Related papers: Basic Subtoposes of the Effective Topos
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…
This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…
We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite…
To have a robot actively supporting a human during a collaborative task, it is crucial that robots are able to identify the current action in order to predict the next one. Common approaches make use of high-level knowledge, such as object…
This survey paper examines the effective model theory obtained with the BSS model of real number computation. It treats the following topics: computable ordinals, satisfaction of computable infinitary formulas, forcing as a construction…
Localic and realizability toposes are two central classes of toposes in categorical logic, both arising through the Hyland-Johnstone-Pitts tripos-to-topos construction. We investigate their shared geometric features by providing an…
Deep learning operators are fundamental components of modern deep learning frameworks. With the growing demand for customized operators, it has become increasingly common for developers to create their own. However, designing and…
We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
The main purpose of this paper is to introduce and study minimal and maximal ideals defined on ideal topological spaces. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of $2^X$, where $2^X$…
The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…
The aim of this paper is to inter-relate several algebraic and analytic objects, such as real-type algebraic curves, quadrature domains, functions on them and rational matrix functions with special properties, and some objects from Operator…
We prove in this paper that every $p$-local compact group is approximated by transporter systems over finite $p$-groups. To do so, we use unstable Adams operations acting on a given $p$-local compact group and study the structure of…
We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…
We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence…
This research builds on work in anticipatory human-machine interaction, a subfield of human-machine interaction where machines can facilitate advantageous interactions by anticipating a user's future state. The aim of this research is to…
This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior…
We study conditions under which a space that has a good property and a courser topology with another good property admits a continuous bijection onto a space with both properties.
There is a well-known inclusion $\iota_\mathscr{E}$ of a topos $\mathscr{E}$ in the linguistic topos $\mathscr{T}(\Sigma)$ of its internal language $\Sigma$ that proves both toposes to be equivalent. There is also a canonical translation…
This paper deals with the problem of classifying signals. The new method for building so called local classifiers and local features is presented. The method is a combination of the lifting scheme and the support vector machines. Its main…