In the general population, irritability is associated with later depression. Despite irritability being more prevalent in autistic children, the long-term sequelae are not well explored. We tested whether irritability in early childhood predicted depression symptoms in autistic adolescents, and whether associations could be explained by difficulties in peer relationships and lower educational engagement. Analyses tested the longitudinal associations between early childhood irritability (ages 3–5) and adolescent depression symptoms (age 14) in a prospective inception cohort of autistic children (N = 390), followed from early in development shortly after they received a clinical diagnosis. Mediators were measured in mid-childhood (age 10) by a combination of measures, from which latent factors for peer relationships and educational engagement were estimated. Results showed early childhood irritability was positively associated with adolescent depression symptoms, and this association remained when adjusting for baseline depression. A significant indirect pathway through peer relationships was found, which accounted for around 13% of the association between early childhood irritability and adolescent depression, suggesting peer problems may partially mediate the association between irritability and later depression. No mediation effects were found for education engagement. Results highlight the importance of early screening and intervention for co-occurring irritability and peer problems in young autistic children.

We prove that uniform hyperbolicity is invariant under topological conjugacy for dissipative polynomial automorphisms of $\mathbb {C}^2$ . Along the way we also show that a sufficient condition for hyperbolicity is that local stable and unstable manifolds of saddle points have uniform geometry.

Through autonomic and affective mechanisms, adverse childhood experiences (ACEs) may disrupt the capacity to regulate negative emotions, increasing craving and exacerbating risk for opioid use disorder (OUD) among individuals with chronic pain who are receiving long-term opioid analgesic pharmacotherapy. This study examined associations between ACEs, heart rate variability (HRV) during emotion regulation, and negative emotional cue-elicited craving among a sample of female opioid-treated chronic pain patients at risk for OUD. A sample of women (N = 36, mean age = 51.2 ± 9.5) with chronic pain receiving long-term opioid analgesic pharmacotherapy (mean morphine equivalent daily dose = 87.1 ± 106.9 mg) were recruited from primary care and pain clinics to complete a randomized task in which they viewed and reappraised negative affective stimuli while HRV and craving were assessed. Both ACEs and duration of opioid use significantly predicted blunted HRV during negative emotion regulation and increased negative emotional cue-elicited craving. Analysis of study findings from a multiple-levels-of-analysis approach suggest that exposure to childhood abuse occasions later emotion dysregulation and appetitive responding toward opioids in negative affective contexts among adult women with chronic pain, and thus this vulnerable clinical population should be assessed for OUD risk when initiating a course of extended, high-dose opioids for pain management.

We consider the family of quadratic Hénon diffeomorphisms of the plane $\mathbb{R}^{2}$. A map will be said to be a ‘horseshoe’ if its restriction to the non-wandering set is hyperbolic and conjugate to the full 2-shift. We give a criterion for being a horseshoe based on an auxiliary coding which describes positions of points relative to the stable manifold of one of the fixed points. In addition we describe the topological conjugacy type of maps on the boundary of the horseshoe locus. We use complex techniques and we work with maps in a parameter region which is a two-dimensional analog of the familiar ‘$1/2$-wake’ for the quadratic family $p_{c}(z)=z^{2}$.

Let A be an integer matrix, and let fA be the associated monomial map. We give a connection between the eigenvalues of A and the existence of a linear recurrence relation in the sequence of degrees.

Let $\{h_{a,b} : a,b \in \mathbb{R}, b \neq 0\}$ denote the Hénon family of quadratic polynomial diffeomorphisms of $\mathbb{R}^2$, with $b$ equal to the Jacobian of $h_{a,b}$. In this paper, we describe the locus of parameter values $(a,b)$ such that $0 < |b| < 0.06$, and the restriction of $h_{a,b}$ to its non-wandering set is topologically conjugate to the horseshoe map. The boundary of the horseshoe locus is shown to be characterized by a homoclinic tangency which is part of a generic unfolding.