The K\"ahler-Ricci flow with positive bisectional curvature

We show that the K\"ahler-Ricci flow on a manifold with positive first Chern class converges to a K\"ahler-Einstein metric assuming positive bisectional curvature and certain stability conditions.Comment: 15 page

Enhanced osteoblast adhesion on nanostructured selenium compacts for anti-cancer orthopedic applications

Metallic bone implants possess numerous problems limiting their long-term efficacy, such as poor prolonged osseointegration, stress shielding, and corrosion under in vivo environments. Such problems are compounded for bone cancer patients since numerous patients receive orthopedic implants after cancerous bone resection. Unfortunately, current orthopedic materials were not originally developed to simultaneously increase healthy bone growth (as in traditional orthopedic implant applications) while inhibiting cancerous bone growth. The long-term objective of the present research is to investigate the use of nano-rough selenium to prevent bone cancer from re-occurring while promoting healthy bone growth for this select group of cancer patients. Selenium is a well known anti-cancer chemical. However, what is not known is how healthy bone cells interact with selenium. To determine this, selenium, spherical or semispherical shots, were pressed into cylindrical compacts and these compacts were then etched using 1N NaOH to obtain various surface structures ranging from the micron, submicron to nano scales. Changes in surface chemistry were also analyzed. Through these etching techniques, results of this study showed that biologically inspired surface roughness values were created on selenium compacts to match that of natural bone roughness. Moreover, results showed that healthy bone cell adhesion increased with greater nanometer selenium roughness (more closely matching that of titanium). In this manner, this study suggests that nano-rough selenium should be further tested for orthopedic applications involving bone cancer treatment

Selenium nanoparticles inhibit Staphylococcus aureus growth

Staphylococcus aureus is a key bacterium commonly found in numerous infections. S. aureus infections are difficult to treat due to their biofilm formation and documented antibiotic resistance. While selenium has been used for a wide range of applications including anticancer applications, the effects of selenium nanoparticles on microorganisms remain largely unknown to date. The objective of this in vitro study was thus to examine the growth of S. aureus in the presence of selenium nanoparticles. Results of this study provided the first evidence of strongly inhibited growth of S. aureus in the presence of selenium nanoparticles after 3, 4, and 5 hours at 7.8, 15.5, and 31 μg/mL. The percentage of live bacteria also decreased in the presence of selenium nanoparticles. Therefore, this study suggests that selenium nanoparticles may be used to effectively prevent and treat S. aureus infections and thus should be further studied for such applications

Quantum Geometric Oscillations in Two-Dimensional Flat-Band Solids

Two-dimensional van der Waals heterostructures can be engineered into artificial superlattices that host flat bands with significant Berry curvature and provide a favorable environment for the emergence of novel electron dynamics. In particular, the Berry curvature can induce an oscillating trajectory of an electron wave packet transverse to an applied static electric field. Though analogous to Bloch oscillations, this novel oscillatory behavior is driven entirely by quantum geometry in momentum space instead of band dispersion. While the orbits of Bloch oscillations can be localized by increasing field strength, the size of the geometric orbits saturates to a nonzero plateau in the strong-field limit. In non-magnetic materials, the geometric oscillations are even under inversion of the applied field, whereas the Bloch oscillations are odd, a property that can be used to distinguish these two co-existing effects.Comment: 6 + 7 pages, 2 figures. Comments are greatly appreciated

Protected Fermionic Zero Modes in Periodic Gauge Fields

It is well-known that macroscopically-normalizable zero-energy wavefunctions of spin-$\frac{1}{2}$ particles in a two-dimensional inhomogeneous magnetic field are spin-polarized and exactly calculable with degeneracy equaling the number of flux quanta linking the whole system. Extending this argument to massless Dirac fermions subjected to magnetic fields that have \textit{zero} net flux but are doubly periodic in real space, we show that there exist \textit{only two} Bloch-normalizable zero-energy eigenstates, one for each spin flavor. This result is immediately relevant to graphene multilayer systems subjected to doubly-periodic strain fields, which at low energies, enter the Hamiltonian as periodic pseudo-gauge vector potentials. Furthermore, we explore various related settings including nonlinearly-dispersing band structure models and systems with singly-periodic magnetic fields.Comment: 9 pages, 1 figure. Comments are very appreciate

Boundary Modes from Periodic Magnetic and Pseudomagnetic Fields in Graphene

Single-layer graphenes subject to periodic lateral strains are artificial crystals that can support boundary spectra with an intrinsic polarity. These are analyzed by comparing the effects of periodic magnetic fields and strain-induced pseudomagnetic fields that respectively break and preserve time-reversal symmetry. In the former case, a Chern classification of the superlattice minibands with zero total magnetic flux enforces {\it single} counter-propagating modes traversing each bulk gap on opposite boundaries of a nanoribbon. For the pseudomagnetic field, pairs of counter-propagating modes migrate to the {\it same} boundary where they provide well-developed valley-helical transport channels on a single zigzag edge. We discuss possible schemes for implementing this situation and their experimental signatures.Comment: 5+12 pages; 3+6 figures; version accepted to Physical Review Letter

Factorizing LambdaMART for cold start recommendations

Recommendation systems often rely on point-wise loss metrics such as the mean squared error. However, in real recommendation settings only few items are presented to a user. This observation has recently encouraged the use of rank-based metrics. LambdaMART is the state-of-the-art algorithm in learning to rank which relies on such a metric. Despite its success it does not have a principled regularization mechanism relying in empirical approaches to control model complexity leaving it thus prone to overfitting. Motivated by the fact that very often the users' and items' descriptions as well as the preference behavior can be well summarized by a small number of hidden factors, we propose a novel algorithm, LambdaMART Matrix Factorization (LambdaMART-MF), that learns a low rank latent representation of users and items using gradient boosted trees. The algorithm factorizes lambdaMART by defining relevance scores as the inner product of the learned representations of the users and items. The low rank is essentially a model complexity controller; on top of it we propose additional regularizers to constraint the learned latent representations that reflect the user and item manifolds as these are defined by their original feature based descriptors and the preference behavior. Finally we also propose to use a weighted variant of NDCG to reduce the penalty for similar items with large rating discrepancy. We experiment on two very different recommendation datasets, meta-mining and movies-users, and evaluate the performance of LambdaMART-MF, with and without regularization, in the cold start setting as well as in the simpler matrix completion setting. In both cases it outperforms in a significant manner current state of the art algorithms