Three equivalent ordinal notation systems in cubical Agda

We present three ordinal notation systems representing ordinals below epsilon zero in type theory, using recent type-theoretical innovations such as mutual inductive-inductive definitions and higher inductive types. We show how ordinal arithmetic can be developed for these systems, and how they admit a transfinite induction principle. We prove that all three notation systems are equivalent, so that we can transport results between them using the univalence principle. All our constructions have been implemented in cubical Agda

Suspected retinopathies in Norwegian optometric practice with emphasis on patients with diabetes: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>The scope of optometry differs worldwide. In Norway the vast majority of optometrists perform ophthalmoscopy as part of their routine examinations. The aim of this study was to describe the frequency of <it>suspected </it>retinopathies in patients seen for routine optometric examination and to determine how optometrists deal with these patients.</p> <p>Methods</p> <p>212 optometrists participated in a questionnaire survey and a practice registration during November 2004 – May 2005. In the practice registration, details for 20 consecutive patient encounters were recorded. Data were analysed by chi-square tests and multiple logistic regression.</p> <p>Results</p> <p>All optometrist stated that ocular history taking was an integrated part of their routine examination, while general health and diabetes history were routinely addressed by 59% and 42% of the optometrists, respectively. During the practice registration 4,052 patient encounters were recorded. Ophthalmoscopy was performed in 88% of the patients, of which 2% were dilated fundus examinations. Retinopathy was <it>suspected </it>in 106 patients, of whom 31 did not report a previous history of ocular or systemic disease. Old age (75+), hypertension and diabetes strongly predicted retinopathy with odds ratio (95% CI) of 6.4 (4.2 to 9.9), 3.8 (2.4 to 6.0) and 2.5 (1.4 to 4.7), respectively. Diabetic retinopathy was seen in 10% of diabetic patients and <it>suspected </it>in 0.2% of patients with no established history of diabetes. Retinopathy was not confirmed in 9 out 18 patients with a history of diabetic retinopathy; seven of these had undergone laser treatment. Out of the 106 patients with findings of retinopathy, 28 were referred to an ophthalmologist or a general practitioner (GP), written reports were sent to a GP in 16 cases, ten patients were urged to contact their GP for further follow up, while 52 were considered in need of routine optometric follow up only.</p> <p>Conclusion</p> <p>Optometric practice provides a low threshold setting for detecting cases of ocular disease and retinal manifestations of systemic disease in the population. At present diagnosis of retinopathy in Norwegian optometric practice is unreliable. There are potentials for improving the optometrists' routine examination, their patient management patterns and collaboration routines with medical doctors.</p

Care of vision and ocular health in diabetic members of a national diabetes organization: A cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Regular examination and early treatment of diabetic retinopathy can prevent visual loss. The aim of the study was to describe the care of vision and ocular health in people with diabetes in Norway.</p> <p>Methods</p> <p>A cross-sectional questionnaire survey of a random sample (n = 1,887) of the Norwegian Diabetic Associations' (NDA) members was carried out in 2005. Questions were asked about care of vision and ocular health, history of ocular disease and visual symptoms, general medical history and diabetes management. The study was approved by the Regional Committee for Medical Research Ethics.</p> <p>Results</p> <p>The response rate was 74%. Forty-four questionnaires with incomplete data regarding gender, age or type of diabetes were excluded, leaving 1352 cases (52% females) for analysis. 451 (33%) had type 1 and 901 (67%) had type 2 diabetes, the mean duration of diabetes was respectively, 22 (sd ± 14) and 10 (sd ± 9) years. In all 1,052 (78%) had their eyes examined according to guidelines and 1,169 (87%) confirmed to have received information about regular eye examinations. One in two recalled to have received such information from their general practitioner. To have received information about the importance of eye examinations (PR 3.1, 95% CI 2.4 to 4.0), and diabetes duration > 10 years (PR 1.2, 95% CI 1.2 to 1.3), were independently associated with reporting regular eye examinations. A history of diabetic retinopathy was reported by 178 (13%) responders, of which 101 (57%) reported a history of laser treatment. Responders who had regular eye examinations reported more frequently a history of diabetic retinopathy (19% vs. 5%, p < 0.001). The frequency of retinopathy was significantly higher in responders with reported HbA1c values above treatment target (23% vs. 13%, p = 0.001). However, in responders who were not regularly examined, there was no difference in reported frequency of retinopathy with regard to HbA1c level.</p> <p>Conclusion</p> <p>Eight out of ten diabetic members of the NDA had their eyes examined according to current guidelines and the majority was well informed about the risk of vision loss due to diabetes. The results indicate that the reported history of diabetic retinopathy likely underestimates the prevalence of retinopathy.</p

Empirical correlation of triggered activity and spatial and temporal re-entrant substrates with arrhythmogenicity in a murine model for Jervell and Lange-Nielsen syndrome

