Inducing Effect on the Percolation Transition in Complex Networks

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always causes a discontinuous percolation transition. We precisely predict the percolation threshold and core size for uncorrelated random networks with arbitrary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation occurs. The core sizes of real-world networks can also be well predicted using degree distribution as the only input. Our work therefore provides a theoretical framework for quantitatively understanding discontinuous breakdown phenomena in various complex systems.Comment: Main text and appendices. Title has been change

Majorana neutrino signals at Belle-II and ILC

For some theoretical and experimental considerations, the relatively light Majorana neutrinos at the GeV scale have been attracting some interest. In this article we consider a scenario with only one Majorana neutrino $N$, negligible mixing with the active neutrinos $\nu_{L}$, where the Majorana neutrino interactions could be described in a model independent approach based on an effective theory. Under such a framework, we particularly study the feasibility of observing the $N$ with mass in the range 0$-$30 GeV via the process e^+ e^- \to \nu N \to\gamma + \slashed E in the future Belle-II and ILC experiments. The results show that it is unpromising for Belle-II to observe the signal, while ILC may easily make a discovery for the Majorana neutrino.Comment: 14 pages, 7 figures, 2 table

Model-Independent Constraints on Lorentz Invariance Violation via the Cosmographic Approach

Since Lorentz invariance plays an important role in modern physics, it is of interest to test the possible Lorentz invariance violation (LIV). The time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray bursts (GRBs) has been extensively used to this end. However, to our best knowledge, one or more particular cosmological models were assumed {\it a priori} in (almost) all of the relevant works in the literature. So, this makes the results on LIV in those works model-dependent and hence not so robust in fact. In the present work, we try to avoid this problem by using a model-independent approach. We calculate the time delay induced by LIV with the cosmic expansion history given in terms of cosmography, without assuming any particular cosmological model. Then, we constrain the possible LIV with the observational data, and find weak hints for LIV.Comment: 15 pages, 4 figures, 3 tables, revtex4; v2: discussions added, Phys. Lett. B in pres