Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential

The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" singularities in the "oil domain" of the Schwarz function are stationary, and the "physical" singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17] (1989). A generalization is also given for the so-called "elliptic growth" problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n - techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing "globalizing families". We make three conjectures in potential theory relating to our investigation

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

Policy Experimentation and Innovation as a Response to Complexity in China’s Management of Health Reforms

There are increasing criticisms of dominant models for scaling up health systems in developing countries and a recognition that approaches are needed that better take into account the complexity of health interventions. Since Reform and Opening in the late 1970s, Chinese government has managed complex, rapid and intersecting reforms across many policy areas. As with reforms in other policy areas, reform of the health system has been through a process of trial and error. There is increasing understanding of the importance of policy experimentation and innovation in many of China’s reforms; this article argues that these processes have been important in rebuilding China’s health system. While China’s current system still has many problems, progress is being made in developing a functioning system able to ensure broad population access. The article analyses Chinese thinking on policy experimentation and innovation and their use in management of complex reforms. It argues that China’s management of reform allows space for policy tailoring and innovation by sub-national governments under a broad agreement over the ends of reform, and that shared understandings of policy innovation, alongside informational infrastructures for the systemic propagation and codification of useful practices, provide a framework for managing change in complex environments and under conditions of uncertainty in which ‘what works’ is not knowable in advance. The article situates China’s use of experimentation and innovation in management of health system reform in relation to recent literature which applies complex systems thinking to global health, and concludes that there are lessons to be learnt from China’s approaches to managing complexity in development of health systems for the benefit of the poor

How is success achieved by individuals innovating for patient safety and quality in the NHS?

Background: Innovation in healthcare is said to be notoriously difficult to achieve and sustain yet simultaneously the health service is under intense pressure to innovate given the ever increasing demands placed upon it. Whilst many studies have looked at diffusion of innovation from an organisational perspective, few have sought to understand how individuals working in healthcare innovate successfully. We took a positive deviance approach to understand how innovations are achieved by individuals working in the NHS. Method: We conducted in depth interviews in 2015 with 15 individuals who had received a national award for being a successful UK innovator in healthcare. We invited only those people who were currently (or had recently) worked in the NHS and whose innovation focused on improving patient safety or quality. Thematic analysis was used. Findings: Four themes emerged from the data: personal determination, the ability to broker relationships and make connections, the ways in which innovators were able to navigate organisational culture to their advantage and their ability to use evidence to influence others. Determination, focus and persistence were important personal characteristics of innovators as were skills in being able to challenge the status quo. Innovators were able to connect sometimes disparate teams and people, being the broker between them in negotiating collaborative working. The culture of the organisation these participants resided in was important with some being able to use this (and the current patient safety agenda) to their advantage. Gathering robust data to demonstrate their innovation had a positive impact and was seen as essential to its progression. Conclusions: This paper reveals a number of factors which are important to the success of innovators in healthcare. We have uncovered that innovators have particular personal traits which encourage a propensity towards change and action. Yet, for fruitful innovation to take place, it is important for relational networks and organisational culture to be receptive to change