How Many Topics? Stability Analysis for Topic Models

Topic modeling refers to the task of discovering the underlying thematic structure in a text corpus, where the output is commonly presented as a report of the top terms appearing in each topic. Despite the diversity of topic modeling algorithms that have been proposed, a common challenge in successfully applying these techniques is the selection of an appropriate number of topics for a given corpus. Choosing too few topics will produce results that are overly broad, while choosing too many will result in the "over-clustering" of a corpus into many small, highly-similar topics. In this paper, we propose a term-centric stability analysis strategy to address this issue, the idea being that a model with an appropriate number of topics will be more robust to perturbations in the data. Using a topic modeling approach based on matrix factorization, evaluations performed on a range of corpora show that this strategy can successfully guide the model selection process.Comment: Improve readability of plots. Add minor clarification

The critical dimension for a 4th order problem with singular nonlinearity

We study the regularity of the extremal solution of the semilinear biharmonic equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under Dirichlet boundary conditions $u=\partial_\nu u=0$ on $\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the identification of a "pull-in voltage" \la^*>0 such that a stable classical solution u_\la with 0 exists for \la\in (0,\la^*), while there is none of any kind when \la>\la^*. Our main result asserts that the extremal solution $u_{\lambda^*}$ is regular $(\sup_B u_{\lambda^*} <1)$ provided $N \le 8$ while $u_{\lambda^*}$ is singular ($\sup_B u_{\lambda^*} =1$) for $N \ge 9$, in which case $1-C_0|x|^{4/3}\leq u_{\lambda^*} (x) \leq 1-|x|^{4/3}$ on the unit ball, where $C_0:= (\frac{\lambda^*}{\overline{\lambda}})^{1/3}$ and $\bar{\lambda}:= {8/9} (N-{2/3}) (N- {8/3})$.Comment: 19 pages. This paper completes and replaces a paper (with a similar title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this author's papers can be downloaded at this http://www.birs.ca/~nassif

Accelerated increase in the Arctic tropospheric warming events surpassing stratospheric warming events during winter

In January 2016, a robust reversal of the Arctic Oscillation (AO) took place associated with a rapid tropospheric warming in the Arctic region; this was followed by the occurrence of a classic sudden stratospheric warming in March-April. The succession of these two distinct Arctic warming events provides a stimulating opportunity to examine their characteristics in terms of similarities and differences. Historical cases of these two types of Arctic warming were identified and validated based upon tropical linkages with the Madden-Julian Oscillation and El Niño as well as those documented in previous studies. Our results indicate a recent and accelerated increase in the tropospheric warming type versus a flat trend in stratospheric warming type. The relatively shorter duration and rapid transition of tropospheric warming events suggest a link to the documented increase in midlatitude weather extremes during boreal winter. Forced simulations with an atmospheric general circulation model suggest that the reduced Arctic sea ice contributes to the observed increase in the tropospheric warming events and associated impact on the anomalously cold Siberia

Macrospin approximation and quantum effects in models for magnetization reversal

The thermal activation of magnetization reversal in magnetic nanoparticles is controlled by the anisotropy-energy barrier. Using perturbation theory, exact diagonalization and stability analysis of the ferromagnetic spin-s Heisenberg model with coupling or single-site anisotropy, we study the effects of quantum fluctuations on the height of the energy barrier. Opposed to the classical case, there is no critical anisotropy strength discriminating between reversal via coherent rotation and via nucleation/domain-wall propagation. Quantum fluctuations are seen to lower the barrier depending on the anisotropy strength, dimensionality and system size and shape. In the weak-anisotropy limit, a macrospin model is shown to emerge as the effective low-energy theory where the microscopic spins are tightly aligned due to the ferromagnetic exchange. The calculation provides explicit expressions for the anisotropy parameter of the effective macrospin. We find a reduction of the anisotropy-energy barrier as compared to the classical high spin-s limit.Comment: 10 pages, 11 figure

