Approximate Capacities of Two-Dimensional Codes by Spatial Mixing

We apply several state-of-the-art techniques developed in recent advances of counting algorithms and statistical physics to study the spatial mixing property of the two-dimensional codes arising from local hard (independent set) constraints, including: hard-square, hard-hexagon, read/write isolated memory (RWIM), and non-attacking kings (NAK). For these constraints, the strong spatial mixing would imply the existence of polynomial-time approximation scheme (PTAS) for computing the capacity. It was previously known for the hard-square constraint the existence of strong spatial mixing and PTAS. We show the existence of strong spatial mixing for hard-hexagon and RWIM constraints by establishing the strong spatial mixing along self-avoiding walks, and consequently we give PTAS for computing the capacities of these codes. We also show that for the NAK constraint, the strong spatial mixing does not hold along self-avoiding walks

Pulsar Timing Probes of Primordial Black Holes and Subhalos

Pulsars act as accurate clocks, sensitive to gravitational redshift and acceleration induced by transiting clumps of matter. We study the sensitivity of pulsar timing arrays (PTAs) to single transiting compact objects, focusing on primordial black holes and compact subhalos in the mass range from $10^{-12} M _{\odot}$ to well above $100~M_\odot$. We find that the Square Kilometer Array can constrain such objects to be a subdominant component of the dark matter over this entire mass range, with sensitivity to a dark matter sub-component reaching the sub-percent level over significant parts of this range. We also find that PTAs offer an opportunity to probe substantially less dense objects than lensing because of the large effective radius over which such objects can be observed, and we quantify the subhalo concentration parameters which can be constrained.Comment: 18 pages, 6 figure

Challenges and Opportunities for Trade and Financial Integration in Asia and the Pacific

The aim of this chapter is to explore whether there are principles that can be brought to bear in negotiating the services and investment provisions of trade agreements, and which can help to ensure that the partial reforms achieved under those agreements add to, rather than detract from economic well-being. These principles might be seen as the services and investment equivalents of the "top-down" principle for tariff reform. It is not intended to go as far as developing a negotiating modality for services or investment, as that would be premature. However, the principles developed here could be used by individual countries on a voluntary basis when undertaking negotiations in services and investment.negotiate, service, investment, trade agreement, tariff reform, liberalization