Related papers: The descriptive theory of represented spaces
The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
The paper outlines ongoing research on logic-based tools for the analysis and representation of legal contracts of the kind frequently encountered in large-scale engineering projects and complex, long-term trading agreements. We consider…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
The diversity of painting styles represents a rich visual vocabulary for the construction of an image. The degree to which one may learn and parsimoniously capture this visual vocabulary measures our understanding of the higher level…
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
We propose a novel shape representation useful for analyzing and processing shape collections, as well for a variety of learning and inference tasks. Unlike most approaches that capture variability in a collection by using a template model…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
3D scatterplots are a well-established plotting technique that can be used to represent data with three or more dimensions. On paper and computer monitors they are essentially two-dimensional projections of the three-dimensional Cartesian…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
Diffusion Models are popular generative modeling methods in various vision tasks, attracting significant attention. They can be considered a unique instance of self-supervised learning methods due to their independence from label…
Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…
We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can…
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Thye theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and much more, as well as being a fruitful area of research in abstract mathematics. In this…