Linear treesCaterpillarsdoi:10.1016/j.disc.2020.112284Tanay WakhareEric WitykCharles R. JohnsonDiscrete Mathematics
obtain basic geometric and graph-theoretic results, and compare these results to those in the classical phylogenetic setting. In particular, we focus on ranked trees, discrete time-trees (as defined above), and the ultrametric versions of those types of trees. We establish size bounds for neighbo...
This paper introduces new MIP formulations for learning optimal decision trees with multivariate branching rules and no assumptions on the feature types. We first propose a strong baseline MIP formulation that still uses big-M constraints, but yields a stronger LP relaxation than its counterparts in ...
Fig. 9. (a) CBT7 in 1-M7 with a leaf being 0000000 and its parent being 0000001. (b) CBT7 in 1-M7 with a leaf being 0000000 and its parent being 0000001. (c) Tx. (d) Ty. Case 3. n=4k+9 and k≥1. Similarly, Type-0-1-(1,1) CBTn−4 can be constructed by building...
substances in the same spectral band, VIS–NIR spectroscopy is widely used to detect chemical substances [20,21], soil [22], minerals [23] and food [24]. The following articles in this section describe the principle of VIS–NIR spectroscopy and its application in the study of fruit tree ...
The regulatory processes that govern cell proliferation and differentiation are central to developmental biology. Particularly well studied in this respect is the lymphoid system due to its importance for basic biology and for clinical applications. Gene expression measured in lymphoid cells in several dis...
purple flowers and are particularly well represented in eastern Brazil—where are found ~30% of all species of this genus9,10. In the Atlantic Forest, species ofPleromaare commonly known asManacá da serraandQuaresmeira, the latter meaning literally ’tree of Lent’ because its blossoms ...
Machine Learning techniques are widely used today for many different tasks. Different types of data require different methods.Yandexrelies on Gradient Boosting to power many of our market-leading products and services including search, music streaming, ride-hailing, self-driving cars, weather prediction...
If e is not in any edge-cut separating T of size f(k) then we may simply delete it. So, let us assume that δ(X) is an edge-cut of G separating T with size f(k) and e∈δ(X). Since both X and its complement contain a point in T and an end of e, we have |X|,|V...
Moreover, if H is a tree, then H is a tree as well (and its size is at most the size of H). Hence, it suffices to work with trees that are cores. Hell and Nesˇetˇril proved that deciding whether a given digraph is a core is coNP- complete [42]. However, it follows ...