Moyal star product approach to the Bohr-Sommerfeld approximation

The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The Hamiltonian need only have a Weyl transform (or symbol) that is a power series in $\hbar$, starting with $\hbar^0$, with a generic fixed point in phase space. The Hamiltonian is not restricted to the kinetic-plus-potential form. The method involves transforming the Hamiltonian to a normal form, in which it becomes a function of the harmonic oscillator Hamiltonian. Diagrammatic and other techniques with potential applications to other normal form problems are presented for manipulating higher order terms in the Moyal series.Comment: 27 pages, no figure

DenseNet and Support Vector Machine classifications of major depressive disorder using vertex-wise cortical features

Major depressive disorder (MDD) is a complex psychiatric disorder that affects the lives of hundreds of millions of individuals around the globe. Even today, researchers debate if morphological alterations in the brain are linked to MDD, likely due to the heterogeneity of this disorder. The application of deep learning tools to neuroimaging data, capable of capturing complex non-linear patterns, has the potential to provide diagnostic and predictive biomarkers for MDD. However, previous attempts to demarcate MDD patients and healthy controls (HC) based on segmented cortical features via linear machine learning approaches have reported low accuracies. In this study, we used globally representative data from the ENIGMA-MDD working group containing an extensive sample of people with MDD (N=2,772) and HC (N=4,240), which allows a comprehensive analysis with generalizable results. Based on the hypothesis that integration of vertex-wise cortical features can improve classification performance, we evaluated the classification of a DenseNet and a Support Vector Machine (SVM), with the expectation that the former would outperform the latter. As we analyzed a multi-site sample, we additionally applied the ComBat harmonization tool to remove potential nuisance effects of site. We found that both classifiers exhibited close to chance performance (balanced accuracy DenseNet: 51%; SVM: 53%), when estimated on unseen sites. Slightly higher classification performance (balanced accuracy DenseNet: 58%; SVM: 55%) was found when the cross-validation folds contained subjects from all sites, indicating site effect. In conclusion, the integration of vertex-wise morphometric features and the use of the non-linear classifier did not lead to the differentiability between MDD and HC. Our results support the notion that MDD classification on this combination of features and classifiers is unfeasible

White matter disturbances in major depressive disorder : a coordinated analysis across 20 international cohorts in the ENIGMA MDD working group

