The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $\beta$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta- \beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2, \gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $\alpha$.Comment: Version accepted for publication in PRE, revtex

Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization

The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in $^{40}$Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affects the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.Comment: 14 pages, 4 Figures, Illinois preprint P-93-12-106, Figures available from the author

The Information Geometry of the Spherical Model

Motivated by previous observations that geometrizing statistical mechanics offers an interesting alternative to more standard approaches,we have recently calculated the curvature (the fundamental object in this approach) of the information geometry metric for the Ising model on an ensemble of planar random graphs. The standard critical exponents for this model are alpha=-1, beta=1/2, gamma=2 and we found that the scalar curvature, R, behaves as epsilon^(-2),where epsilon = beta_c - beta is the distance from criticality. This contrasts with the naively expected R ~ epsilon^(-3) and the apparent discrepancy was traced back to the effect of a negative alpha on the scaling of R. Oddly,the set of standard critical exponents is shared with the 3D spherical model. In this paper we calculate the scaling behaviour of R for the 3D spherical model, again finding that R ~ epsilon^(-2), coinciding with the scaling behaviour of the Ising model on planar random graphs. We also discuss briefly the scaling of R in higher dimensions, where mean-field behaviour sets in.Comment: 7 pages, no figure

Statistics of pre-localized states in disordered conductors

The distribution function of local amplitudes of single-particle states in disordered conductors is calculated on the basis of the supersymmetric $\sigma$-model approach using a saddle-point solution of its reduced version. Although the distribution of relatively small amplitudes can be approximated by the universal Porter-Thomas formulae known from the random matrix theory, the statistics of large amplitudes is strongly modified by localization effects. In particular, we find a multifractal behavior of eigenstates in 2D conductors which follows from the non-integer power-law scaling for the inverse participation numbers (IPN) with the size of the system. This result is valid for all fundamental symmetry classes (unitary, orthogonal and symplectic). The multifractality is due to the existence of pre-localized states which are characterized by power-law envelopes of wave functions, $|\psi_t(r)|^2\propto r^{-2\mu}$, $\mu <1$. The pre-localized states in short quasi-1D wires have the power-law tails $|\psi (x)|^2\propto x^{-2}$, too, although their IPN's indicate no fractal behavior. The distribution function of the largest-amplitude fluctuations of wave functions in 2D and 3D conductors has logarithmically-normal asymptotics.Comment: RevTex, 17 twocolumn pages; revised version (several misprint corrected

Both “illness and temptation of the enemy”: melancholy, the medieval patient and the writings of King Duarte of Portugal (r. 1433–38)

Recent historians have rehabilitated King Duarte of Portugal, previously maligned and neglected, as an astute ruler and philosopher. There is still a tendency, however, to view Duarte as a depressive or a hypochondriac, due to his own description of his melancholy in his advice book, the Loyal Counselor. This paper reassesses Duarte's writings, drawing on key approaches in the history of medicine, such as narrative medicine and the history of the patient. It is important to take Duarte's views on his condition seriously, placing them in the medical and theological contexts of his time and avoiding modern retrospective diagnosis. Duarte's writings can be used to explore the impact of plague, doubt and death on the life of a well-educated and conscientious late-medieval ruler

Rare Coding Variants Associated With Electrocardiographic Intervals Identify Monogenic Arrhythmia Susceptibility Genes: A Multi-Ancestry Analysis

Background: Alterations in electrocardiographic (ECG) intervals are well-known markers for arrhythmia and sudden cardiac death (SCD) risk. While the genetics of arrhythmia syndromes have been studied, relations between electrocardiographic intervals and rare genetic variation at a population level are poorly understood. Methods: Using a discovery sample of 29 000 individuals with whole-genome sequencing from Trans-Omics in Precision Medicine and replication in nearly 100 000 with whole-exome sequencing from the UK Biobank and MyCode, we examined associations between low-frequency and rare coding variants with 5 routinely measured electrocardiographic traits (RR, P-wave, PR, and QRS intervals and corrected QT interval). Results: We found that rare variants associated with population-based electrocardiographic intervals identify established monogenic SCD genes (KCNQ1, KCNH2, and SCN5A), a controversial monogenic SCD gene (KCNE1), and novel genes (PAM and MFGE8) involved in cardiac conduction. Loss-of-function and pathogenic SCN5A variants, carried by 0.1% of individuals, were associated with a nearly 6-fold increased odds of the first-degree atrioventricular block (P=8.4×10-5). Similar variants in KCNQ1 and KCNH2 (0.2% of individuals) were associated with a 23-fold increased odds of marked corrected QT interval prolongation (P=4×10-25), a marker of SCD risk. Incomplete penetrance of such deleterious variation was common as over 70% of carriers had normal electrocardiographic intervals. Conclusions: Our findings indicate that large-scale high-depth sequence data and electrocardiographic analysis identifies monogenic arrhythmia susceptibility genes and rare variants with large effects. Known pathogenic variation in conventional arrhythmia and SCD genes exhibited incomplete penetrance and accounted for only a small fraction of marked electrocardiographic interval prolongation

Track D Social Science, Human Rights and Political Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd

Whole-exome sequence analysis of anthropometric traits illustrates challenges in identifying effects of rare genetic variants

Anthropometric traits, measuring body size and shape, are highly heritable and significant clinical risk factors for cardiometabolic disorders. These traits have been extensively studied in genome-wide association studies (GWASs), with hundreds of genome-wide significant loci identified. We performed a whole-exome sequence analysis of the genetics of height, body mass index (BMI) and waist/hip ratio (WHR). We meta-analyzed single-variant and gene-based associations of whole-exome sequence variation with height, BMI, and WHR in up to 22,004 individuals, and we assessed replication of our findings in up to 16,418 individuals from 10 independent cohorts from Trans-Omics for Precision Medicine (TOPMed). We identified four trait associations with single-nucleotide variants (SNVs; two for height and two for BMI) and replicated the LECT2 gene association with height. Our expression quantitative trait locus (eQTL) analysis within previously reported GWAS loci implicated CEP63 and RFT1 as potential functional genes for known height loci. We further assessed enrichment of SNVs, which were monogenic or syndromic variants within loci associated with our three traits. This led to the significant enrichment results for height, whereas we observed no Bonferroni-corrected significance for all SNVs. With a sample size of ∼20,000 whole-exome sequences in our discovery dataset, our findings demonstrate the importance of genomic sequencing in genetic association studies, yet they also illustrate the challenges in identifying effects of rare genetic variants

Multi-ancestry GWAS of the electrocardiographic PR interval identifies 202 loci underlying cardiac conduction

The electrocardiographic PR interval reflects atrioventricular conduction, and is associated with conduction abnormalities, pacemaker implantation, atrial fibrillation (AF), and cardiovascular mortality. Here we report a multi-ancestry (N = 293,051) genome-wide association meta-analysis for the PR interval, discovering 202 loci of which 141 have not previously been reported. Variants at identified loci increase the percentage of heritability explained, from 33.5% to 62.6%. We observe enrichment for cardiac muscle developmental/contractile and cytoskeletal genes, highlighting key regulation processes for atrioventricular conduction. Additionally, 8 loci not previously reported harbor genes underlying inherited arrhythmic syndromes and/or cardiomyopathies suggesting a role for these genes in cardiovascular pathology in the general population. We show that polygenic predisposition to PR interval duration is an endophenotype for cardiovascular disease, including distal conduction disease, AF, and atrioventricular pre-excitation. These findings advance our understanding of the polygenic basis of cardiac conduction, and the genetic relationship between PR interval duration and cardiovascular disease