Wright meets Markowitz: How standard portfolio theory changes when assets are technologies following experience curves

We consider how to optimally allocate investments in a portfolio of competing technologies using the standard mean-variance framework of portfolio theory. We assume that technologies follow the empirically observed relationship known as Wright's law, also called a "learning curve" or "experience curve", which postulates that costs drop as cumulative production increases. This introduces a positive feedback between cost and investment that complicates the portfolio problem, leading to multiple local optima, and causing a trade-off between concentrating investments in one project to spur rapid progress vs. diversifying over many projects to hedge against failure. We study the two-technology case and characterize the optimal diversification in terms of progress rates, variability, initial costs, initial experience, risk aversion, discount rate and total demand. The efficient frontier framework is used to visualize technology portfolios and show how feedback results in nonlinear distortions of the feasible set. For the two-period case, in which learning and uncertainty interact with discounting, we compare different scenarios and find that the discount rate plays a critical role

Composition-solubility-structure relationships in calcium (alkali) aluminosilicate hydrate (C-(N,K-)A-S-H)

The interplay between the solubility, structure and chemical composition of calcium (alkali) aluminosilicate hydrate (C-(N,K-)A-S-H) equilibrated at 50 °C is investigated in this paper. The tobermorite-like C-(N,K-)A-S-H products are more crystalline in the presence of alkalis, and generally have larger basal spacings at lower Ca/Si ratios. Both Na and K are incorporated into the interlayer space of the C-(N,K-)A-S-H phases, with more alkali uptake observed at higher alkali and lower Ca content. No relationship between Al and alkali uptake is identified at the Al concentrations investigated (Al/Si ≤ 0.1). More stable C-(N,K-)A-S-H is formed at higher alkali content, but this factor is only significant in some samples with Ca/Si ratios ≤1. Shorter chain lengths are formed at higher alkali and Ca content, and cross-linking between (alumino)silicate chains in the tobermorite-like structure is greatly promoted by increasing alkali and Al concentrations. The calculated solubility products do not depend greatly on the mean chain length in C-(N,K-)A-S-H at a constant Ca/(Al + Si) ratio, or the Al/Si ratio in C-(N,K-)A-S-H. These results are important for understanding the chemical stability of C-(N,K-)A-S-H, which is a key phase formed in the majority of cements and concretes used worldwide

A thermodynamic model for C-(N-)A-S-H gel: CNASH_ss. Derivation and validation

The main reaction product in Ca-rich alkali-activated cements and hybrid Portland cement (PC)-based materials is a calcium (alkali) aluminosilicate hydrate (C-(N-)A-S-H) gel. Thermodynamic models without explicit definitions of structurally-incorporated Al species have been used in numerous past studies to describe this gel, but offer limited ability to simulate the chemistry of blended PC materials and alkali-activated cements. Here, a thermodynamic model for C-(N-)A-S-H gel is derived and parameterised to describe solubility data for the CaO–(Na2O,Al2O3)–SiO2–H2O systems and alkali-activated slag (AAS) cements, and chemical composition data for C-A-S-H gels. Simulated C-(N-)A-S-H gel densities and molar volumes are consistent with the corresponding values reported for AAS cements, meaning that the model can be used to describe chemical shrinkage in these materials. Therefore, this model can provide insight into the chemistry of AAS cements at advanced ages, which is important for understanding the long-term durability of these materials

Effectiveness of a national quality improvement programme to improve survival after emergency abdominal surgery (EPOCH): a stepped-wedge cluster-randomised trial

Background: Emergency abdominal surgery is associated with poor patient outcomes. We studied the effectiveness of a national quality improvement (QI) programme to implement a care pathway to improve survival for these patients. Methods: We did a stepped-wedge cluster-randomised trial of patients aged 40 years or older undergoing emergency open major abdominal surgery. Eligible UK National Health Service (NHS) hospitals (those that had an emergency general surgical service, a substantial volume of emergency abdominal surgery cases, and contributed data to the National Emergency Laparotomy Audit) were organised into 15 geographical clusters and commenced the QI programme in a random order, based on a computer-generated random sequence, over an 85-week period with one geographical cluster commencing the intervention every 5 weeks from the second to the 16th time period. Patients were masked to the study group, but it was not possible to mask hospital staff or investigators. The primary outcome measure was mortality within 90 days of surgery. Analyses were done on an intention-to-treat basis. This study is registered with the ISRCTN registry, number ISRCTN80682973. Findings: Treatment took place between March 3, 2014, and Oct 19, 2015. 22 754 patients were assessed for elegibility. Of 15 873 eligible patients from 93 NHS hospitals, primary outcome data were analysed for 8482 patients in the usual care group and 7374 in the QI group. Eight patients in the usual care group and nine patients in the QI group were not included in the analysis because of missing primary outcome data. The primary outcome of 90-day mortality occurred in 1210 (16%) patients in the QI group compared with 1393 (16%) patients in the usual care group (HR 1·11, 0·96–1·28). Interpretation: No survival benefit was observed from this QI programme to implement a care pathway for patients undergoing emergency abdominal surgery. Future QI programmes should ensure that teams have both the time and resources needed to improve patient care. Funding: National Institute for Health Research Health Services and Delivery Research Programme