Altres ajuts: The ENIGMA-Major Depressive Disorder working group gratefully acknowledges support from the NIH Big Data to Knowledge (BD2K) award (U54 EB020403 to PMT) and NIH grant R01 MH116147 (PMT). LS is supported by an NHMRC MRFF Career Development Fellowship (APP1140764). We wish to acknowledge the patients and control subjects that have particiaped int the study. We thank Rosa Schirmer, Elke Schreiter, Reinhold Borschke and Ines Eidner for image acquisition and data preparation, and Anna Oliynyk for quality checks. We thank Dorothee P. Auer and F. Holsboer for initiation of the RUD study. We wish to acknowledge the patients and control subjects that have particiaped int the study. We thank Rosa Schirmer, Elke Schreiter, Reinhold Borschke and Ines Eidner for image acquisition and data preparation, and Anna Oliynyk for quality checks. We thank Dorothee P. Auer and F. Holsboer for initiation of the RUD study. NESDA: The infrastructure for the NESDA study (www.nesda.nl) is funded through the Geestkracht program of the Netherlands Organisation for Health Research and Development (Zon-Mw, grant number 10-000-1002) and is supported by participating universities (VU University Medical Center, GGZ inGeest, Arkin, Leiden University Medical Center, GGZ Rivierduinen, University Medical Center Groningen) and mental health care organizations, see www.nesda.nl. M-JvT was supported by a VENI grant (NWO grant number 016.156.077). UCSF: This work was supported by the Brain and Behavior Research Foundation (formerly NARSAD) to TTY; the National Institute of Mental Health (R01MH085734 to TTY; K01MH117442 to TCH) and by the American Foundation for Suicide Prevention (PDF-1-064-13) to TCH. Stanford: This work was supported by NIMH Grants R01MH59259 and R37101495 to IHG. MS is partially supported by an award funded by the Phyllis and Jerome Lyle Rappaport Foundation. Muenster: This work was funded by the German Research Foundation (SFB-TRR58, Projects C09 and Z02 to UD) and the Interdisciplinary Center for Clinical Research (IZKF) of the medical faculty of Münster (grant Dan3/012/17 to UD). Marburg: This work was funded by the German Research Foundation (DFG, grant FOR2107 DA1151/5-1 and DA1151/5-2 to UD; KI 588/ 14-1, KI 588/14-2 to TK; KR 3822/7-1, KR 3822/7-2 to AK; JA 1890/ 7-1, JA 1890/7-2 to AJ). IMH-MDD: This work was supported by the National Healthcare Group Research Grant (SIG/15012) awarded to KS. Barcelona: This study was funded by two grants of the Fondo de Investigación Sanitaria from the Instituto de Salud Carlos III, by the Centro de Investigación Biomédica en Red de Salud Mental (CIBERSAM). The author is funded through 'Miguel Servet' research contract (CP16-0020), co-financed by the European Regional Development Fund (ERDF) (2016-2019). QTIM: We thank the twins and singleton siblings who gave generously of their time to participate in the QTIM study. We also thank the many research assistants, radiographers, and IT support staff for data acquisition and DNA sample preparation. This study was funded by White matter disturbances in major depressive disorder: a coordinated analysis across 20 international. . . 1521 the National Institute of Child Health & Human Development (RO1 HD050735); National Institute of Biomedical Imaging and Bioengineering (Award 1U54EB020403-01, Subaward 56929223); National Health and Medical Research Council, Australia (Project Grants 496682, 1009064). NIH ENIGMA-BD2K U54 EB020403 (Thompson); R01 MH117601 (Jahanshad/Schmaal). Magdeburg: M.L. and M.W. are funded by SFB 779. Bipolar Family Study: This study has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013). This paper reflects only the author's views and the European Union is not liable for any use that may be made of the information contained therein. This work was also supported by a Wellcome Trust Strategic Award (104036/Z/14/Z). Minnesota Adolescent Depression Study: The study was funded by the National Institute of Mental Health (K23MH090421), the National Alliance for Research on Schizophrenia and Depression, the University of Minnesota Graduate School, the Minnesota Medical Foundation, and the Biotechnology Research Center (P41 RR008079 to the Center for Magnetic Resonance Research), University of Minnesota, and the Deborah E. Powell Center for Women's Health Seed Grant, University of Minnesota. Dublin: This study was supported by Science Foundation Ireland through a Stokes Professorhip grant to TF. MPIP: The MPIP Sample comprises patients included in the Recurrent Unipolar Depression (RUD) Case-Control study at the clinic of the Max Planck Institute of Psychiatry, Munich, German. The RUD study was supported by GlaxoSmithKline.Alterations in white matter (WM) microstructure have been implicated in the pathophysiology of major depressive disorder (MDD). However, previous findings have been inconsistent, partially due to low statistical power and the heterogeneity of depression. In the largest multi-site study to date, we examined WM anisotropy and diffusivity in 1305 MDD patients and 1602 healthy controls (age range 12-88 years) from 20 samples worldwide, which included both adults and adolescents, within the MDD Working Group of the Enhancing Neuroimaging Genetics through Meta-Analysis (ENIGMA) consortium. Processing of diffusion tensor imaging (DTI) data and statistical analyses were harmonized across sites and effects were meta-analyzed across studies. We observed subtle, but widespread, lower fractional anisotropy (FA) in adult MDD patients compared with controls in 16 out of 25 WM tracts of interest (Cohen's d between 0.12 and 0.26). The largest differences were observed in the corpus callosum and corona radiata. Widespread higher radial diffusivity (RD) was also observed (all Cohen's d between 0.12 and 0.18). Findings appeared to be driven by patients with recurrent MDD and an adult age of onset of depression. White matter microstructural differences in a smaller sample of adolescent MDD patients and controls did not survive correction for multiple testing. In this coordinated and harmonized multisite DTI study, we showed subtle, but widespread differences in WM microstructure in adult MDD, which may suggest structural disconnectivity in MDD

