Essential Incompleteness of Arithmetic Verified by Coq

A constructive proof of the Goedel-Rosser incompleteness theorem has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive functions are proved to be representable in a weak axiom system. Formulas and proofs are encoded as natural numbers, and functions operating on these codes are proved to be primitive recursive. The weak axiom system is proved to be essentially incomplete. In particular, Peano arithmetic is proved to be consistent in Coq's type theory and therefore is incomplete.Comment: This paper is part of the proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005). For the associated Coq source files see the TeX sources, or see <http://r6.ca/Goedel20050512.tar.gz

The Relative Value of AER P&P Economic Education Papers

The CEE had been allocated one session in the AER Papers and Proceedings (P&P) since 1964. In 2008, the American Economic Association evaluated the allocation of AER Papers and Proceedings sessions to various AEA Committees. In response, the CEE was asked to prepare a one-page rationale for keeping that session. Their response (Committee on Economic Education, 2008) made several important defenses of the session, including that the quality of the papers published in these sessions must speak for itself. In this paper, we propose to evaluate the relative quality of AER P&P papers through citation analysis. Using the Social Science Citation Index, the citation counts of CEE AER P&P papers are compared to other papers included in the issue

Advanced Characterization of Fractured Reservoirs in Carbonate Rocks: The Michigan Basin

The main objective of this project is for a university-industry consortium to develop a comprehensive model for fracture carbonate reservoirs based on the ''data cube'' concept using the Michigan Basin as a prototype. This project combined traditional historical data with 2D and 3D seismic data as well as data from modern logging tools in a novel way to produce a new methodology for characterizing fractured reservoirs in carbonate rocks. Advanced visualization software was used to fuse the data and to image it on a variety of scales, ranging from basin-scale to well-scales

The Importance of Time Congruity in the Organisation.

In 1991 Kaufman, Lane, and Lindquist proposed that time congruity in terms of an individual's time preferences and the time use methods of an organisation would lead to satisfactory performance and enhancement of quality of work and general life. The research reported here presents a study which uses commensurate person and job measures of time personality in an organisational setting to assess the effects of time congruity on one aspect of work life, job-related affective well-being. Results show that time personality and time congruity were found to have direct effects on well-being and the influence of time congruity was found to be mediated through time personality, thus contributing to the person–job (P–J) fit literature which suggests that direct effects are often more important than indirect effects. The study also provides some practical examples of ways to address some of the previously cited methodological issues in P–J fit research

Identifying and prioritising services in European terrestrial and freshwater ecosystems

Ecosystems are multifunctional and provide humanity with a broad array of vital services. Effective management of services requires an improved evidence base, identifying the role of ecosystems in delivering multiple services, which can assist policy-makers in maintaining them. Here, information from the literature and scientific experts was used to systematically document the importance of services and identify trends in their use and status over time for the main terrestrial and freshwater ecosystems in Europe. The results from this review show that intensively managed ecosystems contribute mostly to vital provisioning services (e.g. agro-ecosystems provide food via crops and livestock, and forests provide wood), while semi-natural ecosystems (e.g. grasslands and mountains) are key contributors of genetic resources and cultural services (e.g. aesthetic values and sense of place). The most recent European trends in human use of services show increases in demand for crops from agro-ecosystems, timber from forests, water flow regulation from rivers, wetlands and mountains, and recreation and ecotourism in most ecosystems, but decreases in livestock production, freshwater capture fisheries, wild foods and virtually all services associated with ecosystems which have considerably decreased in area (e.g. semi-natural grasslands). The condition of the majority of services show either a degraded or mixed status across Europe with the exception of recent enhancements in timber production in forests and mountains, freshwater provision, water/erosion/natural hazard regulation and recreation/ecotourism in mountains, and climate regulation in forests. Key gaps in knowledge were evident for certain services across all ecosystems, including the provision of biochemicals and natural medicines, genetic resources and the regulating services of seed dispersal, pest/disease regulation and invasion resistance

Fluctuations in the Cosmic Microwave Background I: Form Factors and their Calculation in Synchronous Gauge

