Related papers: Spatiotemporal Persistence Landscapes
Persistent homology is a way of determining the topological properties of a data set. It is well known that each persistence module admits the structure of a representation of a finite totally ordered set. In previous work, the authors…
Topological invariants have played a fundamental role in the advancement of theoretical high energy physics. Physicists have used several kinematic techniques to distinguish new physics predictions from the Standard Model (SM) of particle…
We propose and implement a method to analyze time series with a neural network using a matrix of area-normalized persistence landscapes obtained through topological data analysis. We include a gating layer in the network's architecture that…
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Ripser. The cup product operation which is available at…
The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map…
In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Video diffusion models have recently shown promise for world modeling through autoregressive frame prediction conditioned on actions. However, they struggle to maintain long-term memory due to the high computational cost associated with…
Latent space matching, which consists of matching distributions of features in latent space, is a crucial component for tasks such as adversarial attacks and defenses, domain adaptation, and generative modelling. Metrics for probability…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
Interactive world models continually generate video by responding to a user's actions, enabling open-ended generation capabilities. However, existing models typically lack a 3D representation of the environment, meaning 3D consistency must…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
Recently, bipath persistent homology has been proposed as an extension of standard persistent homology, along with its visualization (bipath persistence diagram) and computational methods. In the setting of standard persistent homology, the…
This sketch shows that the usual generating function based capacities have an interpretation in the language of persistent homology as persistences of certain homology classes in the persistence module formed by the corresponding generating…
In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under…
Pose Machines provide a sequential prediction framework for learning rich implicit spatial models. In this work we show a systematic design for how convolutional networks can be incorporated into the pose machine framework for learning…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…