Efficient Compilation of a Class of Variational Forms

We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler (FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC.Comment: ACM Transactions on Mathematical Software 33(3), 20 pages (2007

Interim report on the ground-water resources of Manatee County, Florida

A large part of western Manatee County is devoted to the growing of winter vegetables and citrus fruits. As in most of peninsular Florida, rainfall in the county during the growing season is not sufficient for crop production and large quantites of artesian water are used for irrigation. The large withdrawals of artesian water for irrigation result in a considerable decline of the artesian head in the western part of the county. This seasonal decline of the artesian head has become larger as the withdrawal of artesian water has increased. The lowering of the fresh-water head in some coastal areas in the State has resulted in an infiltration of sea water into the water-bearing formations. The presence of salty water in the artesian aquifer in parts of the coastal area of Manatee County indicates that sea water may also have entered the waterbearing formations in this area as a result of the decline of artesian pressure during the growing season. The purpose of the investigation is to make a detailed study of the geology and ground-water resources of the county, primarily to determine whether salt-water encroachment has occurred or is likely to occur in the coastal area. (PDF contains 38 pages.

Transition from a two-dimensional superfluid to a one-dimensional Mott insulator

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.Comment: 4 pages, 4 figures. Slightly revised according to referee request

Recent evidence that TADs and chromatin loops are dynamic structures.

Mammalian genomes are folded into spatial domains, which regulate gene expression by modulating enhancer-promoter contacts. Here, we review recent studies on the structure and function of Topologically Associating Domains (TADs) and chromatin loops. We discuss how loop extrusion models can explain TAD formation and evidence that TADs are formed by the ring-shaped protein complex, cohesin, and that TAD boundaries are established by the DNA-binding protein, CTCF. We discuss our recent genomic, biochemical and single-molecule imaging studies on CTCF and cohesin, which suggest that TADs and chromatin loops are dynamic structures. We highlight complementary polymer simulation studies and Hi-C studies employing acute depletion of CTCF and cohesin, which also support such a dynamic model. We discuss the limitations of each approach and conclude that in aggregate the available evidence argues against stable loops and supports a model where TADs are dynamic structures that continually form and break throughout the cell cycle

Testing for co-integration in vector autoregressions with non-stationary volatility

Many key macro-economic and financial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with nonstationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics of Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identified inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform remarkably well in practice.Cointegration; non-stationary volatility; trace and maximum eigenvalue tests; wild bootstrap

Capacity building in economics : education and research in transition economies

The development of the institutional capacity to create and evaluate economic policies remains a critical need-and constraint-in most transition economies if they are to complete the successful passage to fully functioning market economies. To take an active role in the transition process, economic policymakers, business leaders, government officials, and others need a thorough grounding in market-based economics. This requires strengthening economics education and providing support for qualified economists to teach economics at all levels and to carry out high-quality research and policy analysis. Although the education systems in a handful of countries have already risen to the challenge, in many other transition countries, the structure of educational and research institutes remains grounded in the Communist model. This paper presents findings from a comprehensive study assessing the state of economics education and research in 24 countries in East-Central Europe and the former Soviet Union. While 20 countries were initially included because preliminary assessments showed that they lacked the capability to offer high-quality economics education, four additional countries-the Czech Republic, Hungary, Russia, and Ukraine-were included to highlight five centers of excellence that they already host. Based on the experience of these successful centers, the study's findings, and information gathered from a series of donor meetings in Berlin, New York, and Washington, D.C., this paper presents an approach to building new indigenous capacity for teaching and research on market-based economics in regions where the need is particularly critical-the Caucasus, Central Asia, and Southeast Europe.Curriculum&Instruction,Decentralization,Agricultural Knowledge&Information Systems,Teaching and Learning,Public Health Promotion,Tertiary Education,Health Monitoring&Evaluation,Agricultural Knowledge&Information Systems,Teaching and Learning,Curriculum&Instruction

Quadratic performance of generalized first-order systems

In this note we formulate the Kalman-Yakubovic-Popov lemma for generalized first-order systems, both in continuous- and discrete-tim

Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility

Many key macro-economic and ?nancial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identi?ed inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice.co-integration; non-stationary volatility; trace and maximum eigenvalue tests; wild bootstrap

Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters

We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning beam of concentrated energy. The analytical solution is written in a dimensionless form as a sum of integrals over (dimensionless) time. For the numerical computation of these integrals we suggest a quadrature scheme that utilizes pre-calculated look-up tables for the required quadrature orders. Such a scheme is efficient because the required quadrature orders are strongly dependent on the parameters in the heat flux. The possibilities of using the obtained computational technique for the control and optimization of powder bed fusion processes are discussed