Genetic architecture of subcortical brain structures in 38,851 individuals

Subcortical brain structures are integral to motion, consciousness, emotions and learning. We identified common genetic variation related to the volumes of the nucleus accumbens, amygdala, brainstem, caudate nucleus, globus pallidus, putamen and thalamus, using genome-wide association analyses in almost 40,000 individuals from CHARGE, ENIGMA and UK Biobank. We show that variability in subcortical volumes is heritable, and identify 48 significantly associated loci (40 novel at the time of analysis). Annotation of these loci by utilizing gene expression, methylation and neuropathological data identified 199 genes putatively implicated in neurodevelopment, synaptic signaling, axonal transport, apoptosis, inflammation/infection and susceptibility to neurological disorders. This set of genes is significantly enriched for Drosophila orthologs associated with neurodevelopmental phenotypes, suggesting evolutionarily conserved mechanisms. Our findings uncover novel biology and potential drug targets underlying brain development and disease

The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder

Structural brain correlates of childhood inhibited temperament: an ENIGMA-Anxiety Mega-analysis

NWORubicon 019.201SG.022Pathways through Adolescenc

Multi-site benchmark classification of major depressive disorder using machine learning on cortical and subcortical measures

Machine learning (ML) techniques have gained popularity in the neuroimaging field due to their potential for classifying neuropsychiatric disorders. However, the diagnostic predictive power of the existing algorithms has been limited by small sample sizes, lack of representativeness, data leakage, and/or overfitting. Here, we overcome these limitations with the largest multi-site sample size to date (N = 5365) to provide a generalizable ML classification benchmark of major depressive disorder (MDD) using shallow linear and non-linear models. Leveraging brain measures from standardized ENIGMA analysis pipelines in FreeSurfer, we were able to classify MDD versus healthy controls (HC) with a balanced accuracy of around 62%. But after harmonizing the data, e.g., using ComBat, the balanced accuracy dropped to approximately 52%. Accuracy results close to random chance levels were also observed in stratified groups according to age of onset, antidepressant use, number of episodes and sex. Future studies incorporating higher dimensional brain imaging/phenotype features, and/or using more advanced machine and deep learning methods may yield more encouraging prospects

Subcortical volumes across the lifespan: Data from 18,605 healthy individuals aged 3–90 years

Age has a major effect on brain volume. However, the normative studies available are constrained by small sample sizes, restricted age coverage and significant methodological variability. These limitations introduce inconsistencies and may obscure or distort the lifespan trajectories of brain morphometry. In response, we capitalized on the resources of the Enhancing Neuroimaging Genetics through Meta‐Analysis (ENIGMA) Consortium to examine age‐related trajectories inferred from cross‐sectional measures of the ventricles, the basal ganglia (caudate, putamen, pallidum, and nucleus accumbens), the thalamus, hippocampus and amygdala using magnetic resonance imaging data obtained from 18,605 individuals aged 3–90 years. All subcortical structure volumes were at their maximum value early in life. The volume of the basal ganglia showed a monotonic negative association with age thereafter; there was no significant association between age and the volumes of the thalamus, amygdala and the hippocampus (with some degree of decline in thalamus) until the sixth decade of life after which they also showed a steep negative association with age. The lateral ventricles showed continuous enlargement throughout the lifespan. Age was positively associated with inter‐individual variability in the hippocampus and amygdala and the lateral ventricles. These results were robust to potential confounders and could be used to examine the functional significance of deviations from typical age‐related morphometric patterns

Cortical thickness across the lifespan: Data from 17,075 healthy individuals aged 3-90 years

Delineating the association of age and cortical thickness in healthy individuals is critical given the association of cortical thickness with cognition and behavior. Previous research has shown that robust estimates of the association between age and brain morphometry require large‐scale studies. In response, we used cross‐sectional data from 17,075 individuals aged 3–90 years from the Enhancing Neuroimaging Genetics through Meta‐Analysis (ENIGMA) Consortium to infer age‐related changes in cortical thickness. We used fractional polynomial (FP) regression to quantify the association between age and cortical thickness, and we computed normalized growth centiles using the parametric Lambda, Mu, and Sigma method. Interindividual variability was estimated using meta‐analysis and one‐way analysis of variance. For most regions, their highest cortical thickness value was observed in childhood. Age and cortical thickness showed a negative association; the slope was steeper up to the third decade of life and more gradual thereafter; notable exceptions to this general pattern were entorhinal, temporopolar, and anterior cingulate cortices. Interindividual variability was largest in temporal and frontal regions across the lifespan. Age and its FP combinations explained up to 59% variance in cortical thickness. These results may form the basis of further investigation on normative deviation in cortical thickness and its significance for behavioral and cognitive outcomes