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.

The Beveridge Curve

macroeconomics, Beveridge Curve

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

The superluminous supernova SN 2017egm in the nearby galaxy NGC 3191: a metal-rich environment can support a typical SLSN evolution

At redshift z=0.03, the recently-discovered SN 2017egm is the nearest Type I superluminous supernova (SLSN) to date, and first near the center of a massive spiral galaxy (NGC 3191). Using SDSS spectra of NGC 3191, we find a metallicity ~2 Z$_\odot$ at the nucleus and ~1.3 Z$_\odot$ for a star forming region at a radial offset similar to SN 2017egm. Archival radio-to-UV photometry reveals a star-formation rate ~15 M$_\odot$ yr$^{-1}$ (with ~70% dust-obscured), which can account for a Swift X-ray detection, and stellar mass ~$10^{10.7}$ M$_\odot$. We model the early UV-optical light curves with a magnetar central-engine model, using the Bayesian light curve fitting tool MOSFiT. The fits indicate ejecta mass 2-4 M$_\odot$, spin period 4-6 ms, magnetic field (0.7-1.7)$\times 10^{14}$G, and kinetic energy 1-2 $\times10^{51}$ erg. These parameters are consistent with the overall distributions for SLSNe, modeled by Nicholl et al (2017), although the derived mass and spin are towards the low end, possibly indicating enhanced loss of mass and angular momentum before explosion. This has two implications: (i) SLSNe can occur at solar metallicity, although with a low fraction ~10%; and (ii) metallicity has at most a modest effect on their properties. Both conclusions are in line with results for long gamma-ray bursts. Assuming a monotonic rise gives an explosion date MJD $57889\pm1$. However, a short-lived excess in the data relative to the best-fitting models may indicate an early-time `bump'. If confirmed, SN 2017egm would be the first SLSN with a spectrum during the bump-phase; this shows the same O II lines seen at maximum light, which may be an important clue for explaining these bumps.Comment: Accepted for publication in ApJ

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