Diving into the Cats module - some conceptual differences between Catlab v0.16 and v0.17 for modeling categories, functors, (co)limits, and more.| blog.algebraicjulia.org
$$ $$ Analogies in Planning Do X like you would Y. That’s the essence of analogical thinking which can be surprisingly powerful in planning. We often want to restate one task in the language of another to reframe how we think about the problem. This reframing then helps us solve novel problems with solutions we already know. Forming an analogy is a frequent cognitive process humans engage in. In cognitive psychology, this process is described as forming a structured mapping between two inte...| AlgebraicJulia blog
How can we model and solve multi-agent coordination problems in AlgebraicJulia?| blog.algebraicjulia.org
$$ $$ The newest member of the AlgebraicJulia family is CliqueTrees.jl. Originally written as a backend to StructuredDecompositions.jl, the package has taken on a life of its own, and it is now used by packages across the Julia ecosystem. Its dependants include BayesNets.jl CausalInference.jl BandedMatrices.jl SumOfSquares.jl TSSOS.jl OMEinsumContractionOrders.jl SparseMatrixColorings.jl as well as the AlgebraicJulia packages StructuredDecompositions.jl and CategoricalTensorNetworks.jl. Cliqu...| AlgebraicJulia blog
Looking at using ACSets to structure and solve a fundamental network optimization model.| blog.algebraicjulia.org
Examples of theories and models for sets and functions in Catlab.jl.| blog.algebraicjulia.org
An introduction to some big upcoming changes in Catlab, with a focus on GATlab.jl.| blog.algebraicjulia.org
How can we tackle relational algebra of the sort seen in optimization models using tools from AlgebraicJulia?| blog.algebraicjulia.org
Announcing the first version of InterTypes: a package for cross-language serialization for ADTs and ACSets| blog.algebraicjulia.org
Rewrite rules are organized via a graphical syntax into discrete-time simulations which can be understood as agent-based models. This representation is transparent, compositional, and serializable.| blog.algebraicjulia.org
Acsets are great, but what if attributes could be variables?| blog.algebraicjulia.org
A follow-up to Algebraic Geometry for the Working Programmer, this post explains a category-theoretic approach to symbolic open dynamical systems.| blog.algebraicjulia.org
In this series of posts, we investigate the duality between algebra and geometry in order to develop new types of lenses. In this first post, we review some basic ideas about algebraic geometry that will be needed in the coming posts.| blog.algebraicjulia.org
It’s breakfast time! You wake up and walk to your kitchen and notice a loaf of bread, a knife, a raw egg (in its shell), a skillet, and a stove burner sitting on the counter. You’re hungry and your preferred state of existence is to, instead, have an egg sandwich sitting on your counter. You are saddened by the situation, but feel empowered to change it! You compare what you have and what you want, recall what cooking skills you have, and devise the following steps:| blog.algebraicjulia.org
The chase in an algorithm in the context of databases that has applications in Catlab for model exploration, term rewriting, and enforcing schema axioms.| blog.algebraicjulia.org
For graphs and C-sets more generally, the most useful notion of equivalence differs from strict equality of the underlying data structures. Finding automorphism classes of C-sets addresses this problem; we explore how to compute automorphism classes and applications of them.| blog.algebraicjulia.org
Nonclassical logics are often thought to be abstruse and exotic, but they arise naturally as the logic of connected spaces. In this post, we introduce the propositional logic of subgraphs, and more generally of sub-C-sets, and illustrate it with computational examples. The nonclassicality of this logic is seen to be not just natural but inevitable, and also surprisingly useful.| blog.algebraicjulia.org
Reflexive graphs are graphs where every vertex has a distinguished self-loop. While this may seem inconsequential, reflexive graphs have interestingly different properties than ordinary graphs owing to their different morphisms. We will see that reflexive graphs are more geometrical than graphs and also review the general notion of homomorphism between C-sets.| blog.algebraicjulia.org
In the previous post, we defined a general approach for composing dynamical systems based on the mathematics of operads and operad algebras. In this post, we explore an undirected composition syntax in which dynamical systems compose by sharing resources. We also get a taste of hierarchical composition, i.e. composing systems which are themselves composites.| blog.algebraicjulia.org
Informally, many models are specified as compositions of primitive dynamical systems. In this series of posts, we make this modular specification formal by introducing a computing framework from composing open dynamical systems. In this first post of the series, we examine directed theories for composition.| blog.algebraicjulia.org
Not just useful for graphs, C-sets are a general-purpose tool for data analysis offering the functionality of an in-memory relational database. In this post, we illustrate Catlab’s new capabilities for querying C-sets and we explain the categorical underpinnings of conjunctive queries.| blog.algebraicjulia.org
Following up the original post, we explain how modeling is simplified by a shift in perspective from composing structured cospans in categorical style to composing structured multicospans in operadic style.| blog.algebraicjulia.org
We present an approach to scientific data management that utilizes category theory to seamlessly integrate workflow creation, database generation, and database querying. We use Catlab as a backend to provide this more continuous and consistent database experience.| blog.algebraicjulia.org
Structured cospans are a categorical method for turning closed systems into open ones. We show how structured cospans of Petri nets can be used to construct complex epidemiological models in a compositional way.| blog.algebraicjulia.org
In this post we unveil the category of attributed C-sets. It is an upgrade to the category of C-sets that makes each element of a component set (e.g. each vertex or edge in a graph) have attributes, which may be elements of arbitrary sets/Julia types. In order to formalize attributed C-sets, we also take a tour of double category theory and profunctors.| blog.algebraicjulia.org
Graphs are made up of vertices and edges, but an important variation on this concept is based on “half-edges” or “darts.” We explain how half-edge graphs are implemented as C-sets in Catlab.jl and how they are used in topological graph theory to represent embeddings of graphs in surfaces.| blog.algebraicjulia.org
What is a scientific model? This post considers how mathematical logic and category theory can help us understand scientific models, and how AlgebraicJulia aims to build modeling frameworks based on this understanding.| blog.algebraicjulia.org
Through the course of this blog we will encounter a diverse cast of algebraic structures generalizing the concept of a graph. In this post we start at the very beginning, with how category theorists understand graphs, how graphs are an example of a general class of structures called “C-sets,” and how C-sets can be used as data structures in Julia through Catlab.jl.| blog.algebraicjulia.org