Improved Algorithms for Time Decay Streams

In the time-decay model for data streams, elements of an underlying data set arrive sequentially with the recently arrived elements being more important. A common approach for handling large data sets is to maintain a coreset, a succinct summary of the processed data that allows approximate recovery of a predetermined query. We provide a general framework that takes any offline-coreset and gives a time-decay coreset for polynomial time decay functions. We also consider the exponential time decay model for k-median clustering, where we provide a constant factor approximation algorithm that utilizes the online facility location algorithm. Our algorithm stores O(k log(h Delta)+h) points where h is the half-life of the decay function and Delta is the aspect ratio of the dataset. Our techniques extend to k-means clustering and M-estimators as well

Electroweak Chiral Lagrangian for a Hypercharge-universal Topcolor Model

Electroweak chiral Lagrangian for a hypercharge-universal topcolor model is investigated. We find that the assignments of universal hypercharge improve the results obtained previously from K.Lane's prototype natural TC2 model by allowing a larger Z' mass resulting in a very small T parameter and the S parameter is still around the order of +1Comment: 12 pages, 7 figure

Neyman Smooth-Type Goodness of Fit Tests in Complex Surveys

In our study, we have extended the Neyman smooth-type goodness of fit tests by Eubank (1997) from simple random sample to complex surveys (Methodologies have been provided for complex surveys, and theorems have been provided only for stratified random samples.) by incorporating consistent estimators under the survey design, which is accomplished by a data-driven nonparametric order selection method. Simulation results show that these proposed methods potentially improve the statistical power while controlling the type I error very well compared to those commonly used existing test procedures, especially for the cases with slow-varying probabilities. We also derived the large sample properties of the test statistics in stratified sampling

New Frameworks for Offline and Streaming Coreset Constructions

A coreset for a set of points is a small subset of weighted points that approximately preserves important properties of the original set. Specifically, if $P$ is a set of points, $Q$ is a set of queries, and $f:P\times Q\to\mathbb{R}$ is a cost function, then a set $S\subseteq P$ with weights $w:P\to[0,\infty)$ is an $\epsilon$-coreset for some parameter $\epsilon>0$ if $\sum_{s\in S}w(s)f(s,q)$ is a $(1+\epsilon)$ multiplicative approximation to $\sum_{p\in P}f(p,q)$ for all $q\in Q$. Coresets are used to solve fundamental problems in machine learning under various big data models of computation. Many of the suggested coresets in the recent decade used, or could have used a general framework for constructing coresets whose size depends quadratically on what is known as total sensitivity $t$. In this paper we improve this bound from $O(t^2)$ to $O(t\log t)$. Thus our results imply more space efficient solutions to a number of problems, including projective clustering, $k$-line clustering, and subspace approximation. Moreover, we generalize the notion of sensitivity sampling for sup-sampling that supports non-multiplicative approximations, negative cost functions and more. The main technical result is a generic reduction to the sample complexity of learning a class of functions with bounded VC dimension. We show that obtaining an $(\nu,\alpha)$-sample for this class of functions with appropriate parameters $\nu$ and $\alpha$ suffices to achieve space efficient $\epsilon$-coresets. Our result implies more efficient coreset constructions for a number of interesting problems in machine learning; we show applications to $k$-median/$k$-means, $k$-line clustering, $j$-subspace approximation, and the integer $(j,k)$-projective clustering problem

Weyl points and topological nodal superfluids in a face-centered cubic optical lattice

We point out that a face-centered cubic (FCC) optical lattice, which can be realised by a simple scheme using three lasers, provides one a highly controllable platform for creating Weyl points and topological nodal superfluids in ultracold atoms. In non-interacting systems, Weyl points automatically arise in the Floquet band structure when shaking such FCC lattices, and sophisticated design of the tunnelling is not required. More interestingly, in the presence of attractive interaction between two hyperfine spin states, which experience the same shaken FCC lattice, a three-dimensional topological nodal superfluid emerges, and Weyl points show up as the gapless points in the quasiparticle spectrum. One could either create a double Weyl point of charge 2, or split it to two Weyl points of charge 1, which can be moved in the momentum space by tuning the interactions. Correspondingly, the Fermi arcs at the surface may be linked with each other or separated as individual ones.Comment: 5 pages, 2 figures in the main text; 2 pages, 2 figures in the supplemental materia

Empirical Research on Information Transmission in the Hang Seng Index Markets: Evidence from Index Futures, Flagship Index and Finance Index

This paper investigates the price discovery mechanism in the Hang Seng Index markets. The analysis is based on the cross-market volatility spillover effects by using the daily sets of Hang Seng Index (HSI), Hang Seng Finance Index (HSFIN), and Hang Seng Index futures (HSCIS00). In order to testify the influence of 2007 financial tsunami on the volatility spillover effect, the study employs the vector autoregressive model (VAR) and the bivariate GARCH model based on the BEKK parameterization. The testing period has been divided into the pre-crisis (1 April, 2003 to 31 July, 2007) and the crisis & recovery period (1 August, 2007 to 1 April, 2013). The empirical results depict that there exists bi-directional volatility spillover effect between HSI and HSCIS00 for the whole testing period. In contrast, a strong bi-directional volatility spillover effect between HSFIN and HSCIS00 is only recognized after the outbreak of the 2007 financial crisis