Integrable models of galactic discs with double nuclei

We introduce a new class of 2-D mass models, whose potentials are of St\"ackel form in elliptic coordinates. Our model galaxies have two separate strong cusps that form double nuclei. The potential and surface density distributions are locally axisymmetric near the nuclei and become {\it highly} non-axisymmetric outside the nucleus. The surface density diverges toward the cuspy nuclei with the law $\Sigma \propto r^{-2}$. Our model is sustained by four general types of regular orbits: {\it butterfly}, {\it nucleuphilic banana}, {\it horseshoe} and {\it aligned loop} orbits. Horseshoes and nucleuphilic bananas support the existence of cuspy regions. Butterflies and aligned loops control the non-axisymmetric shape of outer regions. Without any need for central black holes, our distributed mass models resemble the nuclei of M31 and NGC4486B. It is also shown that the self-gravity of the stellar disc can prevent the double nucleus to collapse.Comment: 8 pages, accepted for publication in MNRA

Local Normal Mode Coupling and Energy Band Splitting in Elliptically Birefringent 1D Magnetophotonic Crystals

An analysis is presented of wave-vector dispersion in elliptically birefringent stratified magneto-optic media having one-dimensional periodicity. It is found that local normal-mode polarization-state differences between adjacent layers lead to mode coupling and impact the wave-vector dispersion and the character of the Bloch states of the system. This coupling produces extra terms in the dispersion relation not present in uniform circularly birefringent magneto-optic stratified media. Normal mode coupling lifts the degeneracy at frequency band cross-over points under certain conditions and induces a magnetization-dependent optical band gap. This study examines the conditions for band gap formation in the system. It shows that such a frequency-split can be characterized by a simple coupling parameter that depends on the relation between polarization states of local normal modes in adjacent layers. The character of the Bloch states and conditions for maximizing the strength of the band splitting in these systems are analyzed.Comment: 15 pages, 4 figure

The Child is Father of the Man: Foresee the Success at the Early Stage

Understanding the dynamic mechanisms that drive the high-impact scientific work (e.g., research papers, patents) is a long-debated research topic and has many important implications, ranging from personal career development and recruitment search, to the jurisdiction of research resources. Recent advances in characterizing and modeling scientific success have made it possible to forecast the long-term impact of scientific work, where data mining techniques, supervised learning in particular, play an essential role. Despite much progress, several key algorithmic challenges in relation to predicting long-term scientific impact have largely remained open. In this paper, we propose a joint predictive model to forecast the long-term scientific impact at the early stage, which simultaneously addresses a number of these open challenges, including the scholarly feature design, the non-linearity, the domain-heterogeneity and dynamics. In particular, we formulate it as a regularized optimization problem and propose effective and scalable algorithms to solve it. We perform extensive empirical evaluations on large, real scholarly data sets to validate the effectiveness and the efficiency of our method.Comment: Correct some typos in our KDD pape