Related papers: Topology of randon linkages
We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descriptor of the topology of a point cloud. So far, convergence…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
We show that birational smooth complex projective varieties with numerically effective canonical bundles along the exceptional loci have the same Betti numbers. In particular, birational smooth minimal models share the same Betti numbers.…
We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the…
We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We…
One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank invariants), is among the most studied metrics in this context,…
Designing an m-bar linkage with a maximal number of assembly modes is important in robot kinematics, and has further applications in structural biology and computational geometry. A related question concerns the number of assembly modes of…
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large $n$, a networked data…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…
We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate definition) the oriented area is a Bott-Morse function on the…
Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated to $n$-manifolds with smooth flows generated by divergence-free p-vector fields,…
A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory.
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
Analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found. We apply the approach to classical random graphs of Erdos and Renyi (ER), evolving networks introduced by…
We consider the moduli spaces $\mathcal{M}_d(\ell)$ of a closed linkage with n links and prescribed lengths in d-dimensional Euclidean space. For d>3 these spaces are no longer manifolds generically, but they have the structure of a…
We generalise the average asymptotic linking number of a pair of divergence-free vector fields on homology three-spheres by considering the linking of a divergence-free vector field on a manifold of arbitrary dimension with a codimension…
In this paper we study a model of random knots obtained by fixing a space curve in $n$-dimensional Euclidean space with $n>3$, and orthogonally projecting the space curve on to random $3$ dimensional subspaces. By varying the space curve we…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…