Operator algebra quantum homogeneous spaces of universal gauge groups

In this paper, we quantize universal gauge groups such as SU(\infty), as well as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely, we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum homogeneous spaces and explain these concepts here. At the same time, we put these definitions in the mathematical context of countably compactly generated spaces as well as C*-compact quantum groups and homogeneous spaces. We also study the representable K-theory of these spaces and compute it for the quantum homogeneous spaces associated to the universal gauge group SU(\infty).Comment: 14 pages. Merged with [arXiv:1011.1073

Spin Calogero models obtained from dynamical r-matrices and geodesic motion

We study classical integrable systems based on the Alekseev-Meinrenken dynamical r-matrices corresponding to automorphisms of self-dual Lie algebras, ${\cal G}$. We prove that these r-matrices are uniquely characterized by a non-degeneracy property and apply a construction due to Li and Xu to associate spin Calogero type models with them. The equation of motion of any model of this type is found to be a projection of the natural geodesic equation on a Lie group $G$ with Lie algebra ${\cal G}$, and its phase space is interpreted as a Hamiltonian reduction of an open submanifold of the cotangent bundle $T^*G$, using the symmetry arising from the adjoint action of $G$ twisted by the underlying automorphism. This shows the integrability of the resulting systems and gives an algorithm to solve them. As illustrative examples we present new models built on the involutive diagram automorphisms of the real split and compact simple Lie algebras, and also explain that many further examples fit in the dynamical r-matrix framework.Comment: 25 pages, with minor stylistic changes and updated references in v

Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.Comment: 15 pages, standard LaTe

Challenges of beta-deformation

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.Comment: 20 page

Comparison of manual and user guided methodologies for the classification and retrieval of construction site images

The amount of original imaging information produced yearly during the last decade has experienced a tremendous growth in all industries due to the technological breakthroughs in digital imaging and electronic storage capabilities. This trend is affecting the construction industry as well, where digital cameras and image databases are gradually replacing traditional photography. Owners demand complete site photograph logs and engineers store thousands of images for each project to use in a number of construction management tasks like monitoring an activity's progress and keeping evidence of the "as built" in case any disputes arise. So far, retrieval methodologies are done manually with the user being responsible for imaging classification according to specific rules that serve a limited number of construction management tasks. New methods that, with the guidance of the user, can automatically classify and retrieve construction site images are being developed and promise to remove the heavy burden of manually indexing images. In this paper, both the existing methods and a novel image retrieval method developed by the authors for the classification and retrieval of construction site images are described and compared. Specifically a number of examples are deployed in order to present their advantages and limitations. The results from this comparison demonstrates that the content based image retrieval method developed by the authors can reduce the overall time spent for the classification and retrieval of construction images while providing the user with the flexibility to retrieve images according different classification schemes

Identification of Materials from Construction Site Images Using Content Based Image Retrieval Techniques

The capability to automatically identify shapes, objects and materials from the image content through direct and indirect methodologies has enabled the development of several civil engineering related applications that assist in the design, construction and maintenance of construction projects. Examples include surface cracks detection, assessment of fire-damaged mortar, fatigue evaluation of asphalt mixes, aggregate shape measurements, velocimentry, vehicles detection, pore size distribution in geotextiles, damage detection and others. This capability is a product of the technological breakthroughs in the area of Image and Video Processing that has allowed for the development of a large number of digital imaging applications in all industries ranging from the well established medical diagnostic tools (magnetic resonance imaging, spectroscopy and nuclear medical imaging) to image searching mechanisms (image matching, content based image retrieval). Content based image retrieval techniques can also assist in the automated recognition of materials in construction site images and thus enable the development of reliable methods for image classification and retrieval. The amount of original imaging information produced yearly in the construction industry during the last decade has experienced a tremendous growth. Digital cameras and image databases are gradually replacing traditional photography while owners demand complete site photograph logs and engineers store thousands of images for each project to use in a number of construction management tasks. However, construction companies tend to store images without following any standardized indexing protocols, thus making the manual searching and retrieval a tedious and time-consuming effort. Alternatively, material and object identification techniques can be used for the development of automated, content based, construction site image retrieval methodology. These methods can utilize automatic material or object based indexing to remove the user from the time-consuming and tedious manual classification process. In this paper, a novel material identification methodology is presented. This method utilizes content based image retrieval concepts to match known material samples with material clusters within the image content. The results demonstrate the suitability of this methodology for construction site image retrieval purposes and reveal the capability of existing image processing technologies to accurately identify a wealth of materials from construction site images

Shape-Based Retrieval of Construction Site Photographs

Digital photographs of construction site activities are gradually replacing their traditional paper based counterparts. Existing digital imaging technologies in hardware and software make it easy for site engineers to take numerous photographs of “interesting” processes and activities on a daily basis. The resulting photographic data are evidence of the “as-built” project, and can therefore be used in a number of project life cycle tasks. However, the task of retrieving the relevant photographs needed in these tasks is often burdened by the sheer volume of photographs accumulating in project databases over time and the numerous objects present in each photograph. To solve this problem, the writers have recently developed a number of complementary techniques that can automatically classify and retrieve construction site images according to a variety of criteria (materials, time, date, location, etc.). This paper presents a novel complementary technique that can automatically identify linear (i.e., beam, column) and nonlinear (i.e., wall, slab) construction objects within the image content and use that information to enhance the performance of the writers’ existing construction site image retrieval approach

Multi-Modal Image Retrieval from Construction Databases and Model-Based Systems

In the modern and dynamic construction environment it is important to access information in a fast and efficient manner in order to improve the decision making processes for construction managers. This capability is, in most cases, straightforward with today’s technologies for data types with an inherent structure that resides primarily on established database structures like estimating and scheduling software. However, previous research has demonstrated that a significant percentage of construction data is stored in semi-structured or unstructured data formats (text, images, etc.) and that manually locating and identifying such data is a very hard and time-consuming task. This paper focuses on construction site image data and presents a novel image retrieval model that interfaces with established construction data management structures. This model is designed to retrieve images from related objects in project models or construction databases using location, date, and material information (extracted from the image content with pattern recognition techniques)