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Heon Lee

Publications and source records attributed to Heon Lee.

15 recordsLinked to original sources
arXiv2025

Projected Subgradient Ascent for Convex Maximization

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex functions over convex sets, we show that projected subgradient ascent converges to a first-order stationary point when using arbitrarily large step sizes. Taking the step sizes to infinity leads to a deterministic variant of the conditional gradient algorithm, and iterated linear optimization as a special case.

math.OC↗
arXiv2024

Laplacians on $ q $-deformations of compact semisimple Lie groups

The problem of formulating a correct notion of Laplacian on compact quantum groups (CQGs) has long been recognized as both fundamental and nontrivial. Existing constructions typically rely on selecting a specific first-order differential calculus (FODC), but the absence of a canonical choice in the noncommutative setting renders these approaches inherently non-canonical. In this work, we propose a simple set of conditions under which a linear operator on a CQG can be recognized as a Laplacian -- specifically, as the formal modulus square of the differential associated with a bicovariant FODC. A key feature of our framework is its generality: it applies to arbitrary finite-dimensional bicovariant $*$-FODCs on \( K_q \), the \( q \)-deformation of a compact semisimple Lie group \( K \). To each such calculus, we associate a Laplacian defined via the formal modulus square of its differential. Under mild additional assumptions, we demonstrate that these operators converge to classical Laplacians on \( K \) in the classical limit \( q \to 1 \), thereby justifying their interpretation as ``$q$-deformed Laplacians." Furthermore, we prove that the spectra of the $q$-deformed Laplacians are discrete, real, bounded from below, and diverge to infinity, much like those of their classical counterparts. However, in contrast to the classical case, the associated heat semigroups do not define quantum Markov semigroups.

math.QA↗
arXiv2024

Analytic subalgebras of Beurling-Fourier algebras and complexification of Lie groups

In this paper, we focus on how we can interpret the actions of the elements in the Gelfand spectrum of a weighted Fourier algebra on connected Lie groups. They can be viewed as evaluations on specific points of the complexification of the underlying Lie group by restricting to a particular dense subalgebra, which we call an analytic subalgebra. We first introduce an analytic subalgebra allowing a ``local" solution for general connected Lie groups. We will demonstrate that a ``global" solution is also possible for connected, simply connected and nilpotent Lie groups through a different choice of an analytic subalgebra. Finally, we examine the case of the $ax+b$-group as an example of a non-nilpotent, non-unimodular Lie group with a ``global" solution.

math.FA↗
arXiv2023

On the Instability of Fractional Reserve Banking

This paper develops a dynamic monetary model to study the (in)stability of the fractional reserve banking system. The model shows that the fractional reserve banking system can endanger stability in that equilibrium is more prone to exhibit endogenous cyclic, chaotic, and stochastic dynamics under lower reserve requirements, although it can increase consumption in the steady-state. Introducing endogenous unsecured credit to the baseline model does not change the main results. The calibrated exercise suggests that this channel could be another source of economic fluctuations. This paper also provides empirical evidence that is consistent with the prediction of the model.

econ.TH↗
arXiv2022

Scalably manufactured high-index atomic layer-polymer hybrid metasurfaces for high-efficiency virtual reality metaoptics in the visible

Metalenses, which exhibit superior light-modulating performance with sub-micrometer-scale thicknesses, are suitable alternatives to conventional bulky refractive lenses. However, fabrication limitations, such as a high cost, low throughput, and small patterning area, hinder their mass production. Here, we demonstrate the mass production of low-cost, high-throughput, and large-aperture visible metalenses using an argon fluoride immersion scanner and wafer-scale nanoimprint lithography. Once a 12-inch master stamp is imprinted, hundreds of centimeter-scale metalenses can be fabricated. To enhance light confinement, the printed metasurface is thinly coated with a high-index film, resulting in drastic increase of conversion efficiency. As a proof of concept, a prototype of a virtual reality device with ultralow thickness is demonstrated with the fabricated metalens.

