Search

By Guan and Zhou’s resolution of the Suita Conjecture, it is known that for any open, hyperbolic Riemann surface X, the Bergman kernel K, the logarithmic capacity c_β, and the analytic capacity c_B, are related by πK ≥ c_β ≥ c_B. When X is a domain in C, we show that c_B ≥ π(Vol(X))^{-1} where Vol is the volume, and determine the conditions for when there exists a point z_0 such that c_B(z_0) = π(Vol(X))^{−1}, c_β(z_0) = π(Vol(X))^{−1}, and πK(z_0) = π(Vol(X))^{−1}. For open Riemann surfaces, we also determine equality conditions for c_B ≤ c_β. A significant portion of this part of the thesis is based on joint work with Dong and Zhang.The second part of the thesis is motivated by Henkin and Leiterer’s question of whether uniform estimates for the ∂-operator hold on the Cartan classical bounded symmetric domains. Using weighted L^2-methods initiated by Berndtsson, we obtain a pointwise estimate for the canonical solutions to the equation ∂u = f when f is bounded in a Bergman-type L∞-norm. This part is based on joint work with Dong and Li.In the third part of the thesis, we extend a theorem of M. Christ and S.-Y. Li on the ∂-equation ∂u = f. Let D ⊂ C^n be a bounded pseudoconvex domain with C∞ boundary which has a Stein neighborhood basis. We show that if f is a (p,q) form defined on Ω whose coefficients lie in a quasi-analytic class C^L(Ω), then there exists a solution u to ∂u = f such that the coefficients of u belong to the same quasi-analytic class.

Health system response to COVID-19 required drastic care delivery changes, but also a substantially altered environment in which to observe implementation of more standard quality improvement efforts. Implementation assessment during disrupted operational norms (“business not as usual”) distills challenges solved by prioritization from those requiring solutions that address more fundamental barriers to change. This commentary retrospectively analyzes health system implementation of a clinical practice guideline intended to support COVID-19 treatment. We use the QUERI roadmap to reflect upon implementation strategy within the context of a nascent LHS framework. In doing so, we identify aspects of implementation that were facilitated by the COVID-19-altered environment, enduring implementation challenges with respect to fidelity and sustainability, and key areas of necessary continued investment to strengthen a responsive system for learning and improvement. Moving forward, COVID-19 response highlighted key investments that bridge learning health system structures to implementation practices. This includes structures that (1) accelerate ideas that emerge from the front lines, (2) promote “living” care guidelines that are supported by continuous review of emergent evidence, and (3) enhance analytic capacity that supports organizational learning. COVID-19 response has offered opportunities for “new norm” thinking around what’s possible to build out a learning health system. Strategic application of implementation frameworks to learning health system infrastructure has highlighted necessary investments that build and sustain a more responsive, improvement-oriented organization.

This exploratory research study employed a mixed methods research design to examine the data-driven decision making supports of data system infrastructure, analytic capacity, and data-use leadership from the perspective of the DDAs (district data administrators that oversee the provisions of data-driven decision making supports throughout the school district) and from the perspective of school and district personnel (teachers, school and district administrators, school support staff, and district staff that actively use data-driven decision making toward their educational practices). Qualitative data were collected through five individual interviews of DDAs. Quantitative data were collected through a district-wide online survey of school and district personnel (N = 218). Qualitative and quantitative data were used together to capture the overall state of the data-driven decision making supports within the school district.Findings indicate the district under study is still in the early phases of implementing quality data-driven decision making supports such that supports are provided, but they have limitations and are “a work in progress.” The quality of the district’s data-driven decision making supports is reflected in the perceptions of the school and district personnel. On average, the school and district personnel were between somewhat disagree to somewhat agree that the district provides quality data driven-decision making supports in the three areas of data system infrastructure, analytic capacity, and data-use leadership. The findings also show predictive relationships between data-driven decision making supports and data-driven decision making processes, indicating the importance of having quality data-driven decision making supports. The findings of the study also highlight notable considerations for implementing quality data-driven decision making supports such as implementation phase, district size and breadth, organizational structures, and time.

