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.

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

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

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

Co-integration rank tests under conditional heteroskedasticity

In this paper we analyse the properties of the conventional Gaussian-based co-integrating rank tests of Johansen (1996) in the case where the vector of series under test is driven by possibly non-stationary, conditionally heteroskedastic (martingale difference) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either i.i.d. or stationary martingale difference innovations. We then propose wild bootstrap implementations of the co-integrating rank tests and demonstrate that the associated bootstrap rank statistics replicate the first- order asymptotic null distributions of the rank statistics. We show that the same is also true of the corresponding rank tests based on the i.i.d. bootstrap of Swensen (2006). The wild bootstrap, however, has the important property that, unlike the i.i.d. bootstrap, it preserves in the re-sampled data the pattern of heteroskedasticity present in the original shocks. Consistent with this, numerical evidence suggests that, relative to tests based on the asymptotic critical values or the i.i.d. bootstrap, the wild bootstrap rank tests perform very well in small samples under a variety of conditionally heteroskedastic innovation processes. An empirical application to the term structure of interest rates is also given.Co-integration; trace and maximum eigenvalue rank tests; conditional heteroskedasticity; IID bootstrap; wild bootstrap

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