Chimera states in complex networks: interplay of fractal topology and delay

Chimera states are an example of intriguing partial synchronization patterns emerging in networks of identical oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. We analyze chimera states in networks of Van der Pol oscillators with hierarchical connectivities, and elaborate the role of time delay introduced in the coupling term. In the parameter plane of coupling strength and delay time we find tongue-like regions of existence of chimera states alternating with regions of existence of coherent travelling waves. We demonstrate that by varying the time delay one can deliberately stabilize desired spatio-temporal patterns in the system.Comment: arXiv admin note: text overlap with arXiv:1603.0017

Chimera states in networks of Van der Pol oscillators with hierarchical connectivities

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 26, 094825 (2016) and may be found at https://doi.org/10.1063/1.4962913.Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in ring networks of Van der Pol oscillators with hierarchical coupling topology. We investigate the stepwise transition from a nonlocal to a hierarchical topology and propose the network clustering coefficient as a measure to establish a link between the existence of chimera states and the compactness of the initial base pattern of a hierarchical topology; we show that a large clustering coefficient promotes the occurrence of chimeras. Depending on the level of hierarchy and base pattern, we obtain chimera states with different numbers of incoherent domains. We investigate the chimera regimes as a function of coupling strength and nonlinearity parameter of the individual oscillators. The analysis of a network with larger base pattern resulting in larger clustering coefficient reveals two different types of chimera states and highlights the increasing role of amplitude dynamics. Chimera states are an example of intriguing partial synchronization patterns appearing in networks of identical oscillators. They exhibit a hybrid structure combining coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics.1,2 Recent studies have demonstrated the emergence of chimera states in a variety of topologies and for different types of individual dynamics. In this paper, we analyze chimera states in networks with complex coupling topologies arising in neuroscience. We provide a systematic analysis of the transition from nonlocal to hierarchical (quasi-fractal) connectivities in ring networks of identical Van der Pol oscillators and use the clustering coefficient and the symmetry properties to classify different topologies with respect to the occurrence of chimera states. We show that symmetric connectivities with large clustering coefficients promote the emergence of chimera states, while they are suppressed by slight topological asymmetries or small clustering coefficient.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Wholeness as a Hierarchical Graph to Capture the Nature of Space

According to Christopher Alexander's theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented that enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating beautiful built and natural environments or with a high degree of wholeness.Comment: 14 pages, 7 figures, 2 table

On environments as systemic exoskeletons: Crosscutting optimizers and antifragility enablers

Classic approaches to General Systems Theory often adopt an individual perspective and a limited number of systemic classes. As a result, those classes include a wide number and variety of systems that result equivalent to each other. This paper introduces a different approach: First, systems belonging to a same class are further differentiated according to five major general characteristics. This introduces a "horizontal dimension" to system classification. A second component of our approach considers systems as nested compositional hierarchies of other sub-systems. The resulting "vertical dimension" further specializes the systemic classes and makes it easier to assess similarities and differences regarding properties such as resilience, performance, and quality-of-experience. Our approach is exemplified by considering a telemonitoring system designed in the framework of Flemish project "Little Sister". We show how our approach makes it possible to design intelligent environments able to closely follow a system's horizontal and vertical organization and to artificially augment its features by serving as crosscutting optimizers and as enablers of antifragile behaviors.Comment: Accepted for publication in the Journal of Reliable Intelligent Environments. Extends conference papers [10,12,15]. The final publication is available at Springer via http://dx.doi.org/10.1007/s40860-015-0006-

Deep Virtual Networks for Memory Efficient Inference of Multiple Tasks

Deep networks consume a large amount of memory by their nature. A natural question arises can we reduce that memory requirement whilst maintaining performance. In particular, in this work we address the problem of memory efficient learning for multiple tasks. To this end, we propose a novel network architecture producing multiple networks of different configurations, termed deep virtual networks (DVNs), for different tasks. Each DVN is specialized for a single task and structured hierarchically. The hierarchical structure, which contains multiple levels of hierarchy corresponding to different numbers of parameters, enables multiple inference for different memory budgets. The building block of a deep virtual network is based on a disjoint collection of parameters of a network, which we call a unit. The lowest level of hierarchy in a deep virtual network is a unit, and higher levels of hierarchy contain lower levels' units and other additional units. Given a budget on the number of parameters, a different level of a deep virtual network can be chosen to perform the task. A unit can be shared by different DVNs, allowing multiple DVNs in a single network. In addition, shared units provide assistance to the target task with additional knowledge learned from another tasks. This cooperative configuration of DVNs makes it possible to handle different tasks in a memory-aware manner. Our experiments show that the proposed method outperforms existing approaches for multiple tasks. Notably, ours is more efficient than others as it allows memory-aware inference for all tasks.Comment: CVPR 201