On realizing diagrams of Pi-algebras

Given a diagram of Pi-algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Pi-algebras. This extends a program begun in [J. Pure Appl. Alg. 103 (1995) 167-188] and [Topology 43 (2004) 857-892] to study the realization of a single Pi-algebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations.Comment: This is the version published by Algebraic & Geometric Topology on 21 June 200

G-protein-coupled receptor solubilization and purification for biophysical analysis and functional studies, in the total absence of detergent

G-protein coupled receptors (GPCRs) constitute the largest class of membrane proteins and are a major drug target. A serious obstacle to studying GPCR structure/function characteristics is the requirement to extract the receptors from their native environment in the plasma membrane, coupled with the inherent instability of GPCRs in the detergents required for their solubilization. In the present study, we report the first solubilization and purification of a functional GPCR [human adenosine A2A receptor (A2AR)], in the total absence of detergent at any stage, by exploiting spontaneous encapsulation by styrene maleic acid (SMA) co-polymer direct from the membrane into a nanoscale SMA lipid particle (SMALP). Furthermore, the A2AR-SMALP, generated from yeast (Pichia pastoris) or mammalian cells, exhibited increased thermostability (∼5°C) compared with detergent [DDM (n-dodecyl-β-D-maltopyranoside)]-solubilized A2AR controls. The A2AR-SMALP was also stable when stored for prolonged periods at 4°C and was resistant to multiple freeze-thaw cycles, in marked contrast with the detergent-solubilized receptor. These properties establish the potential for using GPCR-SMALP in receptor-based drug discovery assays. Moreover, in contrast with nanodiscs stabilized by scaffold proteins, the non-proteinaceous nature of the SMA polymer allowed unobscured biophysical characterization of the embedded receptor. Consequently, CD spectroscopy was used to relate changes in secondary structure to loss of ligand binding ([3H]ZM241385) capability. SMALP-solubilization of GPCRs, retaining the annular lipid environment, will enable a wide range of therapeutic targets to be prepared in native-like state to aid drug discovery and understanding of GPCR molecular mechanisms

Semaglutide and cardiovascular outcomes in patients with obesity and prevalent heart failure: a prespecified analysis of the SELECT trial

Background: Semaglutide, a GLP-1 receptor agonist, reduces the risk of major adverse cardiovascular events (MACE) in people with overweight or obesity, but the effects of this drug on outcomes in patients with atherosclerotic cardiovascular disease and heart failure are unknown. We report a prespecified analysis of the effect of once-weekly subcutaneous semaglutide 2·4 mg on ischaemic and heart failure cardiovascular outcomes. We aimed to investigate if semaglutide was beneficial in patients with atherosclerotic cardiovascular disease with a history of heart failure compared with placebo; if there was a difference in outcome in patients designated as having heart failure with preserved ejection fraction compared with heart failure with reduced ejection fraction; and if the efficacy and safety of semaglutide in patients with heart failure was related to baseline characteristics or subtype of heart failure. Methods: The SELECT trial was a randomised, double-blind, multicentre, placebo-controlled, event-driven phase 3 trial in 41 countries. Adults aged 45 years and older, with a BMI of 27 kg/m2 or greater and established cardiovascular disease were eligible for the study. Patients were randomly assigned (1:1) with a block size of four using an interactive web response system in a double-blind manner to escalating doses of once-weekly subcutaneous semaglutide over 16 weeks to a target dose of 2·4 mg, or placebo. In a prespecified analysis, we examined the effect of semaglutide compared with placebo in patients with and without a history of heart failure at enrolment, subclassified as heart failure with preserved ejection fraction, heart failure with reduced ejection fraction, or unclassified heart failure. Endpoints comprised MACE (a composite of non-fatal myocardial infarction, non-fatal stroke, and cardiovascular death); a composite heart failure outcome (cardiovascular death or hospitalisation or urgent hospital visit for heart failure); cardiovascular death; and all-cause death. The study is registered with ClinicalTrials.gov, NCT03574597. Findings: Between Oct 31, 2018, and March 31, 2021, 17 604 patients with a mean age of 61·6 years (SD 8·9) and a mean BMI of 33·4 kg/m2 (5·0) were randomly assigned to receive semaglutide (8803 [50·0%] patients) or placebo (8801 [50·0%] patients). 4286 (24·3%) of 17 604 patients had a history of investigator-defined heart failure at enrolment: 2273 (53·0%) of 4286 patients had heart failure with preserved ejection fraction, 1347 (31·4%) had heart failure with reduced ejection fraction, and 666 (15·5%) had unclassified heart failure. Baseline characteristics were similar between patients with and without heart failure. Patients with heart failure had a higher incidence of clinical events. Semaglutide improved all outcome measures in patients with heart failure at random assignment compared with those without heart failure (hazard ratio [HR] 0·72, 95% CI 0·60-0·87 for MACE; 0·79, 0·64-0·98 for the heart failure composite endpoint; 0·76, 0·59-0·97 for cardiovascular death; and 0·81, 0·66-1·00 for all-cause death; all pinteraction>0·19). Treatment with semaglutide resulted in improved outcomes in both the heart failure with reduced ejection fraction (HR 0·65, 95% CI 0·49-0·87 for MACE; 0·79, 0·58-1·08 for the composite heart failure endpoint) and heart failure with preserved ejection fraction groups (0·69, 0·51-0·91 for MACE; 0·75, 0·52-1·07 for the composite heart failure endpoint), although patients with heart failure with reduced ejection fraction had higher absolute event rates than those with heart failure with preserved ejection fraction. For MACE and the heart failure composite, there were no significant differences in benefits across baseline age, sex, BMI, New York Heart Association status, and diuretic use. Serious adverse events were less frequent with semaglutide versus placebo, regardless of heart failure subtype. Interpretation: In patients with atherosclerotic cardiovascular diease and overweight or obesity, treatment with semaglutide 2·4 mg reduced MACE and composite heart failure endpoints compared with placebo in those with and without clinical heart failure, regardless of heart failure subtype. Our findings could facilitate prescribing and result in improved clinical outcomes for this patient group. Funding: Novo Nordisk

