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

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

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

Approximating data (Approximating data and statistical procedures

Stochastic models approximate data and are not true representations of the same. Statistical procedure make use of approximate stochastic models to facilitate the analysis of data. --

The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra

The granular silo is one of the many interesting illustrations of the thixotropic property of granular matter: a rapid flow develops at the outlet, propagating upwards through a dense shear flow while material at the bottom corners of the container remains static. For large enough outlets, the discharge flow is continuous; however, by contrast with the clepsydra for which the flow velocity depends on the height of fluid left in the container, the discharge rate of granular silos is constant. Implementing a plastic rheology in a 2D Navier-Stokes solver (following the mu(I)-rheology or a constant friction), we simulate the continuum counterpart of the granular silo. Doing so, we obtain a constant flow rate during the discharge and recover the Beverloo scaling independently of the initial filling height of the silo. We show that lowering the value of the coefficient of friction leads to a transition toward a different behavior, similar to that of a viscous fluid, and where the filling height becomes active in the discharge process. The pressure field shows that large enough values of the coefficient of friction ($\simeq$ 0.3) allow for a low-pressure cavity to form above the outlet, and can thus explain the Beverloo scaling. In conclusion, the difference between the discharge of a hourglass and a clepsydra seems to reside in the existence or not of a plastic yield stress.Comment: 6 pages, 6 figure

NGC 4254: An Act of Harassment Uncovered by the Arecibo Legacy Fast ALFA Survey

We present an HI map constructed from the Arecibo Legacy Fast ALFA (ALFALFA) survey of the surroundings of the strongly asymmetric Virgo cluster Sc galaxy NGC 4254. Noted previously for its lopsided appearance, rich interstellar medium, and extradisk HI emission, NGC 4254 is believed to be entering the Virgo environment for the first time and at high speed. The ALFALFA map clearly shows a long HI tail extending ~250 kpc northward from the galaxy. Embedded as one condensation within this HI structure is the object previously identified as a "dark galaxy": Virgo HI21 (Davies et al. 2004). A body of evidence including its location within and velocity with respect to the cluster and the appearance and kinematics of its strong spiral pattern, extra-disk HI and lengthy HI tail is consistent with a picture of "galaxy harassment" as proposed by Moore et al. (1996a,b; 1998). The smoothly varying radial velocity field along the tail as it emerges from NGC 4254 can be used as a timing tool, if interpreted as resulting from the coupling of the rotation of the disk and the collective gravitational forces associated with the harassment mechanism.Comment: accepted for publication in Ap.J.(Lett.). higher resolution figure available at http://egg.astro.cornell.edu/alfalfa/pubs/figs/n4254_f1.ep

Conceptual design of an airborne laser Doppler velocimeter system for studying wind fields associated with severe local storms

An airborne laser Doppler velocimeter was evaluated for diagnostics of the wind field associated with an isolated severe thunderstorm. Two scanning configurations were identified, one a long-range (out to 10-20 km) roughly horizontal plane mode intended to allow probing of the velocity field around the storm at the higher altitudes (4-10 km). The other is a shorter range (out to 1-3 km) mode in which a vertical or horizontal plane is scanned for velocity (and possibly turbulence), and is intended for diagnostics of the lower altitude region below the storm and in the out-flow region. It was concluded that aircraft flight velocities are high enough and severe storm lifetimes are long enough that a single airborne Doppler system, operating at a range of less than about 20 km, can view the storm area from two or more different aspects before the storm characteristics change appreciably

Massless interacting particles

We show that classical electrodynamics of massless charged particles and the Yang--Mills theory of massless quarks do not experience rearranging their initial degrees of freedom into dressed particles and radiation. Massless particles do not radiate. We consider a version of the direct interparticle action theory for these systems following the general strategy of Wheeler and Feynman.Comment: LaTeX; 20 pages; V4: discussion is slightly modified to clarify some important points, relevant references are adde