KCNE1 encodes the β-subunit of the slow component of the delayed rectifier K+ current. The Jervell and Lange-Nielsen syndrome is characterized by sensorineural deafness, prolonged QT intervals, and ventricular arrhythmogenicity. Loss-of-function mutations in KCNE1 are implicated in the JLN2 subtype. We recorded left ventricular epicardial and endocardial monophasic action potentials (MAPs) in intact, Langendorff-perfused mouse hearts. KCNE1−/− but not wild-type (WT) hearts showed not only triggered activity and spontaneous ventricular tachycardia (VT), but also VT provoked by programmed electrical stimulation. The presence or absence of VT was related to the following set of criteria for re-entrant excitation for the first time in KCNE1−/− hearts: Quantification of APD90, the MAP duration at 90% repolarization, demonstrated alterations in (1) the difference, ∆APD90, between endocardial and epicardial APD90 and (2) critical intervals for local re-excitation, given by differences between APD90 and ventricular effective refractory period, reflecting spatial re-entrant substrate. Temporal re-entrant substrate was reflected in (3) increased APD90 alternans, through a range of pacing rates, and (4) steeper epicardial and endocardial APD90 restitution curves determined with a dynamic pacing protocol. (5) Nicorandil (20 µM) rescued spontaneous and provoked arrhythmogenic phenomena in KCNE1−/− hearts. WTs remained nonarrhythmogenic. Nicorandil correspondingly restored parameters representing re-entrant criteria in KCNE1−/− hearts toward values found in untreated WTs. It shifted such values in WT hearts in similar directions. Together, these findings directly implicate triggered electrical activity and spatial and temporal re-entrant mechanisms in the arrhythmogenesis observed in KCNE1−/− hearts

On Relating Theories: Proof-Theoretical Reduction

The notion of proof-theoretical or finitistic reduction of one theory to another has a long tradition. Feferman and Sieg (Buchholz et al., Iterated inductive definitions and subsystems of analysis. Springer, Berlin, 1981, Chap. 1) and Feferman in (J Symbol Logic 53:364–384, 1988) made first steps to delineate it in more formal terms. The first goal of this paper is to corroborate their view that this notion has the greatest explanatory reach and is superior to others, especially in the context of foundational theories, i.e., theories devised for the purpose of formalizing and presenting various chunks of mathematics. A second goal is to address a certain puzzlement that was expressed in Feferman’s title of his Clermont-Ferrand lectures at the Logic Colloquium 1994: “How is it that finitary proof theory became infinitary?” Hilbert’s aim was to use proof theory as a tool in his finitary consistency program to eliminate the actual infinite in mathematics from proofs of real statements. Beginning in the 1950s, however, proof theory began to employ infinitary methods. Infinitary rules and concepts, such as ordinals, entered the stage. In general, the more that such infinitary methods were employed, the farther did proof theory depart from its initial aims and methods, and the closer did it come instead to ongoing developments in recursion theory, particularly as generalized to admissible sets; in both one makes use of analogues of regular cardinals, as well as “large” cardinals (inaccessible, Mahlo, etc.). (Feferman 1994). The current paper aims to explain how these infinitary tools, despite appearances to the contrary, can be formalized in an intuitionistic theory that is finitistically reducible to (actually Π02 -conservative over) intuitionistic first order arithmetic, also known as Heyting arithmetic. Thus we have a beautiful example of Hilbert’s program at work, exemplifying the Hilbertian goal of moving from the ideal to the real by eliminating ideal elements

Scandinavian society for the study of diabetes Abstracts Seventh Meeting

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46039/1/125_2005_Article_BF01219478.pd

1963:4

ARTIKLAR Gustaf Aulén: Gudsföreställningar i Aniara G. W. H. Lampe: Nattvardsgemenskap. En anglikansk standpunkt Jacob Jervell: Agape og menighetsordning. Omkring i Kor 12–14 TEOLOGISK LITTERATUR La Sainte Bible traduite en français sous la direction de l’Êcole Biblique de Jérusalem. Habaquq. Abdias. Joël, traduits par J. Trinquet. 2:e édition revue. Anm. av Joh. Lindblom Gillis Gerleman: Ruth. Biblischer Kommentar. Altes Testament, XVIII:1. Anm. av Joh. Lindblom Emilia Fogelklou: Minnesbilder och ärenden. Anm. av Joh. Lindblom Hans Volz: Martin Luthers Thesenanschlag und dessen Vorgeschichte. Erwin Iserloh: Luthers Thesenanschlag – Tatsache oder Legende? Anm. av Henrik Caspari D. Martin Luthers Werke. Kritische Gesamtausgabe. 55. Band. Anm. av Bengt Hägglund Kurt Aland (red.): Luther Deutsch. Die Werke Martin Luthers in neuer Auswahl für die Gegenwart. Band 2. Der Reformator. Band 5. Die Schriftauslegung. Anm. av Bengt Hägglund Die Religion in Geschichte und Gegenwart. Handwörterbuch für Theologie und Religionswissenschaft. Anm. av Gottfried Hornig Karl Rahner & Joseph Ratzinger: Episkopat und Primat, Quaestiones Disputatae. Anm. av Vilmos Vajta FRÅN DEN TEOLOGISKA SAMTIDEN Vilmos Vajta: Det teologiska arbetet i Helsingfors Lars Österlin: Angloskandinavisk konferens i Rugb

Multifunctionality of agricultural activities, changin rural identies and new institutional arrangements

This paper builds on the outcomes of a state-of-the-art review of research for the European research project MULTAGRI, with a particular focus on the conceptualisation of Multifunctional Agriculture (MFA) from a 'supply side' perspective. It argues that a consistent and satisfactory conceptual framework for studying the supply of MFA at farm and territorial level is still largely lacking and that, when consistently applied, the recognition of the multifunctionality of agriculture fundamentally challenges the ways in which agricultural activities are observed, analysed and their effects assessed. This is elaborated by discussing five 'critical questions' for studying the supply of MFA: (1) what are relevant functions of agriculture? (2) how to define agricultural activities? (3) how to identify relevant farm/firm categories? (4) how to study the role of changing rural identities? and (5) what is the role of new territorial and institutional arrangements