Spatial, temporal, and energy characteristics of copper vapor laser radiation

Abstract

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.

Direct instantons and nucleon magnetic moments

“…The resulting functions µ p,n (M) specify the value of the magnetic moment which is required to make both sides of the sum rule (10) This fit predicts χ ≃ −4.96 GeV −2 for the proton and χ ≃ −4.73 GeV −2 for the neutron sum rule. These values correspond to the OPE scale µ = 0.5 GeV adopted for our sum rules and lie inside the range obtained from other estimates [8,19,22]. They are somewhat smaller in magnitude than the value χ ≃ −5.7 GeV −2 found in the two-and three-pole models of Ref.…”

“…They are somewhat smaller in magnitude than the value χ ≃ −5.7 GeV −2 found in the two-and three-pole models of Ref. [19]. (Our predicted values for the excited-state transition parameters are A p ≃ 0.28GeV 2 and A n ≃ −0.27GeV −2 .…”

“…[8], for two reasons: first, one of its Wilson coefficients contains, in the "pragmatic" version of the OPE (see below), an infrared divergence. Secondly, the Π 3 sum rule failed to show a fiducial Borel region of stability [18] (even after proper subtraction of the divergence), while the other two sum rules provide stable and accurate values for the nucleon magnetic moments even without directinstanton corrections, and with a value of χ consistent with other, independent estimates [19].…”

Hadronic light-by-light scattering in the muon g-2: a new short-distance constraint on pion exchange

“…As pointed out in Ref. [39], the value of Π VT (p 2 ) at zero momentum is related to the quark condensate magnetic susceptibility χ in QCD in the presence of a constant external electromagnetic field, introduced in Ref. [40]:…”

Electromagnetic decay of vector mesons as derived from QCD sum rules

“…Subsequently Belyaev and Kogan [6] extended the calculation and obtained an improved estimate χ = −5.7 GeV −2 using the two-pole approximation. Chiu et al [7] also estimated the susceptibilities with the two-pole model and obtained…”