Related papers: Kolam Simulation using Angles at Lattice Points
This paper introduces Pulli Kolam, a traditional South Indian craft, as a medium for physical data representation. Grounded in its cultural meaning and embodied practice, Pulli Kolam follows structured geometric rules while allowing…
Pulli kolam is a ubiquitous art form in south India. It involves drawing a line looped around a collection of dots (pullis) place on a plane such that three mandatory rules are followed: all line orbits should be closed, all dots are…
Pulli Kolam is an ancient mathematical artform that is still practiced today in south India by over a quarter million people. "Pulli" in the Tamil language means dots. A specific type of pulli kolam is "sikku" kolam where a series of dots…
In south India, there are traditional patterns of line-drawings encircling dots, called ``Kolam'', among which one-line drawings or the ``infinite Kolam'' provide very interesting questions in mathematics. For example, we address the…
This study extends the mathematical framework of Hridaya Kolam patterns by applying modular arithmetic to even-ordered dot arrangements with arm counts co-prime to the number of dots. We analyze the resulting cyclic sequences that…
This paper extends Hridaya Kolam patterns to cases where the number of dots ($m$) and arms ($n$) are not coprime, i.e., $\gcd(m, n) \ne 1$. Such configurations give rise to multiple disjoint closed loops. We propose a…
Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. This work studies to what extent Large Language Models (LLMs) can…
Tax manipulation comes in a variety of forms with different motivations and of varying complexities. In this paper, we deal with a specific technique used by tax-evaders known as circular trading. In particular, we define algorithms for the…
Vision-Language Models (VLMs) have demonstrated their broad effectiveness thanks to extensive training in aligning visual instructions to responses. However, such training of conclusive alignment leads models to ignore essential visual…
We present Loom, a computer architecture that executes programs compiled from C inside a looped transformer whose weights are derived analytically. The architecture implements a 22-opcode instruction set in 8 transformer layers. Each…
Folding a sequence $S$ into a multidimensional box is a well-known method which is used as a multidimensional coding technique. The operation of folding is generalized in a way that the sequence $S$ can be folded into various shapes and not…
Simulation is essential for developing robotic manipulation systems, particularly for task and motion planning (TAMP), where symbolic reasoning interfaces with geometric, kinematic, and physics-based execution. Recent advances in Large…
In this presentation, we describe the GoSam (Golem/Samurai) framework for the automated computation of multi-particle scattering amplitudes at the one-loop level. The amplitudes are generated analytically in terms of Feynman diagrams, and…
While many algorithms exist for tracing various contours for illustrating a meshed object, few algorithms organize these contours into region-bounding closed loops. Tracing closed-loop boundaries on a mesh can be problematic due to…
This paper presents a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
The Dancing problem requires a swarm of $n$ autonomous mobile robots to form a sequence of patterns, aka perform a choreography. Existing work has proven that some crucial restrictions on choreographies and initial configurations (e.g., on…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
We propose KnotGym, an interactive environment for complex, spatial reasoning and manipulation. KnotGym includes goal-oriented rope manipulation tasks with varying levels of complexity, all requiring acting from pure image observations.…
Origami crease patterns are folding paths that transform flat sheets into spatial objects. Origami patterns with a single degree of freedom (DOF) have creases that fold simultaneously. More often, several substeps are required to…