Related papers: A Homotopy Method Based on Theory of Functional Co…

Tackling unfairness in graph learning models is a challenging task, as the unfairness issues on graphs involve both attributes and topological structures. Existing work on fair graph learning simply assumes that attributes of all nodes are…

The growing population of man-made objects with the build up of mega-constellations not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but above all poses a serious…

Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…

Filterless optical transport networks relies on passive optical interconnections between nodes, i.e., on splitters/couplers and amplifiers. While different studies have investigated their design, none of them offer a solution for an optimal…

In traditional networks, interfaces of network nodes are duplex. But, emerging communication technologies such as visible light communication, millimeter-wave communications, can only provide a unidirectional interface when cost is limited.…

Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…

A novel matching based heuristic algorithm designed to detect specially formulated infeasible zero-one IPs is presented. The algorithm input is a set of nested doubly stochastic subsystems and a set E of instance defining variables set at…

Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a…

Persistent homology, a method from topological data analysis, extracts robust, multi-scale features from data. It produces stable representations of time series by applying varying thresholds to their values (a process known as a…

This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…

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…

The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…

Robotic planning in real-world scenarios typically requires joint optimization of logic and continuous variables. A core challenge to combine the strengths of logic planners and continuous solvers is the design of an efficient interface…

We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory…

This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of Functional Connections is a technique to derive constrained…

The Homotopy Analysis Method (HAM) is a widely used analytical approach for solving nonlinear problems, yet its theoretical foundation lacks rigorous justification, and its intrinsic correlation with perturbation theory remains ambiguous,…

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…

Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…

We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring…

TPC (Three-Phase Consolidation) is here introduced as a simple but effective approach to continually learn new classes (and/or instances of known classes) while controlling forgetting of previous knowledge. Each experience (a.k.a. task) is…