Related papers: Classifying topoi in synthetic guarded domain theo…
We elaborate on the representation theorems of topoi as topoi of discrete actions of various kinds of localic groups and groupoids. We introduce the concept of "proessential point" and use it to give a new characterization of pointed Galois…
This monograph is an ongoing revision of "Lectures On A Mathematical Theory of Computation" by Dana Scott. Scott's monograph uses a formulation of domains called neighborhood systems in which finite elements are selected subsets of a master…
Time-Sensitive Distributed Systems (TSDS), such as applications using autonomous drones, achieve goals under possible environment interference (\eg, winds). Moreover, goals are often specified using explicit time constraints which must be…
Reliability-based topology optimization (RBTO) requires repeated estimation of small failure probabilities and their gradients, making conventional nested Monte Carlo approaches computationally prohibitive for large scale structural…
Real-world processes often generate data that are a mix of categorical and numeric values that are recorded at irregular and informative intervals. Discrete token-based approaches are limited in numeric representation capacity while methods…
The study of dynamical systems has long focused on the characterization of their asymptotic dynamics such as fixed points, limit cycles and other types of attractors and how these invariant sets change their properties as systems parameters…
We consider a weakly coupled gauge theory where charged particles all have large gaps (ie no Higgs condensation to break the gauge "symmetry") and the field strength fluctuates only weakly. We ask what kind of topological terms can be added…
In this chapter we propose Generic Ontology Design Patterns, GODPs, as a methodology for representing and instantiating ontology design patterns in a way that is adaptable, and allows domain experts (and other users) to safely use them…
Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating…
We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry $G$. We argue for a general correspondence between such phases and topological phases of undriven systems…
Node tokenized graph Transformers (GTs) have shown promising performance in node classification. The generation of token sequences is the key module in existing tokenized GTs which transforms the input graph into token sequences,…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is…
We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting gapped quantum many-body systems that…
There is a class of problems that exhibit smooth behavior on macroscopic scales, where only a microscopic evolution law is known. Patch dynamics scheme of `equation-free multiscale modelling' is one of the techniques, which aims to extract…
This paper presents applicability of Strong Stationary Times (SST) techniques in the area of cryptography. The applicability is in three areas: *) Propositions of a new class of cryptographic algorithms (pseudo-random permutation…
A family of repressor networks is proposed as a simple model of gene regulatory networks. We analytically show three topological classes of the repressor networks, each of which exhibits distinctly growing complexity of spatiotemporal…
Generic Ontology Design Patterns, GODPs, are defined in Generic DOL, an extension of DOL, the Distributed Ontology, Model and Specification Language, and implemented using Heterogeneous Tool Set. Parameters such as classes, properties,…
We give a model-theoretic characterisation of the geometric theories classified by \'etendues -- the `locally localic' topoi. They are the theories where each model is determined, syntactically and semantically, by any witness of a fixed…
We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein…