Related papers: A graphical construction of free Markov categories
We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…
We use traced monoidal categories to give a precise general version of "geometry of interaction". We give a number of examples of both "particle-style" and "wave-style" instances of this construction. We relate these ideas to semantics of…
The definition of a holomorphic function over a general measurable space $S$ endowed with a Markov process is defined by Zeghib and Barre. In this article we consider holomorphic functions over graphs whose ranges are a given finite field…
A model of a discrete pregeometry on a microscopic scale is introduced. This model is a finite network of finite elementary processes. The mathematical description is a d-graph that is a generalization of a graph. This is the particular…
This is the first part of a two paper series studying free globularily generated double categories. In this first installment we introduce the free globularily generated double category construction. The free globularily generated double…
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs,…
The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the…
We define a family of structures called "opetopic algebras", which are algebraic structures with an underlying opetopic set. Examples of such are categories, planar operads, and Loday's combinads over planar trees. Opetopic algebras can be…
We introduce the arrow product, a systematic generating function technique for directed graph enumeration. It provides short proofs for previous results of Gessel on the number of directed acyclic graphs and of Liskovets, Robinson and…
We systematically develop the explicit map between string vacua constructed in the Free Fermionic Formulation and their $\mathbb{Z}_2^N$ toroidal orbifold counterparts. We illustrate the map in various example classes of models, including…
One of the most difficult aspects of modeling complex dilemmas in decision-analytic terms is composing a diagram of relevance relations from a set of domain concepts. Decision models in domains such as medicine, however, exhibit certain…
We construct a new class of directed and bipartite random graphs whose topology is governed by the analytic properties of L-functions. The bipartite L-graphs and the multiplicative zeta graphs are relevant examples of the proposed…
In this paper, we construct countably many isolated circular orders on the free products $G = F_{2n} \ast \mathbb{Z}_{m_1} \ast \cdots \ast \mathbb{Z}_{m_k}$ of cyclic groups. Moreover, we prove that these isolated circular orders are not…
This work discusses an approach to solving geometric construction problems in which the given figure is included in a set ordered by construction steps. The flow of information is carried through the chain, allowing the original problem to…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing…
In this paper we show that any $\infty$-operad is equivalent to the localization of a discrete $\Sigma$-free operad, working in the formalism of dendroidal sets. The key point is defining the root functor of a dendroidal set $X$, a functor…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…
We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…