Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations

The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like nonlocal coupling can exhibit more elaborate patterns such as uniformly twisted states. It was discovered by Wiley, Strogatz and Girvan in 2006 that the stability of these twisted states depends on the coupling range of each oscillator. In this paper, we analyze twisted states and their bifurcations in the infinite particle limit of ring-like nonlocal coupling. We not only consider traditional pairwise interactions as in the Kuramoto model but also demonstrate the effects of higher-order nonpairwise interactions, which arise naturally in phase reductions. We elucidate how pairwise and nonpairwise interactions affect the stability of the twisted states, compute bifurcating branches, and show that higher-order interactions can stabilize twisted states that are unstable if the coupling is only pairwise.Comment: 36 pages, 7 figure

Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions

Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bifurcations of twisted states in ring networks of phase oscillators with nonpairwise higher-order interactions. Hopf bifurcations give rise to quasiperiodic solutions that move along the oscillator ring at nontrivial speed. Because of the higher-order interactions, these emerging solutions may be stable. Using the Ott--Antonsen approach, we continue the emergent solution branches which approach anti-phase type solutions (where oscillators form two clusters whose phase is $\pi$ apart) as well as twisted states with a different winding number.Comment: 24 pages, 8 figure

Subjektivierendes Arbeitshandeln - "Nice to have" oder ein gesellschaftskritischer Blick auf "das Andere" der Verwertung?

Der Aufsatz zeigt, wie das Konzept des subjektivierenden Arbeitshandelns zur Analyse der Entwicklung von Arbeit in kritischer Reflexion und mit neuen Ansätzen beiträgt: Mit der Untersuchung des Arbeitshandelns als Referenzrahmen wird die Perspektive des Subjekts eingenommen, und damit wird der Blick auf sinnlich-körperliche Erfahrung im Arbeitsprozess möglich. Theoretisch wie empirisch begründet der Artikel die eigenständige Bedeutung subjektivierenden Handelns. In umfangreichen empirischen Untersuchungen erweist sich die Bewältigung von Unwägbarkeiten und Unbestimmtheiten als zentrale Anforderung an menschliche Arbeit, die subjektivierendes Arbeitshandeln und damit verbunden praktisches Erfahrungswissen als wesentliche Elemente menschlichen Arbeitsvermögens benötigt. In der Forderung nach selbstgesteuertem Handeln, das im Sinne kapitalistischer Verwertungslogik transparent und messbar gemacht werden soll, erkennen wir einen in der Subjektivierung von Arbeit angelegten Widerspruch, in den sich subjektivierendes Arbeitshandeln (als nicht formalisierbares Handeln) grundsätzlich nicht einfügt. Mit Bezug auf empirisch fundierte Modelle schließen wir mit einem Plädoyer für eine arbeitspolitische Perspektive, die subjektivierendes Arbeitshandeln als substanzielles Element menschlichen Arbeitsvermögens anerkennt und Formen der Organisation, Technik wie Bildung entwickelt, die dieses Handeln ermöglichen.This article will explain how the concept of subjectifying work action can contribute to critically analyze new developments of work. The concept of subjectifying work action uses work actions of subjects as the point of reference for empirical analysis. Our perspective emphasizes sensual, bodily and embodied human experiences. These sticky and hard to imitate resources are often hidden or neglected. In the first part of our contribution we will show their importance for successful work operations especially in moments of high uncertainties. We will argue on a theoretical and empirical basis that the ability to handle uncertainties is a key requirement for “the working man” and how the dimensions of subjectifying work actions enable researchers to grasp how humans manage these situations. In the second part of our text we will develop an immanent contradiction in new forms of work organization based on self-organized processes. Here subjectifying work actions, capacities which cannot be formalized, are used in form of self-regulation and extended responsibilities for individuals. Yet, management directives require work actions that are performed in an objectifying manner to suit governance structures of transparency and objectivity. We complete our article with perspectives for a labour policy that acknowledges and includes subjectifying work actions as substantial part of human labour capacities

Mathematical analysis of nonlocal PDEs for network generation

In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the degree distribution as time progresses. The evolution of the generating function of this degree distribution can be described by a nonlocal PDE. To address this equation we will rigorously convert it into a local first order PDE. Then, we use theory of characteristics to prove solvability and regularity of the solution. Next, we investigate the existence of steady states of the PDE. We show that this problem reduces to an implicit ODE, which we subsequently analyze. Finally, we perform numerical simulations, which show stability of the steady states

Multi-population phase oscillator networks with higher-order interactions

The classical Kuramoto model consists of finitely many pairwisely coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions take place. Hence, we replace the classical coupling law with a very general coupling function involving higher-order terms. Furthermore, we allow for multiple populations of oscillators interacting with each other through a very general law. In our analysis, we focus on the characteristic system and the mean-field limit of this generalized class of Kuramoto models. While there are several works studying particular aspects of our program, we propose a general framework to work with all three aspects (higher-order, multi-population, and mean-field) simultaneously. In this article, we investigate dynamical properties within the framework of the characteristic system. We identify invariant subspaces of synchrony patterns and study their stability. It turns out that the so called all-synchronized state, which is one special synchrony pattern, is never asymptotically stable. However, under some conditions and with a suitable definition of stability, the all-synchronized state can be proven to be at least locally stable. In summary, our work provides a rigorous mathematical framework upon which the further study of multi-population higher-order coupled particle systems can be based

Random walks and Laplacians on hypergraphs: When do they match?

