Simple Analysis of Sparse, Sign-Consistent JL

Allen-Zhu, Gelashvili, Micali, and Shavit construct a sparse, sign-consistent Johnson-Lindenstrauss distribution, and prove that this distribution yields an essentially optimal dimension for the correct choice of sparsity. However, their analysis of the upper bound on the dimension and sparsity requires a complicated combinatorial graph-based argument similar to Kane and Nelson\u27s analysis of sparse JL. We present a simple, combinatorics-free analysis of sparse, sign-consistent JL that yields the same dimension and sparsity upper bounds as the original analysis. Our analysis also yields dimension/sparsity tradeoffs, which were not previously known. As with previous proofs in this area, our analysis is based on applying Markov\u27s inequality to the pth moment of an error term that can be expressed as a quadratic form of Rademacher variables. Interestingly, we show that, unlike in previous work in the area, the traditionally used Hanson-Wright bound is not strong enough to yield our desired result. Indeed, although the Hanson-Wright bound is known to be optimal for gaussian degree-2 chaos, it was already shown to be suboptimal for Rademachers. Surprisingly, we are able to show a simple moment bound for quadratic forms of Rademachers that is sufficiently tight to achieve our desired result, which given the ubiquity of moment and tail bounds in theoretical computer science, is likely to be of broader interest

(White) Tyranny and the Democratic Value of Distrust

This paper makes an argument for the democratic value of distrust. It begins by analyzing distrust, since distrust is not merely the negation of trust. The account that it develops is based primarily on Martin Luther King Jr.’s work in Why We Can’t Wait. On this view, distrust is the confident belief that another individual or group of individuals or an institution will not act justly or as justice requires. It is a narrow normative account of distrust, since it concerns a specific normative task. Distinctions between vertical and horizontal distrust, as well as trust and agnostic trust are also discussed. This paper argues that distrust’s democratic value lies in its ability to secure democracy by protecting political minorities from having their voices ignored. As such, distrust can be viewed as a kind of Madisonian “check and balance” that works to prevent tyranny. Distrust also works to secure democracy by forging new or alternative forms of democratic participation. The main example discussed in this paper is King’s involvement in the Birmingham Campaign during the Black Civil Rights movement in America. In this case, King and his supporters’ distrust of fellow White citizens and political institutions led to alternative forms of political expression such as non-violent protests, boycotts, and other forms of civil disobedience, all of which led to greater racial justice by working to alleviate White tyranny

Paying With Our Health: The Real Cost of Freight Transport in California

Examines the health costs of asthma and other illnesses, and the level of economic opportunity provided to affected communities, with the transport of goods in California. Estimates the cost of state-recommended pollution controls to transporters