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Tourette Syndrome (TS) is characterized with chronic motor and vocal tics beginning in childhood. Abnormality of both gray (GM) and white matter (WM) has been observed in cortico-striato-thalamo-cortical circuits and sensory-motor cortex of adult TS patient. It is not clear if these morphological changes are also present in TS children and if there are any microstructural changes of WM. To understand the developmental cause of such changes, we investigated volumetric changes of GM and WM using VBM and microstructural changes of WM using DTI, and correlated these changes with tic severity and duration. T1 images and Diffusion Tensor Images (DTI) from 21 TS children were compared with 20 age and gender matched health control children using a 1.5T Philips scanner. All of the 21 TS children met the DSM-IV-TR criteria. T1 images were analyzed using DARTEL-VBM in conjunction with statistical parametric mapping (SPM). Diffusion tensor imaging (DTI) analysis was performed using Tract-Based Spatial Statistics (TBSS). Brain volume changes were found in left superior temporal gyrus, left and right paracentral gyrus, right precuneous cortex, right pre- and post-central gyrus, left temporal occipital fusiform cortex, right frontal pole, and left lingual gyrus. Significant axial diffusivity (AD) and mean diffusivity (MD) increases were found in anterior thalamic radiation, right cingulum bundle projecting to the cingulate gurus and forceps minor. Decreases in white matter volume (WMV) in the right frontal pole were inversely related with tic severity (YGTSS), and increases in AD and MD were positively correlated with tic severity and duration, respectively. These changes in TS children can be interpreted as signs of neural plasticity in response to the experiential demand. Our findings may suggest that the morphological and microstructural measurements from structural MRI and DTI can potentially be used as a biomarker of the pathophysiologic pattern of early TS children.

The title compound, C26H32O11, is composed of an α,β-unsaturated cyclohexanone ring (A), two cyclohexane rings (B and C), a six-membered lactone ring (D) and tetrahydrofuran ring (E). Ring A exists in a half-chair conformation with a C atom displaced by 0.679 (2) Å from the mean plane through the remaining five atoms. Ring B exists in a normal chair conformation. Both rings C and D exist in a twisted-chair conformation due to the O-atom bridge and the carbonyl group in rings C and D, respectively. Ring E shows an envelope conformation with a C atom displaced by 0.761 (1) Å from the mean plane through the remaining five atoms. The ring junctions are A/B trans, B/C trans, C/D cis and D/E cis. An intramolecular O—H...O hydrogen bond occurs. In the crystal, O—H...O hydrogen bonds involving the hydroxy, lactone and ester groups and C—H...O interactions are observed.

The title compound, C24H30O5, is the didehydro product of the steroid hellebrigenin (systematic name: 3β,5,14-trihydroxy-19-oxo-5β-bufa-20,22-dienolide). It consists of three cyclohexane rings (A, B and C), a five-membered ring (D) and a six-membered lactone ring (E). The stereochemistry of the ring junctions are A/B cis, B/C trans and C/D cis. Cyclohexane rings A, B and C have normal chair conformations. The five-membered ring D with the C=C bond adopts an envelope conformation. Lactone ring E is essentially planar with a mean derivation of 0.006 (4) Å and is β-oriented at the C atom of ring D to which it is attached. There is an O—H...O hydrogen bond in the molecule involving the hydroxy groups. In the crystal, O—H...O hydrogen bonds link the molecules into chains propagating along [010]. The chains are linked by C—H...O contacts into a three-dimensional network.

The title compound, C26H37NO5, was the reaction product of hellebrigenin with N,N-dimethylformamide. It consists of three cyclohexane rings (A, B and C), one five-membered ring (D) and one dihydropyran ring (E). The stereochemistry of the ring junctions is is A/B cis, B/C trans, C/D cis and C/E trans. The cyclohexane rings A, B and C have chair conformations. Both the five-membered ring D and the dihydropyran ring adopt an envelope conformation. Two orientations are found for the aldehyde group with occupancies of 0.608 (10) and 0.392 (10). In the crystal, short O—H...O hydrogen bonds and short C—H...O contacts involving the hydroxy group, terminal methyl group and carbonyl group link the molecules into a three-dimensional network.

Under suitable assumptions, the quantum-phase-estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground-state energy. However, QPE requires a large number of ancilla qubits and a large circuit depth, as well as the ability to perform inverse quantum Fourier transform, making it expensive to implement on an early fault-tolerant quantum computer. We propose an alternative method to estimate the ground-state energy of a Hamiltonian with Heisenberg-limited precision scaling, which employs a simple quantum circuit with one ancilla qubit, and a classical postprocessing procedure. Besides the ground-state energy, our algorithm also produces an approximate cumulative distribution function of the spectral measure, which can be used to compute other spectral properties of the Hamiltonian.