Searcharxiv⌕ Search

arXiv subjects

Jung Hoon Lee

Publications and source records attributed to Jung Hoon Lee.

At least 19 recordsLinked to original sources
arXiv2026

A note on reducing spheres for the genus-4 Heegaard surface in the 3-sphere

For the genus-$4$ Heegaard surface in the $3$-sphere, we present a sufficient condition for a non-separating weak reducing pair to be separated by a reducing sphere for the surface. As a consequence, we reduce the connectivity problem in the reducing sphere complex for the surface to the problem of showing that any two vertices, whose representative reducing spheres are disjoint from a fixed non-separating compressing disk for the surface, are connected in the complex.

math.GT↗
arXiv2025

The rectangle condition does not detect the strong irreducibility

The rectangle condition for a genus $g$ Heegaard splitting of a 3-manifold, defined by Casson and Gordon, provides a sufficient criterion for the Heegaard splitting to be strongly irreducible. However it is unknown whether there exists a strongly irreducible Heegaard splitting which does not satisfy the rectangle condition. In this paper we provide a counterexample of a genus 2 Heegaard splitting of a 3-manifold which is strongly irreducible but fails to satisfy the rectangle condition. The way of constructing such an example is to take a double branched cover of a 3-bridge decomposition of a knot in $S^3$ which is strongly irreducible but does not meet the rectangle condition. This implies that the rectangle condition does not detect the strong irreducibility. As our next goal, we expect that this result provides the weaker version of the rectangle condition which detects the strong irreducibility.

math.GT↗
arXiv2025

Two out of Three (ToT): using self-consistency to make robust predictions

Deep learning (DL) can automatically construct intelligent agents, deep neural networks (alternatively, DL models), that can outperform humans in certain tasks. However, the operating principles of DL remain poorly understood, making its decisions incomprehensible. As a result, it poses a great risk to deploy DL in high-stakes domains in which mistakes or errors may lead to critical consequences. Here, we aim to develop an algorithm that can help DL models make more robust decisions by allowing them to abstain from answering when they are uncertain. Our algorithm, named `Two out of Three (ToT)', is inspired by the sensitivity of the human brain to conflicting information. ToT creates two alternative predictions in addition to the original model prediction and uses the alternative predictions to decide whether it should provide an answer or not.

cs.LG↗
arXiv2025

Spiking Neural Network: a low power solution for physical layer authentication

Deep learning (DL) is a powerful tool that can solve complex problems, and thus, it seems natural to assume that DL can be used to enhance the security of wireless communication. However, deploying DL models to edge devices in wireless networks is challenging, as they require significant amounts of computing and power resources. Notably, Spiking Neural Networks (SNNs) are known to be efficient in terms of power consumption, meaning they can be an alternative platform for DL models for edge devices. In this study, we ask if SNNs can be used in physical layer authentication. Our evaluation suggests that SNNs can learn unique physical properties (i.e., `fingerprints') of RF transmitters and use them to identify individual devices. Furthermore, we find that SNNs are also vulnerable to adversarial attacks and that an autoencoder can be used clean out adversarial perturbations to harden SNNs against them.

cs.LG↗
arXiv2025

On the Invalidity of Lemma 2.5 in our previous work on the Powell Conjecture

In our previous version entitled ``The reducing sphere complexes for the 3-sphere are connected: a proof of the Powell Conjecture", we claimed to prove the Powell Conjecture, which states that the Goeritz group of the genus-$g$ Heegaard splitting of the 3-sphere is finitely generated for any non-negative integer $g$. However, we have found a critical error in the proof of Lemma 2.5 in that version. In this note, we prove that the statement of Lemma 2.5 does not hold in general. This invalidates a key step in our argument and leaves the proof of the Powell Conjecture incomplete. Consequently, the Powell Conjecture remains an open problem in the case of $g \geq 4$.

math.GT↗
arXiv2025

User-Centric Association and Feedback Bit Allocation for FDD Cell-Free Massive MIMO

