Indexing methods for efficient processing of multidimensional data are very requested in many fields, like geographical information systems, drawing documentations etc. Well-known R-tree is one of the multidimensional data structures. The R-tree is based on bounding of spatial near points by multidimensional rectangles. This data structure supports various types of queries, e.g. point and range...

Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227–240] as a generalization of median graphs. We present some incorrectnesses from that article. In particular we point to a gap in the proof of the theorem about the dismantlability of the cube graph of a tree-like partial cube and ...

The spatially explicit and mechanistic model TREEGRASS was used to test the effects of tree density, tree spatial distribution, and tree size distribution on radiation absorption, net primary production (NPP), and, water fluxes for a West African savanna . The model has previously been shown to adequately predict radiation absorption, production, and soil water balance in humid savannas . Using...

In this paper, we provide a method to accelerate the power of splicing systems. We introduce the splicing systems on trees to be built as partially annealed single strands, that is a quite similar notion and a natural extension of splicing systems on strings. Trees are a common and useful data structure in computer science and have a biological counterpart such as molecular sequences with secon...

We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations encoded in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new property of conditional independence that hol...

In [Vieira et al. 2004] we presented a new dynamic Metric Access Method (MAM) called DBM-tree. This structure, unlike any other MAM, explores the varying density of elements in the dataset that allows creating, in a controlled way, unbalanced trees. Every dynamic MAM that works with persistent data proposed so far uses the same principle employed in conventional trees, like the B-tree [Comer 19...

Many kinds of variable-sized data we would like to model contain an internal hierarchical structure in the form of a tree, including source code, formal logical statements, and natural language sentences with parse trees. For such data it is natural to consider a model with matching computational structure. In this work, we introduce a variational autoencoder-based generative model for tree-str...