Related papers: Algorithms and topological invariants for dynamic …

We settle two problems of reconstructing a biholomorphic type of a manifold. In the first problem we use graphs associated to Riemann surfaces of a particular class. In the second one we use the semigroup structure of analytic endomorphisms…

We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and…

We compute the Donaldson-Thomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the…

We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting…

We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject…

Mapping is an important part of many robotic applications. In order to measure the performance of the mapping process we have to measure the quality of its result: the map. The map is essential for robotic algorithms like localization and…

The paper introduces a new differential-geometric system which originates from the theory of $m$-Hessian operators. The core of this system is a new notion of invariant differentiation on multidimensional surfaces. This novelty gives rise…

Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as…

The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links…

Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…

In the paper we introduce the construction of invariants for 3-manifolds, based on the same key concepts as the classical Dijkgraaf-Witten invariant. We introduce the notion of a special $G$-system and describe how each system induces the…

We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…

In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…

Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…

Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…

We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…