Lepskii Principle in Supervised Learning

In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the least-square (prediction) error and for the reproducing kernel Hilbert space (reconstruction) norm error. It is based on a modified Lepskii balancing principle using a varying family of norms

Ranking, Unemployment Duration, and Wages

Firms often receive multiple acceptable applications for vacancies, requiring a choice among candidates. This paper contrasts equilibria when firms select workers at random and when firms select the worker with the shortest spell of unemployment, called ranking. With the filling of vacancies unaffected by the selection rule, both equilibria have the same aggregate dynamics, but different distributions of unemployment durations. With the threat point for the Nash bargained wage being a worker with zero unemployment duration, the wage with ranking is much more sensitive to changes in the tightness of the labor market. The same holds for efficiency wages.

On Regressive Ramsey Numbers

AbstractWe prove the following relation between regressive and classical Ramsey numbers Rregn(n+2)=Rn−1(n)+2. This is used to compute Rreg3(5)=8, Rreg4 (6)=15, and Rreg5(7)⩾36. We prove that Rx+k2(4)⩽2k+1(3+k)−(k+1), and use this to compute R2reg(5)=15. Finally, we provide the bounds 195⩽Rreg2(6)⩽ 5·242+239−2

Investigating the local structure of B-site cations in (1-x) BaTiO3exBiScO3 and (1-x)PbTiO3exBiScO3 using X-ray absorption spectroscopy

NSERCThe structural properties of (1-x)BaTiO3exBiScO3 and (1-x)PbTiO3exBiScO3 were investigated using powder X-ray diffraction and X-ray absorption spectroscopy. Diffraction measurements confirmed that substituting small amounts of BiScO3 into BaTiO3 initially stabilizes a cubic phase at x 1⁄4 0.2 before im- purity phases begin to form at x 1⁄4 0.5. BiScO3 substitution also resulted in noticeable changes in the local coordination environment of Ti4þ. X-ray absorption near-edge spectroscopy (XANES) analysis showed that replacing Ti4þ with Sc3þ results in an increase in the off-centre displacement of Ti4þ cations. Sur- prisingly, BiScO3 substitution has no effect on the displacement of the Ti4þ cation in the (1-x)PbTiO3 exBiScO3 solid solution

Convergence analysis of Tikhonov regularization for non-linear statistical inverse problems

We study a non-linear statistical inverse problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization) approach to estimate the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the concept of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions

Fish lost at sea: the effect of soak time on pelagic longline catches

Our analyses of observer records reveal that abundance estimates are strongly influenced by the timing of longline operations in relation to dawn and dusk and soak time— the amount of time that baited hooks are available in the water. Catch data will underestimate the total mortality of several species because hooked animals are “lost at sea.” They fall off, are removed, or escape from the hook before the longline is retrieved. For example, longline segments with soak times of 20 hours were retrieved with fewer skipjack tuna and seabirds than segments with soak times of 5 hours. The mortality of some seabird species is up to 45% higher than previously estimated. The effects of soak time and timing vary considerably between species. Soak time and exposure to dusk periods have strong positive effects on the catch rates of many species. In particular, the catch rates of most shark and billfish species increase with soak time. At the end of longline retrieval, for example, expected catch rates for broadbill swordfish are four times those at the beginning of retrieval. Survival of the animal while it is hooked on the longline appears to be an important factor determining whether it is eventually brought on board the vessel. Catch rates of species that survive being hooked (e.g. blue shark) increase with soak time. In contrast, skipjack tuna and seabirds are usually dead at the time of retrieval. Their catch rates decline with time, perhaps because scavengers can easily remove hooked animals that are dead. The results of our study have important implications for fishery management and assessments that rely on longline catch data. A reduction in soak time since longlining commenced in the 1950s has introduced a systematic bias in estimates of mortality levels and abundance. The abundance of species like seabirds has been over-estimated in recent years. Simple modifications to procedures for data collection, such as recording the number of hooks retrieved without baits, would greatly improve mortality estimates

Searching for Cooling Signatures in Strong Lensing Galaxy Clusters: Evidence Against Baryons Shaping the Matter Distribution in Cluster Cores

The process by which the mass density profile of certain galaxy clusters becomes centrally concentrated enough to produce high strong lensing (SL) cross-sections is not well understood. It has been suggested that the baryonic condensation of the intra-cluster medium (ICM) due to cooling may drag dark matter to the cores and thus steepen the profile. In this work, we search for evidence of ongoing ICM cooling in the first large, well-defined sample of strong lensing selected galaxy clusters in the range 0.1 < z < 0.6. Based on known correlations between the ICM cooling rate and both optical emission line luminosity and star formation, we measure, for a sample of 89 strong lensing clusters, the fraction of clusters that have [OII]3727 emission in their brightest cluster galaxy (BCG). We find that the fraction of line-emitting BCGs is constant as a function of redshift for z > 0.2 and shows no statistically significant deviation from the total cluster population. Specific star formation rates, as traced by the strength of the 4000 angstrom break, D_4000, are also consistent with the general cluster population. Finally, we use optical imaging of the SL clusters to measure the angular separation, R_arc, between the arc and the center of mass of each lensing cluster in our sample and test for evidence of changing [OII] emission and D_4000 as a function of R_arc, a proxy observable for SL cross-sections. D_4000 is constant with all values of R_arc, and the [OII] emission fractions show no dependence on R_arc for R_arc > 10" and only very marginal evidence of increased weak [OII] emission for systems with R_arc < 10". These results argue against the ability of baryonic cooling associated with cool core activity in the cores of galaxy clusters to strongly modify the underlying dark matter potential, leading to an increase in strong lensing cross-sections.Comment: 9 Pages, 5 Figures, 1 Tabl

The Intermediate Luminosity Optical Transient SN 2010da: The Progenitor, Eruption and Aftermath of a Peculiar Supergiant High-mass X-ray Binary

We present optical spectroscopy, ultraviolet to infrared imaging and X-ray observations of the intermediate luminosity optical transient (ILOT) SN 2010da in NGC 300 (d=1.86 Mpc) spanning from -6 to +6 years relative to the time of outburst in 2010. Based on the light curve and multi-epoch SEDs of SN 2010da, we conclude that the progenitor of SN 2010da is a ~10-12 Msol yellow supergiant possibly transitioning into a blue loop phase. During outburst, SN 2010da had a peak absolute magnitude of M<-10.4 mag, dimmer than other ILOTs and supernova impostors. We detect multi-component hydrogen Balmer, Paschen, and Ca II emission lines in our high-resolution spectra, which indicate a dusty and complex circumstellar environment. Since the 2010 eruption, the star has brightened by a factor of ~5 and remains highly variable in the optical. Furthermore, we detect SN 2010da in archival Swift and Chandra observations as an ultraluminous X-ray source (L~6x10^{39} erg/s). We additionally attribute He II 4686 Angstrom and coronal Fe emission lines in addition to a steady X-ray luminosity of ~10^{37} erg/s to the presence of a compact companion.Comment: published; updated citations and other minor edit