In this paper we study the connection between the analytic capacity of a set and the size of its orthogonal projections. More precisely, we prove that if $E\subset \mathbb C$ is compact and $\mu$ is a Borel measure supported on $E$, then the analytic capacity of $E$ satisfies $$ \gamma(E) \geq c\,\frac{\mu(E)^2}{\int_I \|P_\theta\mu\|_2^2\,d\theta}, $$ where $c$ is some positive constant, $I\subset [0,\pi)$ is an arbitrary interval, and $P_\theta\mu$ is the image measure of $\mu$ by $P_\theta$, the orthogonal projection onto the line $\{re^{i\theta}:r\in\mathbb R\}$. This result is related to an old conjecture of Vitushkin about the relationship between the Favard length and analytic capacity. We also prove a generalization of the above inequality to higher dimensions which involves related capacities associated with signed Riesz kernels., Comment: Minor corrections and adjustments. An additional appendix where we estimate $L^2$ densities of projections in terms of a conical Riesz energy plus an 'error term'

River basins often extend over several regions connected by both water flows and socioeconomic factors. Therefore, water policy and diverse hydrological scenarios can affect socioeconomic variables in other parts of a river basin. This paper proposes a tool combining hydro-economic and input–output models to analyze the socioeconomic impacts of different hydrologic scenarios from a multiregional standpoint. To this end, we have built a monthly-basis hydro-economic model to fit a multiregional input–output table to estimate direct and indirect impacts on value added and employment, bringing together data on water flow and regional demand, sector-based economic analysis and macroeconomic impacts. In a given hydrological scenario, the hydro-economic model determines the output of irrigated farmland in each region and the value added generated by each crop. These data are then processed using the multiregional input–output model to determine socio-economic impacts in each of the regions forming the river basin. This methodology allows evaluation of different water policies, providing a tool for policymakers to estimate socio-economic impacts. Finally, we apply this methodology in two scenarios reflecting the opportunity costs of diverse hydrological scenarios in terms of value added and employment terms to demonstrate its excellent analytic capacity. Graphic abstract: [Figure not available: see fulltext.].

COVID-19 has caused 100s of millions of infections and millions of deaths worldwide, overwhelming health and economic capacities in many countries and at multiple scales. The immediacy and magnitude of this crisis has resulted in government officials, practitioners and applied scholars turning to reflexive learning exercises to generate insights for managing the reverberating effects of this disease as well as the next inevitable pandemic. We contribute to both tasks by assessing COVID-19 as a “super wicked” problem denoted by four features we originally formulated to describe the climate crisis: time is running out, no central authority, those causing the problem also want to solve it, and policies irrationally discount the future (Levin et al. in Playing it forward: path dependency, progressive incrementalism, and the “super wicked” problem of global climate change, 2007; Levin et al. in Playing it forward: Path dependency, progressive incrementalism, and the "super wicked" problem of global climate change, 2009; Levin et al. in Policy Sci 45(2):123–152, 2012). Doing so leads us to identify three overarching imperatives critical for pandemic management. First, similar to requirements to address the climate crisis, policy makers must establish and maintaindurablepolicy objectives. Second, in contrast to climate, management responses must always allow for swiftchangesin policy settings and calibrations given rapid and evolving knowledge about a particular disease’s epidemiology. Third, analogous to, but with swifter effects than climate, wide-ranging global efforts, if well designed, will dramatically reduce domestic costs and resource requirements by curbing the spread of the disease and/or fostering relevant knowledge for managing containment and eradication. Accomplishing these tasks requires building the analytic capacity for engaging in reflexive anticipatory policy design exercises aimed at maintaining, or building, life-saving thermostatic institutions at the global and domestic levels.

Criteria for approximability of functions by solutions of homogeneous second order elliptic equations (with constant complex coefficients) in the norms of the Whitney $$C^1$$ -spaces on compact sets in $$\mathbb {R}^2$$ are obtained in terms of the respective $$C^1$$ -capacities. It is proved that the mentioned $$C^1$$ -capacities are comparable to the classic C-analytic capacity, and so have a proper geometric measure characterization.