physics.optics↗
arXiv2022

Daylong sub-ambient radiative cooling with full color exterior

Terrestrial radiative cooling is an intriguing way to mitigate the accelerating cooling demands in the residential and commercial sectors by offering zero-energy cooling. However, the ultra-white or mirror-like appearance of radiative coolers can be visually sterile and raise safety issues when broadly applied to building facades and vehicles. To overcome the fundamental trade-off between color diversity and cooling performance, we propose a radiatively integrated, conductively insulated system that exploits thermal non-equilibrium between colorants and thermal emitters. This allows such radiative coolers to be cooled below the ambient temperature at all times of the day while exhibiting any desired exterior color including black. We experimentally demonstrate that even black coolers, absorbing 646 Wm-2 of solar power under AM1.5 conditions, cools down to a maximum of 6.9 K (average of 3.5 K) below the ambient temperature during the daytime. These systems can potentially be used in outdoor applications, especially in commercial buildings and residential houses, where carbon-free thermal management is in high demand but diversity of colors is also important for visual appeal and comfort.

physics.app-ph↗
arXiv2022

Bundle Theoretic Descriptions of Massless Single-Particle State Spaces; How do we perceive a moving quantum particle

Recently, a bundle theoretic description of massive single-particle state spaces, which is better suited for Relativistic Quantum Information Theory than the ordinary Hilbert space description, has been suggested. However, the mathematical framework presented in that work does not apply to massless particles. It is because, unlike massive particles, massless particles cannot assume the zero momentum state and hence the mass shell associated with massless particles has non-trivial cohomology. To overcome this difficulty, this paper suggests a new framework that can be applied to massless particles. Applications to the cases of massless particles with spin-1 and 2, namely photon and graviton, will reveal that the field equations, the gauge conditions, and the gauge freedoms of Electromagnetism and General Relativity naturally arise as manifestations of an inertial observer's perception of the internal quantum states of a photon and a graviton, respectively. Finally, we show that gauge freedom is exhibited by all massless particles, except those with spin-0 and 1/2.

math-ph↗
arXiv2022

Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory

Relativistic Quantum Information Theory (RQI) is a flourishing research area of physics, yet, there has been no systematic mathematical treatment of the field. In this paper, we suggest bundle theoretic descriptions of massive single-particle state spaces, which are basic building blocks of RQI. In the language of bundle theory, one can construct a vector bundle over the set of all possible motion states of a massive particle, in whose fibers the moving particle's internal quantum state as perceived by a fixed inertial observer is encoded. A link between the usual Hilbert space description is provided by a generalized induced representation construction on the $L^2$-section space of the bundle. The aim of this paper is two-fold. One is to communicate the basic ideas of RQI to mathematicians and the other is to suggest an improved formalism for single-particle state spaces that encompasses all known massive particles including those which have never been dealt with in the RQI literature. Some of the theoretical implications of the formalism will be explored at the end of the paper.

math-ph↗
arXiv2022

Relativistic massive particle with spin-1/2, a vector bundle point of view

Recently, in the context of Relativistic Quantum Information Theory (RQI) of massive spin-1/2 particles, it has been suggested that it is impossible to perform a momentum-independent spin measurement, showing the inadequacy of the spin reduced density matrix as a legitimate information resource. This is because there is an unavoidable ambiguity in the definition of the spin of a moving particle. In this paper, by introducing a vector bundle theoretic way to view the single-particle state space, we try to rule out this ambiguity. The discrete degree of freedom of the resulting representation space contains information about the Pauli-Lubansky four-vector of the particle instead of the ambiguous spin. Comparing this representation with the standard one used in the RQI literature, we show that the discrete degree of freedom of the standard representation space attains the meaning of the Newton-Wigner spin. Also using this viewpoint, we give a mathematical proof of why the spin reduced density matrix is meaningless, which is stronger than the previous claims in that it asserts that the matrix is void of any meaning at all, not just in terms of the impossibility of measurement or Lorentz non-covariance. We give a way (which turns out to be the only way) to modify it to obtain the Pauli-Lubansky reduced density matrix, which is covariant under Lorentz transformations.

