The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results

The mathematically correct computation of the spin glasses free energy in the infinite range limit crowns 25 years of mathematic efforts in solving this model. The exact solution of the model was found many years ago by using a heuristic approach; the results coming from the heuristic approach were crucial in deriving the mathematical results. The mathematical tools used in the rigorous approach are quite different from those of the heuristic approach. In this note we will review the heuristic approach to spin glasses in the light of the rigorous results; we will also discuss some conjectures that may be useful to derive the solution of the model in an alternative way.Comment: 12 pages, 1 figure; lecture at the Flato Colloquia Day, Thursday 27 November, 200

Statistical distribution of quantum entanglement for a random bipartite state

We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping the problem to a random matrix model and then using a Coulomb gas method. We identify three different regimes in the entropy distribution, which correspond to two phase transitions in the associated Coulomb gas. The two critical points correspond to sudden changes in the shape of the Coulomb charge density: the appearance of an integrable singularity at the origin for the first critical point, and the detachement of the rightmost charge (largest eigenvalue) from the sea of the other charges at the second critical point. Analytical results are verified by Monte Carlo numerical simulations. A short account of some of these results appeared recently in Phys. Rev. Lett. {\bf 104}, 110501 (2010).Comment: 7 figure

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phy

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

The Ising Susceptibility Scaling Function

We have dramatically extended the zero field susceptibility series at both high and low temperature of the Ising model on the triangular and honeycomb lattices, and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and, for the square and honeycomb lattices, the antiferromagnetic critical point.Comment: PDFLaTeX, 50 pages, 5 figures, zip file with series coefficients and background data in Maple format provided with the source files. Vs2: Added dedication and made several minor additions and corrections. Vs3: Minor corrections. Vs4: No change to eprint. Added essential square-lattice series input data (used in the calculation) that were removed from University of Melbourne's websit

Is metabolic syndrome predictive of prevalence, extent, and risk of coronary artery disease beyond its components? results from the multinational coronary ct angiography evaluation for clinical outcome: An international multicenter registry (confirm)

Although metabolic syndrome is associated with increased risk of cardiovascular disease and events, its added prognostic value beyond its components remains unknown. This study compared the prevalence, severity of coronary artery disease (CAD), and prognosis of patients with metabolic syndrome to those with individual metabolic syndrome components. The study cohort consisted of 27125 consecutive individuals who underwent ≥64-detector row coronary CT angiography (CCTA) at 12 centers from 2003 to 2009. Metabolic syndrome was defined as per NCEP/ATP III criteria. Metabolic syndrome patients (n=690) were matched 1:1:1 to those with 1 component (n=690) and 2 components (n=690) of metabolic syndrome for age, sex, smoking status, and family history of premature CAD using propensity scoring. Major adverse cardiac events (MACE) were defined by a composite of myocardial infarction (MI), acute coronary syndrome, mortality and late target vessel revascularization. Patients with 1 component of metabolic syndrome manifested lower rates of obstructive 1-, 2-, and 3-vessel/left main disease compared to metabolic syndrome patients (9.4% vs 13.8%, 2.6% vs 4.5%, and 1.0% vs 2.3%, respectively; p0.05). At 2.5 years, metabolic syndrome patients experienced a higher rate of MACE compared to patients with 1 component (4.4% vs 1.6%; p=0.002), while no difference observed compared to individuals with 2 components (4.4% vs 3.2% p=0.25) of metabolic syndrome. In conclusion, Metabolic syndrome patients have significantly greater prevalence, severity, and prognosis of CAD compared to patients with 1 but not 2 components of metabolic syndrome

Prognostic implications of coronary artery calcium in the absence of coronary artery luminal narrowing

Background and aims: Coronary artery calcium (CAC) scoring is a predictor of future adverse clinical events, and a surrogate measure of overall coronary artery plaque burden. Coronary computed tomographic angiography (CCTA) is a contrast-enhanced method that allows for visualization of plaque as well as whether that plaque causes luminal narrowing. To date, the prognosis of individuals with CAC but without stenosis has not been reported. We explored the prevalence of CAC>0 and its prognostic utility for future mortality for patients without luminal narrowing by CCTA. Methods: From 17 sites in 9 countries, we identified patients without known coronary artery disease, who underwent CAC scoring and CCTA, and were followed for >3 years. CCTA was graded for % stenosis according to a modified American Heart Association 16-segment model. We calculated hazard ratios (HR) with 95% confidence intervals (95% CI) for incident mortality and compared risk of death for patients as a function of presence or absence of CAC and presence or absence of luminal narrowing by CCTA. Results: Among 6656 patients who underwent CCTA and CAC scoring, 399 patients (6.0%) had no coronary luminal narrowing but CAC>0. During a median follow-up of 5.1 years (IQR: 3.9-5.9 years), 456 deaths occurred. Compared to individuals without luminal narrowing or CAC, individuals without luminal narrowing but CAC>0 were older, more likely to be male and had higher rates of diabetes, hypertension, and dyslipidemia. Individuals without luminal narrowing but CAC experienced a 2-fold increased risk of mortality, with increasing risk of mortality with higher CAC score. Following adjustment, incident death persisted (HR, 1.8; 95% CI, 1.1-2.9, p = 0.02) among patients without luminal narrowing but with CAC>0 compared with patients whose CACS = 0. Individuals without luminal narrowing but CAC ≥100 had mortality risks similar to individuals with non-obstructive CAD (0 < stenosis<50%) by CCTA [HR 2.5 (95% CI 1.3-4.9) and 2.2 (95% CI 1.6-3.0), respectively]. Conclusions: Patients without luminal narrowing but with CAC experienc

