Chimeras in a Network of Three Oscillator Populations with Varying Network Topology

We study a network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring populations than to those in their own population. Using this system as a model system, we discuss for the first time the influence of network topology on the existence of so called chimera states. In this context, the network with three populations represents an interesting case because the populations may either be connected as a triangle, or as a chain, thereby representing the simplest discrete network of either a ring or a line segment of oscillator populations. We introduce a special parameter that allows us to study the effect of breaking the triangular network structure, and to vary the network symmetry continuously such that it becomes more and more chain-like. By showing that chimera states only exist for a bounded set of parameter values we demonstrate that their existence depends strongly on the underlying network structures. We conclude that chimeras exist on networks with a chain-like character, which indicates that it might be possible to observe chimeras on a continuous line segment of oscillators.Comment: 9 pages, 4 figure

Transitions from trees to cycles in adaptive flow networks

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins

Directed Flow of Information in Chimera States

We investigated interactions within chimera states in a phase oscillator network with two coupled subpopulations. To quantify interactions within and between these subpopulations, we estimated the corresponding (delayed) mutual information that -- in general -- quantifies the capacity or the maximum rate at which information can be transferred to recover a sender's information at the receiver with a vanishingly low error probability. After verifying their equivalence with estimates based on the continuous phase data, we determined the mutual information using the time points at which the individual phases passed through their respective Poincar\'{e} sections. This stroboscopic view on the dynamics may resemble, e.g., neural spike times, that are common observables in the study of neuronal information transfer. This discretization also increased processing speed significantly, rendering it particularly suitable for a fine-grained analysis of the effects of experimental and model parameters. In our model, the delayed mutual information within each subpopulation peaked at zero delay, whereas between the subpopulations it was always maximal at non-zero delay, irrespective of parameter choices. We observed that the delayed mutual information of the desynchronized subpopulation preceded the synchronized subpopulation. Put differently, the oscillators of the desynchronized subpopulation were 'driving' the ones in the synchronized subpopulation. These findings were also observed when estimating mutual information of the full phase trajectories. We can thus conclude that the delayed mutual information of discrete time points allows for inferring a functional directed flow of information between subpopulations of coupled phase oscillators

Complex dynamics in adaptive phase oscillator networks

Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adjust coupling strengths between units in accordance with their activity arises naturally in a variety of contexts, including neural plasticity in the brain, and adds an additional layer of complexity: the dynamics on the nodes influence the dynamics of the network and vice versa. We study a model of Kuramoto phase oscillators with a general adaptive learning rule with three parameters (strength of adaptivity, adaptivity offset, adaptivity shift). This rule includes as special cases learning paradigms such as (anti-)Hebbian learning and spike time dependent plasticity (STDP). Importantly, the adaptivity parameter allows to study the impact of adaptation on the collective dynamics as we move away from the non-adaptive case given by stationary coupling. First, we carry out a detailed bifurcation analysis for N = 2 oscillators with (un-)directed coupling strengths. Adaptation dynamics in terms of nontrivial bifurcations arises only when the strength of adaptation exceeds a critical threshold. Whereas the paradigms of (anti-)Hebbian learning and STDP result in non-trivial multi-stability and bifurcation scenarios, mixed-type learning rules exhibit even more complicated and rich dynamics including a period doubling cascade to chaotic dynamics as well as oscillations displaying features of both librational and rotational character. Second, we numerically investigate a larger system with N = 50 oscillators and explore dynamic similarities with the case of N = 2 oscillators

CONCEPTUAL MODEL AND OPERATIONAL PROCESSES OF CUSTOMER VALUE-BASED REVENUE MANAGEMENT IN TRANSPORT AND LOGISTICS

The approach presented in this article addresses the shortcomings of transaction-based revenue management and proposes a conceptual model of customer value-based revenue management to allow for both an efficient utilization of limited capacity resources and the establishment of profitable customer relationships. Furthermore, process models are developed for the operational tasks as well as results of a prototypical implementation are presented. Finally, some concluding remarks and an outlook on remaining research are given

The Sound of Feelings:Electrophysiological Responses Emotional Speech in Alexithymia

BACKGROUND: Alexithymia is a personality trait characterized by difficulties in the cognitive processing of emotions (cognitive dimension) and in the experience of emotions (affective dimension). Previous research focused mainly on visual emotional processing in the cognitive alexithymia dimension. We investigated the impact of both alexithymia dimensions on electrophysiological responses to emotional speech in 60 female subjects. METHODOLOGY: During unattended processing, subjects watched a movie while an emotional prosody oddball paradigm was presented in the background. During attended processing, subjects detected deviants in emotional prosody. The cognitive alexithymia dimension was associated with a left-hemisphere bias during early stages of unattended emotional speech processing, and with generally reduced amplitudes of the late P3 component during attended processing. In contrast, the affective dimension did not modulate unattended emotional prosody perception, but was associated with reduced P3 amplitudes during attended processing particularly to emotional prosody spoken in high intensity. CONCLUSIONS: Our results provide evidence for a dissociable impact of the two alexithymia dimensions on electrophysiological responses during the attended and unattended processing of emotional prosody. The observed electrophysiological modulations are indicative of a reduced sensitivity to the emotional qualities of speech, which may be a contributing factor to problems in interpersonal communication associated with alexithymia

Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators

Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked -- a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions. Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos

Transfusion of red blood cells: the impact on short-term and long-term survival after coronary artery bypass grafting, a ten-year follow-up.

Transfusion of red blood cells (RBC) and other blood products in patients undergoing coronary artery bypass grafting (CABG) is associated with increased mortality and morbidity. We retrospectively analyzed data of patients who underwent an isolated coronary bypass graft operation between January 1998 and December 2007. Mean follow-up was 1696±1026 days, with exclusion of 122 patients lost to follow-up and 80 patients who received 10 units of RBC. Of the remaining patients, 8001 (76.7%) received no RBC, 1621 (15.2%) received 1–2 units of RBC, 593 (5.7%) received 3–5 units and 220 (2.1%) received 6–10 units. The number of transfused RBC was a predictor for early but not for late mortality. When compared to expected survival, survival of patients not receiving any blood product was better, while survival of patients receiving >3 units of RBC was worse. Transfusion of RBC is an independent, dose-dependent risk factor for early mortality after revascularization. Compared to expected survival, receiving no RBC improves patient long-term survival, whereas receiving three or more units of RBC significantly decreases patient survival

Coupled vortex oscillations in spatially separated permalloy squares

We experimentally study the magnetization dynamics of pairs of micron-sized permalloy squares coupled via their stray fields. The trajectories of the vortex cores in the Landau-domain patterns of the squares are mapped in real space using time-resolved scanning transmission x-ray microscopy. After excitation of one of the vortex cores with a short magnetic-field pulse, the system behaves like coupled harmonic oscillators. The coupling strength depends on the separation between the squares and the configuration of the vortex-core polarizations. Considering the excitation via a rotating in-plane magnetic field, it can be understood that only a weak response of the second vortex core is observed for equal core polarizations