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Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is…
Cohomology and cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical…
In this work, we propose an approach to the spatiotemporal localisation (detection) and classification of multiple concurrent actions within temporally untrimmed videos. Our framework is composed of three stages. In stage 1, appearance and…
In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the…
We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$,…
The recent technological progress in acquisition, modeling and processing of 3D data leads to the proliferation of a large number of 3D objects databases. Consequently, the techniques used for content based 3D retrieval has become…
Recent advances in diffusion-based generation techniques enable AI models to produce highly realistic videos, heightening the need for reliable detection mechanisms. However, existing detection methods provide only limited exploration of…
Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as…
Given a graph embedded in an orientable surface, a process consisting of random excitations and random node and face balancing is constructed and analyzed. It is shown that given a priori bounds g' on the genus and n' on the number of…
Robots equipped with situational awareness can help humans efficiently find their lost objects by leveraging spatial and temporal structure. Existing approaches to video and image retrieval do not take into account the unique constraints…
We propose a self-supervised framework that learns to group visual entities based on their rate of co-occurrence in space and time. To model statistical dependencies between the entities, we set up a simple binary classification problem in…
In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the \textit{time-varying non-linear spatio-temporal correlations} found in multivariate time series data . In multivariate time series data, an anomaly may be…
This study presents an open source method for detecting 3D printing anomalies by comparing images of printed layers from a stationary monocular camera with G-code-based reference images of an ideal process generated with Blender, a physics…
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…
In this paper we study the application of convolutional neural networks for jointly detecting objects depicted in still images and estimating their 3D pose. We identify different feature representations of oriented objects, and energies…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Recently, a new set of multigraph parameters was defined, called "gonalities". Gonality bears some similarity to treewidth, and is a relevant graph parameter for problems in number theory and multigraph algorithms. Multigraphs of gonality 1…
Discovering causal structures from multivariate time series is a key problem because interactions span across multiple lags and possibly involve instantaneous dependencies. Additionally, the search space of the dynamic graphs is…
Inductive representation learning on temporal graphs is an important step toward salable machine learning on real-world dynamic networks. The evolving nature of temporal dynamic graphs requires handling new nodes as well as capturing…
Dominators provide a general mechanism for identifying reconverging paths in graphs. This is useful for a number of applications in Computer-Aided Design (CAD) including signal probability computation in biased random simulation, switching…