Problem (P) and pathological gambling (PG) symptoms wax and wane. Past symptoms are a risk for future symptoms even after controlling for familial influences. To address the genetic architecture of lifetime PG and current PG symptoms, we tested for common and unique genetic factors to lifetime PG symptoms at baseline and past year PG symptoms at 10-year follow-up. Diagnostic and Statistical Manual of Mental Disorders (3rd ed., Rev.; DSM-III-R; American Psychiatric Association, 1987) lifetime criteria of one or more PG symptoms were derived in 1992 and past year PG symptoms in 2002 from 1675 individual twins from the Vietnam Era Twin Registry. Cholesky decomposition models were fit to baseline and past year PG symptoms. Under the best fitting model we observed that 49% of the risk for one or more baseline PG symptoms in 1992 was due to a genetic factor and 51% of the risk was due to a unique environmental factor. All of the genetic variance (57.5%) in risk to past year PG symptoms in 2002 was common with baseline PG symptoms. Unique environment accounted for the remaining variance in past year PG symptoms with 13% common to baseline and 30% specific to past year PG symptoms. The genetic contributions to lifetime and past year gambling symptoms 10 years later are similar. There is no evidence for genetic contributions unique to past year PG symptoms. However, most of the unique environmental influences to past year PG are not shared with lifetime PG. This may reflect the changed social–cultural environment between 1992 and 2002, characterized by increasing access to legalized gambling.

An example is given of an operator weight W that satisfies the dyadic operator Hunt–Muckenhoupt–Wheeden condition [Aopf]d2 for which there exists a dyadic martingale transform on L2 (W) that is unbounded. The construction relates weighted boundedness to the boundedness of dyadic vector Hankel operators.

Let $f : V \to U$ be a (generalized) polynomial-like map. Suppose thatharmonic measure $\omega= \omega(\cdot,\infty)$ on the Julia set $J_{f}$ is equal tothe measure of maximal entropy $m$ for $f : J_{f} \hookleftarrow$. Then thedynamics $(f,V,U)$ is called maximal. We are going to give a criterion for thedynamics to be conformally equivalent to a maximal one, that is to beconformally maximal. In the second part of this paper we construct aninvariant ‘harmonic’ measure $\mu$ such that ${d\mu}/{d\omega}$ is Hölderfor certain dynamics. This allows us to prove in this class of dynamicalsystems that $\omega\approx m$ is necessary and sufficient for $(f,V,U)$ to beconformally maximal. In the particular case when $f$ is expanding and $J_{f}$is a circle, our result becomes a theorem of Shub and Sullivan; so throughoutthe paper we are dealing with an analog of a theorem of Shub and Sullivan on‘wild’ (e.g. totally disconnected) $J_{f}$ and for certain non-expanding$f$. We also construct (under certain assumptions) invariant harmonic measure on$J_{f}$. In this respect, our work stems from one of the works of Carleson.