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Jung Hoon Lee

Publications and source records attributed to Jung Hoon Lee.

At least 37 records · Page 2Linked to original sources
arXiv2019

Complementary reinforcement learning towards explainable agents

Reinforcement learning (RL) algorithms allow agents to learn skills and strategies to perform complex tasks without detailed instructions or expensive labelled training examples. That is, RL agents can learn, as we learn. Given the importance of learning in our intelligence, RL has been thought to be one of key components to general artificial intelligence, and recent breakthroughs in deep reinforcement learning suggest that neural networks (NN) are natural platforms for RL agents. However, despite the efficiency and versatility of NN-based RL agents, their decision-making remains incomprehensible, reducing their utilities. To deploy RL into a wider range of applications, it is imperative to develop explainable NN-based RL agents. Here, we propose a method to derive a secondary comprehensible agent from a NN-based RL agent, whose decision-makings are based on simple rules. Our empirical evaluation of this secondary agent's performance supports the possibility of building a comprehensible and transparent agent using a NN-based RL agent.

cs.LG↗
arXiv2018

Disk surgery and the primitive disk complexes of the $3$-sphere

Given a genus-$g$ Heegaard splitting of the $3$-sphere with $g \ge 3$, we show that the primitive disk complex for the splitting is not weakly closed under disk surgery operation. That is, there exist two primitive disks in one of the handlebodies of the splitting such that any disk surgery on one along the other one yields no primitive disks.

math.GT↗
arXiv2018

On weak reducing disks and disk surgery

Let $K$ be an unknot in $8$-bridge position in the $3$-sphere. We give an example of a pair of weak reducing disks $D_1$ and $D_2$ for $K$ such that both disks obtained from $D_i$ ($i = 1, 2$) by a surgery along any outermost disk in $D_{3-i}$, cut off by an outermost arc of $D_i \cap D_{3-i}$ in $D_{3-i}$, are not weak reducing disks, i.e. the property of weak reducibility of compressing disks is not preserved by a disk surgery.

math.GT↗
arXiv2016

Reduction of bridge positions along a bridge disk

Suppose a knot in a $3$-manifold is in $n$-bridge position. We consider a reduction of the knot along a bridge disk $D$ and show that the result is an $(n-1)$-bridge position if and only if there is a bridge disk $E$ such that $(D, E)$ is a cancelling pair. We apply this to an unknot $K$, in $n$-bridge position with respect to a bridge sphere $S$ in the $3$-sphere, to consider the relationship between a bridge disk $D$ and a disk in the $3$-sphere that $K$ bounds. We show that if a reduction of $K$ along $D$ yields an $(n-1)$-bridge position, then $K$ bounds a disk that contains $D$ as a subdisk and intersects $S$ in $n$ arcs.

math.GT↗
arXiv2014

Linearly embedded graphs in 3-space with homotopically free exteriors

An embedding of a graph into $\mathbb{R}^3$ is said to be linear, if any edge of the graph is sent 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. It was known that for any complete graph its linear embedding is always free. In this paper we investigate the freeness of linear embeddings considering the number of vertices. It is shown that for any simple connected graph with at most 6 vertices, if its minimal valency is at least 3, then its linear embedding is always free. On the contrary when the number of vertices is much larger than the minimal valency or connectivity, the freeness may not be an intrinsic property of such graphs. In fact we show that for any $n \geq 1$ there are infinitely many connected graphs with minimal valency $n$ which have non-free linear embeddings, and furthermore, that there are infinitely many $n$-connected graphs which have non-free linear embeddings.

math.GT↗
arXiv2014

On the connectedness of subcomplexes of a disk complex

For a boundary-reducible $3$-manifold $M$ with $\partial M$ a genus $g$ surface, we show that if $M$ admits a genus $g+1$ Heegaard surface $S$, then the disk complex of $S$ is simply connected. Also we consider the connectedness of the complex of reducing spheres. We investigate the intersection of two reducing spheres for a genus three Heegaard splitting of $\mathrm{(torus)} \times I$.

math.GT↗
arXiv2013

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection -- Secure DoF and Jammer Scaling Law

In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of $S$ jammers among which Bob selects $K$ jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than $KN_j$ receive antennas, where $N_j$ is the number of jammer's transmit antenna each, and hence $KN_j$ can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals.

cs.IT↗
arXiv2013

Multiuser Diversity in Interfering Broadcast Channels: Achievable Degrees of Freedom and User Scaling Law

