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Jiho Hong

Publications and source records attributed to Jiho Hong.

18 recordsLinked to original sources

Instance-Enriched Semantic Maps for Visual Language Navigation

Visual Language Navigation (VLN) aims to enable an embodied agent to navigate complex environments by following natural language instructions. Recent approaches build semantic spatial maps and leverage Large Language Models (LLMs) for reasoning and decision making. Despite these advances, existing systems lack instance-level object detail and robustness to diverse user queries, limiting reliable navigation in complex indoor environments. To address these limitations, we propose Instance-Enriched Semantic Maps, a unified framework with three key contributions: (1) Instance-level two-and-a-half-dimensional (2.5D) rich information mapping that constructs maps from color and depth observations via open-vocabulary panoptic segmentation, preserving vertical distinctions and capturing small objects, while storing diverse semantic attributes and natural language captions enriched with room-level context. (2) Robust query processing via LLM-based target selection, which dynamically routes queries across type-specialized experts and integrates their outputs through score-level fusion, enabling consistent goal selection across diverse query formulations. (3) Storage-efficient semantic representation that achieves approximately 96% reduction compared to three-dimensional (3D) scene-graph approaches while preserving sufficient spatial information for navigation. The proposed 2.5D representation outperforms the 3D baseline by over 27% in prediction-normalized Area Under the Curve (AUC). In navigation experiments, our method achieves over 17% improvement in object retrieval and over 23% in navigation success compared to the baseline across diverse query types. The project page is available at https://rcilab.github.io/iesm_vln.

cs.RO

Unique Determination of Variable Order in Subdiffusion from a Single Measurement

We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of heterogeneous media in anomalous diffusion processes. In this work, we establish several new uniqueness results for the inverse problem in the case of piecewise constant variable orders, without any monotonicity condition. The analysis follows a new approach that combines properties of harmonic functions, a linearization technique in the Laplace domain, and tools from complex, asymptotic, and geometrical analysis. In addition, we weaken the regularity assumptions on the problem data and extend the analysis of previous contributions to higher-dimensional settings.

math.AP

Solving Inverse Acoustic Obstacle Scattering Problem with Phaseless Far-Field Measurement Using Deep Neural Network Surrogates

In this work, we investigate the use of deep neural networks (DNNs) as surrogates for solving the inverse acoustic scattering problem of recovering a sound-soft obstacle from phaseless far-field measurements. We approximate the forward maps from the obstacle to the far-field data using DNNs, and for star-shaped domains in two and three dimensions, we establish the expression rates for fully connected feedforward neural networks with the ReLU activation for approximating the forward maps. The analysis is based on the weak formulation of the direct problem, and can handle variable coefficients. Numerically we validate the accuracy of the DNN surrogates of the forward maps, and demonstrate the use of DNN surrogates in the Bayesian treatment of the inverse obstacle scattering problem. Numerical experiments indicate that the surrogates are effective in both two- and three-dimensional cases, and can significantly speed up the exploration of the posterior distribution of the shape parameters using Markov chain Monte Carlo.

math.NA

Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion

In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from the observation at one point on the boundary without / with the knowledge of medium properties, and a conditional Lipschitz stability estimate when the observation is available on the whole boundary. The analysis crucially employs resolvent estimates in the $L^r(\Omega)$ ($r>d$) spaces, solution representation in the Laplace domain and novel asymptotic expansions of the Laplace transform of the boundary flux at $p= 0$ and $p=1$.

math.AP

Direct Algorithms for Reconstructing Small Conductivity Inclusions in Subdiffusion

