Maximum Skew-Symmetric Flows and Matchings

The maximum integer skew-symmetric flow problem (MSFP) generalizes both the maximum flow and maximum matching problems. It was introduced by Tutte in terms of self-conjugate flows in antisymmetrical digraphs. He showed that for these objects there are natural analogs of classical theoretical results on usual network flows, such as the flow decomposition, augmenting path, and max-flow min-cut theorems. We give unified and shorter proofs for those theoretical results. We then extend to MSFP the shortest augmenting path method of Edmonds and Karp and the blocking flow method of Dinits, obtaining algorithms with similar time bounds in general case. Moreover, in the cases of unit arc capacities and unit ``node capacities'' the blocking skew-symmetric flow algorithm has time bounds similar to those established in Even and Tarjan (1975) and Karzanov (1973) for Dinits' algorithm. In particular, this implies an algorithm for finding a maximum matching in a nonbipartite graph in $O(\sqrt{n}m)$ time, which matches the time bound for the algorithm of Micali and Vazirani. Finally, extending a clique compression technique of Feder and Motwani to particular skew-symmetric graphs, we speed up the implied maximum matching algorithm to run in $O(\sqrt{n}m\log(n^2/m)/\log{n})$ time, improving the best known bound for dense nonbipartite graphs. Also other theoretical and algorithmic results on skew-symmetric flows and their applications are presented.Comment: 35 pages, 3 figures, to appear in Mathematical Programming, minor stylistic corrections and shortenings to the original versio

A Palladium-Catalyzed Vinylcyclopropane (3 + 2) Cycloaddition Approach to the Melodinus Alkaloids

A palladium-catalyzed (3 + 2) cycloaddition of a vinylcyclopropane and a β-nitrostyrene is employed to rapidly assemble the cyclopentane core of the Melodinus alkaloids. The ABCD ring system of the natural product family is prepared in six steps from commercially available materials

Pulmonary embolism and mortality following total ankle replacement: a data linkage study using the NJR data set

OBJECTIVE: To determine the mortality rate following total ankle replacement (TAR) and incidence of 90 day pulmonary embolism (PE) along with the associated risk factors.  DESIGN: Data-linkage study of the UK National Joint Registry (NJR) data and Hospital Episodes Statistics (HES) database. Linkage was performed in a deterministic fashion. HES episodes 90 days after the index procedure were analysed for PE. Mortality data were obtained pertaining to all the index procedures from the NJR for analysis.  PARTICIPANTS: All primary and revision ankle replacement patients captured on the NJR between February 2008 and February 2013.  RESULTS: The 90-day mortality following TAR was 0.13% (95% CI 0.03 to 0.52) and 1-year mortality was 0.72% (95% CI 0.40 to 1.30); no deaths were as a result of PE. The incidence of PE within 90 days following primary TAR was 0.51% (95% CI 0.23 to 1.13). There was only one PE following revision surgery. Patients with an Royal College of Surgeons Charlson score greater than zero were at 13 times greater risk of PE (p=0.003).  CONCLUSIONS: There is low incidence of PE following TAR, but multiple comorbidities are a leading risk factor for its occurrence

How do patients with end-stage ankle arthritis decide between two surgical treatments?:A qualitative study

To examine how patients decide between ankle fusion and ankle replacement in end-stage ankle arthritis

Lattice-corrected strain-induced vector potentials in graphene

The electronic implications of strain in graphene can be captured at low energies by means of pseudovector potentials which can give rise to pseudomagnetic fields. These strain-induced vector potentials arise from the local perturbation to the electronic hopping amplitudes in a tight-binding framework. Here we complete the standard description of the strain-induced vector potential, which accounts only for the hopping perturbation, with the explicit inclusion of the lattice deformations or, equivalently, the deformation of the Brillouin zone. These corrections are linear in strain and are different at each of the strained, inequivalent Dirac points, and hence are equally necessary to identify the precise magnitude of the vector potential. This effect can be relevant in scenarios of inhomogeneous strain profiles, where electronic motion depends on the amount of overlap among the local Fermi surfaces. In particular, it affects the pseudomagnetic field distribution induced by inhomogeneous strain configurations, and can lead to new opportunities in tailoring the optimal strain fields for certain desired functionalities.Comment: Errata for version

Multi-unit Bilateral Trade

We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular. Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1-e) approximation mechanism, matching the best known bounds for the single-item setting

Anisotropic noise

Programmable graphics hardware makes it possible to generate procedural noise textures on the fly for interactive rendering. However, filtering and antialiasing procedural noise involves a tradeoff between aliasing artifacts and loss of detail. In this paper we present a technique, targeted at interactive applications, that provides high-quality anisotropic filtering for noise textures. We generate noise tiles directly in the frequency domain by partitioning the frequency domain into oriented subbands. We then compute weighted sums of the subband textures to accurately approximate noise with a desired spectrum. This allows us to achieve high-quality anisotropic filtering. Our approach is based solely on 2D textures, avoiding the memory overhead of techniques based on 3D noise tiles. We devise a technique to compensate for texture distortions to generate uniform noise on arbitrary meshes. We develop a GPU-based implementation of our technique that achieves similar rendering performance as state-of-the-art algorithms for procedural noise. In addition, it provides anisotropic filtering and achieves superior image quality.National Science Foundation (U.S.) (CAREER Award 0447561)Microsoft Research (New Faculty Fellowship)Alfred P. Sloan Foundation (Fellowship

Hemoptysis - a Rare Complication of Pacemaker Implantation

We describe a case of hemoptysis as a rare complication of pacemaker lead insertion via the axillary approach in a patient with difficult chest anatomy