Related papers: A "Symbolic" Representation of Object-Nets (Extend…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
This work models named entity distribution from a way of visualizing topological structure of embedding space, so that we make an assumption that most, if not all, named entities (NEs) for a language tend to aggregate together to be…
We study the link structure of on-line social networks (OSNs), and introduce a new model for such networks which may help infer their hidden underlying reality. In the geo-protean (GEO-P) model for OSNs nodes are identified with points in…
We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer…
This paper presents a unified algebraic, topological, and logical framework for electrical one-port networks based on \v{S}are's $m$-theory. Within this formalism, networks are represented by $m$-words (jorbs) over an ordered alphabet,…
We build on the correspondence between Petri nets and free symmetric strict monoidal categories already investigated in the literature, and present a categorical semantics for Petri nets with guards. This comes in two flavors: Deterministic…
Every transformation monoid comes equipped with a canonical topology-the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This…
Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate…
In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and…
Step net bisimilarity \cite{Gor23} is a truly concurrent behavioral equivalence for finite Petri nets, which is defined as a smooth generalization of standard step bisimilarity \cite{NT84} on Petri nets, but with the property of relating…
Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S^2 and the torus T,…
Recent progress on the question of the size of the class of connected and hyperconnected geometric morphisms from a given topos has led to the definition of {\em local state classifier}. We discuss a historical precedent which leads to the…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
We propose MetroSets, a new, flexible online tool for visualizing set systems using the metro map metaphor. We model a given set system as a hypergraph $\mathcal{H} = (V, \mathcal{S})$, consisting of a set $V$ of vertices and a set…
We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as…
We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…
For every finite Petri net, we construct a commutative polynomial in two variables and with coefficients from the semiring of natural numbers. We also present an inverse construction and show that multiplication of polynomials…
Autonomous robots that interact with their environment require a detailed semantic scene model. For this, volumetric semantic maps are frequently used. The scene understanding can further be improved by including object-level information in…
Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on…
Software-defined networking is finding its way into optical networks. Here, it promises a simplification and unification of network management for optical networks allowing automation of operational tasks despite the highly diverse and…