arXiv subjects

Donggyu Kim

Publications and source records attributed to Donggyu Kim.

68 records · Page 4Linked to original sources

arXiv2020

Unified Discrete-Time Factor Stochastic Volatility and Continuous-Time Ito Models for Combining Inference Based on Low-Frequency and High-Frequency

This paper introduces unified models for high-dimensional factor-based Ito process, which can accommodate both continuous-time Ito diffusion and discrete-time stochastic volatility (SV) models by embedding the discrete SV model in the continuous instantaneous factor volatility process. We call it the SV-Ito model. Based on the series of daily integrated factor volatility matrix estimators, we propose quasi-maximum likelihood and least squares estimation methods. Their asymptotic properties are established. We apply the proposed method to predict future vast volatility matrix whose asymptotic behaviors are studied. A simulation study is conducted to check the finite sample performance of the proposed estimation and prediction method. An empirical analysis is carried out to demonstrate the advantage of the SV-Ito model in volatility prediction and portfolio allocation problems.

stat.ME↗

arXiv2020

Volatility Analysis with Realized GARCH-Ito Models

This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump-diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in the continuous instantaneous volatility process. The key feature of the proposed model is that the corresponding conditional daily integrated volatility adopts an autoregressive structure where both integrated volatility and jump variation serve as innovations. We name it as the realized GARCH-Ito model. Given the autoregressive structure in the conditional daily integrated volatility, we propose a quasi-likelihood function for parameter estimation and establish its asymptotic properties. To improve the parameter estimation, we propose a joint quasi-likelihood function that is built on the marriage of daily integrated volatility estimated by high-frequency data and nonparametric volatility estimator obtained from option data. We conduct a simulation study to check the finite sample performance of the proposed methodologies and an empirical study with the S&P500 stock index and option data.

stat.ME↗

arXiv2019

Gravitational effect on the advancing and receding angle of a 2D Cassie-Baxter droplet on a textured surface

Advancing and receding angles are physical quantities frequently measured to characterize the wetting properties of a rough surface. Thermodynamically, the advancing and receding angles are often interpreted as the maximum and minimum contact angles that can be formed by a droplet without losing its stability. Despite intensive research on wetting of rough surfaces, the gravitational effect on these angles has been overlooked because most studies have considered droplets smaller than the capillary length. In this study, however, by combining theoretical and numerical modeling, we show that the shape of a droplet smaller than the capillary length can be substantially modified by gravity under advancing and receding conditions. First, based on the Laplace pressure equation, we predict the shape of a two-dimensional Cassie-Baxter droplet on a textured surface with gravity at each pinning point. Then the stability of the droplet is tested by examining the interference between the liquid surface and neighboring pillars as well as analyzing the free energy change upon depinning. Interestingly, it turns out that the apparent contact angles under advancing and receding conditions are not affected by gravity, while the overall shape of a droplet and the position of the pinning point is affected by gravity. In addition, the advancing and receding of the droplet with continuously increasing or decreasing volume is analyzed, and it is showed that the gravitational effect plays a key role on the movement of the droplet tip. Finally, the theoretical predictions were validated against line-tension based front tracking modeling that seamlessly captures the attachment and detachment between the liquid surface and the solid substrate.

cond-mat.soft↗

arXiv2019

Domain-agnostic Question-Answering with Adversarial Training

Adapting models to new domain without finetuning is a challenging problem in deep learning. In this paper, we utilize an adversarial training framework for domain generalization in Question Answering (QA) task. Our model consists of a conventional QA model and a discriminator. The training is performed in the adversarial manner, where the two models constantly compete, so that QA model can learn domain-invariant features. We apply this approach in MRQA Shared Task 2019 and show better performance compared to the baseline model.

cs.CL↗

arXiv2019

Large-Scale Uniform Optical Focus Array Generation with a Phase Spatial Light Modulator

We report a new method to generate uniform large-scale optical focus arrays (LOFAs). By identifying and removing undesired phase rotation in the iterative Fourier-transform algorithm (IFTA), our approach rapidly produces computer-generated holograms of highly uniform LOFAs. The new algorithm also shows faster compensation of system-induced LOFA intensity inhomogeneity than the conventional IFTA. After just three adaptive correction steps, we demonstrate LOFAs consisting of $\mathcal{O}(10^3)$ optical foci with $> 98\ \%$ intensity uniformity.

