Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.Comment: 4 pages, 7 figure

Orthogonality Catastrophe in Parametric Random Matrices

We study the orthogonality catastrophe due to a parametric change of the single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian is modeled by a suitable random matrix ensemble. We show that the overlap between the original and the parametrically modified many-body ground states, $S$, taken as Slater determinants, decreases like $n^{-k x^2}$, where $n$ is the number of electrons in the systems, $k$ is a numerical constant of the order of one, and $x$ is the deformation measured in units of the typical distance between anticrossings. We show that the statistical fluctuations of $S$ are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure

Assessment of Brain Age in Posttraumatic Stress Disorder: Findings from the ENIGMA PTSD and Brain Age Working Groups

Background Posttraumatic stress disorder (PTSD) is associated with markers of accelerated aging. Estimates of brain age, compared to chronological age, may clarify the effects of PTSD on the brain and may inform treatment approaches targeting the neurobiology of aging in the context of PTSD. Method Adult subjects (N = 2229; 56.2% male) aged 18–69 years (mean = 35.6, SD = 11.0) from 21 ENIGMA-PGC PTSD sites underwent T1-weighted brain structural magnetic resonance imaging, and PTSD assessment (PTSD+, n = 884). Previously trained voxel-wise (brainageR) and region-of-interest (BARACUS and PHOTON) machine learning pipelines were compared in a subset of control subjects (n = 386). Linear mixed effects models were conducted in the full sample (those with and without PTSD) to examine the effect of PTSD on brain predicted age difference (brain PAD; brain age − chronological age) controlling for chronological age, sex, and scan site. Results BrainageR most accurately predicted brain age in a subset (n = 386) of controls (brainageR: ICC = 0.71, R = 0.72, MAE = 5.68; PHOTON: ICC = 0.61, R = 0.62, MAE = 6.37; BARACUS: ICC = 0.47, R = 0.64, MAE = 8.80). Using brainageR, a three-way interaction revealed that young males with PTSD exhibited higher brain PAD relative to male controls in young and old age groups; old males with PTSD exhibited lower brain PAD compared to male controls of all ages. Discussion Differential impact of PTSD on brain PAD in younger versus older males may indicate a critical window when PTSD impacts brain aging, followed by age-related brain changes that are consonant with individuals without PTSD. Future longitudinal research is warranted to understand how PTSD impacts brain aging across the lifespan

A Comparison of Methods to Harmonize Cortical Thickness Measurements Across Scanners and Sites

Results of neuroimaging datasets aggregated from multiple sites may be biased by site-specific profiles in participants’ demographic and clinical characteristics, as well as MRI acquisition protocols and scanning platforms. We compared the impact of four different harmonization methods on results obtained from analyses of cortical thickness data: (1) linear mixed-effects model (LME) that models site-specific random intercepts (LME INT), (2) LME that models both site-specific random intercepts and age-related random slopes (LME INT+SLP), (3) ComBat, and (4) ComBat with a generalized additive model (ComBat-GAM). Our test case for comparing harmonization methods was cortical thickness data aggregated from 29 sites, which included 1,340 cases with posttraumatic stress disorder (PTSD) (6.2–81.8 years old) and 2,057 trauma-exposed controls without PTSD (6.3–85.2 years old). We found that, compared to the other data harmonization methods, data processed with ComBat-GAM was more sensitive to the detection of significant case-control differences (Χ 2(3) = 63.704, p < 0.001) as well as case-control differences in age-related cortical thinning (Χ 2(3) = 12.082, p = 0.007). Both ComBat and ComBat-GAM outperformed LME methods in detecting sex differences (Χ 2(3) = 9.114, p = 0.028) in regional cortical thickness. ComBat-GAM also led to stronger estimates of age-related declines in cortical thickness (corrected p-values < 0.001), stronger estimates of case-related cortical thickness reduction (corrected p-values < 0.001), weaker estimates of age-related declines in cortical thickness in cases than controls (corrected p-values < 0.001), stronger estimates of cortical thickness reduction in females than males (corrected p-values < 0.001), and stronger estimates of cortical thickness reduction in females relative to males in cases than controls (corrected p-values < 0.001). Our results support the use of ComBat-GAM to minimize confounds and increase statistical power when harmonizing data with non-linear effects, and the use of either ComBat or ComBat-GAM for harmonizing data with linear effects

Remodeling of the Cortical Structural Connectome in Posttraumatic Stress Disorder:Results from the ENIGMA-PGC PTSD Consortium

BACKGROUND: Posttraumatic stress disorder (PTSD) is accompanied by disrupted cortical neuroanatomy. We investigated alteration in covariance of structural networks associated with PTSD in regions that demonstrate the case-control differences in cortical thickness (CT) and surface area (SA). METHODS: Neuroimaging and clinical data were aggregated from 29 research sites in >1,300 PTSD cases and >2,000 trauma-exposed controls (age 6.2-85.2 years) by the ENIGMA-PGC PTSD working group. Cortical regions in the network were rank-ordered by effect size of PTSD-related cortical differences in CT and SA. The top-n (n = 2 to 148) regions with the largest effect size for PTSD > non-PTSD formed hypertrophic networks, the largest effect size for PTSD < non-PTSD formed atrophic networks, and the smallest effect size of between-group differences formed stable networks. The mean structural covariance (SC) of a given n-region network was the average of all positive pairwise correlations and was compared to the mean SC of 5,000 randomly generated n-region networks. RESULTS: Patients with PTSD, relative to non-PTSD controls, exhibited lower mean SC in CT-based and SA-based atrophic networks. Comorbid depression, sex and age modulated covariance differences of PTSD-related structural networks. CONCLUSIONS: Covariance of structural networks based on CT and cortical SA are affected by PTSD and further modulated by comorbid depression, sex, and age. The structural covariance networks that are perturbed in PTSD comport with converging evidence from resting state functional connectivity networks and networks impacted by inflammatory processes, and stress hormones in PTSD

