Related papers: Splitting the Kunneth formula
Phylogenetic networks are generalizations of trees that allow for the modeling of non-tree like evolutionary processes. Split networks give a useful way to construct networks with intuitive distance structures induced from the associated…
The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for pm(n) for…
We develop exact piecewise polynomial sequences on Alfeld splits in any spatial dimension and any polynomial degree. An Alfeld split of a simplex is obtained by connecting the vertices of an $n$-simplex with its barycenter. We show that, on…
A split system on a multiset $\mathcal M$ is a set of bipartitions of $\mathcal M$. Such a split system $\mathfrak S$ is compatible if it can be represented by a tree in such a way that the vertices of the tree are labelled by the elements…
We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a…
Intersection numbers of twisted cocycles arise in mathematics in the field of algebraic geometry. Quite recently, they appeared in physics: Intersection numbers of twisted cocycles define a scalar product on the vector space of Feynman…
Cycle expansions are an efficient scheme for computing the properties of chaotic systems. When enumerating the orbits for a cycle expansion not all orbits that one would expect at first are present --- some are pruned. This pruning leads to…
We present a property satisfied by a large variety of complex continued fraction algorithms (the "finite building property") and use it to explore the structure of bijectivity domains for natural extensions of Gauss maps. Specifically, we…
The questions of the measure and finding open intervals in certain sets of sums and products of elements of the middle third Cantor set (or a variant of it), have generated considerable interest recently. A broad general framework that…
Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear…
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…
Based on the presentation of the Kauffman bracket skein module of the torus given by the third author in previous work, Charles D. Frohman and R\u{a}zvan Gelca established a complete description of the multiplicative operation leading to a…
Two simple predicates are adopted and certain real-valued piecewise continuous functions are constructed from them. This type of maps will be called quasi-step maps and aim to separate the fixed points of an iteration map in an interval.…
We introduce the notion of brick-splitting torsion pairs as a modern analogue and generalization of the classical notion of splitting torsion pairs. A torsion pair is called brick-splitting if any given brick is either torsion or…
The splitting algorithms of monotone operator theory find zeros of sums of relations. This corresponds to solving series or parallel one-port electrical circuits, or the negative feedback interconnection of two subsystems. One-port circuits…
Given a stochastic matrix $P$ partitioned in four blocks $P_{ij}$, $i,j=1,2$, Kemeny's constant $\kappa(P)$ is expressed in terms of Kemeny's constants of the stochastic complements $P_1=P_{11}+P_{12}(I-P_{22})^{-1}P_{21}$, and…
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…
When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the states-of-knowledge of the respective observers. Here…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…