Process chain approach to high-order perturbation calculus for quantum lattice models

A method based on Rayleigh-Schroedinger perturbation theory is developed that allows to obtain high-order series expansions for ground-state properties of quantum lattice models. The approach is capable of treating both lattice geometries of large spatial dimensionalities d and on-site degrees of freedom with large state space dimensionalities. It has recently been used to accurately compute the zero-temperature phase diagram of the Bose-Hubbard model on a hypercubic lattice, up to arbitrary large filling and for d=2, 3 and greater [Teichmann et al., Phys. Rev. B 79, 100503(R) (2009)].Comment: 11 pages, 6 figure

Feynman-diagram evaluation in the electroweak theory with computer algebra

The evaluation of quantum corrections in the theory of the electroweak and strong interactions via higher-order Feynman diagrams requires complicated and laborious calculations, which however can be structured in a strictly algorithmic way. These calculations are ideally suited for the application of computer algebra systems, and computer algebra has proven to be a very valuable tool in this field already over several decades. It is sketched how computer algebra is presently applied in evaluating the predictions of the electroweak theory with high precision, and some recent results obtained in this way are summarized.Comment: 7 pages, updated version of proceedings contribution to ACAT 2000, Fermilab, October 200

Tensor Networks for Lattice Gauge Theories with continuous groups

We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge invariant states that can be used in actual numerical computation. Our construction is also applied to the simplest realization of the quantum link models/gauge magnets and provides a clear way to understand their microscopic relation with Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge invariant operators that modify continuously Rokshar-Kivelson wave functions and can be used to extend the phase diagram of known models. As an example we characterize the transition between the deconfined phase of the $Z_2$ lattice gauge theory and the Rokshar-Kivelson point of the U(1) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.Comment: 27 pages, 25 figures, 2nd version the same as the published versio

Goal sketching: towards agile requirements engineering

This paper describes a technique that can be used as part of a simple and practical agile method for requirements engineering. The technique can be used together with Agile Programming to develop software in internet time. We illustrate the technique and introduce lazy refinement, responsibility composition and context sketching. Goal sketching has been used in a number of real-world development projects, one of which is described here

Integrating Multiple Sketch Recognition Methods to Improve Accuracy and Speed

Sketch recognition is the computer understanding of hand drawn diagrams. Recognizing sketches instantaneously is necessary to build beautiful interfaces with real time feedback. There are various techniques to quickly recognize sketches into ten or twenty classes. However for much larger datasets of sketches from a large number of classes, these existing techniques can take an extended period of time to accurately classify an incoming sketch and require significant computational overhead. Thus, to make classification of large datasets feasible, we propose using multiple stages of recognition. In the initial stage, gesture-based feature values are calculated and the trained model is used to classify the incoming sketch. Sketches with an accuracy less than a threshold value, go through a second stage of geometric recognition techniques. In the second geometric stage, the sketch is segmented, and sent to shape-specific recognizers. The sketches are matched against predefined shape descriptions, and confidence values are calculated. The system outputs a list of classes that the sketch could be classified as, along with the accuracy, and precision for each sketch. This process both significantly reduces the time taken to classify such huge datasets of sketches, and increases both the accuracy and precision of the recognition

Integrating Multiple Sketch Recognition Methods to Improve Accuracy and Speed

Sketch recognition is the computer understanding of hand drawn diagrams. Recognizing sketches instantaneously is necessary to build beautiful interfaces with real time feedback. There are various techniques to quickly recognize sketches into ten or twenty classes. However for much larger datasets of sketches from a large number of classes, these existing techniques can take an extended period of time to accurately classify an incoming sketch and require significant computational overhead. Thus, to make classification of large datasets feasible, we propose using multiple stages of recognition. In the initial stage, gesture-based feature values are calculated and the trained model is used to classify the incoming sketch. Sketches with an accuracy less than a threshold value, go through a second stage of geometric recognition techniques. In the second geometric stage, the sketch is segmented, and sent to shape-specific recognizers. The sketches are matched against predefined shape descriptions, and confidence values are calculated. The system outputs a list of classes that the sketch could be classified as, along with the accuracy, and precision for each sketch. This process both significantly reduces the time taken to classify such huge datasets of sketches, and increases both the accuracy and precision of the recognition