It is shown that the fluctuation in the temperature of the cosmic microwave background in any direction may be evaluated as an integral involving scalar and dipole form factors, which incorporate all relevant information about acoustic oscillations before the time of last scattering. A companion paper gives asymptotic expressions for the multipole coefficient $C_\ell$ in terms of these form factors. Explicit expressions are given here for the form factors in a simplified hydrodynamic model for the evolution of perturbations.Comment: 35 pages, no figures. Improved treatment of damping, including both Landau and Silk damping; inclusion of late-time effects; several references added; minor changes and corrections made. Accepted for publication in Phys. Rev. D1

Large-scale Roll Out of Electronic Longitudinal Mood-Monitoring for Research in Affective Disorders: Report From the UK Bipolar Disorder Research Network

Background Electronic longitudinal mood monitoring has been shown to be acceptable to patients with affective disorders within clinical settings, but its use in large-scale research has not yet been established. Methods Using both postal and email invitations, we invited 4080 past research participants with affective disorders who were recruited into the Bipolar Disorder Research Network (BDRN) over a 10 year period to participate in online weekly mood monitoring. In addition, since January 2015 we have invited all newly recruited BDRN research participants to participate in mood monitoring at the point they were recruited into BDRN. Results Online mood monitoring uptake among past participants was 20, and among new participants to date was 46 with participants recruited over the last year most likely to register (61). More than 90 mood monitoring participants engaged for at least one month, with mean engagement period greater than one year (58 weeks) and maximum engagement for longer than three years (165 weeks). There were no significant differences in the proportion of past and new BDRN participants providing data for at least 4 weeks (91, 92 respectively), 3 months (78, 82), 6 months (65, 54) or one year (51, 44). Limitations Our experiences with recruiting participants for electronic prospective mood monitoring may not necessarily generalise fully to research situations that are very different from those we describe. Conclusions Large-scale electronic longitudinal mood monitoring in affective disorders for research purposes is feasible with uptake highest among newly recruited participants

Toroidal modelling of plasma response and RMP field penetration

The penetration dynamics of the resonant magnetic perturbation (RMP) field is sim- ulated in the full toroidal geometry, under realistic plasma conditions in MAST experiments. The physics associated with several aspects of the RMP penetration - the plasma response and rotational screening, the resonant and non-resonant torques and the toroidal momentum balance - are highlighted. In particular, the plasma response is found to significantly amplify the non-resonant component of the RMP field for some of the MAST plasmas. A fast rotating plasma, in response to static external magnetic fields, experiences a more distributed electro- magnetic torque due to the resonance with continuum waves in the plasma. At fast plasma flow (such as for the MAST plasma), the electromagnetic torque is normally dominant over the neoclassical toroidal viscous (NTV) torque. However, at sufficiently slow plasma flow, the NTV torque can play a significant role in the toroidal momentum balance, thanks to the precession drift resonance enhanced, so called superbanana plateau regime

The use of dose quantities in radiological protection: ICRP publication 147 Ann ICRP 50(1) 2021.

The International Commission on Radiological Protection has recently published a report (ICRP Publication 147;Ann. ICRP50, 2021) on the use of dose quantities in radiological protection, under the same authorship as this Memorandum. Here, we present a brief summary of the main elements of the report. ICRP Publication 147 consolidates and clarifies the explanations provided in the 2007 ICRP Recommendations (Publication 103) but reaches conclusions that go beyond those presented in Publication 103. Further guidance is provided on the scientific basis for the control of radiation risks using dose quantities in occupational, public and medical applications. It is emphasised that best estimates of risk to individuals will use organ/tissue absorbed doses, appropriate relative biological effectiveness factors and dose-risk models for specific health effects. However, bearing in mind uncertainties including those associated with risk projection to low doses or low dose rates, it is concluded that in the context of radiological protection, effective dose may be considered as an approximate indicator of possible risk of stochastic health effects following low-level exposure to ionising radiation. In this respect, it should also be recognised that lifetime cancer risks vary with age at exposure, sex and population group. The ICRP report also concludes that equivalent dose is not needed as a protection quantity. Dose limits for the avoidance of tissue reactions for the skin, hands and feet, and lens of the eye will be more appropriately set in terms of absorbed dose rather than equivalent dose

Simulating Cosmic Microwave Background maps in multi-connected spaces

This article describes the computation of cosmic microwave background anisotropies in a universe with multi-connected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multi-connected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps.Comment: 33 pages, 55 figures, submitted to PRD. Higher resolution figures available on deman