Related papers: Neural category
We describe the endomorphism rings in an additive category whose objects are right $R$-modules $M$ with a fixed chain of submodules $0=M^{(0)}\leq M^{(1)}\leq M^{(2)} \leq \dots \leq M^{(n)}=M$ and the behaviour of these objects as far as…
Determining the types of neurons within a nervous system plays a significant role in the analysis of brain connectomics and the investigation of neurological diseases. However, the efficiency of utilizing anatomical, physiological, or…
Understanding how people represent categories is a core problem in cognitive science. Decades of research have yielded a variety of formal theories of categories, but validating them with naturalistic stimuli is difficult. The challenge is…
Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…
Let $R$ be a right notherian ring. We introduce the concept of relative singularity category $\Delta_{\mathcal{X}}(R)$ of $R$ with respect to a contravariantly finite subcategory $\mathcal{X}$ of $\rm{mod}\mbox{-}R.$ Along with some…
Category theory in homotopy type theory is intricate as categorical laws can only be stated "up to homotopy", and thus require coherences. The established notion of a univalent category (Ahrens, Kapulkin, Shulman) solves this by considering…
This study investigates the ability of perceptron-type neurons in language models to perform intra-neuronal attention; that is, to identify different homogeneous categorical segments within the synthetic thought category they encode, based…
Rings form a bicategory [Rings], with classes of bimodules as horizontal arrows, and bimodule maps as vertical arrows. The notion of Morita equivalence for rings can be translated in terms of bicategories in the following way. Two rings are…
Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code $C$ can be represented by its neural ideal $J_C$. In turn, the polynomials in $J_C$ can be used to…
In the case of $(\infty,1)$-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories. This shows that homotopy coherent diagrams of…
Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the semidualizing modules, we define and study new classes of modules and homological dimensions and investigate the relations between them. In…
Understanding how genes interact and relate to each other is a fundamental question in biology. However, current practices for describing these relationships, such as drawing diagrams or graphs in a somewhat arbitrary manner, limit our…
Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information via the collective behavior of populations of neurons. A…
The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…
Neural coding is a field of study that concerns how sensory information is represented in the brain by networks of neurons. The link between external stimulus and neural response can be studied from two parallel points of view. The first,…
We show how the notion of intercategory encompasses a wide variety of three-dimensional structures from the literature, notably duoidal categories, monoidal double categories, cubical bicategories, double bicategories and Gray categories.…
Neural systems show a modular and typically also a hierarchical organisation across different levels and across different species. Topology relates to function, but it is also influences dynamics as earlier studies showed its effect on…
In colored range counting (CRC), the input is a set of points where each point is assigned a ``color'' (or a ``category'') and the goal is to store them in a data structure such that the number of distinct categories inside a given query…
The polysemantic nature of synthetic neurons in artificial intelligence language models is currently understood as the result of a necessary superposition of distributed features within the latent space. We propose an alternative approach,…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…