Effectiveness of a national quality improvement programme to improve survival after emergency abdominal surgery (EPOCH): a stepped-wedge cluster-randomised trial

BACKGROUND: Emergency abdominal surgery is associated with poor patient outcomes. We studied the effectiveness of a national quality improvement (QI) programme to implement a care pathway to improve survival for these patients. METHODS: We did a stepped-wedge cluster-randomised trial of patients aged 40 years or older undergoing emergency open major abdominal surgery. Eligible UK National Health Service (NHS) hospitals (those that had an emergency general surgical service, a substantial volume of emergency abdominal surgery cases, and contributed data to the National Emergency Laparotomy Audit) were organised into 15 geographical clusters and commenced the QI programme in a random order, based on a computer-generated random sequence, over an 85-week period with one geographical cluster commencing the intervention every 5 weeks from the second to the 16th time period. Patients were masked to the study group, but it was not possible to mask hospital staff or investigators. The primary outcome measure was mortality within 90 days of surgery. Analyses were done on an intention-to-treat basis. This study is registered with the ISRCTN registry, number ISRCTN80682973. FINDINGS: Treatment took place between March 3, 2014, and Oct 19, 2015. 22 754 patients were assessed for elegibility. Of 15 873 eligible patients from 93 NHS hospitals, primary outcome data were analysed for 8482 patients in the usual care group and 7374 in the QI group. Eight patients in the usual care group and nine patients in the QI group were not included in the analysis because of missing primary outcome data. The primary outcome of 90-day mortality occurred in 1210 (16%) patients in the QI group compared with 1393 (16%) patients in the usual care group (HR 1·11, 0·96-1·28). INTERPRETATION: No survival benefit was observed from this QI programme to implement a care pathway for patients undergoing emergency abdominal surgery. Future QI programmes should ensure that teams have both the time and resources needed to improve patient care. FUNDING: National Institute for Health Research Health Services and Delivery Research Programme

Dynamics in the Hopf bundle, the geometric phase and implications for dynamical systems.

A Hopf bundle framework is constructed within Cn, in terms of which general paths on Cn ____ {0} are viewed and analyzed. The resulting hierarchy of spaces is addressed both theoretically and numerically, and the consequences for numerics and applications are investigated through a wide range of numerical experiments. The geometric reframing of Cn in this way - in terms of an intrinsic fibre bundle - allows for the introduction of bundle-theoretic quantities in a general dynamical setting. The roles of the various structural elements of the bundle are explored, including horizontal and vertical subspaces, parallel translation and connections. These concepts lead naturally to the association of a unique geometric phase with each path on Cn ____ {0}. This phase quantity is interpreted as a measure of the spinning in the S1 fibre of the Hopf bundle induced by paths on Cn ____ {0}, relative to a given connection, and is shown to be an important quantity. The implications of adopting this bundle viewpoint are investigated in two specific contexts. The first is the case of the lowest-dimensional Hopf bundle, S1 → S3 → S2. Here the quaternionic matrices are used to develop a simplified, geometrically intuitive formulation of the bundle structure, and a reduced expression for the phase is used to compute numerical phase results in three example systems. The second is the case where paths in Cn ____ {0} are generated by solutions to a particular class of parameter-dependent first-order ODEs. This establishes a direct link between the dynamical characteristics of such systems and the underlying bundle geometry. A variety of systems are examined and numerical phase results compiled. The numerics reveal an important correlation between the spectral properties of the path-generating ODEs and the resultant geometric phase change values. The details of this observed link are recorded in a conjecture

Dynamiccs in the Hopf Bundle, The Geometric Phase and Implications for Dynamical Systems

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Comparing expert elicitation and model-based probabilistic technology cost forecasts for the energy transition.

We conduct a systematic comparison of technology cost forecasts produced by expert elicitation methods and model-based methods. Our focus is on energy technologies due to their importance for energy and climate policy. We assess the performance of several forecasting methods by generating probabilistic technology cost forecasts rooted at various years in the past and then comparing these with observed costs in 2019. We do this for six technologies for which both observed and elicited data are available. The model-based methods use either deployment (Wright's law) or time (Moore's law) to forecast costs. We show that, overall, model-based forecasting methods outperformed elicitation methods. Their 2019 cost forecast ranges contained the observed values much more often than elicitations, and their forecast medians were closer to observed costs. However, all methods underestimated technological progress in almost all technologies, likely as a result of structural change across the energy sector due to widespread policies and social and market forces. We also produce forecasts of 2030 costs using the two types of methods for 10 energy technologies. We find that elicitations generally yield narrower uncertainty ranges than model-based methods. Model-based 2030 forecasts are lower for more modular technologies and higher for less modular ones. Future research should focus on further method development and validation to better reflect structural changes in the market and correlations across technologies