Related papers: Exploring the Topology of Dynamical Reconstruction…
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes…
To understand, predict, and control complex networked systems, a prerequisite is to reconstruct the network structure from observable data. Despite recent progress in network reconstruction, binary-state dynamics that are ubiquitous in…
The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever…
We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…
A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…
This paper examines the reconstruction of a family of dynamical systems with neuromorphic behavior using a single scalar time series. A model of a physiological neuron based on the Hodgkin-Huxley formalism is considered. Single time series…
Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…
The systems without symmetries, e.g. the spatial and chiral symmetries, are generally thought to be improper for topological study and no conventional integral topological invariant can be well defined. In this work, with multi-band…
We address 2D floorplan reconstruction from 3D scans. Existing approaches typically employ heuristically designed multi-stage pipelines. Instead, we formulate floorplan reconstruction as a single-stage structured prediction task: find a…
Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens'…
Topology change is a challenging problem for 4D reconstruction of dynamic scenes. In the classic volumetric fusion-based framework, a mesh is usually extracted from the TSDF volume as the canonical surface representation to help estimating…
Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…
Samples from intimate (non-linear) mixtures are generally modeled as being drawn from a smooth manifold. Scenarios where the data contains multiple intimate mixtures with some constituent materials in common can be thought of as manifolds…
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…