In a group of 831 participants from the general population in the Human Connectome Project, smokers exhibited low overall functional connectivity, and more specifically of the lateral orbitofrontal cortex which is associated with non-reward mechanisms, the adjacent inferior frontal gyrus, and the precuneus. Participants who drank a high amount had overall increases in resting state functional connectivity, and specific increases in reward-related systems including the medial orbitofrontal cortex and the cingulate cortex. Increased impulsivity was found in smokers, associated with decreased functional connectivity of the non-reward-related lateral orbitofrontal cortex; and increased impulsivity was found in high amount drinkers, associated with increased functional connectivity of the reward-related medial orbitofrontal cortex. The main findings were cross-validated in an independent longitudinal dataset with 1176 participants, IMAGEN. Further, the functional connectivities in 14-year-old non-smokers (and also in female low-drinkers) were related to who would smoke or drink at age 19. An implication is that these differences in brain functional connectivities play a role in smoking and drinking, together with other factors.

The first voxel-level resting-state functional connectivity (FC) neuroimaging analysis of depression of the anterior cingulate cortex (ACC) showed in 282 patients with major depressive disorder compared with 254 controls, some higher, and some lower FCs. However, in 125 unmedicated patients, primarily increases of FC were found: of the subcallosal anterior cingulate with the lateral orbitofrontal cortex, of the pregenual/supracallosal anterior cingulate with the medial orbitofrontal cortex, and of parts of the anterior cingulate with the inferior frontal gyrus, superior parietal lobule, and with early cortical visual areas. In the 157 medicated patients, these and other FCs were lower than in the unmedicated group. Parcellation was performed based on the FC of individual ACC voxels in healthy controls. A pregenual subdivision had high FC with medial orbitofrontal cortex areas, and a supracallosal subdivision had high FC with lateral orbitofrontal cortex and inferior frontal gyrus. The high FC in depression between the lateral orbitofrontal cortex and the subcallosal parts of the ACC provides a mechanism for more non-reward information transmission to the ACC, contributing to depression. The high FC between the medial orbitofrontal cortex and supracallosal ACC in depression may also contribute to depressive symptoms.

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In this paper, to describe the uncertainty from external environment, we propose a stochastic Dullin-Gottwald-Holm (SDGH) equation by adding an additive noise to the well-known DGH equation. Using regularization, the local existence and uniqueness of the solution of SDGH are proved. By means of a priori estimates, we find that the local solution may blow up in a finite time if the initial value satisfies certain conditions.

The non-sequential double ionization (NSDI) of He in a chirped few-cycle laser pulse is studied using a full-dimensional semi-classical model. The NSDI probability is found to be very sensitive to the rate of wavelength change. An abrupt jump is found in the probability distribution during the crossover from up- to down-chirped pulse, followed with a further increase of the probability when keep increasing the rate of wavelength change. In the meantime, the correlated electron momentum distribution transfers from anti-correlated to a correlated pattern. Further analysis reveals the underlying mechanism to be the increase of the kinetic energy of returned electron acquired from the chirped pulse in the re-collision process. The dominant NSDI mechanism transfers from recollision-induced excitation with subsequent field ionization (RESI) to electron-impact ionization (EI). Therefore, the chirped laser pulse could be a useful tool for controlling the electron dynamics in NSDI and beyond.