Related papers: A Homotopy Method Based on Theory of Functional Co…
Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
Data-driven machine learning approaches have recently been proposed to facilitate wireless network optimization by learning latent knowledge from historical optimization instances. However, existing methods do not well handle the topology…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
We observe that the notion of two sets being equal up to finitely many elements is a homotopy equivalence relation in a model category, and suggest a homotopy-invariant variant of Generalised Continuum Hypothesis about which more can be…
Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…
To address the gaps between the static pre-set "thinking-planning-action" of humanoid robots in unfamiliar scenarios and the highly programmed "call tool-return result" due to the lack of autonomous coding capabilities, this work designs a…
We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start…
We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and…
Although modern imaging technologies allow us to study connectivity between two distinct brain regions in-vivo, an in-depth understanding of how anatomical structure supports brain function and how spontaneous functional fluctuations emerge…
The solution space of any set of power flow equations may contain different number of real-valued solutions. The boundaries that separate these regions are referred to as power flow solution space boundaries. Knowledge of these boundaries…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
In the present work, a highly efficient Moving Morphable Component (MMC) based approach for multi-resolution topology optimization is proposed. In this approach, high-resolution optimization results can be obtained with much less number of…
A fundamental question in search-guided AI: what topology should guide Monte Carlo Tree Search (MCTS) in puzzle solving? Prior work applied topological features to guide MCTS in ARC-style tasks using grid topology -- the Laplacian spectral…
We prove in this work that the well-known lasso problem can be solved exactly without homotopy using novel differential inclusions techniques. Specifically, we show that a selection principle from the theory of differential inclusions…
Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has…
Aiming at the binary classification of functional data, we propose the continuum centroid classifier (CCC) built upon projections of functional data onto one specific direction. This direction is obtained via bridging the regression and…
Force-directed layouts belong to a popular class of methods used to position nodes in a node-link diagram. However, they typically lack direct consideration of global structures, which can result in visual clutter and the overlap of…
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological…