Hilbert's tenth problem for weak theories of arithmetic

AbstractHilbert's tenth problem for a theory T asks if there is an algorithm which decides for a given polynomial p(x̄) from Z[x̄] whether p(x̄) has a root in some model of T. We examine some of the model-theoretic consequences that an affirmative answer would have in cases such as T = Open Induction and others, and apply these methods by providing a negative answer in the cases when T is some particular finite fragment of the weak theories IE1 (bounded existential induction) or IU-1 (parameter-free bounded universal induction)

The Universal Cloud and Aerosol Sounding System (UCASS): a low-cost miniature optical particle counter for use in dropsonde or balloon-borne sounding systems

© Author(s) 2019. This work is distributed under the Creative Commons Attribution 4.0 License. An earlier version of this work was published in Atmospheric Measurement Techniques Discussions: https://dx.doi.org/10.5194/amt-2019-70.A low-cost miniaturized particle counter has been developed by The University of Hertfordshire (UH) for the measurement of aerosol and droplet concentrations and size distributions. The Universal Cloud and Aerosol Sounding System (UCASS) is an optical particle counter (OPC), which uses wide-angle elastic light scattering for the high-precision sizing of fluid-borne particulates. The UCASS has up to 16 configurable size bins, capable of sizing particles in the range 0.4–40 µm in diameter. Unlike traditional particle counters, the UCASS is an open-geometry system that relies on an external air flow. Therefore, the instrument is suited for use as part of a dropsonde, balloon-borne sounding system, as part of an unmanned aerial vehicle (UAV), or on any measurement platform with a known air flow. Data can be logged autonomously using an on-board SD card, or the device can be interfaced with commercially available meteorological sondes to transmit data in real time. The device has been deployed on various research platforms to take measurements of both droplets and dry aerosol particles. Comparative results with co-located instrumentation in both laboratory and field settings show good agreement for the sizing and counting ability of the UCASS.Peer reviewe

Incidence of rough and irregular atmospheric ice particles from Small Ice Detector 3 measurements

NERC, NE/E011225/1 © Author(s) 2013. This work is distributed under the Creative Commons Attribution 3.0 LicenseThe knowledge of properties of ice crystals such as size, shape, concavity and roughness is critical in the context of radiative properties of ice and mixed phase clouds. Limitations of current cloud probes to measure these properties can be circumvented by acquiring two-dimensional light scattering patterns instead of particle images. Such patterns were obtained in situ for the first time using the Small Ice Detector 3 (SID-3) probe during several flights in a variety of mid-latitude mixed phase and cirrus clouds. The patterns are analyzed using several measures of pattern texture, selected to reveal the magnitude of particle roughness or complexity. The retrieved roughness is compared to values obtained from a range of well-characterized test particles in the laboratory. It is found that typical in situ roughness corresponds to that found in the rougher subset of the test particles, and sometimes even extends beyond the most extreme values found in the laboratory. In this study we do not differentiate between small-scale, fine surface roughness and large-scale crystal complexity. Instead, we argue that both can have similar manifestations in terms of light scattering properties and also similar causes. Overall, the in situ data is consistent with ice particles with highly irregular or rough surfaces being dominant. Similar magnitudes of roughness were found in growth and sublimation zones of cirrus. The roughness was found to be negatively correlated with the halo ratio, but not with other thermodynamic or microphysical properties found in situ. Slightly higher roughness was observed in cirrus forming in clean oceanic airmasses than in a continental, polluted one. Overall, the roughness and complexity is expected to lead to increased shortwave cloud reflectivity, in comparison with cirrus composed of more regular, smooth ice crystal shapes. These findings put into question suggestions that climate could be modified through aerosol seeding to reduce cirrus cover and optical depth, as the seeding may result in decreased shortwave reflectivity.Peer reviewe

