The WAY theorem and the quantum resource theory of asymmetry

The WAY theorem establishes an important constraint that conservation laws impose on quantum mechanical measurements. We formulate the WAY theorem in the broader context of resource theories, where one is constrained to a subset of quantum mechanical operations described by a symmetry group. Establishing connections with the theory of quantum state discrimination we obtain optimal unitaries describing the measurement of arbitrary observables, explain how prior information can permit perfect measurements that circumvent the WAY constraint, and provide a framework that establishes a natural ordering on measurement apparatuses through a decomposition into asymmetry and charge subsystems.Comment: 11 pages, 3 figure

Dynamics of a Quantum Reference Frame

We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyze the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in time which scales linearly with the size of the reference. This contrasts a recent conclusion of Bartlett et al. that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles

Estimating hypothetical estimands with causal inference and missing data estimators in a diabetes trial

The recently published ICH E9 addendum on estimands in clinical trials provides a framework for precisely defining the treatment effect that is to be estimated, but says little about estimation methods. Here we report analyses of a clinical trial in type 2 diabetes, targeting the effects of randomised treatment, handling rescue treatment and discontinuation of randomised treatment using the so-called hypothetical strategy. We show how this can be estimated using mixed models for repeated measures, multiple imputation, inverse probability of treatment weighting, G-formula and G-estimation. We describe their assumptions and practical details of their implementation using packages in R. We report the results of these analyses, broadly finding similar estimates and standard errors across the estimators. We discuss various considerations relevant when choosing an estimation approach, including computational time, how to handle missing data, whether to include post intercurrent event data in the analysis, whether and how to adjust for additional time-varying confounders, and whether and how to model different types of ICE separately

An in-situ pilot study to investigate the native clinical resistance of enamel to erosion

OBJECTIVES: To investigate the differences in susceptibility of the surface of native and polished enamel to dietary erosion using an in-situ model.METHODS: Thirty healthy volunteers (n = 10 per group) wore mandibular appliances containing 2 native and 2 polished enamel samples for 30 min after which, the samples were exposed to either an ex-vivo or in-vivo immersion in orange juice for 5, 10 or 15 min and the cycle repeated twice with an hour's interval between them. Samples were scanned with a non-contacting laser profilometer and surface roughness was extracted from the data, together with step height and microhardness change on the polished enamel samples.RESULTS: All volunteers completed the study. For native enamel there were no statistical difference between baseline roughness values versus post erosion. Polished enamel significantly increased mean (SD) Sa roughness from baseline for each group resulting in roughness change of 0.04 (0.03), 0.06 (0.04), 0.04 (0.03), 0.06 (0.03), 0.08 (0.05) and 0.09 (0.05) μm respectively. With statistical differences between roughness change 45 min in-vivo versus 45 min ex-vivo (p &lt; 0.05). Microhardness significantly decreased for each polished group, with statistical differences in hardness change between 30 min in-vivo versus 30 min ex-vivo (p &lt; 0.05), 45 min in-vivo versus 30 min ex-vivo (p &lt; 0.01), 45 min in-vivo versus 45 min ex-vivo (p &lt; 0.01).CONCLUSIONS: The native resistance to erosion provided clinically is a combination of the ultrastructure of outer enamel, protection from the salivary pellicle and the overall effects of the oral environment. CLINICALTRIALS.GOV IDENTIFIER: NCT03178968.CLINICAL SIGNIFICANCE: This study demonstrates that outer enamel is innately more resistant to erosion which is clinically relevant as once there has been structural breakdown at this level the effects of erosive wear will be accelerated.</p

Diagnosing students' difficulties in learning mathematics

This study considers the results of a diagnostic test of student difficulty and contrasts the difference in performance between the lower attaining quartile and the higher quartile. It illustrates a difference in qualitative thinking between those who succeed and those who fail in mathematics, illustrating a theory that those who fail are performing a more difficult type of mathematics (coordinating procedures) than those who succeed (manipulating concepts). Students who have to coordinate or reverse processes in time will encounter far greater difficulty than those who can manipulate symbols in a flexible way. The consequences of such a dichotomy and implications for remediation are then considered

New Technologies for Space Avionics, 1993

The report reviews a 1993 effort that investigated issues associated with the development of requirements, with the practice of concurrent engineering and with rapid prototyping, in the development of a next-generation Reaction Jet Drive Controller. This report details lessons learned, the current status of the prototype, and suggestions for future work. The report concludes with a discussion of the vision of future avionics architectures based on the principles associated with open architectures and integrated vehicle health management

In vitro influence of stem surface finish and mantle conformity on pressure generation in cemented hip arthroplasty

Background and purpose Under physiological loads, debonded cemented femoral stems have been shown to move within their cement mantle and generate a fluid pump that may facilitate peri-prosthetic osteolysis by pressurizing fluid and circulating wear debris. The long-term physiological loading of rough and polished tapered stems in vitro has shown differences in performance, with greater interface pressures generated by the rough stems. In this study we investigated the individual effects of stem surface finish, degree of mantle wear, and mode of loading on the stem pump mechanism

Technical Support Document for Version 3.9.0 of the COMcheck Software

COMcheck provides an optional way to demonstrate compliance with commercial and high-rise residential building energy codes. Commercial buildings include all use groups except single family and multifamily not over three stories in height. COMcheck was originally based on ANSI/ASHRAE/IES Standard 90.1-1989 (Standard 90.1-1989) requirements and is intended for use with various codes based on Standard 90.1, including the Codification of ASHRAE/IES Standard 90.1-1989 (90.1-1989 Code) (ASHRAE 1989a, 1993b) and ASHRAE/IESNA Standard 90.1-1999 (Standard 90.1-1999). This includes jurisdictions that have adopted the 90.1-1989 Code, Standard 90.1-1989, Standard 90.1-1999, or their own code based on one of these. We view Standard 90.1-1989 and the 90.1-1989 Code as having equivalent technical content and have used both as source documents in developing COMcheck. This technical support document (TSD) is designed to explain the technical basis for the COMcheck software as originally developed based on the ANSI/ASHRAE/IES Standard 90.1-1989 (Standard 90.1-1989). Documentation for other national model codes and standards and specific state energy codes supported in COMcheck has been added to this report as appendices. These appendices are intended to provide technical documentation for features specific to the supported codes and for any changes made for state-specific codes that differ from the standard features that support compliance with the national model codes and standards. Beginning with COMcheck version 3.8.0, support for 90.1-1989, 90.1-1999, and the 1998 IECC are no longer included, but those sections remain in this document for reference purposes