On the distribution of the nodal sets of random spherical harmonics

We study the length of the nodal set of eigenfunctions of the Laplacian on the \spheredim-dimensional sphere. It is well known that the eigenspaces corresponding to \eigval=n(n+\spheredim-1) are the spaces \eigspc of spherical harmonics of degree $n$, of dimension \eigspcdim. We use the multiplicity of the eigenvalues to endow \eigspc with the Gaussian probability measure and study the distribution of the \spheredim-dimensional volume of the nodal sets of a randomly chosen function. The expected volume is proportional to \sqrt{\eigval}. One of our main results is bounding the variance of the volume to be O(\frac{\eigval}{\sqrt{\eigspcdim}}). In addition to the volume of the nodal set, we study its Leray measure. For every $n$, the expected value of the Leray measure is $\frac{1}{\sqrt{2\pi}}$. We are able to determine that the asymptotic form of the variance is \frac{const}{\eigspcdim}.Comment: 47 pages, accepted for publication in the Journal of Mathematical Physics. Lemmas 2.5, 2.11 were proved for any dimension, some other, suggested by the referee, modifications and corrections, were mad

The defect variance of random spherical harmonics

The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is obtaining the asymptotic shape of the defect variance, in the high frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern Cosmological data analysis.Comment: 19 page

On the transience of stability of subthreshold psychopathology

Symptoms of psychopathology lie on a continuum ranging from mental health to psychiatric disorders. Although much research has focused on progression along this continuum, for most individuals, subthreshold symptoms do not escalate into full-blown disorders. This study investigated how the stability of psychopathological symptoms (attractor strength) varies across severity levels (homebase). Data were retrieved from the TRAILS TRANS-ID study, where 122 at-risk young adults (mean age 23.6 years old, 57% males) monitored their mental states daily for a period of six months (± 183 observations per participant). We estimated each individual’s homebase and attractor strength using generalized additive mixed models. Regression analyses showed no association between homebases and attractor strengths (linear model: B = 0.02, p = 0.47, R(2) < 0.01; polynomial model: B < 0.01, p = 0.61, R(2) < 0.01). Sensitivity analyses where we (1) weighed estimates according to their uncertainty and (2) removed individuals with a DSM-5 diagnosis from the analyses did not change this finding. This suggests that stability is similar across severity levels, implying that subthreshold psychopathology may resemble a stable state rather than a transient intermediate between mental health and psychiatric disorder. Our study thus provides additional support for a dimensional view on psychopathology, which implies that symptoms differ in degree rather than kind

Mild psychotic experiences among ethnic minority and majority adolescents and the role of ethnic density

Despite evidence of the increased risk of psychotic disorders among ethnic minority adults, little is known about the effect of ethnic minority status to mild psychotic experiences among adolescents. This study investigated mild psychotic experiences in ethnic minority and majority adolescents in a Dutch representative general population sample, and tested the ethnic density effect in the classroom.The CAPE was used to assess mild psychotic experiences among Dutch (n = 3,606) and non-Western ethnic minority pupils (n = 769).Ethnic minority adolescents showed higher levels of grandiosity and delusions than their ethnic majority peers, whereas no differences were found for hallucinations, paranormal beliefs and paranoia between both groups of adolescents. The ethnic density effect was partly confirmed for the ethnic majority: a decrease of ethnic majority pupils in class increased their feelings of paranoia.Because only some dimensions of mild psychotic experiences were affected by ethnic minority status or the interaction between ethnic minority status and ethnic class composition, our findings emphasize that mild psychotic experiences are multifactorial in origin, with different underlying processes.</p

Anticipating Transitions in Mental Health in At-Risk Youths:A 6-Month Daily Diary Study Into Early-Warning Signals

If psychopathology behaves like a complex dynamic system, sudden onset or worsening of symptoms may be preceded by early-warning signals (EWSs). EWSs could thus reflect personalized warning signals for impending psychopathology. We empirically investigated this hypothesis in at-risk youths (N = 122, mean age = 23.6 ± 0.7 years, 57% males) from the clinical cohort of Tracking Adolescents’ Individual Lives Survey (TRAILS-CC), who provided daily emotion assessments for 6 months. We analyzed whether EWSs (rising autocorrelations and standard deviations in emotions) preceded transitions toward psychopathology. Across indicators and a range of analytical options, EWSs had low sensitivity (M = 26%, SD = 11%) and moderate specificity (M = 75%, SD = 14%). Thus, in the present sample, the proposed generic nature and clinical utility of EWSs could not be substantiated. Given this finding, we call for a more nuanced view on the application of complex-dynamic-systems principles to psychopathology and lay out key questions to be addressed in the future

