Integer programs with bounded subdeterminants and two nonzeros per row

We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our approach is the first polynomial-time algorithm for the weighted stable set problem on graphs that do not contain more than $k$ vertex-disjoint odd cycles, where $k$ is any constant. Previously, polynomial-time algorithms were only known for $k=0$ (bipartite graphs) and for $k=1$. We observe that integer linear programs defined by coefficient matrices with bounded subdeterminants and two nonzeros per column can be also solved in strongly polynomial-time, using a reduction to $b$-matching

Quantum computing by optical control of electron spins

We review the progress and main challenges in implementing large-scale quantum computing by optical control of electron spins in quantum dots (QDs). Relevant systems include self-assembled QDs of III-V or II-VI compound semiconductors (such as InGaAs and CdSe), monolayer fluctuation QDs in compound semiconductor quantum wells, and impurity centres in solids, such as P-donors in silicon and nitrogen-vacancy centres in diamond. The decoherence of the electron spin qubits is discussed and various schemes for countering the decoherence problem are reviewed. We put forward designs of local nodes consisting of a few qubits which can be individually addressed and controlled. Remotely separated local nodes are connected by photonic structures (microcavities and waveguides) to form a large-scale distributed quantum system or a quantum network. The operation of the quantum network consists of optical control of a single electron spin, coupling of two spins in a local nodes, optically controlled quantum interfacing between stationary spin qubits in QDs and flying photon qubits in waveguides, rapid initialization of spin qubits and qubit-specific single-shot non-demolition quantum measurement. The rapid qubit initialization may be realized by selectively enhancing certain entropy dumping channels via phonon or photon baths. The single-shot quantum measurement may be in situ implemented through the integrated photonic network. The relevance of quantum non-demolition measurement to large-scale quantum computation is discussed. To illustrate the feasibility and demand, the resources are estimated for the benchmark problem of factorizing 15 with Shor's algorithm. © 2010 Taylor & Francis.postprin

A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea

Includes bibliographical references.Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnoea. The anatomy of the tongue and other upper airway tissues, and the ability to model their behaviour, is central to such investigations. In this thesis, details of the construction and development of a three-dimensional finite element model of soft tissues of the human upper airway, as well as a simplified fluid model of the airway, are provided. The anatomical data was obtained from the Visible Human Project, and its underlying micro-histological data describing tongue musculature were also extracted from the same source and incorporated into the model. An overview of the mathematical models used to describe tissue behaviour, both at a macro- and microscopic level, is given. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group to a priori unknown external forces was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. The response of the various muscles of the tongue to the complex loading developed during breathing is determined, with a particular focus being placed to that of the genioglossus. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. A comparison is then made to the response determined under quasi-static conditions using the pressure distribution extracted from computational fluid-dynamics results. An analytical model describing the time-dependent response of the components of the tongue musculature most active during oral breathing is developed and validated. It is then modified to simulate the activity of the tongue during sleep and under conditions relating to various possible neural and physiological pathologies. The retroglossal movement of the tongue resulting from the pathologies is quantified and their role in the potential to induce airway collapse is discussed