Related papers: Deconstructing Bataknese Gorga Computationally
Galled trees, directed acyclic graphs that model evolutionary histories with isolated hybridization events, have become very popular due to both their biological significance and the existence of polynomial time algorithms for their…
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…
This paper presents a bridge between the theories of wonderful models associated with toric arrangements and wonderful models associated with hyperplane arrangements. In a previous work, the same authors noticed that the model of the toric…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple operations on a set of sequences called orthology relations may be employed. In addition to being…
We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences of numbers in {-1,0,1}, and introduce several natural generalizations. We study the relationships between these properties and…
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous hulls resulting from these tilings are all topologically…
Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of…
A proper vertex coloring of a graph is a mapping of its vertices on a set of colors, such that two adjacent vertices are not mapped to the same color. This constraint may be interpreted in terms of the distance between to vertices and so a…
We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as tree topologies; a tree topology can also be thought of as a tree combinatorial type, which is…
Understanding the patterns and processes of diversification of life in the planet is a key challenge of science. The Tree of Life represents such diversification processes through the evolutionary relationships among the different taxa, and…
This study aims to investigate geometrical concepts related to ethnomathematics in Indonesia. The research design used in this study is to summarize, review, and analyze 24 papers that discussed ethnomathematics. We selected either journal…
We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of…
We construct polyhedral families of valuations on the branching algebra of a morphism of reductive groups. This establishes a connection between the combinatorial rules for studying a branching problem and the tropical geometry of the…
Tree-decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. The main property of tree-decompositions is the width (the maximum size of a bag minus 1). We show that every graph has a…
Based on solid theoretical foundations, we present strong evidences that a number of real-life networks, taken from different domains like Internet measurements, biological data, web graphs, social and collaboration networks, exhibit…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
The paper reports the possibility of Indonesian traditional artisans of weaving designs and crafts to explore the cellular automata, a dynamical model in computation that may yield similar patterns. The reviews of the cellular automata due…