Related papers: Toward an Algebraic Theory of Systems
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
In this work, we introduce a compositional framework for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on the joint dissipativity-type…
As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
Quantum processes with indefinite causal structure emerge when we wonder which are the most general evolutions, allowed by quantum theory, of a set of local systems which are not assumed to be in any particular causal order. These processes…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
The ability to continually learn, retain and deploy skills to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of…
This paper presents a compositional framework for the construction of symbolic models for a network composed of a countably infinite number of finite-dimensional discrete-time control subsystems. We refer to such a network as infinite…
We introduce a new algebraic structure for multi-dimensional compositional embeddings, built on directional non-commutative monoidal operators. The core contribution of this work is this novel framework, which exhibits appealing theoretical…
Complex systems of systems (SoS) are characterized by multiple interconnected subsystems. Typically, each subsystem is designed and analyzed using methodologies and formalisms that are specific to the particular subsystem model of…
Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce…
The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic…
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…
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of…
In this paper, we introduce a compositional scheme for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In…
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 we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…
According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…