Related papers: Cluster duality between Calkin-Wilf tree and Stern…
Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…
This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting…
We introduce the continuum self-similar tree (CSST) and characterize it topologically. We apply this to answer a question of Curien about the topology of the continuum random tree (CRT). We also give a topological characterization of other…
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…
Let $C$ be a symmetrizable generalized Cartan matrix. We introduce four different versions of double Bott-Samelson cells for every pair of positive braids in the generalized braid group associated to $C$. We prove that the decorated double…
In this paper, we consider random trees associated with the genealogy of Crump-Mode-Jagers processes and perform Bernoulli bond-percolation whose parameter depends on the size of the tree. Our purpose is to show the existence of a giant…
Following Poupard's study of strictly ordered binary trees with respect to two parameters, namely, "end of minimal chain" and "parent of maximum leaf" a true Tree Calculus is being developed to solve a partial difference equation system and…
Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to…
The existence of apparently coincidental equalities (also called Wilf-equivalences) between the enumeration sequences, or generating functions, of various hereditary classes of combinatorial structures has attracted significant interest. We…
The dynamics of a close binary system of globular clusters is considered. It is shown that the star transfer process from one of the components to the other should lead to the decrease of dimension of the first cluster with simultaneous…
Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…
This is a very brief survey of some results in the geometry of string duality delivered at a lecture given at ICM 1998, Berlin. String Duality is the statement that one kind of string theory compactified on one space is equivalent in some…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights…
A hyperbinary expansion of a positive integer n is a partition of n into powers of 2 in which each part appears at most twice. In this paper, we consider a generalization of this concept and a certain statistic on the corresponding set of…
In this paper, we study tree--like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of…
Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and…
The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a…
We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance…
Algorithms can be used to prove and to discover new theorems. This paper shows how algorithmic skills in general, and the notion of invariance in particular, can be used to derive many results from Euclid's algorithm. We illustrate how to…