Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples

Restrictive ID policies: implications for health equity

We wish to thank Synod Community Services for their critical work to develop, support, and implement a local government-issued ID in Washtenaw County, MI. We also thank Yousef Rabhi of the Michigan House of Representatives and Janelle Fa'aola of the Washtenaw ID Task Force, Lawrence Kestenbaum of the Washtenaw County Clerk's Office, Sherriff Jerry Clayton of the Washtenaw County Sherriff's Office, and the Washtenaw ID Task Force for their tireless commitment to developing and supporting the successful implementation of the Washtenaw ID. Additionally, we thank Vicenta Vargas and Skye Hillier for their contributions to the Washtenaw ID evaluation. We thank the Curtis Center for Research and Evaluation at the University of Michigan School of Social Work, the National Center for Institutional Diversity at the University of Michigan, and the University of California-Irvine Department of Chicano/Latino Studies and Program in Public Health for their support of the Washtenaw ID community-academic research partnership. Finally, we thank the reviewers for their helpful comments on earlier drafts of this manuscript. (Curtis Center for Research and Evaluation at the University of Michigan School of Social Work; National Center for Institutional Diversity at the University of Michigan; University of California-Irvine Department of Chicano/Latino Studies; Program in Public Health)https://link.springer.com/content/pdf/10.1007/s10903-017-0579-3.pdfPublished versio

Microstructure and oxide particle stability in a novel ODS γ-TiAl alloy processed by spark plasma sintering and laser additive manufacturing

In this work, a novel oxide dispersion strengthened titanium aluminide alloy (Ti-45Al-3Nb-<0.2Y2O3 at.%) was developed for powder-based processing technologies with a focus on spark plasma sintering and additive manufacturing. Titanium aluminides are promising structural intermetallics for weight reduction and an increased performance of high temperature components. The alloy design and selection process was supported by computational thermodynamics based on the CALPHAD approach, taking into account requirements for processing as well as long term alloy behavior under service conditions. Processing trials using spark plasma sintering, direct metal deposition and selective laser melting were conducted to study the alloy behavior, microstructure formation and introduction as well as stability of the ODS particles. Additionally, thermal annealing on the sintered and laser consolidated material was performed. Conventional dual phase α2-Ti3Al and γ-TiAl duplex and near-lamellar microstructures were obtained from the processed material. The ODS particles were homogeneously distributed in the alloy matrix after processing in the liquid state. For the direct metal deposition process, the novel alloy was compared to the established GE48-2-2 alloy (Ti-48Al-2Cr-2Nb) in terms of phases, microstructure and texture after processing. A significantly reduced texture formation was observed with the novel alloy. The hardness of the consolidated material shows superior properties for ODS-containing TiAl compared to ODS-free material. This work provides a first step towards tailored alloys for AM and the production of ODS TiAl alloys

How mothers feel: validation of a measure of maternal mood

© 2019 The Authors. Journal of Evaluation in Clinical Practice published by John Wiley & Sons Ltd Rationale: Low mood may affect developing relationships with a new baby, partner and family. Early identification of mood disturbance is crucial to improve outcomes for women perinatally. Instruments such as the Edinburgh Postnatal Depression Scale (EPDS) are used routinely, with evidence that some women do not feel comfortable with how they are asked about their mental health. Objective: To develop a mood checklist as a user-friendly, effective measure of well-being in post-partum women, for use by health professionals. Methods: Cognitive interviews with women who had recently given birth assessed response format and face validity of a prototype measure. A cross-sectional survey followed. A random split-half instrument development protocol was used. Exploratory factor analysis determined factor structure with the first sample,. The second sample confirmed factor structure and evaluationof key psychometric variables and known-groups discriminant validity (KGDV), requiring a supplementary between-subjects design with stratification based on case negative/case positive classification using EPDSscreening cut-off criteria. Results: Cognitive interview data confirmed the face validity of the measure. Exploratory factor analysis indicated an 18 item two-factor model with two (negatively) correlated factors. Factor 1 loaded with items reflecting positive mood and factor 2 negative items. Confirmatory factor analysis showed a good fit to the two-factor model across the full spectrum of fit indices. Statistically significant differences between groups were observed in relation to as EPDS caseness classification. Cronbach alpha coefficients for the positive and negative subscales revealed acceptable internal consistency of 0.79 and 0.72, respectively. Conclusion: The outcome checklist may be appropriate for use in clinical practice. It demonstrated effective psychometric properties and clear cross-validation with existing commonly used measures

