International Business Cycles with Mutliple Input Investment Technologies

Backus, Kehoe, and Kydland (International Real Business Cycles, JPE, 100 (4), 1992) documented several discrepancies between the observed post-war business cycles of developed countries and the predictions of a two-country, complete-market model. The main discrepancy dubbed as the quantity anomaly, that cross-country consumption correlations are higher than that of output in the model as opposed to the data, has remained a central puzzle in international economics. The main thesis of this paper is that when the standard two-country model with traded and non-traded goods and complete ¯nancial markets, as in Stockman and Tesar (Tastes and Technology in a Two Country Model of the Business Cycles: Explaining International Comovements, 85 (1), AER, 1995) is extended to include capital goods sectors that utilize both traded and non-traded goods as intermediates, and when the non-traded aggregate is reclassi¯ed to include distribution and transportation services, the model produces the correct ordering of the cross-country correlations of consumption and output.International business cycles; Quantity anomaly; Distribution costs; Cross-country correlations.

Towards Optimal Moment Estimation in Streaming and Distributed Models

One of the oldest problems in the data stream model is to approximate the p-th moment ||X||_p^p = sum_{i=1}^n X_i^p of an underlying non-negative vector X in R^n, which is presented as a sequence of poly(n) updates to its coordinates. Of particular interest is when p in (0,2]. Although a tight space bound of Theta(epsilon^-2 log n) bits is known for this problem when both positive and negative updates are allowed, surprisingly there is still a gap in the space complexity of this problem when all updates are positive. Specifically, the upper bound is O(epsilon^-2 log n) bits, while the lower bound is only Omega(epsilon^-2 + log n) bits. Recently, an upper bound of O~(epsilon^-2 + log n) bits was obtained under the assumption that the updates arrive in a random order. We show that for p in (0, 1], the random order assumption is not needed. Namely, we give an upper bound for worst-case streams of O~(epsilon^-2 + log n) bits for estimating |X |_p^p. Our techniques also give new upper bounds for estimating the empirical entropy in a stream. On the other hand, we show that for p in (1,2], in the natural coordinator and blackboard distributed communication topologies, there is an O~(epsilon^-2) bit max-communication upper bound based on a randomized rounding scheme. Our protocols also give rise to protocols for heavy hitters and approximate matrix product. We generalize our results to arbitrary communication topologies G, obtaining an O~(epsilon^2 log d) max-communication upper bound, where d is the diameter of G. Interestingly, our upper bound rules out natural communication complexity-based approaches for proving an Omega(epsilon^-2 log n) bit lower bound for p in (1,2] for streaming algorithms. In particular, any such lower bound must come from a topology with large diameter

Mechanics-Based Modeling Approach for Rapid Prediction of Low Velocity Impact Damage in Composite Laminates

A mechanics-based modeling approach is developed to rapidly predict damage in polymer matrix composites resulting from a low velocity impact event. The approach is incorporated into a computer code that provides an efficient means to assess the damage resistance for a range of material systems, layup configurations, and impact scenarios. It is envisioned that the developed approach will aid in early design and analysis of composite structures where sizing and layup decisions must be made, and evaluating the feasibility of a large number of laminate configurations using numerical approaches such as finite element analysis (FEA) is prohibitively expensive. Therefore, the goal of the modeling approach is to predict the impact damage size given the laminate configuration and impact scenario. This information can then be used to determine the residual strength of the material. To be useful in such a context, the tool is designed to run quickly (<2 minutes) to allow a large number of design cases to be investigated. The results presented demonstrate that the model is capable of efficiently predicting low velocity impact damage size, shape, and location within an acceptable accuracy suitable for preliminary design and analysis of composite structures