For $K\subset\Bbb C$ compact, we say that $K$ has vanishing analytic capacity (or $\gamma(K)=0$) when all bounded analytic functions on $\Bbb C\backslash K$ are constant. We would like to characterize $\gamma (K)=0$ geometrically. Easily, $\gamma(K) > 0$ when $K$ has Hausdorff dimension larger than 1, and $\gamma(K)=0$ when $\dim (K) < 1$. Thus only the case when $\dim (K)=1$ is interesting. So far there is no characterization of $\gamma (K)=0$ in general, but the special case when the Hausdorff measure $H^1(K)$ is finite was recently settled. In this case, $\gamma(K)=0$ if and only if $K$ is unrectifiable (or Besicovitch-irregular), i.e., if $H^1(K\cap \Gamma)=0$ for all $C^1$-curves $\Gamma$, as was conjectured by Vitushkin. In the present text, we try to explain the structure of the proof of this result, and present the necessary techniques. These include the introduction to Menger curvature in this context (by M. Melnikov and co-authors), and the important use of geometric measure theory (results on quantitative rectifiability), but we insist most on the role of Calderón-Zygmund operators and $T(b)$-Theorems.

Resource allocation and capacity to implement policies are very important in social policy reforms. In many cases, the fiscal resource allocation is neither enough nor efficient. Information capacity and analytic capacity in managing social programs is another important issue. There are also institutional reasons behind this insufficient capacity. This chapter discusses issues in the policy capacity in managing and allocating resources. This chapter also argues that policy capacity could be endogenously determined by the structure of bureaucrats’ incentives.

We study the removable singularities for solutions to the Beltrami equation $\bar\partial f=\mu \partial f$, assuming that the coefficient $\mu$ lies on some Sobolev space $W^{1,p}$, $p\leq 2$. Our results are based on an extended version of the well known Weyl's lemma, asserting that distributional solutions are actually true solutions. Our main result is that quasiconformal mappings with compactly supported Beltrami coefficient $\mu\in W^{1,2}$ preserve compact sets of $\sigma$-finite length and vanishing analytic capacity, even though they need not be bilipschitz., Comment: 1 figure

We show that if a Cantor set $E$ as considered by Garnett in \cite{G2} has positive Hausdorff $h$-measure for a non-decreasing function $h$ satisfying $\int^1_0r^{-3}\,h(r)^2\,dr < \infty$, then the analytic capacity of $E$ is positive. Our tool will be the Menger three-point curvature and Melnikov's identity relating it to the Cauchy kernel. We shall also prove some related more general results.

We study the behavior of the analytic capacity of a compact set under deformations obtained by families of conformal maps depending holomorphically on the complex parameter. We show that, under those deformations, the logarithm of the analytic capacity varies harmonically. We also show that the hypotheses in this result cannot be substantially weakened.

The ability to analyze data to identify best practices is key to improving quality of care for community-based health care organizations (CBOs). Leading commercial statistical software remains too costly for many CBOs operating in underserved communities. The St Louis Integrated Health Network (IHN) collaborates with CBOs to increase access to health care. IHN and a local university developed the Community Analytics Academy (CAA), a training collaborative designed to meet the need for data-informed decision making among CBOs. Establishing analytics training collaboratives for CBOs empowers organizations to respond to the ever-growing amounts of health care data and the need for data-driven decision making.

We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity may not., Comment: 12 pages

We show that, given a family of discs centered at a chord-arc curve, the analytic capacity of a union of subsets of these discs (one subset in each disc) is comparable with the sum of their analytic capacities. However, we need the discs in question to be separated, and it is not clear whether the separation condition is essential. We apply this result to find families {μj} of measures in ℂ with the following property. If the Cauchy integral operators $${C_{{\mu _j}}}$$ from L2(μj) to itself are bounded uniformly in j, then Cμ, μ = Σμj, is also bounded from L2(μ) to itself.

