Veech surfaces and simple closed curves

We study the SL(2,R)-infimal lengths of simple closed curves on half-translation surfaces. Our main result is a characterization of Veech surfaces in terms of these lengths. We also revisit the "no small virtual triangles" theorem of Smillie and Weiss and establish the following dichotomy: the virtual triangle area spectrum of a half-translation surface either has a gap above zero or is dense in a neighborhood of zero. These results make use of the auxiliary polygon associated to a curve on a half-translation surface, as introduced by Tang and Webb.Comment: 12 pages. v2: added proof of continuity of infimal length functions on quadratic differential space; 16 pages, one figure; to appear in Israel J. Mat

International macroeconomic adjustment, 1987-1992 : a world model approach

In forecasting key economic indicators for the major industrial countries, the Bank's Economic Analysis and Prospects Division (IECAP) does not rely on a completely linked global macroeconomic model. This paper asks if IECAP forecasts are consistent with those produced by linked models. To answer this, Bank assumptions about exchange rates and commodity prices are introduced into three global models (OECD, Project Link, and Wharton Econometrics). Following the introduction, section 2 explains the structure of each model. Section 3begins the process of explaining and elaborating on the differences in the forecasts, through a comparison of the key assumptions used in each model. Section 4 presents a comparison of the IECAP baseline with the baseline presented by each organization. In section 5, the results of model simulations using IECAP's assumptions for exchange rates and commodity prices are discussed. In section 6, an attempt is made to explain the differences in the projection results; following this a set of alternative scenarios using each model is presented. Finally, in the last section, the main conclusions are presented.Economic Theory&Research,Environmental Economics&Policies,Economic Stabilization,Macroeconomic Management,Financial Intermediation

Why Do Proteins Look Like Proteins?

Protein structures in nature often exhibit a high degree of regularity (secondary structures, tertiary symmetries, etc.) absent in random compact conformations. We demonstrate in a simple lattice model of protein folding that structural regularities are related to high designability and evolutionary stability. We measure the designability of each compact structure by the number of sequences which can design the structure, i.e., which possess the structure as their nondegenerate ground state. We find that compact structures are drastically different in terms of their designability; highly designable structures emerge with a number of associated sequences much larger than the average. These structures are found to have ``protein like'' secondary structure and even tertiary symmetries. In addition, they are also thermodynamically more stable than ordinary structures. These results suggest that protein structures are selected because they are easy to design and stable against mutations, and that such a selection simutaneously leads to thermodynamic stability.Comment: 5 pages, 4 figures, RevTex, some minor changes from the original version, also available at http://www.neci.nj.nec.com/homepages/tang.htm

Variable Powder Flow Rate Control in Laser Metal Deposition Processes

This paper proposes a novel technique, called Variable Powder Flow Rate Control (VPFRC), for the regulation of powder flow rate in laser metal deposition processes. The idea of VPFRC is to adjust the powder flow rate to maintain a uniform powder deposition per unit length even when disturbances occur (e.g., the motion system accelerates and decelerates). Dynamic models of the powder delivery system motor and the powder transport system (i.e., five–meter pipe, powder dispenser, and cladding head) are first constructed. A general tracking controller is then designed to track variable powder flow rate references. Since the powder flow rate at the nozzle exit cannot be directly measured, it is estimated using the powder transport system model. The input to this model is the DC motor rotation speed, which is estimated on–line using a Kalman filter. Experiments are conducted to examine the performance of the proposed control methodology. The experimental results demonstrate that VPFRC is successful in maintaining a uniform track morphology, even when the motion control system accelerates and decelerates.Mechanical Engineerin