This paper investigates how multiuser dimensions can effectively be exploited for target degrees of freedom (DoF) in interfering broadcast channels (IBC) consisting of K-transmitters and their user groups. First, each transmitter is assumed to have a single antenna and serve a singe user in its user group where each user has receive antennas less than K. In this case, a K-transmitter single-input multiple-output (SIMO) interference channel (IC) is constituted after user selection. Without help of multiuser diversity, K-1 interfering signals cannot be perfectly removed at each user since the number of receive antennas is smaller than or equal to the number of interferers. Only with proper user selection, non-zero DoF per transmitter is achievable as the number of users increases. Through geometric interpretation of interfering channels, we show that the multiuser dimensions have to be used first for reducing the DoF loss caused by the interfering signals, and then have to be used for increasing the DoF gain from its own signal. The sufficient number of users for the target DoF is derived. We also discuss how the optimal strategy of exploiting multiuser diversity can be realized by practical user selection schemes. Finally, the single transmit antenna case is extended to the multiple-input multiple-output (MIMO) IBC where each transmitter with multiple antennas serves multiple users.

cs.IT↗
arXiv2013

Optimal Feedback Rate Sharing Strategy in Zero-Forcing MIMO Broadcast Channels

In this paper, we consider a multiple-input multiple-output broadcast channel with limited feedback where all users share the feedback rates. Firstly, we find the optimal feedback rate sharing strategy using zero-forcing transmission scheme at the transmitter and random vector quantization at each user. We mathematically prove that equal sharing of sum feedback size among all users is the optimal strategy in the low signal-to-noise ratio (SNR) region, while allocating whole feedback size to a single user is the optimal strategy in the high SNR region. For the mid-SNR region, we propose a simple numerical method to find the optimal feedback rate sharing strategy based on our analysis and show that the equal allocation of sum feedback rate to a partial number of users is the optimal strategy. It is also shown that the proposed simple numerical method can be applicable to finding the optimal feedback rate sharing strategy when different path losses of the users are taken into account. We show that our proposed feedback rate sharing scheme can be extended to the system with stream control and is still useful for the systems with other techniques such as regularized zero-forcing and spherical cap codebook.

cs.IT↗
arXiv2013

On the Achievable DoF and User Scaling Law of Opportunistic Interference Alignment in 3-Transmitter MIMO Interference Channels

In this paper, we propose opportunistic interference alignment (OIA) schemes for three-transmitter multiple-input multiple-output (MIMO) interference channels (ICs). In the proposed OIA, each transmitter has its own user group and selects a single user who has the most aligned interference signals. The user dimensions provided by multiple users are exploited to align interfering signals. Contrary to conventional IA, perfect channel state information of all channel links is not required at the transmitter, and each user just feeds back one scalar value to indicate how well the interfering channels are aligned. We prove that each transmitter can achieve the same degrees of freedom (DoF) as the interference free case via user selection in our system model that the number of receive antennas is twice of the number of transmit antennas. Using the geometric interpretation, we find the required user scaling to obtain an arbitrary non-zero DoF. Two OIA schemes are proposed and compared with various user selection schemes in terms of achievable rate/DoF and complexity.

cs.IT↗
arXiv2011

Critical Heegaard surfaces obtained by amalgamation

Critical surfaces are defined by Bachman as topological index 2 surfaces, generalizing incompressible surfaces and strongly irreducible surfaces. In this paper we give a condition to obtain critical Heegaard surfaces by amalgamation. As a special case, we obtain critical Heegaard surfaces by boundary stabilization. It gives critical Heegaard surfaces of non-minimal genus, for 3-manifolds which do not admit distinct Heegaard splittings (up to isotopy).

math.GT↗
arXiv2010

Rectangle condition for compression body and 2-fold branched covering

We give the rectangle condition for strong irreducibility of Heegaard splittings of $3$-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a $2$-fold covering of $S^3$ branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of knot width holds for a composite knot satisfying the condition.

math.GT↗
arXiv2010

A novel boundary element method using surface conductive absorbers for full-wave analysis of 3-D nanophotonics

Fast surface integral equation (SIE) solvers seem to be ideal approaches for simulating 3-D nanophotonic devices, as these devices generate fields both in an interior channel and in the infinite exterior domain. However, many devices of interest, such as optical couplers, have channels that can not be terminated without generating reflections. Generating absorbers for these channels is a new problem for SIE methods, as the methods were initially developed for problems with finite surfaces. In this paper we show that the obvious approach for eliminating reflections, making the channel mildly conductive outside the domain of interest, is inaccurate. We describe a new method, in which the absorber has a gradually increasing surface conductivity; such an absorber can be easily incorporated in fast integral equation solvers. Numerical experiments from a surface-conductivity modified FFT-accelerated PMCHW-based solver are correlated with analytic results, demonstrating that this new method is orders of magnitude more effective than a volume absorber, and that the smoothness of the surface conductivity function determines the performance of the absorber. In particular, we show that the magnitude of the transition reflection is proportional to 1/L^(2d+2), where L is the absorber length and d is the order of the differentiability of the surface conductivity function.

physics.comp-ph↗