Related papers: Cubical token systems
We study two variants of the problem of contact representation of planar graphs with axis-aligned boxes. In a cube-contact representation we realize each vertex with a cube, while in a proportional box-contact representation each vertex is…
Moebius number systems represent points using sequences of Moebius transformations. Thorough the paper, we are mainly interested in representing the unit circle (which is equivalent to representing R\cup\{\infty\}). The main aim of the…
Quantum Bayesian networks provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
We undertake a detailed numerical study of the twin phenomena of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…
The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…
Topos quantum theory provides representations of quantum states as direct generalizations of the probability distribution, namely probability valuation. In this article, we consider extensions of a known bijective correspondence between…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…
Toric differential inclusions play a pivotal role in providing a rigorous interpretation of the connection between weak reversibility and the persistence of mass-action systems and polynomial dynamical systems. We introduce the notion of…
In this paper we define and study a ring associated to a graph that we call the cographic toric face ring, or simply the cographic ring. The cographic ring is the toric face ring defined by the following equivalent combinatorial structures…
Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a generalization of birgraphs intended to be a model of concurrency that incorporates vagueness. More specifically, this model assumes that agents are similar,…
A graph is called $k$-representable if there exists a word $w$ over the nodes of the graph, each node occurring exactly $k$ times, such that there is an edge between two nodes $x,y$ if and only after removing all letters distinct from…
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…