Smaller total and subregional cerebellar volumes in posttraumatic stress disorder:a mega-analysis by the ENIGMA-PGC PTSD workgroup

Although the cerebellum contributes to higher-order cognitive and emotional functions relevant to posttraumatic stress disorder (PTSD), prior research on cerebellar volume in PTSD is scant, particularly when considering subregions that differentially map on to motor, cognitive, and affective functions. In a sample of 4215 adults (PTSD n = 1642; Control n = 2573) across 40 sites from the ENIGMA-PGC PTSD working group, we employed a new state-of-the-art deep-learning based approach for automatic cerebellar parcellation to obtain volumetric estimates for the total cerebellum and 28 subregions. Linear mixed effects models controlling for age, gender, intracranial volume, and site were used to compare cerebellum volumes in PTSD compared to healthy controls (88% trauma-exposed). PTSD was associated with significant grey and white matter reductions of the cerebellum. Compared to controls, people with PTSD demonstrated smaller total cerebellum volume, as well as reduced volume in subregions primarily within the posterior lobe (lobule VIIB, crus II), vermis (VI, VIII), flocculonodular lobe (lobule X), and corpus medullare (all p -FDR &lt; 0.05). Effects of PTSD on volume were consistent, and generally more robust, when examining symptom severity rather than diagnostic status. These findings implicate regionally specific cerebellar volumetric differences in the pathophysiology of PTSD. The cerebellum appears to play an important role in higher-order cognitive and emotional processes, far beyond its historical association with vestibulomotor function. Further examination of the cerebellum in trauma-related psychopathology will help to clarify how cerebellar structure and function may disrupt cognitive and affective processes at the center of translational models for PTSD.</p

Smaller total and subregional cerebellar volumes in posttraumatic stress disorder:a mega-analysis by the ENIGMA-PGC PTSD workgroup

Although the cerebellum contributes to higher-order cognitive and emotional functions relevant to posttraumatic stress disorder (PTSD), prior research on cerebellar volume in PTSD is scant, particularly when considering subregions that differentially map on to motor, cognitive, and affective functions. In a sample of 4215 adults (PTSD n = 1642; Control n = 2573) across 40 sites from the ENIGMA-PGC PTSD working group, we employed a new state-of-the-art deep-learning based approach for automatic cerebellar parcellation to obtain volumetric estimates for the total cerebellum and 28 subregions. Linear mixed effects models controlling for age, gender, intracranial volume, and site were used to compare cerebellum volumes in PTSD compared to healthy controls (88% trauma-exposed). PTSD was associated with significant grey and white matter reductions of the cerebellum. Compared to controls, people with PTSD demonstrated smaller total cerebellum volume, as well as reduced volume in subregions primarily within the posterior lobe (lobule VIIB, crus II), vermis (VI, VIII), flocculonodular lobe (lobule X), and corpus medullare (all p -FDR &lt; 0.05). Effects of PTSD on volume were consistent, and generally more robust, when examining symptom severity rather than diagnostic status. These findings implicate regionally specific cerebellar volumetric differences in the pathophysiology of PTSD. The cerebellum appears to play an important role in higher-order cognitive and emotional processes, far beyond its historical association with vestibulomotor function. Further examination of the cerebellum in trauma-related psychopathology will help to clarify how cerebellar structure and function may disrupt cognitive and affective processes at the center of translational models for PTSD.</p

A population genetic interpretation of GWAS findings for human quantitative traits.

Human genome-wide association studies (GWASs) are revealing the genetic architecture of anthropomorphic and biomedical traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes-notably, by mutation, natural selection, and genetic drift. Because many quantitative traits are subject to stabilizing selection and because genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabilizing selection in a multidimensional trait space. We solve the model for the phenotypic distribution and allelic dynamics at steady state and derive robust, closed-form solutions for summary statistics of the genetic architecture. Our results provide a simple interpretation for missing heritability and why it varies among traits. They predict that the distribution of variances contributed by loci identified in GWASs is well approximated by a simple functional form that depends on a single parameter: the expected contribution to genetic variance of a strongly selected site affecting the trait. We test this prediction against the results of GWASs for height and body mass index (BMI) and find that it fits the data well, allowing us to make inferences about the degree of pleiotropy and mutational target size for these traits. Our findings help to explain why the GWAS for height explains more of the heritable variance than the similarly sized GWAS for BMI and to predict the increase in explained heritability with study sample size. Considering the demographic history of European populations, in which these GWASs were performed, we further find that most of the associations they identified likely involve mutations that arose shortly before or during the Out-of-Africa bottleneck at sites with selection coefficients around s = 10-3