This paper establishes a Coding Theorem in the context of symmetry groups and develops a connection between subgroups of a group and subsets of binary strings.

The paper introduces and demonstrates that leveraging dynamic symmetry—the uniformity of attainable center-of-mass accelerations—significantly enhances a robot's agility, robustness, and multifunction…

This paper presents a polynomial-time Monte Carlo algorithm to determine the symmetry Lie algebra of a parametrized variety directly from the parametrization.

This paper introduces DDC, a Dead-Direction Conditioner that keeps a deep network's optimization on the symmetry quotient by conditioning the optimizer's state in the orbit decomposition of a $G$-inva…

The paper proposes a novel symmetry-aware, category-level method for 9D object pose estimation that accurately estimates translation and size first, followed by rotation, achieving state-of-the-art re…

The paper introduces Move First, Commit Later, a selective layer for Global LiDAR-to-BIM initialization that decides whether to commit to a registration based on evidence from multiple submaps, reduci…

The paper introduces a novel padding method that leverages crystal symmetry to enhance the encoding of complex inorganic structures, significantly improving the generation of stable, novel materials.

This paper introduces and implements variants of the symmetric lexicographic symmetric-subset reverse search framework for enumerating symmetric feasible subsets of a finite set, applying it to cocirc…

This paper presents an algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes for certain dimensions.

The paper resolves three conjectures related to arrow pattern avoidance in permutations using two different proof methods.

This paper studies the structural expressivity and parameterized complexity of counting homomorphisms from small temporal patterns to large temporal graphs, proving a temporal Lovász-style theorem, in…

The paper proves that the reversible elementary second order cellular automaton rule 115 is periodic when started on finite initial configurations.

This paper provides a uniform construction for counting the number of flat-foldable assignments in an origami Miura-ori crease pattern with a specific number of single face flips.

This paper completely characterizes cyclic equalizability for two words over any finite alphabet by proving that the words must share the same Parikh vector.

This paper explores the effects of geometric perturbations on the stability of diffusion architectures, specifically Diffusion Transformers and Convolutional UNets, using a unified framework and contr…

This paper studies the decidability and complexity properties of unary three-way and two-way deterministic and nondeterministic two-dimensional automata.