Decifrando mapas:sobre o conceito de "território" e suas vinculações com a cartografia

This essay studies the cartographic documentation left by military engineers in Portugal, during the 18th Century. The technical dimension of map making is analysed, focusing on the instruments and the methods employed both in field surveys and in subsequent graphic representations. From the point of view of Material Culture, maps are understood as cultural artefacts, therefore historical artefacts; in this sense, the particularities of cartographic language reveal the world conceptions particular to each period. This article proposes a methodology of morphological analysis of the cartographic language, deconstructing the several strata in the organisation of this kind of visual representation. In order to do so, a vast array of heterogeneous correlate documents is mobilised, such as practical geometry, drawing and architecture treatises, contemporary to the period studied.O ensaio versa sobre a documentação cartográfica legada pelos engenheiros militares, em Portugal, no século XVIII. Analisa a dimensão técnica da produção de mapas, focalizando os instrumentos e os métodos empregados nos levantamentos de campo e no desenho de gabinete. Do ponto de vista da cultura material, os mapas são interpretados como artefatos culturais e, portanto, históricos; dessa forma, as particularidades da linguagem cartográfica revelam as concepções de mundo, o estado do conhecimento científico, as convenções e os códigos de representação próprios de cada período. Propõe uma metodologia de análise morfológica da linguagem cartográfica, desconstruindo os diversos estratos da tessitura desse tipo de representação visual. Para tanto, mobiliza um vasto campo de documentos correlatos, heterogêneos, tais como tratados de geometria prática, desenho e arquitetura, contemporâneos ao objeto de estudo

Signatures, Lifts, and Eigenvalues of Graphs

We study the spectra of cyclic signatures of finite graphs and the corresponding cyclic lifts. Starting from a bipartite Ramanujan graph, we prove the existence of an infinite tower of 3-cyclic lifts, each of which is again Ramanujan

Three-Dimensional Grid Drawings with Sub-Quadratic Volume

A three-dimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line-segments representing the edges are pairwise non-crossing. A O(n^{3/2}) volume bound is proved for three-dimensional grid drawings of graphs with bounded degree, graphs with bounded genus, and graphs with no bounded complete graph as a minor. The previous best bound for these graph families was O(n^2). These results (partially) solve open problems due to Felsner, Wismath, and Liotta [Graph Drawing 2001] and Pach, Thiele, and Toth [Graph Drawing 1997]