Active Learning for Hidden Attributes in Networks

In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing which vertex to query in order to learn as much as possible about the attributes of the other vertices. We assume the network is generated by a stochastic block model, but we make no assumptions about its assortativity or disassortativity. We choose which vertex to query using two methods: 1) maximizing the mutual information between its attributes and those of the others (a well-known approach in active learning) and 2) maximizing the average agreement between two independent samples of the conditional Gibbs distribution. Experimental results show that both these methods do much better than simple heuristics. They also consistently identify certain vertices as important by querying them early on

Berry phase and Anomalous Hall Effect in a Three-orbital Tight-binding Hamiltonian

We consider the Anomalous Hall (AH) state induced by interactions in a three-orbital per unit-cell model. To be specific we consider a model appropriate for the Copper-Oxide lattice to highlight the necessary conditions for time-reversal breaking states which are AH states and which are not. We compare the singularities of the wave-functions of the three-orbital model, which are related to the nonzero Berry curvature, and their variation with a change of gauge to those in the two-orbital model introduced in a seminal paper by Haldane. Explicit derivation using wave-functions rather than the more powerful abstract methods may provide additional physical understanding of the phenomena

Geometric engineering of (framed) BPS states

BPS quivers for N=2 SU(N) gauge theories are derived via geometric engineering from derived categories of toric Calabi-Yau threefolds. While the outcome is in agreement of previous low energy constructions, the geometric approach leads to several new results. An absence of walls conjecture is formulated for all values of N, relating the field theory BPS spectrum to large radius D-brane bound states. Supporting evidence is presented as explicit computations of BPS degeneracies in some examples. These computations also prove the existence of BPS states of arbitrarily high spin and infinitely many marginal stability walls at weak coupling. Moreover, framed quiver models for framed BPS states are naturally derived from this formalism, as well as a mathematical formulation of framed and unframed BPS degeneracies in terms of motivic and cohomological Donaldson-Thomas invariants. We verify the conjectured absence of BPS states with "exotic" SU(2)_R quantum numbers using motivic DT invariants. This application is based in particular on a complete recursive algorithm which determine the unframed BPS spectrum at any point on the Coulomb branch in terms of noncommutative Donaldson-Thomas invariants for framed quiver representations.Comment: 114 pages; v2:minor correction

New Insight into Metformin Mechanism of Action and Clinical Application

Metformin is the first-line medication for Type 2 diabetes (T2D) treatment, and it is the only US FDA approved oral antidiabetic medication for pediatric patients with T2D 10 years and older. Metformin is also used to treat polycystic ovary syndrome (PCOS), another condition with underlying insulin resistance. The clinical applications of metformin are continuing to expand into other fields including cancer, aging, cardiovascular diseases, and neurodegenerative diseases. Metformin modulates multiple biological pathways. Its novel properties and effects continue to evolve; however, its molecular mechanism of action remains incompletely understood. In this chapter, we focus on the recent translational research and clinical data on the molecular action of metformin and the evidence linking the effects of metformin on insulin resistance, prediabetes, diabetes, aging, cancer, PCOS, cardiovascular diseases, and neurodegenerative diseases

Sunspot rotation, filament, and flare: The event on 2000 February 10

We find that a sunspot with positive polarity had an obvious counter-clockwise rotation and resulted in the formation and eruption of an inverse S-shaped filament in NOAA active region (AR) 08858 from 2000 February 9 to 10. The sunspot had two umbrae which rotated around each other by 195 degrees within about twenty-four hours. The average rotation rate was nearly 8 degrees per hour. The fastest rotation in the photosphere took place during 14:00UT to 22:01UT on February 9, with the rotation rate of nearly 16 degrees per hour. The fastest rotation in the chromosphere and the corona took place during 15:28UT to 19:00UT on February 9, with the rotation rate of nearly 20 degrees per hour. Interestingly, the rapid increase of the positive magnetic flux just occurred during the fastest rotation of the rotating sunspot, the bright loop-shaped structure and the filament. During the sunspot rotation, the inverse S-shaped filament gradually formed in the EUV filament channel. The filament experienced two eruptions. In the first eruption, the filament rose quickly and then the filament loops carrying the cool and the hot material were seen to spiral into the sunspot counterclockwise. About ten minutes later, the filament became active and finally erupted. The filament eruption was accompanied with a C-class flare and a halo coronal mass ejection (CME). These results provide evidence that sunspot rotation plays an important role in the formation and eruption of the sigmoidal active-region filament.Comment: 20 pages, 9 figures, Accepted for publication in Ap

Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering

A strongly interacting plasma of linearly dispersing electron and hole excitations in two spatial dimensions (2D), also known as a Dirac fluid, can be captured by relativistic hydrodynamics and shares many universal features with other quantum critical systems. We propose a one-dimensional (1D) model to capture key aspects of the 2D Dirac fluid while including lattice effects and being amenable to non-perturbative computation. When interactions are added to the Dirac-like 1D dispersion without opening a gap, we show that this kind of irrelevant interaction is able to preserve Fermi-liquid-like quasi-particle features while relaxing a zero-momentum charge current via collisions between particle-hole excitations, leading to resistivity that is linear in temperature via a mechanism previously discussed for large-diameter metallic carbon nanotubes. We further provide a microscopic lattice model and obtain numerical results via density-matrix renormalization group (DMRG) simulations, which support the above physical picture. The limits on such fast relaxation at strong coupling are of considerable interest because of the ubiquity of bad metals in experiments.Comment: 7 pages, 3 figures plus supplemental material