Related papers: Webs and Posets
Circuits are fundamental objects in linear programming and oriented matroid theory, representing the elementary difference vectors of a polyhedron between points in its affine space. A recent concept introduced by Ekbatani, Natura, and…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Kwasniewski's cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation…
We present a triangulation--independent area--ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two--form ``connection'' should carry three ``color'' indices…
How do sequence models represent their decision-making process? Prior work suggests that Othello-playing neural network learned nonlinear models of the board state (Li et al., 2023). In this work, we provide evidence of a closely related…
We define bipartite and monopartite relational networks of chemical elements and compounds using two different datasets of inorganic chemical and material compounds, as well as study their topology. We discover that the connectivity between…
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…
Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might…
Regarding the Specht modules associated to the two-row partition $(n,n)$, we provide a combinatorial path model to study the transitioning matrix from the tableau basis to the $A_1$-web basis (i.e. cup diagrams), and prove that the entries…
We introduce multi-tribrackets, algebraic structures for region coloring of diagrams of knots and links with different operations at different kinds of crossings. In particular we consider the case of component multi-tribrackets which have…
We explore the application of graph coloring to biological networks, specifically protein-protein interaction (PPI) networks. First, we find that given similar conditions (i.e. number of nodes, number of links, degree distribution and…
Interaction nets are a form of restricted graph rewrite system that can serve as a graphical or textual programming language. As such, benefits include one-step confluence, ease of parallelism and explicit garbage collection. However, some…
Van der Waerden's (VDW) colouring theorem in combinatoric number theory [1] has scope for physical applications.The solution of the two colour case has enabled the construction of an explicit mapping of an infinite, one dimensional…
In this paper we illuminate some algebraic-combinatorial structure underlying the second order networks (SONETS) random graph model of Nykamp, Zhao and collaborators. In particular we show that this algorithm is deeply connected with a…
The increased quantity of data has led to a soaring use of networks to model relationships between different objects, represented as nodes. Since the number of nodes can be particularly large, the network information must be summarised…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type…
Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables) and computing the outcome in other…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the…