In this paper, we introduce a novel approach to user-centric association and feedback bit allocation for the downlink of a cell-free massive MIMO (CF-mMIMO) system, operating under limited feedback constraints. In CF-mMIMO systems employing frequency division duplexing, each access point (AP) relies on channel information provided by its associated user equipments (UEs) for beamforming design. Since the uplink control channel is typically shared among UEs, we take account of each AP's total feedback budget, which is distributed among its associated UEs. By employing the Saleh-Valenzuela multi-resolvable path channel model with different average path gains, we first identify necessary feedback information for each UE, along with an appropriate codebook structure. This structure facilitates adaptive quantization of multiple paths based on their dominance. We then formulate a joint optimization problem addressing user-centric UE-AP association and feedback bit allocation. To address this challenge, we analyze the impact of feedback bit allocation and derive our proposed scheme from the solution of an alternative optimization problem aimed at devising long-term policies, explicitly considering the effects of feedback bit allocation. Numerical results show that our proposed scheme effectively enhances the performance of conventional approaches in CF-mMIMO systems.

cs.IT↗
arXiv2024

The Powell Conjecture for the genus-three Heegaard splitting of the $3$-sphere

The Powell Conjecture states that the Goeritz group of the Heegaard splitting of the $3$-sphere is finitely generated; furthermore, four specific elements suffice to generate the group. Zupan demonstrated that the conjecture holds if and only if the reducing sphere complexes are all connected. In this work, we establish the connectivity of the reducing sphere complex for the genus-$3$ case, thereby confirming the Powell Conjecture in genus $3$. Additionally, we propose a potential framework for extending this approach to Heegaard splittings of higher genera.

math.GT↗
arXiv2024

Generalization ability and Vulnerabilities to adversarial perturbations: Two sides of the same coin

Deep neural networks (DNNs), the agents of deep learning (DL), require a massive number of parallel/sequential operations, which makes it difficult to comprehend them and impedes proper diagnosis. Without better knowledge of DNNs' internal process, deploying DNNs in high-stakes domains may lead to catastrophic failures. Therefore, to build more reliable DNNs/DL, it is imperative that we gain insights into their underlying decision-making process. Here, we use the self-organizing map (SOM) to analyze DL models' internal codes associated with DNNs' decision-making. Our analyses suggest that shallow layers close to the input layer map onto homogeneous codes and that deep layers close to the output layer transform these homogeneous codes in shallow layers to diverse codes. We also found evidence indicating that homogeneous codes may underlie DNNs' vulnerabilities to adversarial perturbations.

cs.LG↗
arXiv2024

The primitive curve complex for a handlebody

A simple closed curve in the boundary surface of a handlebody is called primitive if there exists an essential disk in the handlebody whose boundary circle intersects the curve transversely in a single point. The primitive curve complex is then defined to be the full subcomplex of the curve complex for the boundary surface, spanned by the vertices of primitive curves. Given any two primitive curves, we construct a sequence of primitive curves from one to the other one satisfying a certain property. As a consequence, we prove that the primitive curve complex for the handlebody is connected.

math.GT↗
arXiv2023

One-two-way pass-move for knots and links

We define a local move for knots and links called the {\em one-two-way pass-move}, abbreviated briefly as the {\em $1$-$2$-move}. The $1$-$2$-move is motivated from the pass-move and the $\#$-move, and it is a hybrid of them. We show that the equivalence under the $1$-$2$-move for knots is the same as that of the pass-move: a knot $K$ is $1$-$2$-move equivalent to an unknot (a trefoil respectively) if and only if the Arf invariant of $K$ is $0$ ($1$ respectively). On the other hand, we show that the number of $1$-$2$-moves behaves differently from the number of pass-moves.

