result by Fleischner et al. (2018) gives a su cient condition for the existence of a compatible circuit decomposition in a transitioned 2-connected Eulerian graph, which is based on an extension of the de nition of K5-minors to transitioned graphs. Graphs satisfying this condition are called SUD-K5-minor-free graphs. In this work we formulate a generalization of this property by replacing the K5 by a 4-regular transitioned graph H, which is part of the input. Furthermore, we consider the decision problem of checking for two given graphs if the extended property holds. We prove that this problem is NP- complete and xed parameter tractable with the size of H as parameter. We then formulate an equivalent problem, present a mathematical model for it, and prove its correctness. This mathematical model is then translated into a mixed integer linear program (MIP) for solving it in practice. Computational results show that the MIP formulation can be solved for small instances in reasonable time. In our computations we found snarks with perfect matchings whose contraction leads to SUD-K5-minor-free graphs that contain K5-minors. Furthermore, we veri ed that there exists a perfect pseudo-matching whose contraction leads to a SUD-K5-minor-free graph for all snarks with up to 22 vertices. Keywords: Transition Minor, Cycle Double Cover, Compatible Circuit Decomposition, Integer Programmin

A lower bound for the smallest uniquely hamiltonian planar graph with minimum degree three

Bondy and Jackson conjectured in 1998 that every planar uniquely hamiltonian graph must have a vertex of degree two. In this work we verify computationally Bondy and Jackson's conjecture for graphs with up to 25 vertices. Using a reduction we search for graphs that contain a stable fixed-edge cycle or equivalently a stable cycle with one vertex of degree two. For generating candidate graphs we use plantri and for checking if they contain a stable fixed-edge cycle we propose three approaches. Two of them are based on integer linear programming (ILP) and the other is a cycle enumeration algorithm. To reduce the search space we prove several properties a minimum planar graph with minimum degree at least three containing a stable fixed-edge cycle must satisfy, the most significant being triangle freeness. Comparing the three algorithms shows that the enumeration is more effective on small graphs while for larger graphs the ILP-based approaches perform better. Finally, we use the enumeration approach together with plantri to check that there does not exist a planar graph with minimum degree at least three which contains a stable fixed- edge cycle with 24 or fewer vertices