Related papers: MuRiT: Efficient Computation of Pathwise Persisten…
Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes…
Recently, vision transformer (ViT) and its variants have achieved promising performances in various computer vision tasks. Yet the high computational costs and training data requirements of ViTs limit their application in…
The $\gamma$-linear projected barcode was recently introduced as an alternative to the well-known fibered barcode for multiparameter persistence, in which restrictions of the modules to lines are replaced by pushforwards of the modules…
Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems -- a…
Hybrid precoding plays a key role in realizing massive multiple-input multiple-output (MIMO) transmitters with controllable cost. MIMO precoders are required to frequently adapt based on the variations in the channel conditions. In hybrid…
The mutual interference between similar radar systems can result in reduced radar sensitivity and increased false alarm rates. To address the synchronous and asynchronous interference mitigation problems in similar radar systems, we first…
Given a graph, finding the distance-2 maximal independent set (MIS-2) of the vertices is a problem that is useful in several contexts such as algebraic multigrid coarsening or multilevel graph partitioning. Such multilevel methods rely on…
We introduce a theoretical and computational framework to use discrete Morse theory as an efficient preprocessing in order to compute zigzag persistent homology. From a zigzag filtration of complexes $(K_i)$, we introduce a zigzag Morse…
Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or more scale parameters. The high computational cost of many…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…
We present Multiscale Vision Transformers (MViT) for video and image recognition, by connecting the seminal idea of multiscale feature hierarchies with transformer models. Multiscale Transformers have several channel-resolution scale…
Video-text retrieval has witnessed remarkable progress driven by large-scale vision-language pretraining, yet most existing approaches inherit an implicit assumption from image-text retrieval: that visual semantics can be captured…
We introduce a refinement of persistent homology that detects simple-homotopy-theoretic phenomena invisible to homology. Given a filtered simplicial complex, we define the Morse complexity profile as the minimal number of critical simplices…
We develop novel methods for using persistent homology to infer the homology of an unknown Riemannian manifold $(M, g)$ from a point cloud sampled from an arbitrary smooth probability density function. Standard distance-based filtered…
Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. However, both the attention mechanism and multi-layer perceptrons (MLPs) in ViTs are not sufficiently efficient due…
Stochastic simulations need multiple replications in order to build confidence intervals for their results. Even if we do not need a large amount of replications, it is a good practice to speed-up the whole simulation time using the…
We approach the problem of the computation of persistent homology for large datasets by a divide-and-conquer strategy. Dividing the total space into separate but overlapping components, we are able to limit the total memory residency for…
Vision Transformers (ViTs) have demonstrated strong potential in medical imaging; however, their high computational demands and tendency to overfit on small datasets limit their applicability in real-world clinical scenarios. In this paper,…
Background: Deep learning has significantly advanced medical image analysis, with Vision Transformers (ViTs) offering a powerful alternative to convolutional models by modeling long-range dependencies through self-attention. However, ViTs…
Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While persistent homology, as a core tool of TDA, focuses on…