math.GT↗
arXiv2023

Knowledge Distillation for Feature Extraction in Underwater VSLAM

In recent years, learning-based feature detection and matching have outperformed manually-designed methods in in-air cases. However, it is challenging to learn the features in the underwater scenario due to the absence of annotated underwater datasets. This paper proposes a cross-modal knowledge distillation framework for training an underwater feature detection and matching network (UFEN). In particular, we use in-air RGBD data to generate synthetic underwater images based on a physical underwater imaging formation model and employ these as the medium to distil knowledge from a teacher model SuperPoint pretrained on in-air images. We embed UFEN into the ORB-SLAM3 framework to replace the ORB feature by introducing an additional binarization layer. To test the effectiveness of our method, we built a new underwater dataset with groundtruth measurements named EASI (https://github.com/Jinghe-mel/UFEN-SLAM), recorded in an indoor water tank for different turbidity levels. The experimental results on the existing dataset and our new dataset demonstrate the effectiveness of our method.

cs.CV↗
arXiv2023

Normal forms for rational 3-tangles

In this paper, we define the \textit{normal form} of collections of disjoint three \textit{bridge arcs} for a given rational $3$-tangle. We show that there is a sequence of \textit{normal jump moves} which leads one to the other for two normal forms of the same rational 3-tangle.

math.GT↗
arXiv2022

Note on primitive disk complexes

Given a Heegaard splitting of the $3$-sphere, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting. It is an open question whether the primitive disk complex is connected or not when the genus of the splitting is greater than three. In this note, we prove that a quotient of the primitive disk complex, called the homotopy primitive disk complex, is connected.

math.GT↗
arXiv2022

Linearly Free Graphs

In this paper we are interested in an intrinsic property of graphs which is derived from their embeddings into the Euclidean 3-space $\mathbb{R}^3$. An embedding of a graph into $\mathbb{R}^3$ is said to be linear, if it sends every edge to be a line segment. And we say that an embedding $f$ of a graph $G$ into $\mathbb{R}^3$ is free, if $π_1(\mathbb{R}^3-f(G))$ is a free group. Lastly a simple connected graph is said to be linearly free if every its linear embedding is free. In 1980s it was proved that every complete graph is linearly free, by Nicholson. In this paper, we develop Nicholson's arguments into a general notion, and establish a sufficient condition for a linear embedding to be free. As an application of the condition we give a partial answer for a question: how much can the complete graph $K_n$ be enlarged so that the linear freeness is preserved and the clique number does not increase? And an example supporting our answer is provided. As the second application it is shown that a simple connected graph of minimal valency at least $3$ is linearly free, if it has less than 8 vertices. The conditional inequality is strict, because we found a graph with $8$ vertices which is not linearly free. It is also proved that for $n, m \leq 6$ the complete bipartite graph $K_{n,m}$ is linearly free.

math.GT↗
arXiv2022

Unperturbed weakly reducible non-minimal bridge positions

A bridge position of a knot is said to be perturbed if there exists a cancelling pair of bridge disks. Motivated by the examples of knots admitting unperturbed strongly irreducible non-minimal bridge positions due to Jang-Kobayashi-Ozawa-Takao, we derive examples of unperturbed weakly reducible non-minimal bridge positions. Also, a bridge version of Gordon's Conjecture is proposed: the connected sum of unperturbed bridge positions is unperturbed.

math.GT↗
arXiv2020

Non-minimal bridge position of $2$-cable links

Suppose that every non-minimal bridge position of a knot $K$ is perturbed. We show that if $L$ is a $(2, 2q)$-cable link of $K$, then every non-minimal bridge position of $L$ is also perturbed.

math.GT↗
arXiv2020

Library network, a possible path to explainable neural networks

Deep neural networks (DNNs) may outperform human brains in complex tasks, but the lack of transparency in their decision-making processes makes us question whether we could fully trust DNNs with high stakes problems. As DNNs' operations rely on a massive number of both parallel and sequential linear/nonlinear computations, predicting their mistakes is nearly impossible. Also, a line of studies suggests that DNNs can be easily deceived by adversarial attacks, indicating that their decisions can easily be corrupted by unexpected factors. Such vulnerability must be overcome if we intend to take advantage of DNNs' efficiency in high stakes problems. Here, we propose an algorithm that can help us better understand DNNs' decision-making processes. Our empirical evaluations suggest that this algorithm can effectively trace DNNs' decision processes from one layer to another and detect adversarial attacks.

cs.LG↗