Approximating Data with weighted smoothing Splines

Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i, f_n(t_i)), i=1,..., n. If a data set exhibits large variations in local behaviour, for example large peaks as in spectroscopy data, then the method must be able to adapt to the local changes in smoothness. Whilst many methods are able to accomplish this they are less successful at adapting derivatives. In this paper we show how the goal of local adaptivity of the function and its first and second derivatives can be attained in a simple manner using weighted smoothing splines. A residual based concept of approximation is used which forces local adaptivity of the regression function together with a global regularization which makes the function as smooth as possible subject to the approximation constraints

A three dimensional finite element model of wind effects upon higher harmonics of the internal tide.

A non-linear three dimensional unstructured grid model of the M2 tide in the shelf edge area off the west coast of Scotland is used to examine the spatial distribution of the M2 internal tide and its higher harmonics in the region. In addition the spatial variability of the tidally induced turbulent kinetic energy and associated mixing in the area are considered. Initial calculations involve only tidal forcing, although subsequent calculations are performed with up-welling and down-welling favourable winds in order to examine how these influence the tidal distribution (particularly the higher harmonics) and mixing in the region. Both short and long duration winds are used in these calculations. Tidal calculations show that there is significant small scale spatial variability particularly in the higher harmonics of the internal tide in the region. In addition turbulence energy and mixing exhibit appreciable spatial variability in regions of rapidly changing topography, with increased mixing occurring above seamounts. Wind effects significantly change the distribution of the M2 internal tide and its higher harmonics, with appreciable differences found between up- and down-welling winds, and long and short duration winds due to differences in mixing and the presence of wind induced flows. The implications for model validation, particularly in terms of energy transfer to higher harmonics, and mixing are briefly discussed

Infrared diode laser spectroscopy of the fundamental band of NF(a1Δ)

Thirty-one lines of the fundamental vibration–rotation band of the NF free radical in its a 1 state have been detected in absorption near 8.6 µm using a tunable infrared diode laser. Linewidths were Doppler limited and several transitions were accompanied by resolved hyperfine structure due to fluorine and nitrogen nuclear moments. Wave number calibration using accurately determined N2O lines yielded v0 = 1165.952±0.001 cm^−1 for the band center. Rotational and centrifugal distortion constants for both v = 0 and 1 states have also been determined

Nonparametric Regression, Confidence Regions and Regularization

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in that region where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest non-asymptotic confidence bounds which are less informative but conceptually much simpler

A case study of HF radar spectral width in the post midnight magnetic local time sector and its relationship to the polar cap boundary

International audienceThe aim of this paper is to advance the current understanding of the spectral width parameter observed by coherent high frequency (HF) radars. In particular, we address the relationship of a frequently observed gradient, between low ( 200 m/s) spectral width, to magnetospheric boundaries. Previous work has linked this gradient in the spectral width, in the nightside sector of magnetic local time, to the Polar Cap Boundary (PCB), and also to the boundary between the Central Plasma Sheet (CPS) and the Plasma Sheet Boundary Layer (PSBL). The present case study investigates the former by comparison with the 630.0 nm optical emission. No suitable data were available to test the second of the two hypotheses. It is found that during the interval in question the spectral width gradient is within the region of the 630.0 nm optical emission. A comparison of coherent and incoherent scatter radar data is also conducted, which indicates that values of high spectral width are typically collocated with elevated F-region electron temperatures. We conclude that the high spectral width region in the interval under study is associated with particle precipitation and also that the spectral width gradient is not a reliable method for locating the PCB

Modelling failure mechanisms of soft cliff profiles

A large proportion of the 11,000 km coastline of the United Kingdom is backed by soft cliffs. These cliffs are subject to frequent slumping and landslip events, particularly where sea and ground water percolates into the soil and rock. Many of these cliffs are formed from glaciogenic sediments, which experience severe erosion and rapid recession with long-term horizontal recession rates typically up to 2-3 m/year. A series of scaled physical model tests have been conducted using a large centrifuge facility with two-dimensional cliff models. These were tested in a wave flume container located on the centrifuge. Wave loading was created using a quasi-flap paddle system that was located at the opposite end of the centrifuge box. A number of tests were conducted using different cliff materials (i.e. combinations of sand and Portland cement). A parametric study was carried out to assess the influence of variations in cliff geometry and height, soil properties, wave amplitude and period. From these tests, it has been found that generally, failures occurred by progressive undercutting of the cliff toe, followed by global failure of the cliff mass

Shifts in hexapod diversification and what Haldane could have said

Data on species richness and taxon age are assembled for the extant hexapod orders (insects and their six-legged relatives). Coupled with estimates of phylogenetic relatedness, and simple statistical null models, these data are used to locate where, on the hexapod tree, significant changes in the rate of cladogenesis (speciation-minus-extinction rate) have occurred. Significant differences are found between many successive pairs of sister taxa near the base of the hexapod tree, all of which are attributable to a shift in diversification rate after the origin of the Neoptera (insects with wing flexion) and before the origin of the Holometabola (insects with complete metamorphosis). No other shifts are identifiable amongst supraordinal taxa. Whilst the Coleoptera have probably diversified faster than either of their putative sister lineages, they do not stand out relative to other closely related clades. These results suggest that any Creator had a fondness for a much more inclusive clade than the Coleoptera, definitely as large as the Eumetabola (Holometabola plus bugs and their relatives), and possibly as large as the entire Neoptera. Simultaneous, hence probable causative events are discussed, of which the origin of wing flexion has been the focus of much attention

The D234 action for light quarks

We investigate a new light fermion action (the ``D234'' action), which is accurate up to \O(a^3) and tadpole-improved \O(a \alpha_s) errors. Using D234 with Symanzik- and tadpole-improved glue we find evidence that continuum results for the quenched hadron spectrum (pion, rho and nucleon) can be obtained on coarse lattices.Comment: Latex, 4 pages, submitted to Lattice '95 proceeding