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

Probing the Low Surface Brightness Dwarf Galaxy Population of the Virgo Cluster

We have used public data from the Next Generation Virgo Survey (NGVS) to investigate the dwarf galaxy population of the Virgo cluster beyond what has previously been discovered. We initially mask and smooth the data, and then use the object detection algorithm Sextractor to make our initial dwarf galaxy selection. All candidates are then visually inspected to remove artefacts and duplicates. We derive Sextractor parameters to best select low surface brightness galaxies using g band central surface brightness values of 22.5 to 26.0 mag sq arc sec and exponential scale lengths of 3.0 - 10.0 arc sec to identify 443 cluster dwarf galaxies - 303 of which are new detections. These new detections have a surface density that decreases with radius from the cluster centre. We also apply our selection algorithm to 'background', non-cluster, fields and find zero detections. In combination, this leads us to believe that we have isolated a cluster dwarf galaxy population. The range of objects we are able to detect is limited because smaller scale sized galaxies are confused with the background, while larger galaxies are split into numerous smaller objects by the detection algorithm. Using data from previous surveys combined with our data, we find a faint end slope to the luminosity function of -1.35+/-0.03, which does not significantly differ to what has previously been found for the Virgo cluster, but is a little steeper than the slope for field galaxies. There is no evidence for a faint end slope steep enough to correspond with galaxy formation models, unless those models invoke either strong feedback processes or use warm dark matter.Comment: Accepted for publication in MNRA

Parametric dictionary design for sparse coding

Abstract—This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions, e.g. [1], [2]. A problem in using these parametric dictionaries is how to choose the parameters. In practice these parameters have been chosen by an expert or through a set of experiments. In the sparse approximation context, it has been shown that an incoherent dictionary is appropriate for the sparse approximation methods. In this paper we first characterize the dictionary design problem, subject to a constraint on the dictionary. Then we briefly explain that equiangular tight frames have minimum coherence. The complexity of the problem does not allow it to be solved exactly. We introduce a practical method to approximately solve it. Some experiments show the advantages one gets by using these dictionaries

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

Interference between postural control and mental task performance in patients with vestibular disorder and healthy controls

OBJECTIVES - To determine whether interference between postural control and mental task performance in patients with balance system impairment and healthy subjects is due to general capacity limitations, motor control interference, competition for spatial processing resources, or a combination of these.METHOD - Postural stability was assessed in 48 patients with vestibular disorder and 24 healthy controls while they were standing with eyes closed on (a) a stable and (b) a moving platform. Mental task performance was measured by accuracy and reaction time on mental tasks, comprising high and low load, spatial and non-spatial tasks. Interference between balancing and performing mental tasks was assessed by comparing baseline (single task) levels of sway and mental task performance with levels while concurrently balancing and carrying out mental tasks.RESULTS - As the balancing task increased in difficulty, reaction times on both low load mental tasks grew progressively longer and accuracy on both high load tasks declined in patients and controls. Postural sway was essentially unaffected by mental activity in patients and controls.CONCLUSIONS - It is unlikely that dual task interference between balancing and mental activity is due to competition for spatial processing resources, as levels of interference were similar in patients with vestibular disorder and healthy controls, and were also similar for spatial and non-spatial tasks. Moreover, the finding that accuracy declined on the high load tasks when balancing cannot be attributed to motor control interference, as no motor control processing is involved in maintaining accuracy of responses. Therefore, interference between mental activity and postural control can be attributed principally to general capacity limitations, and is hence proportional to the attentional demands of both tasks

The detection of FIR emission from high redshift star-forming galaxies in the ECDF-S

ABRIDGED: We have used the LABOCA Survey of the ECDF-S (LESS) to investigate rest-frame FIR emission from typical SF systems (LBGs) at redshift 3, 4, and 5. We initially concentrate on LBGs at z~3 and select three subsamples on stellar mass, extinction corrected SF and rest-frame UV-magnitude. We produce composite 870micron images of the typical source in our subsamples, obtaining ~4sigma detections and suggesting a correlation between FIR luminosity and stellar mass. We apply a similar procedure to our full samples at z~3, 4, 4.5 and 5 and do not obtain detections - consistent with a simple scaling between FIR luminosity and stellar mass. In order to constrain the FIR SED of these systems we explore their emission at multiple wavelengths spanning the peak of dust emission at z~3 using the Herschel SPIRE observations of the field. We obtain detections at multiple wavelengths for both our stellar mass and UV-magnitude selected samples, and find a best-fit SED with T_dust in the ~33-41K range. We calculate L_FIR, obscured SFRs and M_dust, and find that a significant fraction of SF in these systems is obscured. Interestingly, our extinction corrected SFR sample does not display the large FIR fluxes predicted from its red UV-spectral slope. This suggests that the method of assuming an intrinsic UV-slope and correcting for dust attenuation may be invalid for this sample - and that these are not in fact the most actively SF systems. All of our z~3 samples fall on the `main sequence' of SF galaxies at z~3 and our detected subsamples are likely to represent the high obscuration end of LBGs at their epoch. We compare the FIR properties of our subsamples with various other populations, finding that our stellar mass selected sample shows similar FIR characteristics to SMGs at the same epoch and therefore potentially represents the low L_FIR end of the high redshift FIR luminosity function.Comment: 18 pages, 10 figure, MNRAS accepted, corrected typos, acknowledgements adde

SINFONI's take on Star Formation, Molecular Gas, and Black Hole Masses in AGN

We present some preliminary (half-way) results on our adaptive optics spectroscopic survey of AGN at spatial scales down to 0.085arcsec. Most of the data were obtained with SINFONI which provides integral field capability at a spectral resolution of R~4000. The themes on which we focus in this contribution are: star formation around the AGN, the properties of the molecular gas and its relation to the torus, and the mass of the black hole.Comment: 5 pages, 2 figures. To appear in Science Perspectives for 3D Spectroscopy. ESO Astrophysics Symposia. Ed by M. Kissler-Patig, M. Roth and J. Wals