Multidimensional Cooley–Tukey Algorithms Revisited

AbstractThe representation theory of Abelian groups is used to obtain an algebraic divide-and-conquer algorithm for computing the finite Fourier transform. The algorithm computes the Fourier transform of a finite Abelian group in terms of the Fourier transforms of an arbitrary subgroup and its quotient. From this algebraic algorithm a procedure is derived for obtaining concrete factorizations of the Fourier transform matrix in terms of smaller Fourier transform matrices, diagonal multiplications, and permutations. For cyclic groups this gives as special cases the Cooley–Tukey and Good–Thomas algorithms. For groups with several generators, the procedure gives a variety of multidimensional Cooley–Tukey type algorithms. This method of designing multidimensional fast Fourier transform algorithms gives different data flow patterns from the standard “row–column” approaches. We present some experimental evidence that suggests that in hierarchical memory environments these data flows are more efficient

A rigorous evaluation of crossover and mutation in genetic programming

The role of crossover and mutation in Genetic Programming (GP) has been the subject of much debate since the emergence of the field. In this paper, we contribute new empirical evidence to this argument using a rigorous and principled experimental method applied to six problems common in the GP literature. The approach tunes the algorithm parameters to enable a fair and objective comparison of two different GP algorithms, the first using a combination of crossover and reproduction, and secondly using a combination of mutation and reproduction. We find that crossover does not significantly outperform mutation on most of the problems examined. In addition, we demonstrate that the use of a straightforward Design of Experiments methodology is effective at tuning GP algorithm parameters

Eigenvalues of p-summing and lp-type operators in Banach spaces

AbstractThis paper is a study of the distribution of eigenvalues of various classes of operators. In Section 1 we prove that the eigenvalues (λn(T)) of a p-absolutely summing operator, p ⩾ 2, satisfy ∑n∈N|λn(T)|p1p⩽πp(T). This solves a problem of A. Pietsch. We give applications of this to integral operators in Lp-spaces, weakly singular operators, and matrix inequalities.In Section 2 we introduce the quasinormed ideal Π2(n), P = (p1, …, pn) and show that for T ∈ Π2(n), 2 = (2, …, 2) ∈ Nn, the eigenvalues of T satisfy ∑i∈N|λi(T)|2nn2⩽πn2(T). More generally, we show that for T ∈ Πp(n), P = (p1, …, pn), pi ⩾ 2, the eigenvalues are absolutely p-summable, 1p=∑i=1n1pi and ∑n∈N|λn(T)|p1p⩽CpπnP(T).We also consider the distribution of eigenvalues of p-nuclear operators on Lr-spaces.In Section 3 we prove the Banach space analog of the classical Weyl inequality, namely ∑n∈N|λn(T)|p ⩽ Cp∑n∈N αn(T)p, 0 < p < ∞, where αn denotes the Kolmogoroff, Gelfand of approximation numbers of the operator T. This solves a problem of Markus-Macaev.Finally we prove that Hilbert space is (isomorphically) the only Banach space X with the property that nuclear operators on X have absolutely summable eigenvalues. Using this result we show that if the nuclear operators on X are of type l1 then X must be a Hilbert space

Relativistic many-body calculations of energies of n=3 states in aluminumlike ions

Energies of 3l3l′3l″ states of aluminumlike ions with Z=14?100 are evaluated to second order in relativistic many-body perturbation theory starting from a 1s22s22p6 Dirac-Fock potential. Intrinsic three-particle contributions to the energy are included in the present calculation and found to contribute about 10?20 % of the total second-order energy. Corrections for the frequency-dependent Breit interaction and the Lamb shift are included in lowest order. A detailed discussion of contributions to the energy levels is given for aluminumlike germanium (Z=32). Comparisons are made with available experimental data. We obtain excellent agreement for term splitting, even for low-Z ions. These calculations are presented as a theoretical benchmark for comparison with experiment and theory

Scenario adjustment in stated preference research

AbstractPoorly designed stated preference (SP) studies are subject to a number of well-known biases, but many of these biases can be minimized when they are anticipated ex ante and accommodated in the study's design or during data analysis. We identify another source of potential bias, which we call “scenario adjustment,” where respondents assume that the substantive alternative(s) in an SP choice set, in their own particular case, will be different from what the survey instrument describes. We use an existing survey, developed to ascertain willingness to pay for private health-risk reduction programs, to demonstrate a strategy to control and correct for scenario adjustment in the estimation of willingness to pay. This strategy involves data from carefully worded follow-up questions, and ex post econometric controls, for each respondent's subjective departures from the intended choice scenario. Our research has important implications for the design of future SP surveys

Shikimate pathway in apicomplexan parasites

No abstract available

Constraining the role of early land plants in Palaeozoic weathering and global cooling

How the colonization of terrestrial environments by early land plants over 400 Ma influenced rock weathering, the biogeochemical cycling of carbon and phosphorus, and climate in the Palaeozoic is uncertain. Here we show experimentally that mineral weathering by liverworts—an extant lineage of early land plants—partnering arbuscular mycorrhizal (AM) fungi, like those in 410 Ma-old early land plant fossils, amplified calcium weathering from basalt grains threefold to sevenfold, relative to plant-free controls. Phosphate weathering by mycorrhizal liverworts was amplified 9–13-fold over plant-free controls, compared with fivefold to sevenfold amplification by liverworts lacking fungal symbionts. Etching and trenching of phyllosilicate minerals increased with AM fungal network size and atmospheric CO2 concentration. Integration of grain-scale weathering rates over the depths of liverwort rhizoids and mycelia (0.1 m), or tree roots and mycelia (0.75 m), indicate early land plants with shallow anchorage systems were probably at least 10-fold less effective at enhancing the total weathering flux than later-evolving trees. This work challenges the suggestion that early land plants significantly enhanced total weathering and land-to-ocean fluxes of calcium and phosphorus, which have been proposed as a trigger for transient dramatic atmospheric CO2 sequestration and glaciations in the Ordovician