Classification problems have made significant progress due to the maturity of artificial intelligence (AI). However, differentiating items from categories without noticeable boundaries is still a huge challenge for machines -- which is also crucial f
or machines to be intelligent. In order to study the fuzzy concept on classification, we define and propose a globalness detection with the four-stage operational flow. We then demonstrate our framework on Facebook public pages inter-like graph with their geo-location. Our prediction algorithm achieves high precision (89%) and recall (88%) of local pages. We evaluate the results on both states and countries level, finding that the global node ratios are relatively high in those states (NY, CA) having large and international cities. Several global nodes examples have also been shown and studied in this paper. It is our hope that our results unveil the perfect value from every classification problem and provide a better understanding of global and local nodes in Online Social Networks (OSNs).
We study effects of disorder (randomness) in a 2D square-lattice $S=1/2$ quantum spin system, the $J$-$Q$ model with a 6-spin interaction $Q$ supplementing the Heisenberg exchange $J$. In the absence of disorder the system hosts antiferromagnetic (AF
M) and columnar valence-bond-solid (VBS) ground states. The VBS breaks $Z_4$ symmetry, and in the presence of arbitrarily weak disorder it forms domains. Using QMC simulations, we demonstrate two kinds of such disordered VBS states. Upon dilution, a removed site leaves a localized spin in the opposite sublattice. These spins form AFM order. For random interactions, we find a different state, with no order but algebraically decaying mean correlations. We identify localized spinons at the nexus of domain walls between different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, there is a strong tendency to singlet formation, because of spinon-spinon interactions mediated by the domain walls. Thus, no long-range AFM order forms. We propose that this state is a 2D analog of the well-known 1D random singlet (RS) state, though the dynamic exponent $z$ in 2D is finite. By studying the T-dependent magnetic susceptibility, we find that $z$ varies, from $z=2$ at the AFM--RS phase boundary and larger in the RS phase The RS state discovered here in a system without geometric frustration should correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr$_2$CuTe$_{1-x}$W$_x$O$_6$.
