We study the resilience of complex networks against attacks in which nodes are targeted intelligently, but where disabling a node has a cost to the attacker which depends on its degree. Attackers have to meet these costs with limited resources, which constrains their actions. A network's integrity is quantified in terms of the efficacy of the process that it supports. We calculate how the optimal attack strategy and the most attack-resistant network degree statistics depend on the node removal cost function and the attack resources. The resilience of networks against intelligent attacks is found to depend strongly on the node removal cost function faced by the attacker. In particular, if node removal costs increase sufficiently fast with the node degree, power law networks are found to be more resilient than Poissonian ones, even against optimized intelligent attacks. For cost functions increasing quadratically in the node degrees, intelligent attackers cannot damage the network more than random damages would.
For bulk InSb at the quantum limit, it is shown that the lowering of the Landau levels is associated with excitation of excess electron-hole pairs by the action of the J x H force, when the stimulated emission sets out, and that the value of the gain of the emission becomes extremely high, diverging as w,i-m in accordance with the observation.Recent experiments carried out at the quantum limit [I-31 have revealed for the first time that stimulated interband Landau emission is brought about by the electromagnetic force (EMF) excitation with an outstanding low value of the critical current densities, such that J , = 16-40 A cm-', when a current J is passed through a bulk InSb plate subjected to a transverse, high magnetic field H up to 7T. The stimulated emissions, identified as a, and u2 emissions in figure 1, have been observed at temperatures from 4.2 to 135K a s long as the quantum limit condition hw,, > kT is satisfied, where w c , = eH/m,*c is the cyclotron frequency of electrons with the electric charge e and the effective mass in:, c is the light velocity, h is Planck's cunsiani, k is ihe Boltzmann constant, and T i s temperature (see reference
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