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Recognition of materials has proven to be a challenging problem due to the wide variation in appearance within and between categories. Global image context, such as where the material is or what object it makes up, can be crucial to…
For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…
Multi-layer graphs can capture qualitatively different types of connection between entities, and networks of this kind are prevalent in biological and social systems: for example, a social contact network typically involves both virtual and…
Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object…
Component systems - ensembles of realizations built from a shared repertoire of modular parts - are ubiquitous in biological, ecological, technological, and socio-cultural domains. From genomes to texts, cities, and software, these systems…
In few-shot learning, classifiers are expected to generalize to unseen classes given only a small number of instances of each new class. One of the popular solutions to few-shot learning is metric-based meta-learning. However, it highly…
Although a plethora of architectural variants for deep classification has been introduced over time, recent works have found empirical evidence towards similarities in their training process. It has been hypothesized that neural networks…
Individuals have an intuitive perception of what makes a good coincidence. Though the sensitivity to coincidences has often been presented as resulting from an erroneous assessment of probability, it appears to be a genuine competence,…
We obtain a rigidity phenomena of rational cohomology automorphisms of certain homogeneous spaces, in the presence of external cohomology classes arising from spaces with trivial cup product in rational cohomology algebra. We classify…
We develop \emph{Fra\"iss\'e theory}, namely the theory of \emph{Fra\"iss\'e classes} and \emph{Fra\"iss\'e limits}, in the context of metric structures. We show that a class of finitely generated structures is Fra\"iss\'e if and only if it…
We introduce a new class of (dynamical) systems that inherently capture cascading effects (viewed as consequential effects) and are naturally amenable to combinations. We develop an axiomatic general theory around those systems, and guide…
Let G be a finite group scheme over an algebraically closed field of positive characteristic. Assume further that the connected component of G is unipotent. It is shown that the projectivity of a rational G-module can be detected on a…
This article is concerned with the rigidity properties of geometric realizations of incidence geometries of rank two as points and lines in the Euclidean plane; we care about the distance being preserved among collinear points. We discuss…
Constellations are partial algebras that are one-sided generalisations of categories. It has previously been shown that the category of inductive constellations is isomorphic to the category of left restriction semigroups. Here we consider…
Classical semantic segmentation methods, including the recent deep learning ones, assume that all classes observed at test time have been seen during training. In this paper, we tackle the more realistic scenario where unexpected objects of…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…
Traditional algorithms for detecting differences in source code focus on differences between lines. As such, little can be learned about abstract changes that occur over time within a project. Structural differencing on the program's…
We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…
The Gestalt laws of perceptual organization, which describe how visual elements in an image are grouped and interpreted, have traditionally been thought of as innate despite their ecological validity. We use deep-learning methods to…