Related papers: Towards a homotopy theory of process algebra
Many generative models originally developed in finite-dimensional Euclidean space have functional generalizations in infinite-dimensional settings. However, the extension of rectified flow to infinite-dimensional spaces remains unexplored.…
In [math.AT/9907138] we proved that strongly homotopy algebras are homotopy invariant concepts in the category of chain complexes. Our arguments were based on the fact that strongly homotopy algebras are algebras over minimal cofibrant…
In this paper, we consider a one dimensional pursuit law with delay which is derived from traffic flow modelling. It takes the form of an infinite system of first order coupled delayed equations. Each equation describes the motion of a…
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures,…
This paper combines the classical model of labeled transition systems with the epistemic model for reasoning about knowledge. The result is a unifying framework for modeling and analyzing multi-agent, knowledge-based, dynamic systems. On…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this third part,…
We consider asynchronous networks of identical finite (independent of network's size or topology) automata. Our automata drive any network from any initial configuration of states, to a coherent one in which it can carry efficiently any…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
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…
Algebraic contraction is proposed to realize mappings between models Hamiltonians. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic $XXZ$ Heisenberg…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
In this work, a complete homotopic interpretation on the periodic table of topological insulators and superconductors has been derived by establishing the loop sequence of the corresponding classifying spaces. In our approach, each…
We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
Several constructions on directed graphs originating in the study of flow equivalence in symbolic dynamics (e.g., splittings and delays) are known to preserve the Morita equivalence class of Leavitt path algebras over any coefficient field…
In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
In standard process algebra, parallel components do not share a common state and communicate through synchronisation. The advantage of this type of communication is that it facilitates compositional reasoning. For modelling and analysing…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…