Influence of Carbon Concentration on the Superconductivity in MgCxNi3

The influence of carbon concentration on the superconductivity (SC) in MgC$_{x}$Ni$_3$ has been investigated by measuring the low temperature specific heat combined with first principles electronic structure calculation. It is found that the specific heat coefficient $\gamma_n=C_{en}/T$ of the superconducting sample ($x\approx1$) in normal state is twice that of the non-superconducting one ($x\approx 0.85$). The comparison of measured $\gamma_n$ and the calculated electronic density of states (DOS) shows that the effective mass renormalization changes remarkably as the carbon concentration changes. The large mass renormalization for the superconducting sample and the low $T_{c}$(7K) indicate that more than one kind of boson mediated electron-electron interactions exist in MgC$_{x}$Ni$_3$.Comment: 4 pages, 4 figure

Interaction between M2-branes and Bulk Form Fields

We construct the interaction terms between the world-volume fields of multiple M2-branes and the 3- and 6-form fields in the context of ABJM theory with U($N$)$\times$U($N$) gauge symmetry. A consistency check is made in the simplest case of a single M2-brane, i.e, our construction matches the known effective action of M2-brane coupled to antisymmetric 3-form field. We show that when dimensionally reduced, our couplings coincide with the effective action of D2-branes coupled to R-R 3- and 5-form fields in type IIA string theory. We also comment on the relation between a coupling with a specific 6-form field configuration and the supersymmetry preserving mass deformation in ABJM theory.Comment: 30 pages, version to appear in JHE

Bubbling AdS and Vacuum String Field Theory

We show that a family of 1/2--BPS states of $\N=4$ SYM is in correspondence with a family of classical solutions of VSFT with a $B$--field playing the role of the inverse Planck constant. We show this correspondence by relating the Wigner distributions of the $N$ fermion systems representing such states, to low energy space profiles of systems of VSFT D-branes. In this context the Pauli exclusion principle appears as a consequence of the VSFT projector equation. The family of 1/2--BPS states maps through coarse--graining to droplet LLM supergravity solutions. We discuss the possible meaning of the corresponding coarse graining in the VSFT side.Comment: 23 pages, subsection 4.1 added, Appendix suppressed. to be published in NP

Determination of energy-band offsets between GaN and AlN using excitonic luminescence transition in AlGaN alloys

We report the determination of the energy-band offsets between GaN and AlN using the linewidth (full width at half maximum) of an extremely sharp excitonic luminescence transition in Alx Ga1-x N alloy with x=0.18 at 10 K. Our sample was grown on C -plane sapphire substrate by metal-organic chemical-vapor deposition at 1050 °C. The observed value of the excitonic linewidth of 17 meV is the smallest ever reported in literature. On subtracting a typical value of the excitonic linewidth in high-quality GaN, namely, 4.0 meV, we obtain a value of 13.0 meV, which we attribute to compositional disorder. This value is considerably smaller than that calculated using a delocalized exciton model [S. M. Lee and K. K. Bajaj, J. Appl. Phys. 73, 1788 (1993)]. The excitons are known to be strongly localized by defects and/or the potential fluctuations in this alloy system. We have simulated this localization assuming that the hole, being much more massive than the electron, is completely immobile, i.e., the hole mass is treated as infinite. Assuming that the excitonic line broadening is caused entirely by the potential fluctuations experienced by the conduction electron, the value of the conduction-band offset between GaN and AlN is determined to be about 57% of the total-band-gap discontinuity. Using our model we have calculated the variation of the excitonic linewidth as a function of Al composition in our samples with higher Al content larger than 18% and have compared it with the experimental data. We also compare our value of the conduction-band offset with those recently proposed by several other groups using different techniques. © 2006 American Institute of Physics

Noncommutative Electromagnetism As A Large N Gauge Theory

We map noncommutative (NC) U(1) gauge theory on R^d_C X R^{2n}_{NC} to U(N -> \infty) Yang-Mills theory on R^d_C, where R^d_C is a d-dimensional commutative spacetime while R^{2n}_{NC} is a 2n-dimensional NC space. The resulting U(N) Yang-Mills theory on R^d_C is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang-Mills theory onto R^d_C. We show that the gauge-Higgs system (A_\mu,\Phi^a) in the U(N -> \infty) Yang-Mills theory on R^d_C leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A_\mu,\Phi^a) in half-BPS configurations describes self-dual Einstein gravity.Comment: 25 pages; More clarifications, to appear in Eur. Phys. J.