Analysis of stratospheric ozone, temperature, and minor constituent data

The objective of this research is to use available satellite measurements of temperature and constituent concentrations to test the conceptual picture of stratospheric chemistry and transport. This was originally broken down into two sub-goals: first, to use the constituent data to search for critical tests of our understanding of stratospheric chemistry and second, to examine constituent transport processes emphasizing interactions with chemistry on various time scales. A third important goal which has evolved is to use the available solar backscattered ultraviolet (SBUV) and Total Ozone Mapping Spectrometer (TOMS) data from Nimbus 7 to describe the morphology of recent changes in Antarctic and global ozone with emphasis on searching for constraints to theories. The major effort now being pursued relative to the two original goals is our effort as a theoretical team for the Arctic Airborne Stratospheric Expedition (AASE). Our effort for the AASE is based on the 3D transport and chemistry model at Goddard. Our goal is to use this model to place the results from the mission data in a regional and global context. Specifically, we set out to make model runs starting in late December and running through March of 1989, both with and without heterogeneous chemistry. The transport is to be carried out using dynamical fields from a 4D data assimilation model being developed under separate funding from this task. We have successfully carried out a series of single constituent transport experiments. One of the things demonstrated by these runs was the difficulty in obtaining observed low N2O abundances in the vortex without simultaneously obtaining very high ozone values. Because the runs start in late December, this difficulty arises in the attempt to define consistent initial conditions for the 3D model. To accomplish a consistent set of initial conditions, we are using the 2D photochemistry-transport model of Jackman and Douglass and mapping in potential temperature, potential vorticity space as developed by Schoeberl and coworkers

Patient perceptions of physician empathy, satisfaction with physician, interpersonal trust, and compliance

Objectives: This study was designed to investigate psychometric properties of the Jefferson Scale of Patient Perceptions of Physician Empathy (JSPPPE), and to examine correlations between its scores and measures of overall satisfaction with physicians, personal trust, and indicators of patient compliance. Methods: Research participants included 535 out-patients (between 18-75 years old, 66% female). A survey was mailed to participants which included the JSPPPE (5-item), a scale for measuring overall satisfaction with the primary care physician (10-item), and demographic questions. Patients were also asked about compliance with their physician\u27s recommendation for preventive tests (colonoscopy, mammogram, and PSA for age and gender appropriate patients). Results: Factor analysis of the JSPPPE resulted in one prominent component. Corrected item-total score correlations ranged from .88 to .94. Correlation between scores of the JSPPPE and scores on the patient satisfaction scale was 0.93. Scores of the JSPPPE were highly correlated with measures of physician-patient trust (r \u3e.73). Higher scores of the JSPPPE were significantly associated with physicians\u27 recommendations for preventive tests (colonoscopy, mammogram, and PSA) and with compliance rates which were \u3e .80). Cronbach\u27s coefficient alpha for the JSPPPE ranged from .97 to .99 for the total sample and for patients in different gender and age groups. Conclusions: Empirical evidence supported the psychometrics of the JSPPPE, and confirmed significant links with patients\u27 satisfaction with their physicians, interpersonal trust, and compliance with physicians\u27 recommendations. Availability of this psychometrically sound instrument will facilitate empirical research on empathy in patient care in different countries

Interpretations between ω-logic and second-order arithmetic

AbstractThis paper addresses the structures (M, ω) and (ω, SSy(M)), whereMis a nonstandard model of PA andωis the standard cut. It is known that (ω, SSy(M)) is interpretable in (M, ω). Our main technical result is that there is an reverse interpretation of (M, ω) in (ω, SSy(M)) which is ‘local’ in the sense of Visser [11]. We also relate the model theory of (M, ω) to the study of transplendent models of PA [2].This yields a number of model theoretic results concerning theω-models (M, ω) and their standard systems SSy(M, ω), including the following.•$\left( {M,\omega } \right) \prec \left( {K,\omega } \right)$if and only if$M \prec K$and$\left( {\omega ,{\rm{SSy}}\left( M \right)} \right) \prec \left( {\omega ,{\rm{SSy}}\left( K \right)} \right)$.•$\left( {\omega ,{\rm{SSy}}\left( M \right)} \right) \prec \left( {\omega ,{\cal P}\left( \omega \right)} \right)$if and only if$\left( {M,\omega } \right) \prec \left( {{M^{\rm{*}}},\omega } \right)$for someω-saturatedM*.•$M{ \prec _{\rm{e}}}K$implies SSy(M, ω) = SSy(K, ω), but cofinal extensions do not necessarily preserve standard system in this sense.• SSy(M, ω)=SSy(M) if and only if (ω, SSy(M)) satisfies the full comprehension scheme.• If SSy(M, ω) is uniformly defined by a single formula (analogous to aβfunction), then (ω, SSy(M, ω)) satisfies the full comprehension scheme; and there are modelsMfor which SSy(M, ω) is not uniformly defined in this sense.</jats:p