ISARIC-COVID-19 dataset: A Prospective, Standardized, Global Dataset of Patients Hospitalized with COVID-19

publishedVersio

A Mathematical Framework for Trust Dynamics in Small-Scale Risk-Sharing Communities

This paper develops a rigorous mathematical framework for analyzing trust dynamics and statistical properties in small-scale risk-sharing communities. We establish that small pools with interdependent risks exhibit fundamentally different mathematical properties than large insurance systems, with volatility exceeding stability thresholds by a factor of √(N/Nc) and correlation structures reducing effective pool size by up to 89%. We formalize trust as a mathematically tractable variable with threshold stability properties, proving the existence of critical values TRcritical ∈ [0.65, 0.75] that create bifurcation points in system behavior. Our mathematical analysis demonstrates that network density directly determines trust propagation speed according to precise mathematical relationships. We prove that trust response exhibits asymmetric properties, with negative experiences having 1.5-2.5 times stronger impact than positive experiences of equal magnitude, creating hysteresis effects in system stability. By developing differential equations governing trust evolution and applying network diffusion models, we establish exact conditions for system stability and characterize phase transitions under parameter variation. The mathematical framework enables precise quantification of correlation penalties, network effects, and trust thresholds with applications to community-based risk-sharing systems where conventional statistical approaches fail. Our results transform qualitative concepts of trust and social capital into quantifiable mathematical variables with specific dynamics and stability properties.Diese Arbeit entwickelt ein rigoroses mathematisches Rahmenwerk zur Analyse von Vertrauensdynamiken und statistischen Eigenschaften in kleinskaligen Risikoausgleichsgemeinschaften. Wir zeigen, dass kleine Risikopools mit interdependenten Risiken grundlegend andere mathematische Eigenschaften aufweisen als groß angelegte Versicherungssysteme: Die Volatilität überschreitet die Stabilitätsschwellen um den Faktor √(N/Nc), und Korrelationsstrukturen reduzieren die effektive Poolgröße um bis zu 89%.Wir formalisieren Vertrauen als mathematisch behandelbare Variable mit stabilitätstheoretischen Schwellenwerten und weisen die Existenz kritischer Werte TR_critical ∈ [0,65; 0,75] nach, die als Bifurkationspunkte im Systemverhalten fungieren. Unsere mathematische Analyse zeigt, dass die Netzwerkkonnektivität die Geschwindigkeit der Vertrauensausbreitung direkt bestimmt, gemäß exakt ableitbaren mathematischen Beziehungen. Es wird nachgewiesen, dass die Vertrauensreaktion asymmetrisch verläuft: Negative Erfahrungen wirken sich 1,5- bis 2,5-mal stärker aus als gleichwertige positive Erlebnisse, was Hystereseeffekte in der Systemstabilität verursacht.Durch die Entwicklung von Differentialgleichungen zur Beschreibung der Vertrauensentwicklung sowie die Anwendung von Netzwerkdiffusionsmodellen definieren wir exakte Stabilitätsbedingungen und charakterisieren Phasenübergänge bei Parameterveränderungen. Das mathematische Rahmenwerk ermöglicht eine präzise Quantifizierung von Korrelationsverlusten, Netzwerkeffekten und Vertrauensschwellen – insbesondere in gemeinschaftsbasierten Risikoausgleichssystemen, in denen konventionelle statistische Verfahren versagen. Unsere Ergebnisse überführen qualitative Konzepte wie Vertrauen und Sozialkapital in quantifizierbare mathematische Variablen mit spezifischen Dynamiken und Stabilitätseigenschaften

Testing S=T×C×DB: A Universal Social Law?

This project tests whether societal success (S) follows a universal multiplicative law: S = T × C × DB, where Trust (T), Consensus (C), and Dual Benefit (DB) must ALL function above critical thresholds. The hypothesis predicts that when any component approaches zero, societal success collapses regardless of other components' strength. Building on validated discoveries (trust threshold τ*=0.68, consensus penalty α=0.109, dual benefit predictive accuracy 97.3%), we employ historical natural experiments, cross-national validation, and prospective predictions. All data, code, and analyses are publicly available. We invite collaboration and attempted refutation