Editor's Note: These short, critical reviews of recent papers in the Journal, written exclusively by graduate students or postdoctoral fellows, are intended to summarize the important findings of the paper and provide additional insight and commentary. For more information on the format and purpose of the Journal Club, please see Review of Cappelletti et al. The most basic form of numerical cog...

Running a recursive algorithm on this expression still gives an exponential worst-case running time. Additionally, there is no hope to only explore a local neighborhood of a single vertex u with this recurrence to run an approximate calculation, because the quantity q̆S in some sense indeed depends on all of S. As in the proof of Shearer’s Lemma, however, we can rearrange the recurrence to obtai...

In this paper we consider a weighted harmonic mean of two inconsistent estimators to propose a new estimator of the coefficient of a linear regression model with measurement errors. The proposed estimator is simple and it does not depend on any unknown quantity. The approximate bias and MSE of the estimator are derived. Further, an empirical application is also presented. c © 2001 Peking Univer...

This paper points out that real GDP statisics respond differently to sector-specific demand and supply shocks for the exactly same changes in physical quantities. The paper illustrates how this property arises from the theoretical quantity aggregates that real GDP is designed to approximate. The paper also presents an application to US data suggesting that these factors have contributed signifi...

Exact arithmetic abilities require symbolic numerals, which constitute a precise representation of quantities, such as the Arabic digits. Numerical thinking, however, also engages an intuitive non-linguistic number sense, Approximate Number System (ANS). The ANS allows us to discriminate approximate transformations, and estimate all without counting ...

Constrained efficient provision of an excludable public good is studied in a model where preferences are private information. The provision level is asymptotically deterministic, making it possible to approximate the optimal mechanism with a mechanism that provides a fixed quantity of the good and charges fixed user fees for access. In general, the fixed fees involve third degree price discrimi...

We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimension is large or infinite. Some applications to principal component analysis a...

Abstract. Let X1, X2, . . . , Xn be a sequence of independent random variables, let M be a rearrangement invariant space on the underlying probability space, and let N be a symmetric sequence space. This paper gives an approximate formula for the quantity ‖‖(Xi)‖N‖M whenever Lq embeds into M for some 1 ≤ q < ∞. This extends work of Johnson and Schechtman who tackled the case when N = lp, and re...

This work provides exponential tail inequalities for sums of random matrices that depend only on intrinsic dimensions rather than explicit matrix dimensions. These tail inequalities are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the explicit dimensions are large...

The detection of motion from image sequences is usually performed using a time differential method or calculating the difference from a background reference image. These algorithms often perform poorly in the presence of temporal clutter. This paper describes a technique that measures the irregularity of an intensity sequence to detect motion. We demonstrate that static background, interesting ...