physics.optics↗

arXiv2018

CMOS-Integrated Diamond Nitrogen-Vacancy Quantum Sensor

The nitrogen vacancy (NV) center in diamond has emerged as a leading solid-state quantum sensor for applications including magnetometry, electrometry, thermometry, and chemical sensing. However, an outstanding challenge for practical applications is that existing NV-based sensing techniques require bulky and discrete instruments for spin control and detection. Here, we address this challenge by integrating NV based quantum sensing with complementary metal-oxide-semiconductor (CMOS) technology. Through tailored CMOS-integrated microwave generation and photodetection, this work dramatically reduces the instrumentation footprint for quantum magnetometry and thermometry. This hybrid diamond-CMOS integration enables an ultra-compact and scalable platform for quantum sensing and quantum information processing.

physics.app-ph↗

arXiv2017

Quantum Reference Beacon-Guided Super-Resolution Optical Focusing in Complex Media

Optical random scattering is generally considered to be a nuisance of microscopy that limits imaging depth and spatial resolution. Wavefront shaping techniques have recently enabled optical imaging at unprecedented depth, but a remaining problem is also to attain super-resolution within complex media. To address this challenge, we introduce a new technique to focus inside of complex media by the use of a quantum reference beacon (QRB), consisting of solid-state quantum emitters with spin-dependent fluorescence. This QRB provides subwavelength guidestar feedback for wavefront shaping to achieve an optical focus below the microscope's diffraction limit. We implement the QRB-guided imaging approach using nitrogen-vacancy centers in diamond nanocrystals, which enable optical focusing with a subdiffraction resolution below 186 nm ($\approx λ/3.5\mbox{NA}$), where the microscope's NA=0.8. This QRB-assisted wavefront shaping paves the way for a range of new applications, including deep-tissue quantum enhanced sensing and individual optical excitation of magnetically-coupled spin ensembles for applications in quantum information processing.

physics.optics↗

arXiv2017

Efficient Extraction of Light from a Nitrogen-Vacancy Center in a Diamond Parabolic Reflector

Quantum emitters in solids are being developed for a range of quantum technologies, including quantum networks, computing, and sensing. However, a remaining challenge is the poor photon collection due to the high refractive index of most host materials. Here we overcome this limitation by introducing monolithic parabolic reflectors as an efficient geometry for broadband photon extraction from quantum emitter and experimentally demonstrate this device for the nitrogen-vacancy (NV) center in diamond. Simulations indicate a photon collection efficiency exceeding 75% across the visible spectrum and experimental devices, fabricated using a high-throughput gray-scale lithography process, demonstrate a photon extraction efficiency of $(48\pm 5)$%. This device enables a raw experimental efficiency of $(12\pm 2)$\% with fluorescence detection rates as high as $(4.6 - 5.7)\times 10^6$ counts per second from a single NV center.

quant-ph↗

arXiv2016

Intelligent Initialization and Adaptive Thresholding for Iterative Matrix Completion; Some Statistical and Algorithmic Theory for Adaptive-Impute

Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and empirical excellence, but choosing the right threshold level still remains as a key empirical difficulty. This paper proposes a novel matrix completion algorithm which iterates thresholded SVD with theoretically-justified and data-dependent values of thresholding parameters. The estimate of the proposed algorithm enjoys the minimax error rate and shows outstanding empirical performances. The thresholding scheme that we use can be viewed as a solution to a non-convex optimization problem, understanding of whose theoretical convergence guarantee is known to be limited. We investigate this problem by introducing a simpler algorithm, generalized-\SI, analyzing its convergence behavior, and connecting it to the proposed algorithm.

