Probabilistic formulation of inverse problems leads to the definition of a probability distribution in the model space. This probability distribution combines a priori information with new information obtained by measuring some observable parameters (data). As, in the general case, the theory linking data with model parameters is nonlinear, the a posteriori probability in the model space may not be easy to describe (it may be multimodal, some moments may not be defined, etc.). When analyzing an inverse problem, obtaining a maximum likelihood model is usually not sufficient, as we normally also wish to have information on the resolution power of the data. In the general case we may have a large number of model parameters, and an inspection of the marginal probability densities of interest may be impractical, or even useless. But it is possible to pseudorandomly generate a large collection of models according to the posterior probability distribution and to analyze and display the models in such a way that information on the relative likelihoods of model properties is conveyed to the spectator. This can be accomplished by means of an efficient Monte Carlo method, even in cases where no explicit formula for the a priori distribution is available. The most well known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possibly highly nonlinear) inverse problems with complex a priori information and data with an arbitrary noise distribution.

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I investigate the determinants of business cycles synchronization, across regions and over time. I use both international and intranational data to evaluate the linkages between trade in goods, trade in financial assets, specialization and business cycles synchronization in the context of a system of simultaneous equations. In all specifications, the results are as follows. (i) Simultaneity is important, as both trade and financial openness have a direct and an indirect effect on cycles synchronization. (ii) Countries with liberalized capital accounts (and States with high degree of risk sharing) are significantly more synchronized, even though they are also more specialized. (iii) Specialization patterns have a sizeable effect on business cycles, above and beyond their reflection of intra-industry trade and of openness to goods and assets trade. (iv) The role of trade, in turn, is in line with existing models once intra-industry trade is controlled for. Furthermore, trade-induced specialization has virtually no effect on cycles synchronization. The results obtain in a variety of cross-sections and panels. They relate to a recent strand of International Business Cycles models with incomplete markets and transport costs, and on the empirical side, point to an important omission in the list of criteria defining an Optimal Currency Area, namely specialization patterns.

Many tasks in software engineering can be characterized as source to source transformations. Design recovery, software restructuring, forward engineering, language translation, platform migration and code reuse can all be understood as transformations from one source text to another. TXL, the Tree Transformation Language, is a programming language and rapid prototyping system specifically designed to support rulebased source to source transformation. Originally conceived as a tool for exploring programming language dialects, TXL has evolved into a general purpose source transformation system that has proven well suited to a wide range of software maintenance and reengineering tasks, including the design recovery, analysis and automated reprogramming of billions of lines of commercial Cobol, PL/I and RPG code for the Year 2000. In this paper we introduce the basic features of modern TXL and its use in a range of software engineering applications, with an emphasis on how each task can be achieved by source transformation.

INTRODUCTION People in countries like the United States are richer by a factor of about 10 or 20 than people a century or two ago. Whereas U.S. per capita income today is $33,000, conventional estimates put it at $1800 in 1850. Yet even this difference likely understates the enormous increase in standards of living over this period. Consider the quality of life of the typical American in the year 1850. Life expectancy at birth was a scant 40 years, just over half of what it is today. Refrigeration, electric lights, telephones, antibiotics, automobiles, skyscrapers, and air conditioning did not exist, much less * This is a draft of a chapter for the Handbook of Economic Growth. I am grateful to Philippe Aghion and Paul Romer for helpful comments, and to the National Science Foundation for research support. the more sophisticated technologies that impact our lives daily in the 21st century. Perhaps the central question of the literature on economic growth is "Why is there growth at

A theory of data types and a programming language based on category theory are presented. Data types play a crucial role in programming. They enable us to write programs easily and elegantly. Various programming languages have been developed, each of which may use different kinds of data types. Therefore, it becomes important to organize data types systematically so that we can understand the relationship between one data type and another and investigate future directions which lead us to discover exciting new data types. There have been several approaches to systematically organize data types: algebraic specification methods using algebras, domain theory using complete partially ordered sets and type theory using the connection between logics and data types. Here, we use category theory. Category theory has proved to be remarkably good at revealing the nature of mathematical objects, and we use it to understand the true nature of data types in programming.

This paper describes the history of Haskell, including its genesis and principles, technical contributions, implementations and tools, and applications and impact. 1.

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Fluctuations in GDP are more synchronized internationally than ßuctuations in Consumption, and they remain so even between Þnancially integrated economies, where the ranking should in theory be the reverse. This paper shows this happens because correlations in GDP ßuctuations rise with Þnancial integration. Finance serves to increase international correlations in both consumption and GDP ßuc-tuations, which explains the persistent gap between the two in the data. The positive association between Þnancial integration and GDP correlation consti-tutes a puzzle, as theory suggests a negative relation if anything. Nevertheless, it prevails in the data even after the effects of Þnance on trade and specialization are accounted for.