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We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
Traversing environments with arbitrary obstacles poses significant challenges for bipedal robots. In some cases, whole body motions may be necessary to maneuver around an obstacle, but most existing footstep planners can only select from a…
In this paper, we introduce and study sequential versions of several fibrewise homotopy invariants, including parametrized topological complexity, parametrized (subspace) homotopic distance. We investigate their basic properties, establish…
We investigate a new structure for machine learning classifiers applied to problems in high-energy physics by expanding the inputs to include not only measured features but also physics parameters. The physics parameters represent a…
In this article, we investigate the higher topological complexity of oriented Seifert fibered manifolds that are Eilenberg--MacLane spaces $K(G,1)$ with infinite fundamental group $G$. We first refine the cohomological lower bounds for…
We consider the problem of connected coordinated motion planning for a large collective of simple, identical robots: From a given start grid configuration of robots, we need to reach a desired target configuration via a sequence of…
We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially…
A workflow specification defines a set of steps and the order in which those steps must be executed. Security requirements may impose constraints on which groups of users are permitted to perform subsets of those steps. A workflow…
Sampling-based planning algorithms are the most common probabilistically complete algorithms and are widely used on many robot platforms. Within this class of algorithms, many variants have been proposed over the last 20 years, yet there is…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
Many of the classic problems of coding theory are highly symmetric, which makes it easy to derive sphere-packing upper bounds and sphere-covering lower bounds on the size of codes. We discuss the generalizations of sphere-packing and…
Topological complexity $\TC{B}$ of a space $B$ is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space.…
The Topological complexity a la Farber $\text{TC}(-)$ is a homotopy invariant which have interesting applications in Robotics, specifically, in the robot motion planning problem. In this work we calculate the topological complexity of the…
This paper proposes an adaptive lattice-based motion planning solution to address the problem of generating feasible trajectories for systems, represented by a linearly parameterizable non-linear model operating within a cluttered…
Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing performance metrics such as runtime and…