stat.ME↗

arXiv2016

Wetting theory for small droplets on textured solid surfaces

Conventional wetting theories on rough surfaces with Wenzel, Cassie-Baxter, and Penetrate modes suggest the possibility of tuning the contact angle by adjusting the surface texture. Despite decades of intensive study, there are still many experimental results that are not well understood because conventional wetting theory, which assume an infinite droplet size, has been used to explain measurements of finite-sized droplets. In this study, we suggest a wetting theory that is applicable to any droplet size based on the free energy landscape analysis of various wetting modes of finite-sized droplets on a 2D textured surface. The key finding of our study is that there are many quantized wetting angles with local free energy minima; the implication of this is remarkable. We find that the conventional theories can predict the contact angle at the global free energy minimum if the droplet size is 40 times or larger than the characteristic scale of the surface roughness. Furthermore, we confirm that the pinning origin is the local free energy minima and obtain the energy barriers of pinning as a function of geometric factors. We validate our theory against experimental results on an anisotropic rough surface. In addition, we discuss wetting on a non-uniform rough surface with a rough central region and flat edge. Our findings clarify the extent to which the conventional wetting theory is valid and expand the physical understanding of wetting phenomena of small liquid drops on rough surfaces.

physics.flu-dyn↗

arXiv2016

Asymptotic Theory for Estimating the Singular Vectors and Values of a Partially-observed Low Rank Matrix with Noise

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for statistical analyses and inferences. This paper proposes estimators of these quantities and studies their asymptotic behavior. Under the setting where the dimensions of the matrix increase to infinity and the probability of observing each entry is identical, Theorem 4.1 gives the rate of convergence for the estimated singular vectors; Theorem 4.3 gives a multivariate central limit theorem for the estimated singular values. Even though the estimators use only a partially observed matrix, they achieve the same rates of convergence as the fully observed case. These estimators combine to form a consistent estimator of the full low rank matrix that is computed with a non-iterative algorithm. In the cases studied in this paper, this estimator achieves the minimax lower bound in Koltchinskii et al. (2011). The numerical experiments corroborate our theoretical results.

stat.ME↗

arXiv2016

Optimal large-scale quantum state tomography with Pauli measurements

Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm losses; and show how these rates can be achieved by a common thresholding approach. Numerical performance of the proposed estimator is also investigated.

math.ST↗

arXiv2013

Pixelation-free and real-time endoscopic imaging through a fiber bundle

Endoscopy has been an indispensible tool in medical diagnostics, and yet the demands for reduced unit diameter and enhanced spatial resolution have steadily been growing for the accurate investigation of distal sites with minimal side effects. However, the attempts to make use of thin image-guiding media accompany the degradation in spatial resolution as the micro-optics often induces aberrations. Here, we present a microendoscope that performs real-time correction of severe aberrations induced by image-guiding media such as a bundled fiber. Specifically, we developed a method exploiting the full binary control of a digital micro-mirror device (DMD) for characterizing the input-output response of image-guiding media and subsequently compensating the aberrations. As a proof-of-concept study, we completely eliminated the pixelation artifact, a severe form of aberration, in endoscopic imaging through an image fiber bundle and achieved spatial resolution much better than the diameter of an individual fiber. Our study lays a foundation of applying extremely thin, but highly aberrant image-guiding media for high-resolution microendoscopy.

physics.optics↗

arXiv2013

Enrichment of deeply penetrating waves in disordered media

Waves incident to a highly scattering medium are incapable of penetrating deep into the medium due to the diffusion process induced by multiple scattering. This poses a fundamental limitation to optically imaging, sensing, and manipulating targets embedded in opaque scattering layers such as biological tissues. One strategy for mitigating the shallow wave penetration is to exploit eigenmodes with anomalously high transmittance existing in any disordered medium. When waves are coupled to these eigenmodes, strong constructive wave interference enhances deeply penetrating waves. However, finding such eigenmodes has been a challenging task due to the complexity of disordered media. In this Letter, we present an iterative wavefront control method that selectively enriches the coupling of incident beam to high-transmission eigenmodes. Specifically, we refined the high-transmission eigenmodes from an arbitrary initial wave by either maximizing transmitted wave intensity or minimizing reflected wave intensity. Using the proposed method, we achieved more than a factor of 3 increases in light transmission through a scattering medium exhibiting hundreds of scattering events. Our approach is readily applicable to in vivo applications in which only the detection of reflected waves is available. Enhancing light penetration will lead to improving the working depth of optical imaging and treatment techniques.

physics.optics↗