Robots were originally introduced in the production of industrialized building components and modular housing. Later mobile robots were developed for special on-site construction tasks. Automated construction sites use robotics for logistics and assembly. The technological progress of robotics allows recently the automated production of facades, which is described in this keynote.

Given a weight 2 and level p modular form f , we construct two weight /2 modular forms (possibly zero) of level 4p and non trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imaginary quadratic twists of f . Furthermore, we give a general framework for our construction that appli...

In this note we will show how to compute Up acting on spaces of overconvergent p-adic modular forms when X0(p) has genus 1. We first give a construction of Banach bases for spaces of overconvergent p-adic modular forms, and then give an algorithm to approximate both the characteristic power series of the Up operator and eigenvectors of finite slope for Up, and present some explicit examples. We...

The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this representation, for various (small) values of the genus and the level, into irreducible representations. As a consequence we obtain uniqueness results for cer...

In [Leh], Emma Lehmer constructed a parametric family of units in real quintic fields of prime conductor p = t + 5t + 15t + 25t+ 25, as translates of Gaussian periods. Later, Schoof and Washington [SW] showed that these units were fundamental units. In this note, we observe that Lehmer’s family comes from the covering of modular curves X1(25) −→ X0(25). This gives a conceptual explanation for t...

Modular construction has great potential to address persistent problems in the industry, such as lack of labor and resources. In implementation modular construction, modularization is a crucial task that overwhelms designers. Different solutions influence manufacturing operations significantly, yet this rarely been studied past. This paper proposed an optimization model considering set-up chang...

Distributed data and knowledge base applications need ontology languages and tools that can support collaborative construction, sharing, and use of large ontologies. Modular ontology languages aim to address this challenge by providing language support for organizing complex ontologies into relatively independent modules, selective sharing of information among ontology modules, and reasoning wi...

The aim of this paper is to provide a sound framework for addressing a difficult problem: the automatic construction of an autonomous agent’s modular architecture. We briefly present two apparently uncorrelated frameworks: Autonomous planning through Markov Decision Processes and Kernel Clustering. Our fundamental idea is that the former addresses autonomy whereas the latter allows to tackle se...

We start with a given modular invariantM of a two dimensional ŝu(n)k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE ...