Related papers: Towards a homotopy theory of process algebra
We propose a general framework to extend Flow Matching to homogeneous spaces, i.e. quotients of Lie groups. Our approach reformulates the problem as a flow matching task on the underlying Lie group by lifting the data distributions. This…
This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological and measurable entropy for dynamical systems, it is shown to generalise three previous lower bounds results…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
We extend the signal flow calculus---a compositional account of the classical signal flow graph model of computation---to encompass affine behaviour, and furnish it with a novel operational semantics. The increased expressive power allows…
Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…
The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM…
The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some…
New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…
Workflows constitute an important language to represent knowledge about processes, but also increasingly to reason on such knowledge. On the other hand, there is a limit to which time constraints between activities can be expressed.…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…
Following our previous work, we suggest here a large class of algebras of scalars in which simultaneous and correlated computations can be performed owing to the existence of surjective algebra homomorphisms. This may replace the currently…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
It is shown that path algebras modulo relations of the form $\Lambda = KQ/I$, where $Q$ is a quiver, $K$ a coefficient field, and $I \subseteq KQ$ the ideal generated by all paths of a given length, can be readily analyzed homologically,…
We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event…
The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges…
Hybrid manufacturing (HM) technologies combine additive and subtractive manufacturing (AM/SM) capabilities, leveraging AM's strengths in fabricating complex geometries and SM's precision and quality to produce finished parts. We present a…
Let A be a geometric arrangement such that codim(x) > 1 for every x in A. We prove that, if the complement space M(A) is rationally hyperbolic, then there exists an injective from a free Lie algebra L(u,v) to the homotopy Lie algebra of…