Generating EQ-5D-3L health utility scores from the Edinburgh Postnatal Depression Scale: a perinatal mapping study

Background: Perinatal depression (PND) describes depression experienced by parents during pregnancy or in the first year after a baby is born. The EQ-5D instrument (a generic measure of health status) is not often collected in perinatal research, however disease-specific measures, such as the Edinburgh Postnatal Depression Scale (EPDS) are widely used. Mapping can be used to estimate generic health utility index values from disease-specific measures like the EPDS. Objective: To develop a mapping algorithm to estimate EQ-5D utility index values from the EPDS. Methods: Patient-level data from the BaBY PaNDA study (English observational cohort study) provided 1068 observations with paired EPDS and EQ-5D (3-level version; EQ-5D-3L) responses. We compared the performance of six alternative regression model types, each with four specifications of covariates (EPDS score and age: base, squared, and cubed). Model performance (ability to predict utility values) was assessed by ranking mean error, mean absolute error, and root mean square error. Algorithm performance in 3 external datasets was also evaluated. Results: There was moderate correlation between EPDS score and utility values (coefficient: – 0.42). The best performing model type was a two-part model, followed by ordinary least squared. Inclusion of squared and cubed covariates improved model performance. Based on graphs of observed and predicted utility values, the algorithm performed better when utility was above 0.6. Conclusions: This direct mapping algorithm allows the estimation of health utility values from EPDS scores. The algorithm has good external validity but is likely to perform better in samples with higher health status

Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

A note on completeness of weighted normed spaces of analytic functions

[EN] Given a non-negative weight v, not necessarily bounded or strictly positive, defined on a domain G in the complex plane, we consider the weighted space H-v(infinity) (G)of all holomorphic functions on G such that the product v vertical bar f vertical bar is bounded in G and study the question of when such a space is complete under the canonical sup-seminorm. We obtain both some necessary and some sufficient conditions in terms of the weight v, exhibit several relevant examples, and characterize completeness in the case of spaces with radial weights on balanced domains.The first author was partially supported by MTM2013-43540-P and MTM2016-76647-P by MINECO/FEDER-EU and GVA Prometeo II/2013/013. The second author was partially supported by the MINECO/FEDER-EU Grant MTM2015-65792-P. Both authors were partially supported by Thematic Research Network MTM2015-69323-REDT, MINECO, Spain.Bonet Solves, JA.; Vukotic, D. (2017). A note on completeness of weighted normed spaces of analytic functions. Results in Mathematics. 72(1-2):263-279. https://doi.org/10.1007/s00025-017-0696-2S263279721-2Arcozzi, N., Björn, A.: Dominating sets for analytic and harmonic functions and completeness of weighted Bergman spaces. Math. Proc. R. Ir. Acad. 102A, 175–192 (2002)Berenstein, C.A., Gay, R.: Complex Variables, An Introduction. Springer, New York (1991)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)Björn, A.: Removable singularities for weighted Bergman spaces. Czechoslov. Math. J. 56, 179–227 (2006)Bonet, J., Domański, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Can. Math. Bull. 42(2), 139–148 (1999)Bonet, J., Vogt, D.: Weighted spaces of holomorphic functions and sequence spaces. Note Mat. 17, 87–97 (1997)Conway, J.B.: Functions of One Complex Variable, Second Edition, Graduate Texts in Mathematics, vol. 11. Springer, New York (1978)Gaier, D.: Lectures on Complex Approximation. Birkhäuser, Boston (1987)Grosse-Erdmann, K.-G.: A weak criterion for vector-valued holomorphic functions. Math. Proc. Camb. Philos. Soc. 136, 399–411 (2004)Hörmander, L.: An Introduction to Complex Analysis in Several Variables. North-Holland, Amsterdam (1979)Horváth, J.: Topological Vector Spaces and Distributions. Addison-Wesley, Reading (1966)Lusky, W.: On weighted spaces of harmonic and holomorphic functions. J. Lond. Math. Soc. 51, 309–320 (1995)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175, 19–45 (2006)Nakazi, T.: Weighted Bloch spaces which are Banach spaces. Rend. Circ. Mat. Palermo 62, 427–440 (2013)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971

Quantum Computing

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future.Comment: 26 pages, 7 figures, 291 references. Early draft of Nature 464, 45-53 (4 March 2010). Published version is more up-to-date and has several corrections, but is half the length with far fewer reference

Evaluating The National Land Cover Database Tree Canopy and Impervious Cover Estimates Across the Conterminous United States: A Comparison with Photo-Interpreted Estimates

The 2001 National Land Cover Database (NLCD) provides 30-m resolution estimates of percentage tree canopy and percentage impervious cover for the conterminous United States. Previous estimates that compared NLCD tree canopy and impervious cover estimates with photo-interpreted cover estimates within selected counties and places revealed that NLCD underestimates tree and impervious cover. Based on these previous results, a wall-to-wall comprehensive national analysis was conducted to determine if and how NLCD derived estimates of tree and impervious cover varies from photo-interpreted values across the conterminous United States. Results of this analysis reveal that NLCD significantly underestimates tree cover in 64 of the 65 zones used to create the NCLD cover maps, with a national average underestimation of 9.7% (standard error (SE) = 1.0%) and a maximum underestimation of 28.4% in mapping zone 3. Impervious cover was also underestimated in 44 zones with an average underestimation of 1.4% (SE = 0.4%) and a maximum underestimation of 5.7% in mapping zone 56. Understanding the degree of underestimation by mapping zone can lead to better estimates of tree and impervious cover and a better understanding of the potential limitations associated with NLCD cover estimates

Surface and Temporal Biosignatures

Recent discoveries of potentially habitable exoplanets have ignited the prospect of spectroscopic investigations of exoplanet surfaces and atmospheres for signs of life. This chapter provides an overview of potential surface and temporal exoplanet biosignatures, reviewing Earth analogues and proposed applications based on observations and models. The vegetation red-edge (VRE) remains the most well-studied surface biosignature. Extensions of the VRE, spectral "edges" produced in part by photosynthetic or nonphotosynthetic pigments, may likewise present potential evidence of life. Polarization signatures have the capacity to discriminate between biotic and abiotic "edge" features in the face of false positives from band-gap generating material. Temporal biosignatures -- modulations in measurable quantities such as gas abundances (e.g., CO2), surface features, or emission of light (e.g., fluorescence, bioluminescence) that can be directly linked to the actions of a biosphere -- are in general less well studied than surface or gaseous biosignatures. However, remote observations of Earth's biosphere nonetheless provide proofs of concept for these techniques and are reviewed here. Surface and temporal biosignatures provide complementary information to gaseous biosignatures, and while likely more challenging to observe, would contribute information inaccessible from study of the time-averaged atmospheric composition alone.Comment: 26 pages, 9 figures, review to appear in Handbook of Exoplanets. Fixed figure conversion error