Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I

We study BPS spectra of D-branes on local Calabi-Yau threefolds $$\mathcal {O}(-p)\oplus \mathcal {O}(p-2)\rightarrow \mathbb {P}^1$$ O ( - p ) ⊕ O ( p - 2 ) → P 1 with $$p=0,1$$ p = 0 , 1 , corresponding to $$\mathbb {C}^3/\mathbb {Z}_{2}$$ C 3 / Z 2 and the resolved conifold. Nonabelianization for exponential networks is applied to compute directly unframed BPS indices counting states with D2 and D0 brane charges. Known results on these BPS spectra are correctly reproduced by computing new types of BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their wall-crossing. We also develop the notion of exponential BPS graphs for the simplest toric examples, and show that they encode both the quiver and the potential associated to the Calabi-Yau via geometric engineering.

Non-exponential networks in production

The article describes the characteristics of special types of queuing systems. Special types of queuing systems are listed. The main methods for calculating of non-exponential queuing systems are given.

MODELING CITATION NETWORKS BASED ON VIGOROUSNESS AND DORMANCY

In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors: vigorousness and dormancy. Based on this idea, a citation network model is proposed, in which a node has two discrete stage: vigorous and dormant. Vigorous nodes can be deactivated and dormant nodes may be activated and become vigorous. The evolution of the network couples addition of new nodes and state transitions of old ones. Both analytical calculation and numerical simulation show that the degree distribution of nodes in generated networks displays a good right-skewed behavior. Particularly, scale-free networks are obtained as the deactivated vertex is target selected and exponential networks are realized for the random-selected case. Moreover, the measurement of four real-world citation networks achieves a good agreement with the stochastic model.

ON SYNCHRONIZABILITY OF DYNAMICAL LOCAL-WORLD NETWORKS

Synchronization phenomena in dynamical systems with local-world topologies are investigated. The effect of local-world size M on the synchronizability is studied. A larger M makes networks more synchronizable. Then the ability of dynamical networks to resist random errors and attacks is analyzed and compared with those of scale-free and exponential networks. Two attacking strategies are adopted, and a better quantity is used to measure the changes in synchronizability after node removal.