Learning from networked examples

Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may share some common objects, and hence share the features of these shared objects. We show that the classic approach of ignoring this problem potentially can have a harmful effect on the accuracy of statistics, and then consider alternatives. One of these is to only use independent examples, discarding other information. However, this is clearly suboptimal. We analyze sample error bounds in this networked setting, providing significantly improved results. An important component of our approach is formed by efficient sample weighting schemes, which leads to novel concentration inequalities

Fractional quantum Hall effect of topological surface states under a strong tilted magnetic field

The fractional quantum Hall effect (FQHE) of topological surface-state particles under a tilted strong magnetic field is theoretically studied by using the exact diagonalization method. The Haldane's pseudopotentials for the Coulomb interaction are analytically obtained. The results show that by increasing the in-plane component of the tilted magnetic field, the FQHE state at $n$=0 Landau level (LL) becomes more stable, while the stabilities of $n$=$\pm1$ LLs become weaker. Moreover, we find that the excitation gaps of the $\nu=1/3$ FQHE states increase as the tilt angle is increased.Comment: 4.2 pages, 4 figure

Thermal Conductance for Single Wall Carbon Nanotubes

We report a theoretical analysis of the phonon thermal conductance, \kappa (T), for single wall carbon nanotubes (SWCN). In a range of low temperatues up to 100K, \kappa (T) of perfect SWCN is found to increase with temperature, approximately, in a parabolic fashion. This is qualitatively consistent with recent experimental measurements where the tube-tube interactions are negligibly weak. When the carbon-carbon bond length is slightly varied, \kappa (T) is found to be qualitatively unaltered which implies that the anharmonic effect does not change the qualitative behavior of \kappa (T).Comment: Revtex, 4 figure