The last of the simple remainders

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Single-valued harmonic polylogarithms and the multi-Regge limit

We argue that the natural functions for describing the multi-Regge limit of six-gluon scattering in planar N=4 super Yang-Mills theory are the single-valued harmonic polylogarithmic functions introduced by Brown. These functions depend on a single complex variable and its conjugate, (w,w*). Using these functions, and formulas due to Fadin, Lipatov and Prygarin, we determine the six-gluon MHV remainder function in the leading-logarithmic approximation (LLA) in this limit through ten loops, and the next-to-LLA (NLLA) terms through nine loops. In separate work, we have determined the symbol of the four-loop remainder function for general kinematics, up to 113 constants. Taking its multi-Regge limit and matching to our four-loop LLA and NLLA results, we fix all but one of the constants that survive in this limit. The multi-Regge limit factorizes in the variables (\nu,n) which are related to (w,w*) by a Fourier-Mellin transform. We can transform the single-valued harmonic polylogarithms to functions of (\nu,n) that incorporate harmonic sums, systematically through transcendental weight six. Combining this information with the four-loop results, we determine the eigenvalues of the BFKL kernel in the adjoint representation to NNLLA accuracy, and the MHV product of impact factors to NNNLLA accuracy, up to constants representing beyond-the-symbol terms and the one symbol-level constant. Remarkably, only derivatives of the polygamma function enter these results. Finally, the LLA approximation to the six-gluon NMHV amplitude is evaluated through ten loops.Comment: 71 pages, 2 figures, plus 10 ancillary files containing analytic expressions in Mathematica format. V2: Typos corrected and references added. V3: Typos corrected; assumption about single-Reggeon exchange made explici

Thermodynamics of Competitive Molecular Channel Transport: Application to Artificial Nuclear Pores

In an analytical model channel transport is analyzed as a function of key parameters, determining efficiency and selectivity of particle transport in a competitive molecular environment. These key parameters are the concentration of particles, solvent-channel exchange dynamics, as well as particle-in-channel- and interparticle interaction. These parameters are explicitly related to translocation dynamics and channel occupation probability. Slowing down the exchange dynamics at the channel ends, or elevating the particle concentration reduces the in-channel binding strength necessary to maintain maximum transport. Optimized in-channel interaction may even shift from binding to repulsion. A simple equation gives the interrelation of access dynamics and concentration at this transition point. The model is readily transferred to competitive transport of different species, each of them having their individual in-channel affinity. Combinations of channel affinities are determined which differentially favor selectivity of certain species on the cost of others. Selectivity for a species increases if its in-channel binding enhances the species' translocation probablity when compared to that of the other species. Selectivity increases particularly for a wide binding site, long channels, and fast access dynamics. Recent experiments on competitive transport of in-channel binding and inert molecules through artificial nuclear pores serve as a paradigm for our model. It explains qualitatively and quantitatively how binding molecules are favored for transport at the cost of the transport of inert molecules

Bottom mixed layer oxygen dynamics in the Celtic Sea

The seasonally stratified continental shelf seas are highly productive, economically important environments which are under considerable pressure from human activity. Global dissolved oxygen concentrations have shown rapid reductions in response to anthropogenic forcing since at least the middle of the twentieth century. Oxygen consumption is at the same time linked to the cycling of atmospheric carbon, with oxygen being a proxy for carbon remineralisation and the release of CO2. In the seasonally stratified seas the bottom mixed layer (BML) is partially isolated from the atmosphere and is thus controlled by interplay between oxygen consumption processes, vertical and horizontal advection. Oxygen consumption rates can be both spatially and temporally dynamic, but these dynamics are often missed with incubation based techniques. Here we adopt a Bayesian approach to determining total BML oxygen consumption rates from a high resolution oxygen time-series. This incorporates both our knowledge and our uncertainty of the various processes which control the oxygen inventory. Total BML rates integrate both processes in the water column and at the sediment interface. These observations span the stratified period of the Celtic Sea and across both sandy and muddy sediment types. We show how horizontal advection, tidal forcing and vertical mixing together control the bottom mixed layer oxygen concentrations at various times over the stratified period. Our muddy-sand site shows cyclic spring-neap mediated changes in oxygen consumption driven by the frequent resuspension or ventilation of the seabed. We see evidence for prolonged periods of increased vertical mixing which provide the ventilation necessary to support the high rates of consumption observed