On the existence of orthonormal geodesic bases for Lie algebras

We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand, we give an example of a solvable unimodular Lie algebra of dimension 5 that has no orthonormal geodesic basis, for any inner product

General Relation between Entanglement and Fluctuations in One Dimension

In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size, suggesting that fluctuations are a useful quantity for determining the scaling of entanglement, especially in higher dimensions. We investigate the effects of boundaries and subleading corrections for critical spin and bosonic chains.Comment: 4 pages, 2 figures. Minor changes, references added

Comparison of Information Structures and Completely Positive Maps

A theorem of Blackwell about comparison between information structures in classical statistics is given an analogue in the quantum probabilistic setup. The theorem provides an operational interpretation for trace-preserving completely positive maps, which are the natural quantum analogue of classical stochastic maps. The proof of the theorem relies on the separation theorem for convex sets and on quantum teleportation.Comment: 12 pages. Substantial changes. Accepted for publication in Journal of Physics

Refined Kirby calculus for integral homology spheres

A theorem of Kirby states that two framed links in the 3-sphere produce orientation-preserving homeomorphic results of surgery if they are related by a sequence of stabilization and handle-slide moves. The purpose of the present paper is twofold: First, we give a sufficient condition for a sequence of handle-slides on framed links to be able to be replaced with a sequences of algebraically canceling pairs of handle-slides. Then, using the first result, we obtain a refinement of Kirby's calculus for integral homology spheres which involves only +/-1-framed links with zero linking numbers.Comment: This is the version published by Geometry & Topology on 18 September 200

Ag on Ge(111): 2D X-ray structure analysis of the (Wurzel)3 x (Wurzel)3 superstructure

We have studied the Ag/Ge(111)(Wurzel)3 x (Wurzel)3 superstructure by grazing-incidence X-ray diffraction. In our structural analysis we find striking similarities to the geometry of Au on Si(111). The Ag atoms form trimer clusters with an Ag-Ag distance of 2.94+-0.04°A with the centers of the trimers being located at the origins of the (Wurzel)3 x (Wurzel)3 lattice. The Ag layer is incomplete and at least one substrate layer is distorted

A Mesoscopic Resonating Valence Bond system on a triple dot

We introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly-occupied dot (spin qubit). Two other strongly capacitively islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1,0) and (0,1); this embodies the weight of the pendulum. The triple dot is placed between two superconducting leads as shown in Fig. 1. Under well-defined conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent. Consequences in a SQUID-geometry are carefully investigated.Comment: final version to appear in PR

Treatment of labial soft tissue recession around dental implants in the esthetic zone using guided bone regeneration with mineralized allograft : a retrospective clinical case series

Objectives: Soft tissue augmentation procedures are often performed to correct gingival recesson on the facial aspects of implants in the esthetic zone. This retrospective clinical case series reports on the use of guided bone regeneration (GBR) and coronal advancement flap with resorbable membrane and allograft. Materials and methods: Records of 14 patients (7 male, 7 female) with a mean (SD) age of 36.78 (13.9) years who were treated for soft tissue recessions around implant-supported restorations in the maxillary central or lateral incisor location were analysed. Implant diameters ranged from 3.3-4.7 mm. All patients had bone loss confined to the labial surface of the implant. A solvent-dehydrated particulate mineralized allograft (Puros Cancellous Bone Allograft, Zimmer Biomet Dental, Palm Beach Gardens, FL) and a resorbable membrane (CopiOs Pericardium, Zimmer Biomet Dental) were used in a GBR surgical procedure in combination with a roughened titanium tenting screw placed 3-4 mm below the implant platform to restore unesthetic defects in the anterior maxilla. Results: All postoperative tissue changes from their preoperative states were statistically significant (p < 0.05, Wilcoxon Signed-Rank test). Mean [SD, 95% Confidence Interval (CI)] preoperative crestal bone thickness (measured 2 mm from crest and mid-implant buccal bone thickness) increased by 1.84 (0.89, 1.32-2.35) mm and 2.07 (0.81, 1.60-2.53) mm, respectively, approximately one year after treatment (p <0.001). Significant mean (SD, 95% CI) increases of 1.28 (0.53, 0.97-1.58) mm, 1.29 (0.81, 0.82-1.75) mm and 1.23 (0.53, 0.92-1.53) mm were also noted in soft tissue thickness, keratinized tissue width, and gingival height, respectively (p <0.001). Conclusion: Use of the allograft and xenogenic membrane effectively increased alveolar hard and soft tissue dimensions in the esthetic zone of the anterior maxilla. Future prospective clinical trials with a control group are needed to compare this technique with conventional methods such as connective tissue graft

Quantum network coding for quantum repeaters

This paper considers quantum network coding, which is a recent technique that enables quantum information to be sent on complex networks at higher rates than by using straightforward routing strategies. Kobayashi et al. have recently showed the potential of this technique by demonstrating how any classical network coding protocol gives rise to a quantum network coding protocol. They nevertheless primarily focused on an abstract model, in which quantum resource such as quantum registers can be freely introduced at each node. In this work, we present a protocol for quantum network coding under weaker (and more practical) assumptions: our new protocol works even for quantum networks where adjacent nodes initially share one EPR-pair but cannot add any quantum registers or send any quantum information. A typically example of networks satisfying this assumption is {\emph{quantum repeater networks}}, which are promising candidates for the implementation of large scale quantum networks. Our results thus show, for the first time, that quantum network coding techniques can increase the transmission rate in such quantum networks as well.Comment: 9 pages, 11figure

[Report of] Specialist Committee V.4: ocean, wind and wave energy utilization

The committee's mandate was :Concern for structural design of ocean energy utilization devices, such as offshore wind turbines, support structures and fixed or floating wave and tidal energy converters. Attention shall be given to the interaction between the load and the structural response and shall include due consideration of the stochastic nature of the waves, current and wind