Related papers: Exploring the Topology of Dynamical Reconstruction…
Dynamic Bayesian networks provide a compact and natural representation for complex dynamic systems. However, in many cases, there is no expert available from whom a model can be elicited. Learning provides an alternative approach for…
In this paper, we give the first algorithm that outputs a faithful reconstruction of a submanifold of Euclidean space without maintaining or even constructing complicated data structures such as Voronoi diagrams or Delaunay complexes. Our…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
In this paper we investigate Deep Learning Models using topological dynamical systems, index theory, and computational homology. These mathematical machinery was invented initially by Henri Poincare around 1900 and developed over time to…
The computation of homology groups for evolving simplicial complexes often requires repeated reconstruction of boundary operators, resulting in prohibitive costs for large-scale or frequently updated data. This work introduces MMHM, a…
Reconstructing a dynamic scene from image inputs is a fundamental computer vision task with many downstream applications. Despite recent advancements, existing approaches still struggle to achieve high-quality reconstructions from unseen…
Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…
Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…
Finite volume schemes for hyperbolic balance laws require a piecewise polynomial reconstruction of the cell averaged values, and a reconstruction is termed `well-balanced' if it is able to simulate steady states at higher order than time…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…
Elements composing complex systems usually interact in several different ways and as such the interaction architecture is well modelled by a multiplex network. However often this architecture is hidden, as one usually only has experimental…
In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
A recently proposed nearest neighbor based selection of time delays for phase space reconstruction is extended to multivariate time series, with an iterative selection of variables and time delays. A case study of numerically generated…
We propose a new method for the reconstruction of simplicial complexes (combining points, edges and triangles) from 3D point clouds from Mobile Laser Scanning (MLS). Our main goal is to produce a reconstruction of a scene that is adapted to…
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…
Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…