Contribution to understanding the mathematical structure of quantum mechanics

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, momentum operator, rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems and the postulates of quantum mechanics are also discussed.Comment: 21 page

Epigenetic variance in dopamine D2 receptor: A marker of IQ malleability?

Genetic and environmental factors both contribute to cognitive test performance. A substantial increase in average intelligence test results in the second half of the previous century within one generation is unlikely to be explained by genetic changes. One possible explanation for the strong malleability of cognitive performance measure is that environmental factors modify gene expression via epigenetic mechanisms. Epigenetic factors may help to understand the recent observations of an association between dopamine-dependent encoding of reward prediction errors and cognitive capacity, which was modulated by adverse life events. The possible manifestation of malleable biomarkers contributing to variance in cognitive test performance, and thus possibly contributing to the “missing heritability” between estimates from twin studies and variance explained by genetic markers, is still unclear. Here we show in 1475 healthy adolescents from the IMaging and GENetics (IMAGEN) sample that general IQ (gIQ) is associated with (1) polygenic scores for intelligence, (2) epigenetic modification of DRD2 gene, (3) gray matter density in striatum, and (4) functional striatal activation elicited by temporarily surprising reward-predicting cues. Comparing the relative importance for the prediction of gIQ in an overlapping subsample, our results demonstrate neurobiological correlates of the malleability of gIQ and point to equal importance of genetic variance, epigenetic modification of DRD2 receptor gene, as well as functional striatal activation, known to influence dopamine neurotransmission. Peripheral epigenetic markers are in need of confirmation in the central nervous system and should be tested in longitudinal settings specifically assessing individual and environmental factors that modify epigenetic structure

Bayesian Inference in Processing Experimental Data: Principles and Basic Applications

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; Monte Carlo estimates of expectation, including a short introduction to Markov Chain Monte Carlo methods.Comment: 40 pages, 2 figures, invited paper for Reports on Progress in Physic

Differential predictors for alcohol use in adolescents as a function of familial risk.

Traditional models of future alcohol use in adolescents have used variable-centered approaches, predicting alcohol use from a set of variables across entire samples or populations. Following the proposition that predictive factors may vary in adolescents as a function of family history, we used a two-pronged approach by first defining clusters of familial risk, followed by prediction analyses within each cluster. Thus, for the first time in adolescents, we tested whether adolescents with a family history of drug abuse exhibit a set of predictors different from adolescents without a family history. We apply this approach to a genetic risk score and individual differences in personality, cognition, behavior (risk-taking and discounting) substance use behavior at age 14, life events, and functional brain imaging, to predict scores on the alcohol use disorders identification test (AUDIT) at age 14 and 16 in a sample of adolescents (N = 1659 at baseline, N = 1327 at follow-up) from the IMAGEN cohort, a longitudinal community-based cohort of adolescents. In the absence of familial risk (n = 616), individual differences in baseline drinking, personality measures (extraversion, negative thinking), discounting behaviors, life events, and ventral striatal activation during reward anticipation were significantly associated with future AUDIT scores, while the overall model explained 22% of the variance in future AUDIT. In the presence of familial risk (n = 711), drinking behavior at age 14, personality measures (extraversion, impulsivity), behavioral risk-taking, and life events were significantly associated with future AUDIT scores, explaining 20.1% of the overall variance. Results suggest that individual differences in personality, cognition, life events, brain function, and drinking behavior contribute differentially to the prediction of future alcohol misuse. This approach may inform more individualized preventive interventions

Association of a schizophrenia-risk nonsynonymous variant with putamen volume in adolescents

Importance Deviation from normal adolescent brain development precedes manifestations of many major psychiatric symptoms. Such altered developmental trajectories in adolescents may be linked to genetic risk for psychopathology. Objective To identify genetic variants associated with adolescent brain structure and explore psychopathologic relevance of such associations. Design, Setting, and Participants Voxelwise genome-wide association study in a cohort of healthy adolescents aged 14 years and validation of the findings using 4 independent samples across the life span with allele-specific expression analysis of top hits. Group comparison of the identified gene-brain association among patients with schizophrenia, unaffected siblings, and healthy control individuals. This was a population-based, multicenter study combined with a clinical sample that included participants from the IMAGEN cohort, Saguenay Youth Study, Three-City Study, and Lieber Institute for Brain Development sample cohorts and UK biobank who were assessed for both brain imaging and genetic sequencing. Clinical samples included patients with schizophrenia and unaffected siblings of patients from the Lieber Institute for Brain Development study. Data were analyzed between October 2015 and April 2018. Main Outcomes and Measures Gray matter volume was assessed by neuroimaging and genetic variants were genotyped by Illumina BeadChip. Results The discovery sample included 1721 adolescents (873 girls [50.7%]), with a mean (SD) age of 14.44 (0.41) years. The replication samples consisted of 8690 healthy adults (4497 women [51.8%]) from 4 independent studies across the life span. A nonsynonymous genetic variant (minor T allele of rs13107325 in SLC39A8, a gene implicated in schizophrenia) was associated with greater gray matter volume of the putamen (variance explained of 4.21% in the left hemisphere; 8.66; 95% CI, 6.59-10.81; P = 5.35 × 10−18; and 4.44% in the right hemisphere; t = 8.90; 95% CI, 6.75-11.19; P = 6.80 × 10−19) and also with a lower gene expression of SLC39A8 specifically in the putamen (t127 = −3.87; P = 1.70 × 10−4). The identified association was validated in samples across the life span but was significantly weakened in both patients with schizophrenia (z = −3.05; P = .002; n = 157) and unaffected siblings (z = −2.08; P = .04; n = 149). Conclusions and Relevance Our results show that a missense mutation in gene SLC39A8 is associated with larger gray matter volume in the putamen and that this association is significantly weakened in schizophrenia. These results may suggest a role for aberrant ion transport in the etiology of psychosis and provide a target for preemptive developmental interventions aimed at restoring the functional effect of this mutation

A stable and replicable neural signature of lifespan adversity in the adult brain

Environmental adversities constitute potent risk factors for psychiatric disorders. Evidence suggests the brain adapts to adversity, possibly in an adversity-type and region-specific manner. However, the long-term effects of adversity on brain structure and the association of individual neurobiological heterogeneity with behavior have yet to be elucidated. Here we estimated normative models of structural brain development based on a lifespan adversity profile in a longitudinal at-risk cohort aged 25 years (n = 169). This revealed widespread morphometric changes in the brain, with partially adversity-specific features. This pattern was replicated at the age of 33 years (n = 114) and in an independent sample at 22 years (n = 115). At the individual level, greater volume contractions relative to the model were predictive of future anxiety. We show a stable neurobiological signature of adversity that persists into adulthood and emphasize the importance of considering individual-level rather than group-level predictions to explain emerging psychopathology