Related papers: Some remarks about trunks and morphisms of neural …
This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two…
The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…
Suppose that $X$ and $Y$ are surfaces of finite topological type, where $X$ has genus $g\geq 6$ and $Y$ has genus at most $2g-1$; in addition, suppose that $Y$ is not closed if it has genus $2g-1$. Our main result asserts that every…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Neural network approaches have been applied to computational morphology with great success, improving the performance of most tasks by a large margin and providing new perspectives for modeling. This paper starts with a brief introduction…
Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…
Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…
In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects…
A large body of work has investigated the properties of graph neural networks and identified several limitations, particularly pertaining to their expressive power. Their inability to count certain patterns (e.g., cycles) in a graph lies at…
In the brain, information is encoded, transmitted and used to inform behaviour at the level of timing of action potentials distributed over population of neurons. To implement neural-like systems in silico, to emulate neural function, and…
Classification and quantitative characterization of neuronal morphologies from histological neuronal reconstruction is challenging since it is still unclear how to delineate a neuronal cell class and which are the best features to define…
For finite nilpotent groups $G$ and $G^{\prime}$, and a $G$-adapted ring $S$ (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings $SG$ and $SG^{\prime}$ is monomial, i.e., maps class…
We introduce the notion of solid monoid and rigid monoid in monoidal categories and study the formal properties of these objects in this framework. We show that there is a one to one correspondence between solid monoids, smashing…
We characterize the signature of piecewise continuously differentiable paths transformed by a polynomial map in terms of the signature of the original path. For this aim, we define recursively an algebra homomorphism between two shuffle…
This work deals with the notion of Newton complementary duality as raised originally in the work of the second author and B. Costa. A conceptual revision of the main steps of the notion is accomplished which then leads to a vast…
This short paper examines diagrams describing neural network systems in academic conference proceedings. Many aspects of scholarly communication are controlled, particularly with relation to text and formatting, but often diagrams are not…
We study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals. We start with the standard generic monomial ideals to find invariants for rational maps of spheres and…
Recent neuroimaging studies have shown that functional connectomes are unique to individuals, i.e., two distinct fMRIs taken over different sessions of the same subject are more similar in terms of their connectomes than those from two…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
Modular structure is ubiquitous among real-world networks from related proteins to social groups. Here we analyze the modular organization of brain networks at a large-scale (voxel level) extracted from functional magnetic resonance imaging…