Random Infinite-Volume Gibbs States for the Curie-Weiss Random Field Ising Model

An approach to the definition of infinite-volume Gibbs states for the (quenched) random-field Ising model is considered in the case of a Curie-Weiss ferromagnet. It turns out that these states are random quasi-free measures. They are random convex linear combinations of the free product-measures “shifted” by the corresponding effective mean fields. The conditional self-averaging property of the magnetization related to this randomness is also discussed

Moderate deviations for random field Curie-Weiss models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization $S_n$, which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number $m$, a positive real number $\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha}$ satisfies a moderate deviations principle with speed $n^{1-2k(1-\alpha)}$ and rate function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1)) < \alpha < 1$.Comment: 21 page

Metastates in mean-field models with random external fields generated by Markov chains

We extend the construction by Kuelske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that, for a degenerate non-reversible chain this CLT approximation is not enough and the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.Comment: 20 pages, 2 figure

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p&lt;0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p&lt;0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Effectiveness of thrombectomy in stroke according to baseline prognostic factors: inverse probability of treatment weighting analysis of a population-based registry

Background and Purpose In real-world practice, the benefit of mechanical thrombectomy (MT) is uncertain in stroke patients with very favorable or poor prognostic profiles at baseline. We studied the effectiveness of MT versus medical treatment stratifying by different baseline prognostic factors. Methods Retrospective analysis of 2,588 patients with an ischemic stroke due to large vessel occlusion nested in the population-based registry of stroke code activations in Catalonia from January 2017 to June 2019. The effect of MT on good functional outcome (modified Rankin Score ≤2) and survival at 3 months was studied using inverse probability of treatment weighting (IPTW) analysis in three pre-defined baseline prognostic groups: poor (if pre-stroke disability, age >85 years, National Institutes of Health Stroke Scale [NIHSS] >25, time from onset >6 hours, Alberta Stroke Program Early CT Score 3), good (if NIHSS <6 or distal occlusion, in the absence of poor prognostic factors), or reference (not meeting other groups’ criteria). Results Patients receiving MT (n=1,996, 77%) were younger, had less pre-stroke disability, and received systemic thrombolysis less frequently. These differences were balanced after the IPTW stratified by prognosis. MT was associated with good functional outcome in the reference (odds ratio [OR], 2.9; 95% confidence interval [CI], 2.0 to 4.4), and especially in the poor baseline prognostic stratum (OR, 3.9; 95% CI, 2.6 to 5.9), but not in the good prognostic stratum. MT was associated with survival only in the poor prognostic stratum (OR, 2.6; 95% CI, 2.0 to 3.3). Conclusions Despite their worse overall outcomes, the impact of thrombectomy over medical management was more substantial in patients with poorer baseline prognostic factors than patients with good prognostic factors

Metastates in Disordered Mean-Field Models: Random Field and Hopfield Models

We rigorously investigate the size dependence of disordered mean-field models with finite local spin space in terms of metastates. Thereby we provide an illustration of the framework of metastates for systems of randomly competing Gibbs measures. In particular we consider the thermodynamic limit of the empirical metastate 1/NΣNn=1δµn(η), where µn(η) is the Gibbs measure in the finite volume {1,..., n} and the frozen disorder variable η is fixed. We treat explicitly the Hopfield model with finitely many patterns and the Curie-Weiss random field Ising model. In both examples in the phase transition regime the empirical metastate is dispersed for large N. Moreover, it does not converge for a.e. η, but rather in distribution, for whose limits we give explicit expressions. We also discuss another notion of metastates, due to Aizenman and Wehr.