Reflections on psychological resilience:a comparison of three conceptually different operationalizations in predicting mental health

BACKGROUND: Psychological resilience refers to the ability to maintain mental health or recover quickly after stress. Despite the popularity of resilience research, there is no consensus understanding or operationalization of resilience. OBJECTIVE: We plan to compare three indicators of resilience that each involve a different operationalization of the construct: a) General resilience or one’s self-reported general ability to overcome adversities; b) Daily resilience as momentarily experienced ability to overcome adversities; and c) Recovery speed evident in the pattern of negative affect recovery after small adversities in daily life. These three indicators are constructed per person to investigate their cross-sectional associations, stability over time, and predictive validity regarding mental health. METHODS: Data will be derived from the prospective MIRORR study that comprises 96 individuals at different levels of psychosis risk and contains both single-time assessed questionnaires and 90-days intensive longitudinal data collection at baseline (T0) and three yearly follow-up waves (T1–T3). General resilience is assessed using the Brief Resilience Scale (BRS) at baseline. Daily resilience is measured by averaging daily resilience scores across 90 days. For recovery speed, vector-autoregressive models with consecutive impulse response simulations will be applied to diary data on negative affect and daily stressors to calculate pattern of affect recovery. These indicators will be correlated concurrently (at T0) to assess their overlap and prospectively (between T0 and T1) to estimate their stability. Their predictive potential will be assessed by regression analysis with mental health (SCL-90) as an outcome, resilience indicators as predictors, and stressful life events as a moderator. CONCLUSION: The comparison of different conceptualizations of psychological resilience can increase our understanding of its multifaceted nature and, in future, help improve diagnostic, prevention and intervention strategies aimed at increasing psychological resilience

The added value of daily diary data in 1- and 3-year prediction of psychopathology and psychotic experiences in individuals at risk for psychosis

This study aimed to assess whether adding information on psychological experiences derived from a daily diary to baseline cross-sectional data could improve short- (1-year) and long-term (3-years) prediction of psychopathology and positive psychotic experiences (PEs). We used 90-day daily diary data from 96 individuals in early subclinical risk stages for psychosis. Stepwise linear regression models were built for psychopathology and PEs at 1- and 3-years follow-up, adding: (1) baseline questionnaires, (2) the mean and variance of daily psychological experiences, and (3) individual symptom network density. We assessed whether similar results could be achieved with a subset of the data (7-14- and 30-days). The mean and variance of the diary improved model prediction of short- and long-term psychopathology and PEs, compared to prediction based on baseline questionnaires solely. Similar results were achieved with 7-14- and 30-day subsets. Symptom network density did not improve model prediction except for short-term prediction of PEs. Simple metrics, i.e., the mean and variance from 7 to 14 days of daily psychological experiences assessments, can improve short- and long-term prediction of both psychopathology and PEs in individuals in early subclinical stages for psychosis. Diary data could be a valuable addition to clinical risk prediction models for psychopathology development.</p

The Associations of Affection and Rejection During Adolescence with Interpersonal Functioning in Young Adulthood:A Macro- and Micro-Level Investigation Using the TRAILS TRANS-ID Study

Affection and rejection in close relationships during adolescence are thought to impact adult interpersonal functioning, but few studies focused on how the quality of adolescents' relationships with different people (e.g. parents, peers, and teachers) impacts the daily, micro-level social experiences as well as general, macro-level interpersonal functioning in young adulthood. The present study investigated the associations between: (i) parental, teacher and peer affection and rejection during adolescence and macro-level (over several months) interpersonal functioning as well as different patterns (i.e. mean, variability and inertia) of micro-level (daily social experiences) during young adulthood; (ii) macro-level interpersonal functioning and the patterns of micro-level social experiences during young adulthood. The sample consisted of N = 122 (43% female) youth. At 11.2 +/- 0.4 and 16.0 +/- 0.6 years old, self- and other-reported parental, peer and teacher affection and rejection were assessed. At 23.7 +/- 0.6 years old, participants reported daily social experiences and interpersonal functioning across six months. The results suggested that: (i) higher teacher-reported peer rejection was associated with lower macro-level interpersonal functioning, higher means and higher variability in negative social experiences during adulthood; (ii) higher macro-level interpersonal functioning during young adulthood was associated with higher means and lower inertia in positive and lower variability in negative daily social experiences. These findings indicate that the affection and rejection during adolescence impact interpersonal functioning at macro- and micro-level during adulthood. The present study also shows distinct associations between macro-level interpersonal functioning and dynamics in daily social experiences