We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A 388, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.PACS numbers: 89.75. Da, 02.50.Le, 89.65.Ef In the last century, queueing theory has proved useful for various problems ranging from operations research to telecommunications [1]. There is a recent resurgence of interest for the queueing theory among the statistical physics community with the application to the problems in human dynamics. Specifically, various queueing models based on the prioritization of tasks, or the priority queue models to be short, have been introduced to account for the heavy-tailed distributions observed in the waiting time and response time distributions [2,3,4,5,6,7,8]. The priority queue model is grounded on the assumption that the human dynamics is the result of an inherent decision-making process of the individual, with implicit priorities assigned for every tasks in his/her task queue, according to which he/she decides which task to execute next.To be specific, the priority queue model by Barabási [2] consists of a single fixed-length queue, filled with tasks each of which is assigned a priority value drawn randomly when it enters into the queue. Every step the task with the highest priority is executed and is replaced by a new task with random priority value. Upon execution, the waiting time τ , that is, how long the task has sat (waited) on the queue, is measured. Waiting time distribution P (τ ) of the Barabási model has been shown to exhibit a power-law tail for large τ aswith the exponent α = 1 [2, 3], conforming to the behaviors observed for the e-mail, library loan, and website visitation records [2,9,10,11]. Besides the human dynamics, however, due to the extremal nature of its dynamics the priority queue model would bear implications also to disparate problems in extremal dynamics, such as the Bak-Sneppen model for biological evolution [12] and invasion percolation [4]. * Email: kgoh@korea.ac.krBarabási model purposefully simplified many aspects of potential importance in realistic human dynamics, serving as a starting framework on which various detailed factors can be embedded [13,14,15,16,17]. One important factor that was not been accounted for is the human interaction...

PACS 05.70.Ln -Nonequilibrium and irreversible thermodynamics PACS 89.65.-s -Social and economic systems Abstract -We study the epidemic spreading process following contact dynamics with heavytailed waiting time distributions. We show both analytically and numerically that the temporal heterogeneity of contact dynamics can significantly suppress the disease's transmissibility, hence the size of epidemic outbreak, obstructing the spreading process. Furthermore, when the temporal heterogeneity is strong enough, one obtains the vanishing transmissibility for any finite recovery time and regardless of underlying structure of contacts, the condition of which was derived.

We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche dynamics; the system is critical with an asymptotic powerlaw avalanche size distribution with an exponent τ = 3/2 on duplex random networks. The detailed cascade dynamics, however, is affected by the multiplex coupling. For example, higher-degree nodes such as hubs in scale-free networks fail more often in the multiplex dynamics than in the simplex network counterpart in which different types of edges are simply aggregated. Our results suggest that multiplex modeling would be necessary in order to gain a better understanding of cascading failure phenomena of real-world multiplex complex systems, such as the global economic crisis.

Dodecylamine-intercalated vanadium oxide nanotubes were obtained by distinct synthesis processes. Water intercalation in the nanotube structure was identified in a marked manner by the distortion of the VO x layers in the x-ray diffraction patterns and enhanced V 4+v O absorption in the Fourier-transform infrared spectra. Our electron spin resonance measurements sensitively reflect changes in the microscopic structure and magnetic interactions introduced by the water intercalation in the vanadium oxide nanotubes.

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