Related papers: Category Theory for Genetics
We introduce a model for the linguistic hedges `very' and `quite' within the label semantics framework, and combined with the prototype and conceptual spaces theories of concepts. The proposed model emerges naturally from the…
In this chapter we take a closer look at the distribution of symbolic regression models generated by genetic programming in the search space. The motivation for this work is to improve the search for well-fitting symbolic regression models…
Living systems can be understood as organized entities that capture, transform, and reproduce information. Classical gene-centered models explain adaptation through frequency changes driven by differential fitness, yet they often overlook…
We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
We firstly introduce some key concepts in category theory, such as quotient category, completion of limits, $\mathrm{Mor}$ category, and so on; then give the concept of topology algebras and sheaves, and discuss how to restore the structue…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
Recent advancements in specialized large-scale architectures for training image and language have profoundly impacted the field of computer vision and natural language processing (NLP). Language models, such as the recent ChatGPT and GPT4…
A recent paper (Manceau and Lambert, 2016) developed a novel approach for describing two well-defined notions of 'species' based on a phylogenetic tree and a phenotypic partition. In this paper, we explore some further combinatorial…
The mathematical modeling of generics in Java and other similar nominally-typed object-oriented programming languages is a challenge. In this short paper we present the outline of a novel order-theoretic approach to modeling generics, in…
We study homotopy theory of the category of spectral sequences with respect to the class of weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We introduce the category of extended spectral sequences and show that…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top…
Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are…
Sequence labelling is the task of assigning categorical labels to a data sequence. In Natural Language Processing, sequence labelling can be applied to various fundamental problems, such as Part of Speech (POS) tagging, Named Entity…
We present a deep hierarchical recurrent neural network for sequence tagging. Given a sequence of words, our model employs deep gated recurrent units on both character and word levels to encode morphology and context information, and…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…