Related papers: Abstract composition laws and their modulation spa…
We study composition operators whose symbols are suitable perturbations of the identity and which act between different weighted modulation classes. We consider both modulation spaces formed by tempered distributions and those whose…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
In this work we propose composition products in the class of complex harmonic functions so that the composition of two such functions is again a complex harmonic function. From here we begin the study of the iterations of the functions of…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
We give sufficient conditions on the Lebesgue exponents for compositions of odd numbers of pseudo-differential operators with symbols in modulation spaces. As a byproduct, we obtain sufficient conditions for twisted convolutions of odd…
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…
We derive properties and a characterization of discrete composition matrices which are useful in the field of numerical computation of shape correspondences.
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
Translating continuous control system models into finite automata allows us to use powerful discrete tools to synthesize controllers for complex specifications. The abstraction construction step is unfortunately hamstrung by high runtime…
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…
There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer…
We define localized modulation maps and modulation spaces of symbols suited to the study of Rieffel's deformation quantization pseudodifferential calculus. They are used to generate Hilbert space representations for the quantized…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
In this paper, we propose a compositional approach to construct opacity-preserving finite abstractions (a.k.a symbolic models) for networks of discrete-time nonlinear control systems. Particularly, we introduce new notions of simulation…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known…
Recently, there has been great interest in the application of composition laws to problems in enumerative geometry. Using the moduli space of stable maps, we compute the number of irreducible, reduced, nodal, degree-$d$ genus-$2$ plane…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…