The Path Integral for 1+1-dimensional QCD

We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables. Remainders of the curved space are Jacobians, an effective potential, and sign factors just as for the problem of a particle in a box. Based on this result we derive a Faddeev-Popov like expression for the transition amplitude avoiding standard infinities that are caused by integrations over gauge equivalent configurations.Comment: 16 pages, LaTeX, 3 PostScript figures, uses epsf.st

Vafa-Witten Estimates for Compact Symmetric Spaces

We give an optimal upper bound for the first eigenvalue of the untwisted Dirac operator on a compact symmetric space G/H with rk G-rk H\le 1 with respect to arbitrary Riemannian metrics. We also prove a rigidity statement.Comment: LaTeX, 11 pages. V2: Rigidity statement added, minor changes. To appea

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel

This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP). This intersection, once mapped, will then be used as a boundary within which a path will be planned for coverage to build a map of the Bathymetry. Methods for sequential updates to GP's are described allowing online fitting, prediction and hyper-parameter optimisation on a small embedded PC. New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage. These algorithms are tested both in simulation and in the field with a small twin hull differential thrust vessel built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field Robotic

Query processing of spatial objects: Complexity versus Redundancy

The management of complex spatial objects in applications, such as geography and cartography, imposes stringent new requirements on spatial database systems, in particular on efficient query processing. As shown before, the performance of spatial query processing can be improved by decomposing complex spatial objects into simple components. Up to now, only decomposition techniques generating a linear number of very simple components, e.g. triangles or trapezoids, have been considered. In this paper, we will investigate the natural trade-off between the complexity of the components and the redundancy, i.e. the number of components, with respect to its effect on efficient query processing. In particular, we present two new decomposition methods generating a better balance between the complexity and the number of components than previously known techniques. We compare these new decomposition methods to the traditional undecomposed representation as well as to the well-known decomposition into convex polygons with respect to their performance in spatial query processing. This comparison points out that for a wide range of query selectivity the new decomposition techniques clearly outperform both the undecomposed representation and the convex decomposition method. More important than the absolute gain in performance by a factor of up to an order of magnitude is the robust performance of our new decomposition techniques over the whole range of query selectivity

LINVIEW: Incremental View Maintenance for Complex Analytical Queries

Many analytics tasks and machine learning problems can be naturally expressed by iterative linear algebra programs. In this paper, we study the incremental view maintenance problem for such complex analytical queries. We develop a framework, called LINVIEW, for capturing deltas of linear algebra programs and understanding their computational cost. Linear algebra operations tend to cause an avalanche effect where even very local changes to the input matrices spread out and infect all of the intermediate results and the final view, causing incremental view maintenance to lose its performance benefit over re-evaluation. We develop techniques based on matrix factorizations to contain such epidemics of change. As a consequence, our techniques make incremental view maintenance of linear algebra practical and usually substantially cheaper than re-evaluation. We show, both analytically and experimentally, the usefulness of these techniques when applied to standard analytics tasks. Our evaluation demonstrates the efficiency of LINVIEW in generating parallel incremental programs that outperform re-evaluation techniques by more than an order of magnitude.Comment: 14 pages, SIGMO

Theory of Electron Spin Relaxation in ZnO

Doped ZnO is a promising material for spintronics applications. For such applications, it is important to understand the spin dynamics and particularly the spin coherence of this II-VI semiconductor. The spin lifetime $\tau_{s}$ has been measured by optical orientation experiments, and it shows a surprising non-monotonic behavior with temperature. We explain this behavior by invoking spin exchange between localized and extended states. Interestingly, the effects of spin-orbit coupling are by no means negligible, in spite of the relatively small valence band splitting. This is due to the wurtzite crystal structure of ZnO. Detailed analysis allows us to characterize the impurity binding energies and densities, showing that optical orientation experiments can be used as a characterization tool for semiconductor samples.Comment: 7 pages, 1 figure: minor changes Accepted by Phys. Rev.

Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

Potential predictors of outcome in patients with tissue loss who undergo infrainguinal vein bypass grafting

AbstractPurpose: Aggressive attempts at limb salvage in patients with ischemic tissue loss are justified by favorable initial results in most patients. The identification of patients whose conditions will not benefit from attempted revascularization remains difficult. Methods: This study was designed as a retrospective review of prospectively collected clinical data. The subjects were 210 consecutive patients who underwent infrainguinal vein bypass grafting for ischemic tissue loss in the setting of an academic medical center. Bypass grafting was to the popliteal artery in 56 patients, to the infrapopliteal arteries in 131 patients, and to the pedal arteries in 23 patients. The follow-up examination was complete in 209 of 210 patients. One hundred twenty-five patients underwent blinded review of duplex scan venous mapping and arteriography to determine simplified vein and run-off scores. The outcome measures were the influence of risk factors, venous conduit, and runoff on mortality, limb loss, and graft failure at the 6-month follow-up examination. Results: One hundred seventy patients (81%) were alive and had limb salvage. Nineteen patients (9.1%) died, with need for a simultaneous inflow procedure and end-stage renal disease being most commonly associated with mortality. Thirty-three patients (15.8%) had undergone amputation: 18 after graft failure, and 15 for progressive tissue loss despite a patent graft. Amputation was significantly more common in patients with diabetes (P = .05) and with poor runoff scores (poor runoff, 44.4% vs good runoff, 7.4%; P < .01). Amputation despite a patent graft also correlated with runoff (poor runoff, 41.7% vs good runoff, 4.3%; P < .01). Twenty-five patients had graft failure without amputation, so that only 145 patients (69.4%) were alive, had limb salvage, and had a patent graft. Run-off score was the strongest predictor of outcome, with 70% of patients with poor run-off scores having death, amputation, or graft failure. Conclusion: Aggressive use of infrainguinal vein bypass grafting in patients with ischemic tissue loss results in a high rate of initial limb salvage but significant morbidity and mortality. Arteriographically determined runoff scores appear to potentially identify patients at high risk for a poor initial outcome and may provide a method of selecting patients for primary amputation. (J Vasc Surg 1999;30:427-35.