math-ph↗
arXiv2021

Money Creation and Banking: Theory and Evidence

This paper studies the role of banks' money creation in monetary transmission. I develop a monetary-search model where demand for the monetary base and the money multiplier are endogenously determined through banks' money creation. The model and data show that reserves are not independent of interest rate policy, even with ample reserves. Furthermore, short-term rates and interest on reserves play distinct roles in monetary transmission. I evaluate the theory by matching it with data, and the calibrated model can account for the evolution of reserves, excess reserves, and the money multiplier

econ.TH↗
arXiv2019

Street Crossing Aid Using Light-weight CNNs for the Visually Impaired

In this paper, we address an issue that the visually impaired commonly face while crossing intersections and propose a solution that takes form as a mobile application. The application utilizes a deep learning convolutional neural network model, LytNetV2, to output necessary information that the visually impaired may lack when without human companions or guide-dogs. A prototype of the application runs on iOS devices of versions 11 or above. It is designed for comprehensiveness, concision, accuracy, and computational efficiency through delivering the two most important pieces of information, pedestrian traffic light color and direction, required to cross the road in real-time. Furthermore, it is specifically aimed to support those facing financial burden as the solution takes the form of a free mobile application. Through the modification and utilization of key principles in MobileNetV3 such as depthwise seperable convolutions and squeeze-excite layers, the deep neural network model achieves a classification accuracy of 96% and average angle error of 6.15 degrees, while running at a frame rate of 16.34 frames per second. Additionally, the model is trained as an image classifier, allowing for a faster and more accurate model. The network is able to outperform other methods such as object detection and non-deep learning algorithms in both accuracy and thoroughness. The information is delivered through both auditory signals and vibrations, and it has been tested on seven visually impaired and has received above satisfactory responses.

cs.CV↗
arXiv2019

LYTNet: A Convolutional Neural Network for Real-Time Pedestrian Traffic Lights and Zebra Crossing Recognition for the Visually Impaired

Currently, the visually impaired rely on either a sighted human, guide dog, or white cane to safely navigate. However, the training of guide dogs is extremely expensive, and canes cannot provide essential information regarding the color of traffic lights and direction of crosswalks. In this paper, we propose a deep learning based solution that provides information regarding the traffic light mode and the position of the zebra crossing. Previous solutions that utilize machine learning only provide one piece of information and are mostly binary: only detecting red or green lights. The proposed convolutional neural network, LYTNet, is designed for comprehensiveness, accuracy, and computational efficiency. LYTNet delivers both of the two most important pieces of information for the visually impaired to cross the road. We provide five classes of pedestrian traffic lights rather than the commonly seen three or four, and a direction vector representing the midline of the zebra crossing that is converted from the 2D image plane to real-world positions. We created our own dataset of pedestrian traffic lights containing over 5000 photos taken at hundreds of intersections in Shanghai. The experiments carried out achieve a classification accuracy of 94%, average angle error of 6.35 degrees, with a frame rate of 20 frames per second when testing the network on an iPhone 7 with additional post-processing steps.

cs.CV↗
arXiv2016

Scattering optical elements: stand-alone optical elements exploiting multiple light scattering

Optical design and fabrication techniques are crucial for making optical elements. From conventional lenses to diffractive optical elements, and to recent metasurfaces, various types of optical elements have been proposed to manipulate light where optical materials are fabricated into desired structures. Here, we propose a scattering optical element (SOE) which exploits multiple light scattering and wavefront shaping. Instead of fabricating optical materials, the SOE consists of a disordered medium and a photopolymer-based wavefront recorder, with shapes the wavefront of impinging light on demand. With the proposed stand-alone SOEs, we experimentally demonstrate control of various properties of light, including intensity, polarisation, spectral frequency and near field. Due to the tremendous freedom brought about by disordered media, the proposed approach will provide unexplored routes to manipulate arbitrary optical fields in stand-alone optical elements.

physics.optics↗
arXiv2003

Structural and Electronic Properties of Amorphous and Polycrystalline In2Se3 Films

Structural and electronic properties of amorphous and single-phase polycrystalline films of gamma- and kappa-In2Se3 have been measured. The stable gamma phase nucleates homogeneously in the film bulk and has a high resistivity, while the metastable kappa phase nucleates at the film surface and has a moderate resistivity. The microstructures of hot-deposited and post-annealed cold-deposited gamma films are quite different but the electronic properties are similar. The increase in the resistivity of amorphous In2Se3 films upon annealing is interpreted in terms of the replacement of In-In bonds with In-Se bonds during crystallization. Great care must be taken in the preparation of In2Se3 films for electrical measurements as the presence of excess chalcogen or surface oxidation may greatly affect the film properties.

cond-mat.mtrl-sci↗