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Suyoung Choi

Publications and source records attributed to Suyoung Choi.

At least 37 records · Page 2Linked to original sources
arXiv2024

Toric wedge induction and toric lifting property for piecewise linear spheres with a few vertices

Let $K$ be an $(n-1)$-dimensional piecewise linear sphere on $[m]$, where $m\leq n+4$. There are a canonical action of $m$-dimensional torus $T^m$ on the moment-angle complex $\mathcal{Z}_K$, and a canonical action of $\mathbb{Z}_2^m$ on the real moment-angle complex $\mathbb{R}\mathcal{Z}_K$, where $\mathbb{Z}_2$ is the additive group with two elements. We prove that any subgroup of $\mathbb{Z}_2^m$ acting freely on $\mathbb{R}\mathcal{Z}_K$ is induced by a subtorus of $T^m$ acting freely on $\mathcal{Z}_K$. The proof primarily utilizes a suitably modified method of toric wedge induction and the combinatorial structure of a specific binary matroid of rank $4$.

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arXiv2024

The characterization of $(n-1)$-spheres with $n+4$ vertices having maximal Buchstaber number

We present a computationally efficient algorithm that is suitable for graphic processing unit implementation. This algorithm enables the identification of all weak pseudo-manifolds that meet specific facet conditions, drawn from a given input set. We employ this approach to enumerate toric colorable seeds. Consequently, we achieve a comprehensive characterization of $(n-1)$-dimensional PL spheres with $n+4$ vertices that possess a maximal Buchstaber number. A primary focus of this research is the fundamental categorization of non-singular complete toric varieties of Picard number $4$. This classification serves as a valuable tool for addressing questions related to toric manifolds of Picard number $4$. Notably, we have determined which of these manifolds satisfy equality within an inequality regarding the number of minimal components in their rational curve space. This addresses a question posed by Chen, Fu, and Hwang in 2014 for this specific case.

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arXiv2024

Legged Robot State Estimation With Invariant Extended Kalman Filter Using Neural Measurement Network

This paper introduces a novel proprioceptive state estimator for legged robots that combines model-based filters and deep neural networks. Recent studies have shown that neural networks such as multi-layer perceptron or recurrent neural networks can estimate the robot states, including contact probability and linear velocity. Inspired by this, we develop a state estimation framework that integrates a neural measurement network (NMN) with an invariant extended Kalman filter. We show that our framework improves estimation performance in various terrains. Existing studies that combine model-based filters and learning-based approaches typically use real-world data. However, our approach relies solely on simulation data, as it allows us to easily obtain extensive data. This difference leads to a gap between the learning and the inference domain, commonly referred to as a sim-to-real gap. We address this challenge by adapting existing learning techniques and regularization. To validate our proposed method, we conduct experiments using a quadruped robot on four types of terrain: \textit{flat}, \textit{debris}, \textit{soft}, and \textit{slippery}. We observe that our approach significantly reduces position drift compared to the existing model-based state estimator.

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arXiv2023

Learning Whole-body Manipulation for Quadrupedal Robot

We propose a learning-based system for enabling quadrupedal robots to manipulate large, heavy objects using their whole body. Our system is based on a hierarchical control strategy that uses the deep latent variable embedding which captures manipulation-relevant information from interactions, proprioception, and action history, allowing the robot to implicitly understand object properties. We evaluate our framework in both simulation and real-world scenarios. In the simulation, it achieves a success rate of 93.6 % in accurately re-positioning and re-orienting various objects within a tolerance of 0.03 m and 5 °. Real-world experiments demonstrate the successful manipulation of objects such as a 19.2 kg water-filled drum and a 15.3 kg plastic box filled with heavy objects while the robot weighs 27 kg. Unlike previous works that focus on manipulating small and light objects using prehensile manipulation, our framework illustrates the possibility of using quadrupeds for manipulating large and heavy objects that are ungraspable with the robot's entire body. Our method does not require explicit object modeling and offers significant computational efficiency compared to optimization-based methods. The video can be found at https://youtu.be/fO_PVr27QxU.

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arXiv2023

Learning Vehicle Dynamics from Cropped Image Patches for Robot Navigation in Unpaved Outdoor Terrains

In the realm of autonomous mobile robots, safe navigation through unpaved outdoor environments remains a challenging task. Due to the high-dimensional nature of sensor data, extracting relevant information becomes a complex problem, which hinders adequate perception and path planning. Previous works have shown promising performances in extracting global features from full-sized images. However, they often face challenges in capturing essential local information. In this paper, we propose Crop-LSTM, which iteratively takes cropped image patches around the current robot's position and predicts the future position, orientation, and bumpiness. Our method performs local feature extraction by paying attention to corresponding image patches along the predicted robot trajectory in the 2D image plane. This enables more accurate predictions of the robot's future trajectory. With our wheeled mobile robot platform Raicart, we demonstrated the effectiveness of Crop-LSTM for point-goal navigation in an unpaved outdoor environment. Our method enabled safe and robust navigation using RGBD images in challenging unpaved outdoor terrains. The summary video is available at https://youtu.be/iIGNZ8ignk0.

