Related papers: Category Theory for Genetics
Language Models have ushered a new age of AI gaining traction within the NLP community as well as amongst the general population. AI's ability to make predictions, generations and its applications in sensitive decision-making scenarios,…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…
This is the first draft of a book about higher categories approached by iterating Segal's method, as in Tamsamani's definition of $n$-nerve and Pelissier's thesis. If $M$ is a tractable left proper cartesian model category, we construct a…
Language modeling studies the probability distributions over strings of texts. It is one of the most fundamental tasks in natural language processing (NLP). It has been widely used in text generation, speech recognition, machine…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.
Characterizations of semi-stable and stage extensions in terms of 2-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming…
Language enables humans to share knowledge, reason about the world, and pass on strategies for survival and innovation across generations. At the heart of this process is not just the ability to communicate but also the remarkable…
We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…
The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory,…
This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is…
We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as a potential yoga for dealing with processes and processes of…
There are already many DNA large language models, but most of them still follow traditional uses, such as extracting sequence features for classification tasks. More innovative applications of large language models, such as prompt…
In this paper we obtain several model structures on {\bf DblCat}, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double…
We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalizing the one introduced by…
The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. We enrich this calculus with a type discipline to guarantee the soundness of reduction rules with respect…
We introduce GENomic Encoding REpresentation with Language Model (GENEREL), a framework designed to bridge genetic and biomedical knowledge bases. What sets GENEREL apart is its ability to fine-tune language models to infuse biological…
The application of deep learning methods, particularly foundation models, in biological research has surged in recent years. These models can be text-based or trained on underlying biological data, especially omics data of various types.…
In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…
Living organisms are the most complex, interesting and significant objects regarding all substructures of the universe. Life science is regarded as a science of the 21st century and one can expect great new discoveries in the near futures.…
Phylogenetic reconstruction aims at finding plausible hypotheses of the evolutionary history of genes or species based on genomic sequence information. The distinction of orthologous genes (genes that having a common ancestry and diverged…