Learning health systems (LHS) use digital health and care data to improve care, shorten the timeframe of improvement projects, and ensure these are based on real‐world data. In the United Kingdom, policymakers are depending on digital innovation, driven by better use of data about current health service performance, to enable service transformation and a more sustainable health system. This paper examines what would be needed to develop LHS in the United Kingdom, considering national policy implications and actions, which local organisations and health systems could take. The paper draws on a seminar attended by academics, policymakers, and practitioners, a brief literature review, and feedback from policy experts and National Health Service (NHS) stakeholders. Although there are examples of some aspects of LHS in the UK NHS, it is hard to find examples where there is a continuous cycle of improvement driven by information and where analysis of data and implementing improvements is part of usual ways of working. The seminar and literature identified a number of barriers. Incentives and capacity to develop LHS are limited, and requires a shift in analytic capacity from regulation and performance, to quality improvement and transformation. The balance in priority given to research compared with implementation also needs to change. Policy initiatives are underway which address some barriers, including building analytical capacity, developing infrastructure, and data standards. The NHS and research partners are investing in infrastructure which could support LHS, although clinical buy in is needed to bring about improvement or address operational challenges. We identify a number of opportunities for local NHS organisations and systems to make better use of health data, and for ways that national policy could promote the collaboration and greater use of analytics which underpin the LHS concept.

Retention measures in antiretroviral therapy programs are important, but there is wide variation in their calculation and relatively little systematic discussion of their relative advantages and limitations. We extracted and compared distinctive approaches to quantifying retention through a systematic search in PubMed and undertook a purposive selection of articles published in peer-reviewed journals and policy documents. We also created a simulated dataset and code examples to help illustrate observations about each metric. Among identified retention approaches, were metrics based only on proportions of either visits alone (constancy) or visits and appointments (visit adherence), which are simple and most accessible in settings using only paper records and registries. However, they are generally appropriate for patients with similar potential follow-up times and do not incorporate all available information. Survival analysis techniques such as Kaplan-Meier and competing risk approaches offer more nuanced retention measures over time, and can combine individuals with different potential follow-up times into one summary, but have trouble capturing the dynamic nature of retention. Newer approaches, including multi-state models and trajectory analyses, enable more nuanced examination of retention but are analytically difficult to carry out and do not yield one single summary. Simple analytical approaches are more widely useable but may miss important gaps in retention. Use of complex analytical approaches might be limited by requirements of electronically available data, data management requirements, and analytic capacity. Overall, efforts to evaluate retention may benefit from informed selection of one or more approaches to meet a range of objectives.

Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to introduce the p-continuous analytic capacity and variants of it, $p \in \{ 0, 1, 2, \cdots \} \cup \{ \infty \}$, for compact or closed sets in $\mathbb{C}$. We use these capacities in order to characterize the removability of singularities of functions in the spaces $A^p$., Comment: Corrected some typos and added some new results

We give new sufficient conditions for a compact set $E \subseteq \mathbb{C}$ to satisfy $\gamma(E)=\gamma_c(E)$, where $\gamma$ is the analytic capacity and $\gamma_c$ is the Cauchy capacity. As a consequence, we provide examples of compact plane sets such that the above equality holds but the Ahlfors function is not the Cauchy transform of any complex Borel measure supported on the set., Comment: 16 pages, 6 figures

We present a process to evaluate the continuing development of All Payer Claims Databases (APCDs) using a collaborative evaluation process. Project teams enhanced the Utah APCD with improved analytic capacity to provide online pricing and cost-transparency reports to support health care reform in Utah. Our program evaluation efforts added key methods and tools, building on recommendations in the APCD Development Manual to provide evaluation data facilitating improvements [1]. These additions included a Collaborative Evaluation Model, logic models, and development and use of best practices as measures. Stakeholders found that the added use of best practices, logic models, and frequent feedback to practitioners facilitated the project’s success. Since the Collaborative Evaluation Model served a structural purpose, it was transparent to the project teams.

Curricular theory must evolve to keep pace with the implications of the design, use, and effects of deploying and adapting digital curricular resources, especially when placed within digital learning systems (DLS) with rapid feedback and analytic capacity. We introduce an “agile curriculum” framework describing how to use classroom assessment data to regulate teachers’ practices of iteratively adapting curricula. Our DLS, called Math-Mapper 6–8, is introduced as an example with its diagnostic assessments of students’ progress along learning trajectories. An exploratory video study of middle school teachers reviewing, interpreting, and acting on its data, both during instruction (short cycle feedback) and within professional learning communities (long cycle feedback) illustrates how an agile curriculum framework supports data-driven adjustments based on student learning.