This paper presents the work carried out by a multidisciplinary team of researchers, gathering knowledge in architecture, drawing, geometry, mathematics and computation. The research was directed in order to create a computational tool for architectural visualization a new digital perspectograph with the use of a new theoretical and operative approach to linear perspective. A new kind of projec...

This paper describes a new approach to extracting 3D perspective structure from 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying pointcorrespondence matches. Unification is realised by constructing a mixture model over the bi-partite graph representing the correspondence match and by effecting optimisation using the EM algorithm. Accor...

From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein–Yang–Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher dimensional gravity, we provide the criteria for the local and global statistical stability o...

The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of projections in the proper perspective of noncommutative geometry. keyword: Index problem, crossed product, Fredholm module, pair of projections. MSC 46L87.

We extend Akemann, Anderson, and Weaver’s Spectral Scale definition to include selfadjoint operators from semifinite von Neumann algebras. New illustrations of spectral scales in both the finite and semifinite von Neumann settings are presented. A counterexample to a conjecture made by Akemann concerning normal operators and the geometry of the their perspective spectral scales in the finite se...

This paper is a brief account of the moduli of complex curves from the perspective of noncommutative geometry. We focus on the uniformization of Riemann surfaces by the ordered K-groups of a noncommutative C-algebra. Using this approach, we prove “generic” arithmeticity of the mapping class group and study correspondences between complex and noncommutative tori.

Coset models and their symmetry preserving branes are studied from a representation theoretic perspective, relating e.g. the horizontal branching spaces to a truncation of the space of bulk fields, and accounting for field identification. This allows us to describe the fuzzy geometry of the branes at finite level.

In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosahedral symmetry. We associate to each Ammann tiling two explicitly constructed highly singular symplectic spaces and we show that they are diffeomorphic but not symplectomorphic. These spaces inherit from the tiling its very inte...

Over the past decade, several technologies have emerged to access nucleic acid-tagged libraries and select the fittest compound within such libraries. This perspective focuses on recent development with PNA-tagged small molecules displayed on DNA templates for screening purposes and to probe the optimal geometry in multivalent interactions.

We review how to describe the stable non-BPS D-branes of type II string theory from a classical perspective, and discuss the properties of the space-time geometry associated to these configurations. This is relevant in order to see whether and how the gauge/gravity correspondence can be formulated in non-conformal and non-supersymmetric settings.