We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and analyze general random walk Laplacians for hypergraphs, and we compare them to hypergraph normalized Laplacians that are not necessarily related to random walks, but which are motivated by biological and chemical networks. We show that, although these two classes of Laplacians coincide in the case of graphs, they appear to have important conceptual differences in the general case. We study the spectral properties of both classes, as well as their applications to Coupled Hypergraph Maps: discrete-time dynamical systems that generalize the well-known Coupled Map Lattices on graphs. Our results also show why for some hypergraph Laplacian variants one expects more classical results from (weighted) graphs to generalize directly, while these results must fail for other hypergraph Laplacians

Coupled hypergraph maps and chaotic cluster synchronization

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each node; the maps are often taken as unimodal, e.g., logistic or tent maps. In this letter, we propose a class of higher-order coupled dynamical systems involving the hypergraph Laplacian, which we call coupled hypergraph maps (CHMs). By combining linearized (in-)stability analysis of synchronized states, hypergraph spectral theory, and numerical methods, we detect robust regions of chaotic cluster synchronization occurring in parameter space upon varying coupling strength and the main bifurcation parameter of the unimodal map. Furthermore, we find key differences between Laplacian and hypergraph Laplacian coupling and detect various other classes of periodic and quasi-periodic patterns. The results show the high complexity of coupled graph maps and indicate that they might be an excellent universal model class to understand the similarities and differences between dynamics on classical graphs and dynamics on hypergraphs

Coupled hypergraph maps and chaotic cluster synchronization

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each node; the maps are often taken as unimodal, e.g., logistic or tent maps. In this letter, we propose a class of higher-order coupled dynamical systems involving the hypergraph Laplacian, which we call coupled hypergraph maps (CHMs). By combining linearized (in-)stability analysis of synchronized states, hypergraph spectral theory, and numerical methods, we detect robust regions of chaotic cluster synchronization occurring in parameter space upon varying coupling strength and the main bifurcation parameter of the unimodal map. Furthermore, we find key differences between Laplacian and hypergraph Laplacian coupling and detect various other classes of periodic and quasi-periodic patterns. The results show the high complexity of coupled graph maps and indicate that they might be an excellent universal model class to understand the similarities and differences between dynamics on classical graphs and dynamics on hypergraphs

A Grammar of Kuuk Thaayorre

© 2006 Dr. Alice Rose GabyThis thesis is a comprehensive description of Kuuk Thaayorre, a Paman language spoken on the west coast of Cape York Peninsula, Australia. On the basis of elicited data, narrative and semi-spontaneous conversation recorded between 2002 and 2005, this grammar details the phonetics and phonology, morphosyntax, lexical and constructional semantics and pragmatics of one of the few indigenous Australian languages still used as a primary means of communication. Kuuk Thaayorre possesses features of typological interest at each of these levels. At the phonological level, Kuuk Thaayorre possesses a particularly rich vowel inventory from an Australian perspective, with five distinct vowel qualities and two contrastive lengths producing ten vowel phonemes. It is in the phonotactic combination of sounds that Kuuk Thaayorre phonology is particularly noteworthy, however. Kuuk Thaayorre’s tendency towards closed syllables (with codas containing up to three consonants) frequently leads to consonant clusters of as many as four segments. Kuuk Thaayorre is also cross-linguistically unusual in allowing sequences of its two rhotics (an alveolar tap/trill and retroflex continuant) within the syllable – either as a complex coda or as onset plus syllabic rhotic. Finally, monosyllables are ubiquitous across all Thaayorre word classes, despite being generally rare in Australian languages

COMPASSO - In-orbit Verification of Optical Key Technologies for Future GNSS - Mission Description

All GNSS programs (i.e. Galileo, GPS, BeiDou, GLONASS, etc.) undergo a permanent process of modernization and improvement of their ground and space segments. Driven by increasing user demands, all programs aim at pushing the boundary of today's position, navigation, and timing technologies to pave the way for more flexible, robust, and resilient GNSSs. A promising way to improve GNSS architectures is the use of optical technologies and more specifically: optical clocks and optical inter-satellite links (ISL). Optical clocks could back-up or replace the currently used microwave clocks, having the potential to improve GNSS position determination enabled by their lower frequency instabilities. In combination with optical inter-satellite links, optical clock technologies enable new GNSS architectures, e.g., by synchronization of distant optical frequency references within the satellite constellation using time and frequency transfer techniques. The aim of the COMPASSO mission - which is an ongoing project and has recently finalized the preliminary system design phase (Phase B) - is to demonstrate new optical technologies relating to satellite navigation. Within the mission, various optical technologies will be further developed and tested with regard to space suitability and operational conditions. This paper details the objectives, status, mission scenario, payload setup and the main optical technologies constituting COMPASSO: iodine frequency references, optical frequency comb, and laser terminal for communication and ranging