The subdiffusion model that involves a Caputo fractional derivative in time is widely used to describe anomalously slow diffusion processes. In this work we aim at recovering the locations of small conductivity inclusions in the model from boundary measurement, and develop novel direct algorithms based on the asymptotic expansion of the boundary measurement with respect to the size of the inclusions and approximate fundamental solutions. These algorithms involve only algebraic manipulations and are computationally cheap. To the best of our knowledge, they are first direct algorithms for the inverse conductivity problem in the context of the subdiffusion model. Moreover, we provide relevant theoretical underpinnings for the algorithms. Also we present numerical results to illustrate their performance under various scenarios, e.g., the size of inclusions, noise level of the data, and the number of inclusions, showing that the algorithms are efficient and robust.

math.NA

Approximation of the first Steklov-Dirichlet eigenvalue on eccentric spherical shells in general dimensions

We study the first Steklov-Dirichlet eigenvalue on eccentric spherical shells in $\mathbb{R}^{n+2}$ with $n\geq 1$, imposing the Steklov condition on the outer boundary sphere, denoted by $\Gamma_S$, and the Dirichlet condition on the inner boundary sphere. The first eigenfunction admits a Fourier--Gegenbauer series expansion via the bispherical coordinates, where the Dirichlet-to-Neumann operator on $\Gamma_S$ can be recursively expressed in terms of the expansion coefficients arXiv:2309.09587. In this paper, we develop a finite section approach for the Dirichlet-to-Neumann operator to approximate the first Steklov--Dirichlet eigenvalue on eccentric spherical shells. We prove the exponential convergence of this approach by using the variational characterization of the first eigenvalue. Furthermore, based on the convergence result, we propose a numerical computation scheme as an extension of the two-dimensional result in [Hong et al., Ann. Mat. Pura Appl., 2022] to general dimensions. We provide numerical examples of the first Steklov-Dirichlet eigenvalue on eccentric spherical shells with various geometric configurations.

math.AP

Identification of a Spatially-Dependent Variable Order in One-Dimensional Subdiffusion

In this work we investigate an inverse problem of identifying a spatially variable order in the one-dimensional subdiffusion model from the boundary flux measurement. The model involves a generalized Caputo derivative in time, and arises in the mathematical modeling of anomalous diffusion in heterogeneous media. We prove the unique recovery of a monotone piecewise constant variable order and its range for known and unknown media, respectively. The analysis is based on a delicate asymptotic expansion of the Laplace transform of the data as $p\to0$, which is of independent interest.

math.AP

Monostatic imaging of an extended target with MCMC sampling

We consider the imaging of a planar extended target from far-field data under a monostatic measurement configuration, in which the data is measured by a single moving transducer, as frequently encountered in practical application. In this paper, we develop a Bayesian approach to recover the shape of the extended target with MCMC sampling, where a new shape basis selection is proposed based on the shape derivative analysis for the measurement data. In order to optimize the center and radius of the initial disk, we use the monostatic sampling method for the center and the explicit scattered field expression for disks for the radius. Numerical simulations are presented to validate the proposed method.

math.NA

High Absorptivity Nanotextured Powders for Additive Manufacturing

The widespread application of metal additive manufacturing (AM) is limited by the ability to control the complex interactions between the energy source and the feedstock material. Here we develop a generalizable process to introduce nanoscale grooves to the surface of metal powders which increases the powder absorptivity by up to 70% during laser powder bed fusion. Absorptivity enhancements in copper, copper-silver, and tungsten enables energy efficient manufacturing, with printing of pure copper at relative densities up to 92% using laser energy densities as low as 82 J/mm^3. Simulations show the enhanced powder absorptivity results from plasmon-enabled light concentration in nanoscale grooves combined with multiple scattering events. The approach taken here demonstrates a general method to enhance the absorptivity and printability of reflective and refractory metal powders by changing the surface morphology of the feedstock without altering its composition.

physics.optics

On the first Steklov-Dirichlet eigenvalue on eccentric annuli in general dimensions

We consider the Steklov-Dirichlet eigenvalue problem on eccentric annuli in Euclidean space of general dimensions. In recent work by the same authors of this paper [21], a limiting behavior of the first eigenvalue, as the distance between the two boundary circles of an annulus approaches zero, was obtained in two dimensions. We extend this limiting behavior to general dimensions by employing bispherical coordinates and expressing the first eigenfunction as a Fourier-Gegenbauer series.

