Iterative Row Sampling

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which allows one to solve a poly(d) sized problem instead. In practice, the best performances are often obtained by invoking these routines in an iterative fashion. We show these iterative methods can be adapted to give theoretical guarantees comparable and better than the current state of the art. Our approaches are based on computing the importances of the rows, known as leverage scores, in an iterative manner. We show that alternating between computing a short matrix estimate and finding more accurate approximate leverage scores leads to a series of geometrically smaller instances. This gives an algorithm that runs in $O(nnz(A) + d^{\omega + \theta} \epsilon^{-2})$ time for any $\theta > 0$, where the $d^{\omega + \theta}$ term is comparable to the cost of solving a regression problem on the small approximation. Our results are built upon the close connection between randomized matrix algorithms, iterative methods, and graph sparsification.Comment: 26 pages, 2 figure

Goodness-of-fit tests for a heavy tailed distribution

For testing whether a distribution function is heavy tailed, we study theKolmogorov test, Berk-Jones test, score test and their integratedversions. A comparison is conducted via Bahadur efficiency and simulations.The score test and the integrated score test show the best performance.Although the Berk-Jones test is more powerful than the Kolmogorov-Smirnovtest, this does not hold true for their integrated versions; this differsfrom results in \\citet{EinmahlMckeague2003}, which shows the difference ofBerk-Jones test in testing distributions and tails.Bahadur efficiency;heavy tail;tail index

Crystal Growth in Fluid Flow: Nonlinear Response Effects

We investigate crystal-growth kinetics in the presence of strong shear flow in the liquid, using molecular-dynamics simulations of a binary-alloy model. Close to the equilibrium melting point, shear flow always suppresses the growth of the crystal-liquid interface. For lower temperatures, we find that the growth velocity of the crystal depends non-monotonically on the shear rate. Slow enough flow enhances the crystal growth, due to an increased particle mobility in the liquid. Stronger flow causes a growth regime that is nearly temperature-independent, in striking contrast to what one expects from the thermodynamic and equilibrium kinetic properties of the system, which both depend strongly on temperature. We rationalize these effects of flow on crystal growth as resulting from the nonlinear response of the fluid to strong shearing forces.Comment: to appear in Phys. Rev. Material

An Economic Analysis of the Impacts of Trade Liberalization on Asian Dairy Market

The objective of this paper is to develop an economic analysis of the impacts of further trade liberalization on Asian dairy markets. In order to achieve this, we first make a review of Asian dairy policies from the perspective of domestic support, market access and export subsidy. Then a world dairy model is employed, which reflects both vertical and spatial characteristics of the world dairy sector. We analyze the separate and combined impacts of eliminating Japan's domestic dairy subsidy, removing other Asian countries dairy trade policies excluding Japan, eliminating all Asian countries domestic dairy and trade policies, and multilateral dairy trade liberalization around the world. We find that Japan and Korea's producers will suffer much bigger losses from trade liberalization than other countries in the region; Japan and Korea's producers get much more protection from trade distortions than from domestic subsidy; India is a potential competitive exporter in Asia and the world; China is a potential importer in Asia but a potential competitive exporter in the world; South East Asia and other South Asian countries are potential importers in Asia and the world; greater trade liberalization around the world will help to increase exports for potential exporters and/or ease importing pressure for potential importers; the order of competitiveness of Asian economies from least competitive to most competitive is Japan, Korea, South East Asia, other South Asia, China and India; China and India consumers will lose from world trade liberalization, but the other countries consumer surplus will increase.

Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained

Dilepton Production at Fermilab and RHIC

Some recent results from several fixed-target dimuon production experiments at Fermilab are presented. In particular, we discuss the use of Drell-Yan data to determine the flavor structure of the nucleon sea, as well as to deduce the energy-loss of partons traversing nuclear medium. Future dilepton experiments at RHIC could shed more light on the flavor asymmetry and possible charge-symmetry-violation of the nucleon sea. Clear evidence for scaling violation in the Drell-Yan process could also be revealed at RHIC.Comment: 5 pages, talk presented at the RIKEN-BNL Workshop on 'Hard Parton Physics in Nucleus-Nucleus collisions, March 199