An Algebraic Spin and Statistics Theorem

A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.Comment: 15 pages, plain TeX, an error in the statement of a theorem has been corrected, to appear in Commun. Math. Phy

Metamaterial bricks and quantization of meta-surfaces

Controlling acoustic fields is crucial in diverse applications such as loudspeaker design, ultrasound imaging and therapy or acoustic particle manipulation. The current approaches use fixed lenses or expensive phased arrays. Here, using a process of analogue-to-digital conversion and wavelet decomposition, we develop the notion of quantal meta-surfaces. The quanta here are small, pre-manufactured three-dimensional units—which we call metamaterial bricks—each encoding a specific phase delay. These bricks can be assembled into meta-surfaces to generate any diffraction-limited acoustic field. We apply this methodology to show experimental examples of acoustic focusing, steering and, after stacking single meta-surfaces into layers, the more complex field of an acoustic tractor beam. We demonstrate experimentally single-sided air-borne acoustic levitation using meta-layers at various bit-rates: from a 4-bit uniform to 3-bit non-uniform quantization in phase. This powerful methodology dramatically simplifies the design of acoustic devices and provides a key-step towards realizing spatial sound modulators

Consensus on guidelines for stereotactic neurosurgery for psychiatric disorders

For patients with psychiatric illnesses remaining refractory to 'standard' therapies, neurosurgical procedures may be considered. Guidelines for safe and ethical conduct of such procedures have previously and independently been proposed by various local and regional expert groups

Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known results such as the Clebsh--Gordan--Pieri formula for tensor products, the Plancherel theorem for Hermitian symmetric spaces (also for line bundle cases), the Hua--Kostant--Schmid $K$-type formula, and the canonical representations in the sense of Vershik--Gelfand--Graev. Our method works in a uniform manner for both finite and infinite dimensional cases, for both discrete and continuous spectra, and for both classical and exceptional cases

Short and long term outcome of bilateral pallidal stimulation in chorea-acanthocytosis

BACKGROUND: Chorea-acanthocytosis (ChAc) is a neuroacanthocytosis syndrome presenting with severe movement disorders poorly responsive to drug therapy. Case reports suggest that bilateral deep brain stimulation (DBS) of the ventro-postero-lateral internal globus pallidus (GPi) may benefit these patients. To explore this issue, the present multicentre (n=12) retrospective study collected the short and long term outcome of 15 patients who underwent DBS. METHODS: Data were collected in a standardized way 2-6 months preoperatively, 1-5 months (early) and 6 months or more (late) after surgery at the last follow-up visit (mean follow-up: 29.5 months). RESULTS: Motor severity, assessed by the Unified Huntington's Disease Rating Scale-Motor Score, UHDRS-MS), was significantly reduced at both early and late post-surgery time points (mean improvement 54.3% and 44.1%, respectively). Functional capacity (UHDRS-Functional Capacity Score) was also significantly improved at both post-surgery time points (mean 75.5% and 73.3%, respectively), whereas incapacity (UHDRS-Independence Score) improvement reached significance at early post-surgery only (mean 37.3%). Long term significant improvement of motor symptom severity (≥ 20 % from baseline) was observed in 61.5 % of the patients. Chorea and dystonia improved, whereas effects on dysarthria and swallowing were variable. Parkinsonism did not improve. Linear regression analysis showed that preoperative motor severity predicted motor improvement at both post-surgery time points. The most serious adverse event was device infection and cerebral abscess, and one patient died suddenly of unclear cause, 4 years after surgery. CONCLUSION: This study shows that bilateral DBS of the GPi effectively reduces the severity of drug-resistant hyperkinetic movement disorders such as present in ChAc