math.AP

The Eigenvalue Problem for the Laplacian via Conformal Mapping and the Gohberg--Sigal Theory

We consider the Dirichlet and Neumann eigenvalues of the Laplacian for a planar, simply connected domain. The eigenvalues admit a characterization in terms of a layer potential of the Helmholtz equation. Using the exterior conformal mapping associated with the given domain, we reformulate the layer potential as an infinite-dimensional matrix. Based on this matrix representation, we develop a finite section approach for approximating the Laplacian eigenvalues and provide a convergence analysis by applying the Gohberg--Sigal theory for operator-valued functions. Moreover, we derive an asymptotic formula for the Laplacian eigenvalues on deformed domains that results from the changes in the conformal mapping coefficients.

math.NA

High-Specific-Power Flexible Transition Metal Dichalcogenide Solar Cells

Semiconducting transition metal dichalcogenides (TMDs) are promising for flexible high-specific-power photovoltaics due to their ultrahigh optical absorption coefficients, desirable band gaps and self-passivated surfaces. However, challenges such as Fermi-level pinning at the metal contact-TMD interface and the inapplicability of traditional doping schemes have prevented most TMD solar cells from exceeding 2% power conversion efficiency (PCE). In addition, fabrication on flexible substrates tends to contaminate or damage TMD interfaces, further reducing performance. Here, we address these fundamental issues by employing: 1) transparent graphene contacts to mitigate Fermi-level pinning, 2) $\rm{MoO}_\it{x}$ capping for doping, passivation and anti-reflection, and 3) a clean, non-damaging direct transfer method to realize devices on lightweight flexible polyimide substrates. These lead to record PCE of 5.1% and record specific power of $\rm{4.4\ W\,g^{-1}}$ for flexible TMD ($\rm{WSe_2}$) solar cells, the latter on par with prevailing thin-film solar technologies cadmium telluride, copper indium gallium selenide, amorphous silicon and III-Vs. We further project that TMD solar cells could achieve specific power up to $\rm{46\ W\,g^{-1}}$, creating unprecedented opportunities in a broad range of industries from aerospace to wearable and implantable electronics.

physics.app-ph

Shape monotonicity of the first Steklov-Dirichlet eigenvalue on eccentric annuli

In this paper, we investigate the monotonicity of the first Steklov--Dirichlet eigenvalue on eccentric annuli with respect to the distance, namely $t$, between the centers of the inner and outer boundaries of an annulus. We first show the differentiability of the eigenvalue in $t$ and obtain an integral expression for the derivative value in two and higher dimensions. We then derive an upper bound of the eigenvalue for each $t$, in two dimensions, by the variational formulation. We also obtain a lower bound of the eigenvalue, given a restriction that the two boundaries of the annulus are sufficiently close. The key point of the proof of the lower bound is in analyzing the limit behavior of an infinite series expansion of the first eigenfunction in bipolar coordinates. We also perform numerical experiments that exhibit the monotonicity for two dimensions.

math.AP

Characterization of stress concentration in two-dimensional boundary value problems: Neumann-type and Dirichlet-type

We consider a boundary value problem for the conductivity equation in a bounded domain containing an inclusion which is nearly touching to the domain's boundary. We assume that the domain and the inclusion are disks with conductivity jump on the boundary of the inclusion. By using the layer potential technique and adopting the bipolar coordinates, we derive the asymptotic formulas which explicitly describe the gradient blow-up of the solution as the distance between the inclusion and the domain's boundary tends to zero. It turns out that the gradient blow-up term can be identified with the electric field generated by certain kind of virtual line charges supported on line segments outside of the domain; thereby, the gradient blow-up is completely characterized in terms of both of Neumann-type and Dirichlet-type boundary conditions, conductivities and geometric parameters.

