This paper explores the effectiveness of network attack when the attacker has imperfect information about the network. For Erdős-Rényi networks, we observe that dynamical importance and betweenness centrality-based attacks are surprisingly robust to the presence of a moderate amount of imperfect information and are more effective compared with simpler degree-based attacks even at moderate levels of network information error. In contrast, for scale-free networks the effectiveness of attack is much less degraded by a moderate level of information error. Furthermore, in the Erdős-Rényi case the effectiveness of network attack is much more degraded by missing links as compared with the same number of false links. [6,7], etc.). Interventions that seek to degrade [8][9][10][11][12][13] or protect [13][14][15][16] network connectivity are thus of great interest. In particular, strategies for network attack by node or link removal have been intensively studied. Key issues have been the dependence of the attack effectiveness upon network topology and the strategy for selecting nodes or links for removal. We note, however, that, while such previous studies have predominantly presumed the attacker to have perfect knowledge of the network to be attacked, this is very often not the case. Specifically, networks inferred from measurements typically have false links and miss true links. One might suppose that these errors could very much lower the effectiveness of attack strategies. The purpose of this paper is to address this important issue for the case of node removal attacks of undirected networks (directed networks are treated in the online supplementary material [17]).One example of a network attack problem is an attempt to stop the spread of a disease with a limited number of vaccinations: the people who receive the vaccinations are chosen on the basis of their position in the social network [8][9][10][11][12][13]. Another example is that of deriving gene therapies for cancer. Here the goal is to select those genes whose disabling would most inhibit cancer cell survival and proliferation [18][5]. Yet another example is the study of the resilience of the Internet to intentional attack [8,12]. The typical attack strategy is to calculate some centrality measure of each node, and to then attack (disable, vaccinate, or remove) those nodes with the highest values of this measure. However, an attacker with imperfect network information will determine values of these centrality measures with some error, and using these would be expected to degrade the effectiveness of his attack. Imperfect network information is ubiquitous in applications and can arise in various ways. Examples of link errors can be found in online social networks, where a friendship may be indicated despite the two subjects having never personally met, or inversely, if no online friendship exists between two faceto-face friends. In the previously cited example of cancer gene therapy, genes are selected for disabling based upon an estimated gene interaction net...

CHICO2 (Compact Heavy Ion COunter), is a large solid-angle, charged-particle detector array developed to provide both θ and  angle resolutions matching those of GRETINA (Gamma-Ray Energy Tracking In-beam Nuclear Array). CHICO2 was successfully tested at the Argonne National Laboratory where it was fielded as an auxiliary detector with GRETINA for -ray spectroscopic studies of nuclei using a 252 Cf spontaneous fission source, stable beams, and radioactive beams from CARIBU. In field tests of the 72,76 Ge beams on a 0.5 mg/cm 2 208 Pb target at the sub-barrier energy, CHICO2 provided chargedparticle angle resolutions (FWHM) of 1.55 o in  and 2.47 o in . This achieves the design goal for both coordinates assuming a beam-spot size (> 3 mm) and the target thickness (> 0.5 mg/cm 2). The combined angular resolution of GRETINA/CHICO2 resulted in a Doppler-shift corrected energy resolution of 0.60% for 1 MeV coincident de-excitation rays. This is nearly a factor of two improvement in resolution and sensitivity compared to Gammasphere/CHICO. Kinematically-coincident detection of scattered ions by CHICO2 still maintains the mass resolution (M/M) of ~ 5% that enhanced isolation of scattered weak beams of interest from scattered contaminant beams.

We consider certain elliptical subsets of the square lattice. The recurrent representative of the identity element of the sandpile group on this graph consists predominantly of a biperiodic pattern, along with some noise. We show that as the lattice spacing tends to 0, the fraction of the area taken up by the pattern in the identity element tends to 1.

<p style='text-indent:20px;'>We consider certain elliptical subsets of the square lattice. The recurrent representative of the identity element of the sandpile group on this graph consists predominantly of a biperiodic pattern, along with some noise. We show that as the lattice spacing tends to 0, the fraction of the area taken up by the pattern in the identity element tends to 1.</p>