New perspective on space and time from Lorentz violation

I present a brief review on space and time in different periods of physics, and then talk on the nature of space and time from physical arguments. I discuss the ways to test such a new perspective on space and time through searching for Lorentz violation in some physical processes. I also make an introduce to a newly proposed theory of Lorentz violation from basic considerations.Comment: 10 latex pages. Plenary talk at First LeCosPA Symposium: Towards Ultimate Understanding of the Universe (LeCosPA2012), National Taiwan University, Taipei, Taiwan, February 6-9, 201

The Perfect Perspective: A Mathematical Analysis of Perspective Using Tools Available to Middle School Students

This paper examines the basic properties of perspective drawings, the history of perspective drawings, and the basic mathematics of perspective. Using a side view and a top view of a three-dimensional projection, similar triangles can be used to find distances from the axes and vanishing point in a projection. By breaking the three-dimensional projection into two, two-dimensional planes, one can recreate projections based on actual figures, or create placements of figures in real space based on a projection. Using this method, one \u27can change a projection based on the changing position of the vanishing point. This simple approach to perspective makes it accessible to students of different ability levels, as well as creating a strong connection between art and mathematics

Ambiguities in recurrence-based complex network representations of time series

Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail. We discuss the main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase-space properties. Possible artifacts induced by disregarding these requirements are pointed out and systematically studied. Finally, a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed

Measuring fragmentation of open space in urbanised Flanders: an evaluation of four methods

The open space in Flanders, the northern part of Belgium, can hardly be seen as really open. From the Middle Ages onward this area has been known for its spread out development pattern, which has even strengthened in recent decades. Especially the residential ribbon development and the omnipresent infrastructure are widely recognised. These developments have led to an intense fragmentation of open space. In this paper we present two new methods to analyse and quantify this fragmentation of open space from a spatial planning perspective, and compare them with two existing methods. This comparative analysis evaluates the differentmethods and connects them to different definitions of fragmentation. The average patch size method is more appropriate to describe general fragmentation if the focus is on major line infrastructures, whereas the density of fragmenting structures method matches with the interpretation of fragmentation as spatial heterogeneity. The two described methods to detect enclosed open space fragments as signs of fragmentation give different results depending on the data and methods used. The ribbon method however is more appropriate to detect open space fragments under threat of privatisation, since it works with a stricter definition of continuous ribbon development. All four methods are relevant for Flemish spatial planning policy, as they indicate where actions are needed to safeguard open space from further urbanisation tendencies. Furthermore, they can support a differentiated spatial policy and add to the scientific basis of the debate on alternative interpretations of Flemish open space

Information-Entropic Measure of Energy-Degenerate Kinks in Two-Field Models

We investigate the existence and properties of kink-like solitons in a class of models with two interacting scalar fields. In particular, we focus on models that display both double and single-kink solutions, treatable analytically using the Bogomol'nyi--Prasad--Sommerfield bound (BPS). Such models are of interest in applications that include Skyrmions and various superstring-motivated theories. Exploring a region of parameter space where the energy for very different spatially-bound configurations is degenerate, we show that a newly-proposed momentum-space entropic measure called Configurational Entropy (CE) can distinguish between such energy-degenerate spatial profiles. This information-theoretic measure of spatial complexity provides a complementary perspective to situations where strictly energy-based arguments are inconclusive