Nonlinear ac response of anisotropic composites

When a suspension consisting of dielectric particles having nonlinear characteristics is subjected to a sinusoidal (ac) field, the electrical response will in general consist of ac fields at frequencies of the higher-order harmonics. These ac responses will also be anisotropic. In this work, a self-consistent formalism has been employed to compute the induced dipole moment for suspensions in which the suspended particles have nonlinear characteristics, in an attempt to investigate the anisotropy in the ac response. The results showed that the harmonics of the induced dipole moment and the local electric field are both increased as the anisotropy increases for the longitudinal field case, while the harmonics are decreased as the anisotropy increases for the transverse field case. These results are qualitatively understood with the spectral representation. Thus, by measuring the ac responses both parallel and perpendicular to the uniaxial anisotropic axis of the field-induced structures, it is possible to perform a real-time monitoring of the field-induced aggregation process.Comment: 14 pages and 4 eps figure

L-functions of Symmetric Products of the Kloosterman Sheaf over Z

The classical $n$-variable Kloosterman sums over the finite field ${\bf F}_p$ give rise to a lisse $\bar {\bf Q}_l$-sheaf ${\rm Kl}_{n+1}$ on ${\bf G}_{m, {\bf F}_p}={\bf P}^1_{{\bf F}_p}-\{0,\infty\}$, which we call the Kloosterman sheaf. Let $L_p({\bf G}_{m,{\bf F}_p}, {\rm Sym}^k{\rm Kl}_{n+1}, s)$ be the $L$-function of the $k$-fold symmetric product of ${\rm Kl}_{n+1}$. We construct an explicit virtual scheme $X$ of finite type over ${\rm Spec} {\bf Z}$ such that the $p$-Euler factor of the zeta function of $X$ coincides with $L_p({\bf G}_{m,{\bf F}_p}, {\rm Sym}^k{\rm Kl}_{n+1}, s)$. We also prove similar results for $\otimes^k {\rm Kl}_{n+1}$ and $\bigwedge^k {\rm Kl}_{n+1}$.Comment: 16 page

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education