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We present an active feedback scheme acting continuously on the state of a quantum gas dispersively coupled to a high-finesse optical cavity. The quantum gas is subject to a transverse pump laser field inducing a self-organization phase transition, where the gas acquires a density modulation and photons are scattered into the resonator. Photons leaking from the cavity allow for a real-time and non-destructive readout of the system. We stabilize the mean intra-cavity photon number through a micro-processor controlled feedback architecture acting on the intensity of the transverse pump field. The feedback scheme can keep the mean intra-cavity photon number $n_\text{ph}$ constant, in a range between $n_\text{ph}=0.17\pm 0.04$ and $n_\text{ph}=27.6\pm 0.5$, and for up to 4 s. Thus we can engage the stabilization in a regime where the system is very close to criticality as well as deep in the self-organized phase. The presented scheme allows us to approach the self-organization phase transition in a highly controlled manner and is a first step on the path towards the realization of many-body phases driven by tailored feedback mechanisms., Comment: 15 pages, 5 figures

Apert syndrome is a rare genetic disorder characterised by craniofacial and limb abnormalities. These patients have to undergo multiple surgeries. One of these is cranial vault repair which is done for craniofacial anomalies. These cases pose a challenge to the anaesthesiologists not only because of a difficult airway but also problems like bronchospasm, increased secretion and even a difficulty in securing intravenous access. We present case report of a patient who had undergone cranial vault repair and subsequently developed CSF rhinorrhea and was planned for endonasal correction of skull base defect. Mask ventilation was difficult but intubation was relatively easy. The patient was operated in supine position with 15 degree head up position under hypotensive conditions to minimise bleeding and keep ICP under control. The intraoperative period was uneventful. Patient recovered completely from anaesthesia and was shifted to ICU.

The Selmer varieties of a hyperbolic curve X over ℚ are refinements of the Selmer group arising from replacing the Tate module of the Jacobian with higher quotients of the unipotent étale fundamental group. It is hoped that these refinements carry extra arithmetic information. In particular the nonabelian Chabauty method developed by Kim uses the Selmer variety to give a new method to find the set X(ℚ). This thesis studies certain local and global properties of the Selmer varieties associated to finite dimensional quotients of the unipotent fundamental group of a curve over ℚ. We develop new methods to prove finiteness of the intersection of the Selmer varieties with the set of local points (and hence of the set of rational points) and new methods to implement this explicitly, giving the first examples of explicit nonabelian Chabauty theory for rational points on projective curves.