Is there an S-curve relationship between U.S. trade balance and terms of trade? An analysis across industries and countries

A key relationship in international economics is that between trade flows and exchange rates. This paper examines the empirical evidence of S-curve relationship between U.S. trade balance and terms of trade both at the aggregated and disaggregated level from 1989Q1 to 2010Q4. I find evidence of an S-curve for U.S. total trade in all goods and services with the rest of the world, as well as that for overall manufacturing and non-manufacturing categories. I further examine the top 20 industries at the SITC 3-digit level, and find evidence of an S-curve in 15 industries. Finally, the relationship is explored with the major trading partners in each of these twenty industries, also yielding positive evidence for several nations.S-curve, trade balance, terms-of-trade, real exchange rates

Streaming Verification of Graph Computations via Graph Structure

We give new algorithms in the annotated data streaming setting - also known as verifiable data stream computation - for certain graph problems. This setting is meant to model outsourced computation, where a space-bounded verifier limited to sequential data access seeks to overcome its computational limitations by engaging a powerful prover, without needing to trust the prover. As is well established, several problems that admit no sublinear-space algorithms under traditional streaming do allow protocols using a sublinear amount of prover/verifier communication and sublinear-space verification. We give algorithms for many well-studied graph problems including triangle counting, its generalization to subgraph counting, maximum matching, problems about the existence (or not) of short paths, finding the shortest path between two vertices, and testing for an independent set. While some of these problems have been studied before, our results achieve new tradeoffs between space and communication costs that were hitherto unknown. In particular, two of our results disprove explicit conjectures of Thaler (ICALP, 2016) by giving triangle counting and maximum matching algorithms for n-vertex graphs, using o(n) space and o(n^2) communication

Integral points on Markoff type cubic surfaces

For integers $k$, we consider the affine cubic surface $V_{k}$ given by $M({\bf x})=x_{1}^2 + x_{2}^2 +x_{3}^2 -x_{1}x_{2}x_{3}=k$. We show that for almost all $k$ the Hasse Principle holds, namely that $V_{k}(\mathbb{Z})$ is non-empty if $V_{k}(\mathbb{Z}_p)$ is non-empty for all primes $p$, and that there are infinitely many $k$'s for which it fails. The Markoff morphisms act on $V_{k}(\mathbb{Z})$ with finitely many orbits and a numerical study points to some basic conjectures about these "class numbers" and Hasse failures. Some of the analysis may be extended to less special affine cubic surfaces.Comment: 57 pages, many figures, revised Introduction, Sec. 5 and Appendi

S-DUALITY AND THE ENTROPY OF BLACK HOLES IN HETEROTIC STRING THEORY

Four dimensional heterotic string effective action is known to admit non-rotating electrically and magnetically charged black hole solutions. It is shown that the partition functions and entropies in both the cases are identical when these black hole solutions are related by S-duality transformations. The entropy is computed and is vanishing for each black hole in the extremal limit.Comment: 13 pages, REVTE

Real zeros of holomorphic Hecke cusp forms

This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity