A Class of Periodic Continued Radicals

We compute the limits of a class of periodic continued radicals and we establish a connection between them and the fixed points of the Chebycheff polynomials

Sequential Logistic Principal Component Analysis (SLPCA): Dimensional Reduction in Streaming Multivariate Binary-State System

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional reduction. However, traditional Singular Value Decomposition (SVD) based PCA fails to model data which largely deviates from Gaussian distribution. The Bregman Divergence was recently introduced to achieve a generalized PCA framework. If the random variable under dimensional reduction follows Bernoulli distribution, which occurs in many emerging fields, the generalized PCA is called Logistic PCA (LPCA). In this paper, we extend the batch LPCA to a sequential version (i.e. SLPCA), based on the sequential convex optimization theory. The convergence property of this algorithm is discussed compared to the batch version of LPCA (i.e. BLPCA), as well as its performance in reducing the dimension for multivariate binary-state systems. Its application in building energy end-use profile modeling is also investigated.Comment: 6 pages, 4 figures, conference submissio

The Ascending Double-Cone: A Closer Look at a Familiar Demonstration

The double-cone ascending an inclined V-rail is a common exhibit used for demonstrating concepts related to center-of-mass in introductory physics courses. While the conceptual explanation is well-known--the widening of the ramp allows the center of mass of the cone to drop, overbalancing the increase in altitude due to the inclination of the ramp--there remains rich physical content waiting to be extracted through deeper exploration. Such an investigations seems to be absent from the literature. This article seeks to remedy the omission.Comment: LaTeX, 16 pages, 18 eps figure

Studying Trilinear Gauge Couplings at Linear Collider Energies

We study the sensitivity of the processes `e+ e- -> lepton (l) neutrino (v) quark (u) antiquark (d)', where the lepton is an electron or a muon, on the non-standard trilinear gauge couplings (TGC), using the optimal observables method at Linear Collider energies. Our study is based on the four-fermion generator ERATO. Taking into account all possible correlations between the different trilinear gauge coupling parameters, we show that they can be measured with an accuracy of $10^{-3}$ to $10^{-4}$ for typical Linear Collider energies and luminosities.Comment: 17 pages, LaTeX, version to appear in Zeitschrift fur Physi