Algebrai logika; relativitáselmélet logikai struktúrájának vizsgálata = Algebraic logic; investigating the logical structure of relativity theory

Gödel, Einstein és Tarski hagyományait kívánjuk folytatni, elmélyítve a Gödel-Einstein együttműködés eredményeit is, és folytatva Tarski tudományegyesítési programmját. Ismert, hogy a logika és a matematika modern megalapozása Gödel és Tarski úttörő munkásságára vezethető vissza. Kevésbbé ismert, hogy Gödel 1948-tól majdnem élete végéig Einsteinnel szorosan együttműködve relativitáselméleten dolgozott, ahol ugyanolyan meghökkentő új horizontokat tárt fel mint logikában, és hogy Gödel relativitáselméleti gondolatai folytatásaként fogható fel a forgó fekete lyukak mai elmélete. Ezen előzmények folytatása a jelen projektum, mely Tarskival és munkatársaival való személyes együttműködés (pl. közös könyv) keretében kezdődött. Az alapgondolat a logika, algebra, geometria, téridőelmélet és relativitáselmélet egységben való művelése. Eredményeinkből egy példa: Nagy, lassan forgó fekete lyukakról bizonyítottuk, hogy a belsejében létrejövő un. zárt időszerű görbe (időhurok) létrejöttére vonatkozó szokásos irodalmi magyarázatok tévesek. Nem az un. drag effect (mozgó anyag magával vonszolja a téridőt) okozza a zárt görbéket, hanem egy egészen más jellegű hatás: a fénykúpok kinyílása a forgással ellentétes irányban. Az eredmény a General Relativity and Gravitation című folyóiratban jelenik meg. | The reported project intends to continue traditions of Gödel, Einstein and Tarski continuing the spirit of the Gödel-Einstein collaboration and pursuing Tarski's programme for unifying science. Modern logic and meta-mathematics was created (basically) by Gödel and Tarski. It is less well known that beginning with 1948 Gödel spent much time with Einstein and worked on relativity theory. Of course, he remained a logician in spirit. Gödel obtained fundamental breakthroughs in relativity like his ones in logic and foundations. The theory of general relativistic spacetimes not admitting a global Time was initiated by Gödel, and came to full blossom during the renaissance of black hole physics during the last 25 years. The present project was originally started in personal cooperation with Tarski and his collaborators. The idea is to study logic, algebra, geometry, spacetime theory and relativity in a strong unity. A sample result of ours: We proved about big, slowly rotating black holes that the usual explanation in the literature of why such black holes contain a closed timelike curve (CTC) is flawed. Namely, it is not the gravitational frame dragging effect which creates CTCs, instead, there is a completely different kind of effect in action there: light cones open up in the direction opposite to that of the rotation of the source and this goes on to such an extreme extent that CTCs are created. Our paper on this appears in the journal General Relativity and Gravitation

Development of Risk Prediction Equations for Incident Chronic Kidney Disease

IMPORTANCE ‐ Early identification of individuals at elevated risk of developing chronic kidney disease  could improve clinical care through enhanced surveillance and better management of underlying health  conditions.  OBJECTIVE – To develop assessment tools to identify individuals at increased risk of chronic kidney  disease, defined by reduced estimated glomerular filtration rate (eGFR).  DESIGN, SETTING, AND PARTICIPANTS – Individual level data analysis of 34 multinational cohorts from  the CKD Prognosis Consortium including 5,222,711 individuals from 28 countries. Data were collected  from April, 1970 through January, 2017. A two‐stage analysis was performed, with each study first  analyzed individually and summarized overall using a weighted average. Since clinical variables were  often differentially available by diabetes status, models were developed separately within participants  with diabetes and without diabetes. Discrimination and calibration were also tested in 9 external  cohorts (N=2,253,540). EXPOSURE Demographic and clinical factors.  MAIN OUTCOMES AND MEASURES – Incident eGFR <60 ml/min/1.73 m2.  RESULTS – In 4,441,084 participants without diabetes (mean age, 54 years, 38% female), there were  660,856 incident cases of reduced eGFR during a mean follow‐up of 4.2 years. In 781,627 participants  with diabetes (mean age, 62 years, 13% female), there were 313,646 incident cases during a mean follow‐up of 3.9 years. Equations for the 5‐year risk of reduced eGFR included age, sex, ethnicity, eGFR, history of cardiovascular disease, ever smoker, hypertension, BMI, and albuminuria. For participants  with diabetes, the models also included diabetes medications, hemoglobin A1c, and the interaction  between the two. The risk equations had a median C statistic for the 5‐year predicted probability of  0.845 (25th – 75th percentile, 0.789‐0.890) in the cohorts without diabetes and 0.801 (25th – 75th percentile, 0.750‐0.819) in the cohorts with diabetes. Calibration analysis showed that 9 out of 13 (69%) study populations had a slope of observed to predicted risk between 0.80 and 1.25. Discrimination was  similar in 18 study populations in 9 external validation cohorts; calibration showed that 16 out of 18 (89%) had a slope of observed to predicted risk between 0.80 and 1.25. CONCLUSIONS AND RELEVANCE – Equations for predicting risk of incident chronic kidney disease developed in over 5 million people from 34 multinational cohorts demonstrated high discrimination and  variable calibration in diverse populations

Serum potassium and adverse outcomes across the range of kidney function: a CKD Prognosis Consortium meta-analysis.

Aims: Both hypo- and hyperkalaemia can have immediate deleterious physiological effects, and less is known about long-term risks. The objective was to determine the risks of all-cause mortality, cardiovascular mortality, and end-stage renal disease associated with potassium levels across the range of kidney function and evaluate for consistency across cohorts in a global consortium. Methods and results: We performed an individual-level data meta-analysis of 27 international cohorts [10 general population, 7 high cardiovascular risk, and 10 chronic kidney disease (CKD)] in the CKD Prognosis Consortium. We used Cox regression followed by random-effects meta-analysis to assess the relationship between baseline potassium and adverse outcomes, adjusted for demographic and clinical characteristics, overall and across strata of estimated glomerular filtration rate (eGFR) and albuminuria. We included 1 217 986 participants followed up for a mean of 6.9 years. The average age was 55 ± 16 years, average eGFR was 83 ± 23 mL/min/1.73 m2, and 17% had moderate- to-severe increased albuminuria levels. The mean baseline potassium was 4.2 ± 0.4 mmol/L. The risk of serum potassium of >5.5 mmol/L was related to lower eGFR and higher albuminuria. The risk relationship between potassium levels and adverse outcomes was U-shaped, with the lowest risk at serum potassium of 4-4.5 mmol/L. Compared with a reference of 4.2 mmol/L, the adjusted hazard ratio for all-cause mortality was 1.22 [95% confidence interval (CI) 1.15-1.29] at 5.5 mmol/L and 1.49 (95% CI 1.26-1.76) at 3.0 mmol/L. Risks were similar by eGFR, albuminuria, renin-angiotensin-aldosterone system inhibitor use, and across cohorts. Conclusions: Outpatient potassium levels both above and below the normal range are consistently associated with adverse outcomes, with similar risk relationships across eGFR and albuminuria