Related papers: Multiple arrangements
New aspects of a relation between lattice and dislocation structures are examined within a physically transparent theoretical scheme. Predicted features originating from the lattice discreteness include: (i) multiple core dislocation…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
Science in the 21st century seems to be governed by novel approaches involving interdisciplinary work, systemic perspectives and complexity theory concepts. These new paradigms force us to leave aside our elder mechanistic approaches and…
We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination…
Adopting the global approach to tangent bundles of order two established in[1], we develop this approach to find new results. We also generalize various results of [3], [4] and [6] to the geometry of tangent bundles of order two.
Living systems, particularly multicellular systems, often seem hopelessly complex. But recent studies have suggested that beneath this complexity, there may be unifying quantitative principles that we are only now starting to unravel. All…
Algorithmic modeling relies on limited information in data to extrapolate outcomes for unseen scenarios, often embedding an element of arbitrariness in its decisions. A perspective on this arbitrariness that has recently gained interest is…
The addition-deletion theorems for hyperplane arrangements, which were originally shown in [H. Terao, Arrangements of hyperplanes and their freeness I, II. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 293--320], provide useful ways to…
Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of two-dimensional tiling models in which the tiles…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
There are many papers written on the Two Envelopes Problem that usually study some of its variations. In this paper we will study and compare the most significant variations of the problem. We will see the correct decisions for each player…
In this paper we describe the intersection between the balls of maximal symplectic packings of $\P^2$. This analysis shows the existence of singular points for maximal packings of $\P^2$ by more than three equal balls. It also yields a…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From a tiling, we can construct a dynamical system which encodes…
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
This paper shows that a multiple translative tile in the plane must be a multiple lattice tile.
Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed.…