2D mixed pseudo-random coupling PS map lattice and its application in S-box generation

Author(s):  
Peizhao Zhou ◽  
Junxiao Du ◽  
Kai Zhou ◽  
Shengfei Wei
Keyword(s):  
1974 ◽  
Vol 61 (3) ◽  
pp. 936-946 ◽  
Author(s):  
Eric J. Heller ◽  
Stuart A. Rice

2003 ◽  
Vol 90 (6) ◽  
pp. 3902-3911 ◽  
Author(s):  
Urs Achim Wiedemann ◽  
Anita Lüthi

Even without active pacemaker mechanisms, temporally patterned synchronization of neural network activity can emerge spontaneously and is involved in neural development and information processing. Generation of spontaneous synchronization is thought to arise as an alternating sequence between a state of elevated excitation followed by a period of quiescence associated with neuronal and/or synaptic refractoriness. However, the cellular factors controlling recruitment and timing of synchronized events have remained difficult to specify, although the specific temporal pattern of spontaneous rhythmogenesis determines its impact on developmental processes. We studied spontaneous synchronization in a model of 600–1,000 integrate-and-fire neurons interconnected with a probability of 5–30%. One-third of neurons generated spontaneous discharges and provided a background of intrinsic activity to the network. The heterogeneity and random coupling of these neurons maintained this background activity asynchronous. Refractoriness was modeled either by use-dependent synaptic depression or by cellular afterhyperpolarization. In both cases, the recruitment of neurons into spontaneous synchronized discharges was determined by the interplay of refractory mechanisms with stochastic fluctuations in background activity. Subgroups of easily recruitable neurons served as amplifiers of these fluctuations, thereby initiating a cascade-like recruitment of neurons (“avalanche effect”). In contrast, timing depended on the precise implementation of neuronal refractoriness and synaptic connectivity. With synaptic depression, neuronal synchronization always occurred stochastically, whereas with cellular afterhyperpolarization, stochastic turned into periodic behavior with increasing synaptic strength. These results associate the type of refractory mechanism with the temporal statistics and the mechanism of synchronization, thereby providing a framework for differentiating between cellular mechanisms of spontaneous rhythmogenesis.


2016 ◽  
Vol 30 (18) ◽  
pp. 1650174 ◽  
Author(s):  
Guowei Zhu ◽  
Xianpei Wang ◽  
Meng Tian ◽  
Dangdang Dai ◽  
Jiachuan Long ◽  
...  

Much empirical evidence shows that many real-world networks fall into the broad class of small-world networks and have a modular structure. The modularity has been revealed to have an important effect on cascading failure in isolated networks. However, the corresponding results for interdependent modular small-world networks remain missing. In this paper, we investigate the relationship between cascading failures and the intra-modular rewiring probabilities and inter-modular connections under different coupling preferences, i.e. random coupling with modules (RCWM), assortative coupling in modules (ACIM) and assortative coupling with modules (ACWM). The size of the largest connected component is used to evaluate the robustness from global and local perspectives. Numerical results indicate that increasing intra-modular rewiring probabilities and inter-modular connections can improve the robustness of interdependent modular small-world networks under intra-attacks and inter-attacks. Meanwhile, experiments on three coupling strategies demonstrate that ACIM has a better effect on preventing the cascading failures compared with RCWM and ACWM. These results can be helpful to allocate and optimize the topological structure of interdependent modular small-world networks to improve the robustness of such networks.


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