Related papers: A graphical construction of free Markov categories
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…
In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…
From the point of view of discrete geometry, the class of locally finite transitive graphs is a wide and important one. The subclass of Cayley graphs is of particular interest, as testifies the development of geometric group theory. Recall…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
In this article we gave the notion of particular type of functions on a group termed as class assigned functions . Using class assigned functions, we have constructed several right gyrogroup structures on a given non-abelian group.
We define a free product of connected simple graphs that is equivalent to several existing definitions when the graphs are vertex-transitive but differs otherwise. The new definition is designed for the automorphism group of the free…
Graphical Markov models determined by acyclic digraphs (ADGs), also called directed acyclic graphs (DAGs), are widely studied in statistics, computer science (as Bayesian networks), operations research (as influence diagrams), and many…
In this paper we present cartesian structure for symmetric Gray-monoidal double categories. To do this we first introduce locally cubical Gray categories, which are three-dimensional categorical structures analogous to classical, locally…
We introduce a new computational methodology for the identification and characterization of free volume within/around atomistic configurations. This scheme employs a three-stage workflow, by which spheres are iteratively grown inside of…
Counting and uniform sampling of directed acyclic graphs (DAGs) from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper, we show that these tasks can be performed in polynomial time, solving a…
This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
The field of directed type theory seeks to design type theories capable of reasoning synthetically about (higher) categories, by generalizing the symmetric identity types of Martin-L\"of Type Theory to asymmetric hom-types. We articulate…
We give a conceptual formulation of Kontsevich's `dual construction' producing graph cohomology classes from a differential graded Frobenius algebra with an odd scalar product. Our construction -- whilst equivalent to the original one -- is…
We discuss a class of chain graph models for categorical variables defined by what we call a multivariate regression chain graph Markov property. First, the set of local independencies of these models is shown to be Markov equivalent to…
We extend the modular orbits method of constructing a two-dimensional orbifold conformal field theory to higher genus Riemann surfaces. We find that partition functions on surfaces of arbitrary genus can be constructed by a straightforward…
We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant extension known as '$\Gamma$-species' which incorporates data about 'structural' group actions). This culminates…
An asteroidal triple free graph is a graph such that for every independent triple of vertices no path between any two avoids the third. In a recent result from Corneil and Stacho, these graphs were characterised through a linear vertex…
Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states. Here we extend coarse-graining to open Markov processes. An "open" Markov process is one where probability can…
We present a structural graph reasoning framework that incorporates explicit anatomical priors for explainable vision-based diagnosis. Convolutional feature maps are reinterpreted as patch-level graphs, where nodes encode both appearance…