Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors

This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen--Lo\`eve expansion for square-integrable random variables can be used to sample such measures on quasi-Banach spaces. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger metric upon perturbations of the misfit function and observed data.Comment: To appear in Inverse Problems and Imaging. This preprint differs from the final published version in layout and typographical detail

Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors

The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an infinite-dimensional space, a typical example being a scalar or tensor field coupled to some observed data via an ODE or PDE. This article gives an introduction to the framework of well-posed BIPs in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others. This framework has the advantage of ensuring uniformly well-posed inference problems independently of the finite-dimensional discretisation used for numerical solution. Recently, this framework has been extended to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen--Lo\`eve expansion for square-integrable random variables can be used to sample such measures on quasi-Banach spaces. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger and total variation metrics upon perturbations of the misfit function and observed data.Comment: To appear in the proceedings of the 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017. This preprint differs from the final published version in pagination and typographical detai

Crack growth measured on flat and curved surfaces at cryogenic temperatures

Multiple element continuity gage measures plane stress crack growth plus surface crack growth under plane strain conditions. The gage measures flat and curved surfaces and operates at cryogenic temperatures

Structural qualification testing and operational loading on a fiberglass rotor blade for the Mod-OA wind turbine

Fatigue tests were performed on full- and half-scale root end sections, first to qualify the root retention design, and second to induce failure. Test methodology and results are presented. Two operational blades were proof tested to design limit load to ascertain buckling resistance. Measurements of natural frequency, damping ratio, and deflection under load made on the operational blades are documented. The tests showed that all structural design requirements were met or exceeded. Blade loads measured during 3000 hr of field operation were close to those expected. The measured loads validated the loads used in the fatigue tests and gave high confidence in the ability of the blades to achieve design life

Effect of vortex generators on the power conversion performance and structural dynamic loads of the Mod-2 wind turbine

Applying vortex generators from 20 to 100 percent span of the Mod-2 rotor resulted in a projected increase in annual energy capture of 20 percent and reduced the wind speed at which rated power is reached by nearly 3 m/sec. Application of vortex generators from 20 to 70 percent span, the fixed portion of the Mod-2 rotor, resulted in a projected increase in annual energy capture of about half this. This improved performance came at the cost of a small increase in cyclic blade loads in below rated power conditions. Cyclic blade loads were found to correlate well with the change in wind speed during one rotor revolution

A review of resonance response in large horizontal-axis wind turbines

Field operation of the Mod-0 and Mod-1 wind turbines is described. Operational experience shows that 1 per rev excitation exists in the drive train, high aerodynamic damping prevents resonance response of the blade flatwise modes, and teetering the hub substantially reduces the chordwise blade response to odd harmonic excitation. These results can be used by designer as a guide to system frequency placement. In addition it is found that present analytical techniques can accurately predict wind turbine natural frequencies

Equivalence of weak and strong modes of measures on topological vector spaces

A strong mode of a probability measure on a normed space $X$ can be defined as a point $u$ such that the mass of the ball centred at $u$ uniformly dominates the mass of all other balls in the small-radius limit. Helin and Burger weakened this definition by considering only pairwise comparisons with balls whose centres differ by vectors in a dense, proper linear subspace $E$ of $X$, and posed the question of when these two types of modes coincide. We show that, in a more general setting of metrisable vector spaces equipped with measures that are finite on bounded sets, the density of $E$ and a uniformity condition suffice for the equivalence of these two types of modes. We accomplish this by introducing a new, intermediate type of mode. We also show that these modes can be inequivalent if the uniformity condition fails. Our results shed light on the relationships between among various notions of maximum a posteriori estimator in non-parametric Bayesian inference.Comment: 22 pages, 3 figure

Single-top-quark production at hadron colliders

Single-top-quark production probes the charged-current weak interaction of the top quark, and provides a direct measurement of the CKM matrix element V_{tb}. We perform two independent analyses to quantify the accuracy with which the W-gluon fusion (gq -> t\bar{b}q) and (q\bar{q} -> t\bar{b}) signals can be extracted from the backgrounds at both the Tevatron and the LHC. Although perturbation theory breaks down at low transverse momentum for the W-gluon fusion \bar{b} differential cross section, we show how to obtain a reliable cross section integrated over low \bar{b} transverse momenta up to a cutoff. We estimate the accuracy with which V_{tb} can be measured in both analyses, including theoretical and statistical uncertainties. We also show that the polarization of the top quark in W-gluon fusion can be detected at the Fermilab Tevatron and the CERN LHC.Comment: Version to appear in PRD, 31 pages, LaTeX, 8 ps figure

Relationship science and interventions: Where we are and where we are going

Relationship distress and divorce often have profound effects on couples and their children. Relationship science has long sought to prevent and alleviate relationship distress; this chapter is a summary of many important recent developments in the field. Ongoing challenges in studying and assisting intimate relationships are also discussed

EBIC investigation of hydrogenation of crystal defects in EFG solar silicon ribbons

Changes in the contrast and resolution of defect structures in 205 Ohm-cm EFG polysilicon ribbon subjected to annealing and hydrogenation treatments were observed in a JEOL 733 Superprobe scanning electron microscope, using electron beam induced current (EBIC) collected at an A1 Schottky barrier. The Schottky barrier was formed by evaporation of A1 onto the cleaned and polished surface of the ribbon material. Measurement of beam energy, beam current, and the current induced in the Schottky diode enabled observations to be quantified. Exposure to hydrogen plasma increased charge collection efficiency. However, no simple causal relationship between the hydrogenation and charge collection efficiency could be inferred, because the collection efficiency also displayed an unexpected thermal dependence. Good quality intermediate-magnification (1000X-5400X) EBIC micrographs of several specific defect structures were obtained. Comparison of grown-in and stress-induced dislocations after annealing in vacuum at 500 C revealed that stress-induced dislocations are hydrogenated to a much greater degree than grown-in dislocations. The theoretical approximations used to predict EBIC contrast and resolution may not be entirely adequate to describe them under high beam energy and low beam current conditions