Coronary dominance and prognosis in patients undergoing coronary computed tomographic angiography: Results from the CONFIRM (COronary CTAngiography EvaluatioN for Clinical Outcomes: An InteRnational Multicenter) registry

Aims: Coronary computed tomographic angiography (CCTA) has become an important tool for non-invasive diagnosis of coronary artery disease (CAD). Coronary dominance can be assessed by CCTA; however, the predictive value of coronary dominance is controversially discussed. The aim of this study was to evaluate the prevalence and prognosis of coronary dominance in a large prospective, international multicentre cohort of patients undergoing CCTA. Methods and results: The study population consisted of 6382 patients with or without CAD (47% females, 53% males, mean age 56.9±12.3 years) who underwent CCTA and were followed over a period of 60 months. Right or left coronary dominance was determined. Right dominance was present in 91% (n = 5817) and left in 9% (n = 565) of the study population. At the end of follow-up, outcome in patients with obstructive CAD (>50% luminal stenosis) and right dominance was similar compared with patients with left dominance [hazard ratio (HR) 0.46, 95% CI 0.16-1.32, P = 0.15]. Furthermore, no differences were observed for the type of coronary dominance in patients with non-obstructive CAD(HR 0.95, 95% CI 0.41-2.21, P = 0.8962) or normal coronary arteries (HR 1.04, 95% CI 0.68-1.59, P = 0.9). Subgroup analysis in patients with left main disease revealed an elevated hazard of the combined endpoint for left dominance (HR 6.45, 95% CI 1.66-25.0, P = 0.007), but not for right dominance. Conclusion: In our study population, survival after 5 years of follow-up did not differ significantly between patientswith left or right coronary dominance. Thus, assessment of coronary vessel dominance by CCTA may not enhance risk stratification in patients with normal coronary arteries or obstructive CAD, but may add prognostic information for specific subpopulations

Incremental prognostic value of coronary computed tomography angiography over coronary calcium scoring for major adverse cardiac events in elderly asymptomatic individuals

Aims Coronary computed tomography angiography (CCTA) and coronary artery calcium score (CACS) have prognostic value for coronary artery disease (CAD) events beyond traditional risk assessment. Age is a risk factor with very high weight and little is known regarding the incremental value of CCTA over CAC for predicting cardiac events in older adults. Methods and results Of 27 125 individuals undergoing CCTA, a total of 3145 asymptomatic adults were identified. This study sample was categorized according to tertiles of age (cut-off points: 52 and 62 years). CAD severity was classified as 0, 1-49, and ≥50% maximal stenosis in CCTA, and further categorized according to number of vessels ≥50% stenosis. The Framingham 10-year risk score (FRS) and CACS were employed as major covariates. Major adverse cardiovascular events (MACE) were defined as a composite of all-cause death or non-fatal MI. During a median follow-up of 26 months (interquartile range: 18-41 months), 59 (1.9%) MACE occurred. For patients in the top age tertile, CCTA improved discrimination beyond a model included FRS and CACS (C-statistic: 0.75 vs. 0.70, P-value = 0.015). Likewise, the addition of CCTA improved category-free net reclassification (cNRI) of MACE in patients within the highest age tertile (e.g. cNRI = 0.75; proportion of events/non-events reclassified were 50 and 25%, respectively; P-value <0.05, all). CCTA displayed no incremental benefit beyond FRS and CACS for prediction of MACE in the lower age tertiles. Conclusion CCTA provides added prognostic value beyond cardiac risk factors and CACS for the prediction of MACE in asymptomatic older adults

Avaliação da Vergonha em Adolescentes: ‘The Other as Shamer Scale’

Shame, as a self-conscious, multidimensional and socially focused emotion, plays a central role in the mental health of individuals. In adolescents, shame is also a frequent experience and its assessment is important for research and clinical practice. This study aims to validate a brief measure of external shame (Other as Shamer Scale – brief version for adolescents: (OASB-A). The participants were 834 adolescents with a mean age of 15 years. The final model of the OASB-A (8 items), obtained through CFA, presents a good fit to the data. The OASB-A shows a good internal consistency and an adequate temporal reliability. The OASB-A also reveals significant correlations with traumatic shame experiences (IES-R) and psychopathological symptoms (DASS-21). The OASB-A is an economic and reliable measure to assess external shame in adolescents