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arXiv2022

Strong Cohomological rigidity of Bott manifolds

We show that the strong cohomological rigidity conjecture for Bott manifolds is true. Namely, any graded cohomology ring isomorphism between two Bott manifolds is induced by a diffeomorphism.

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arXiv2021

An algorithmic strategy for finding characteristic maps over wedged simplicial complexes

The puzzle method was introduced by Choi and Park as an effective method for finding non-singular characteristic maps over wedged simplicial complexes $K(J)$ obtained from a given simplicial complex $K$. We study further the mod 2 case of the puzzle method. We firstly describe it completely in terms of linear algebraic language which allows us to develop a constructive puzzle algorithm. We also analyze our algorithm and compare its performances with other known algorithms including the Garrison and Scott algorithm.

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arXiv2020

On the KO-groups of toric manifolds

In this paper we consider the real topological K-groups of a toric manifold M, which turns out to be closely related to the topology of the small cover MR, the fixed points under the canonical conjugation on M . Following the work of Bahri and Bendersky [2], we give an explicit formula for the KO-groups of toric manifolds, and then we characterize the two extreme classes of toric manifolds according to the two A(1) modules shown in [2].

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arXiv2019

Integral cohomology groups of real toric manifolds and small covers

For a simplicial complex $K$ with $m$ vertices, there is a canonical $\mathbb Z_2^m$-space known as a real moment angle complex $\mathbb R \mathcal Z_K$. In this paper, we consider the quotient spaces $Y=\mathbb R \mathcal Z_K / \mathbb Z_2^{k}$, where $K$ is a pure shellable complex and $\mathbb Z_2^k \subset \mathbb Z_2^m$ is a maximal free action on $\mathbb R \mathcal Z_K$. A typical example of such spaces is a small cover, where a small cover is known as a topological analog of a real toric manifold. We compute the integral cohomology group of $Y$ by using the PL cell decomposition obtained from a shelling of $K$. In addition, we compute the Bockstein spectral sequence of $Y$ explicitly.

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arXiv2019

Geometric representations of finite groups on real toric spaces

We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the $G$-module structure of the homology of $X^{\mathbb R}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type $A$ and $B$, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

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arXiv2017

Multiplication structure of the cohomology ring of real toric spaces

A real toric space is a topological space which admits a well-behaved $\mathbb{Z}_2^k$-action. Real moment-angle complexes and real toric varieties are typical examples of real toric spaces. A real toric space is determined by a pair of a simplicial complex $K$ and a characteristic matrix $Λ$. In this paper, we provide an explicit $R$-cohomology ring formula of a real toric space in terms of $K$ and $Λ$, where $R$ is a commutative ring with unity in which $2$ is a unit. Interestingly, it has a natural $(\mathbb{Z} \oplus \operatorname*{row} Λ)$-grading. As corollaries, we compute the cohomology rings of (generalized) real Bott manifolds in terms of binary matroids, and we also provide a criterion for real toric spaces to be cohomology symplectic.

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arXiv2017

Example of C-rigid polytopes which are not B-rigid

A simple polytope $P$ is said to be \emph{B-rigid} if its combinatorial structure is characterized by its Tor-algebra, and is said to be \emph{C-rigid} if its combinatorial structure is characterized by the cohomology ring of a quasitoric manifold over $P$. It is known that a B-rigid simple polytope is C-rigid. In this paper, we, further, show that the B-rigidity is not equivalent to the C-rigidity.

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arXiv2017

Small covers over wedges of polygons

A small cover is a closed smooth manifold of dimension $n$ having a locally standard $\mathbb{Z}_2^n$-action whose orbit space is isomorphic to a simple polytope. A typical example of small covers is a real projective toric manifold (or, simply, a real toric manifold), that is, a real locus of projective toric manifold. In the paper, we classify small covers and real toric manifolds whose orbit space is isomorphic to the dual of the simplicial complex obtainable by a sequence of wedgings from a polygon, using a systematic combinatorial method finding toric spaces called puzzles.

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arXiv2016

Pseudograph and its associated real toric manifold

Given a simple graph $G$, the graph associahedron $P_G$ is a convex polytope whose facets correspond to the connected induced subgraphs of $G$. Graph associahedra have been studied widely and are found in a broad range of subjects. Recently, S. Choi and H. Park computed the rational Betti numbers of the real toric variety corresponding to a graph associahedron under the canonical Delzant realization. In this paper, we focus on a pseudograph associahedron which was introduced by Carr, Devadoss and Forcey, and then discuss how to compute the Poincaré polynomial of the real toric variety corresponding to a pseudograph associahedron under the canonical Delzant realization.

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