Related papers: Connectivity structure of multiple relations
In 2014, during a study on the connectivity structures of quantum entanglement, I specifically introduced the notion of ''the connectivity structure of a family of random variables'' -- a structure that expresses the dependency relations…
We associate at each link a connectivity space which describes its splittability properties. Then, the notion of order for finite connectivity spaces results in the definition of a new numerical invariant for links, their connectivity…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
This paper presents some basic facts about the so-called connectivity spaces. In particular, it studies the generation of connectivity structures, the existence of limits and colimits in the main categories of connectivity spaces, the…
In this paper, we consider to what degree the structure of a linear system is determined by the system's input/output behavior. The structure of a linear system is a directed graph where the vertices represent the variables in the system…
Biological networks are customarily described as structurally robust. This means that they often function extremely well under large forms of perturbations affecting both the concentrations and the kinetic parameters. In order to explain…
Interconnected networks are mathematical representation of systems where two or more simple networks are coupled to each other. Depending on the coupling weight between the two components, the interconnected network can function in two…
The theoretical base for consciousness, in particular an explanation of how consciousness is defined by the brain, has long been sought by science. We propose a partial theory of consciousness as relations defined by typical data. The…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
In this paper, we explore a taxonomy of connectivity for space-like structures. It is inspired by isolating posets of connected pieces of a space and examining its embedding in the ambient space. The taxonomy includes in its scope all…
Structural Entropy (SE) measures the structural information contained in a graph. Minimizing or maximizing SE helps to reveal or obscure the intrinsic structural patterns underlying graphs in an interpretable manner, finding applications in…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…
In this paper, after some recalls about connectivity structures and about the formalisms of quantum mechanics, we associate some families of connectivity structures with any entangled quantum state, and with any "measurement device" on such…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
In functional MRI (fMRI), effective connectivity analysis aims at inferring the causal influences that brain regions exert on one another. A common method for this type of analysis is structural equation modeling (SEM). We here propose a…
A quite flourishing research thread in the recent literature on component-based systems is concerned with the algebraic properties of different classes of connectors. In a recent paper, an algebra of stateless connectors was presented that…
We introduce the concept of matching connectivity as a notion of connectivity in graph admitting perfect matchings which heavily relies on the structural properties of those matchings. We generalise a result of Robertson, Seymour and Thomas…
This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or…