math.AP

Interdimensional optical isospectrality inspired by graph networks

A network picture has been applied to various physical and biological systems to understand their governing mechanisms intuitively. Utilizing discretization schemes, both electrical and optical materials can also be interpreted as abstract 'graph' networks composed of couplings (edges) between local elements (vertices), which define the correlation between material structures and wave flows. Nonetheless, the fertile structural degrees of freedom in graph theory have not been fully exploited in physics owing to the suppressed long-range interaction between far-off elements. Here, by exploiting the mathematical similarity between Hamiltonians in different dimensions, we propose the design of reduced-dimensional optical structures that perfectly preserve the level statistics of disordered graph networks with significant long-range coupling. We show that the disorder-induced removal of the level degeneracy in high-degree networks allows their isospectral projection to one-dimensional structures without any disconnection. This inter-dimensional isospectrality between high- and low-degree graph-like structures enables the ultimate simplification of broadband multilevel devices, from three- to one-dimensional structures.

physics.optics

Bloch-like waves in random-walk potentials based on supersymmetry

Bloch's theorem was a major milestone that established the principle of bandgaps in crystals. Although it was once believed that bandgaps could form only under conditions of periodicity and long-range correlations for Bloch's theorem, this restriction was disproven by the discoveries of amorphous media and quasicrystals. While network and liquid models have been suggested for the interpretation of Bloch-like waves in disordered media, these approaches based on searching for random networks with bandgaps have failed in the deterministic creation of bandgaps. Here, we reveal a deterministic pathway to bandgaps in random-walk potentials by applying the notion of supersymmetry to the wave equation. Inspired by isospectrality, we follow a methodology in contrast to previous methods: we transform order into disorder while preserving bandgaps. Our approach enables the formation of bandgaps in extremely-disordered potentials analogous to Brownian motion, and also allows the tuning of correlations while maintaining identical bandgaps, thereby creating a family of potentials with 'Bloch-like eigenstates'.

physics.optics

Metadisorder for designer light in random-walk systems

Disorder plays a critical role in signal transport, by controlling the correlation of systems. In wave physics, disordered potentials suppress wave transport due to their localized eigenstates from random-walk scattering. Although the variation of localization with tunable disorder has been intensively studied as a bridge between ordered and disordered media, the general trend of disorder-enhanced localization has remained unchanged, failing in envisaging the existence of delocalization in highly-disordered potentials. Here, we propose the concept of 'metadisorder': tunable random-walk systems having a designed eigenstate with unnatural localization. We demonstrate that one of the eigenstates in a randomly-coupled system can always be arbitrarily molded, regardless of the degree of disorder, by adjusting the self-energy of each element. Ordered waves are then achieved in highly-disordered systems, including planewaves and globally- collective resonances. We also devise counterintuitive functionalities in disordered systems, such as 'small-world-like' transport from non-Anderson-type localization, phase-conserving disorder, and phase-controlled beam steering.

physics.optics

Progress toward high-Q perfect absorption: A Fano antilaser

Here we propose a route to the high-Q perfect absorption of light by introducing the concept of a Fano anti-laser. Based on the drastic spectral variation of the optical phase in a Fano-resonant system, a spectral singularity for scatter-free perfect absorption can be achieved with an order of magnitude smaller material loss. By applying temporal coupled mode theory to a Fano-resonant waveguide platform, we reveal that the required material loss and following absorption Q-factor are ultimately determined by the degree of Fano spectral asymmetry. The feasibility of the Fano anti-laser is confirmed using a photonic crystal platform, to demonstrate spatio-spectrally selective heating. Our results utilizing the phase-dependent control of device bandwidths derive a counterintuitive realization of high-Q perfect conversion of light into internal energy, and thus pave the way for a new regime of absorption-based devices, including switches, sensors, thermal imaging, and opto-thermal emitters.

physics.optics