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Dongho Lee

Publications and source records attributed to Dongho Lee.

11 recordsLinked to original sources
arXiv2026

Ornstein-Uhlenbeck Process Driven by Multiple Dichotomous Noises

We study a generalized Ornstein-Uhlenbeck process driven by a superposition of $K$ independent dichotomous noises with arbitrary fixed amplitudes and switching rates. Unlike the classical Ornstein-Uhlenbeck process driven by equilibrium Gaussian white noise, the present system is governed by bounded nonequilibrium fluctuations with finite correlation times. We obtain exact expressions for the stationary position distribution and all cumulants, and show that the stationary state possesses an unexpectedly rich structure, including compact support, algebraic branch-point singularities, edge divergences, and multiple extrema. We establish a mapping onto a heterogeneous random-flight process with bounded jumps, yielding a transparent probabilistic interpretation of the stationary measure. We further analyze several limiting regimes, including the crossover to Gaussian statistics for large numbers of noise sources. For ensembles with exponentially-distributed quenched amplitudes, we derive exact disorder-averaged stationary distributions and show that disorder fundamentally alters the stationary state, producing exponential tails decorated by algebraic prefactors with non-trivial exponents.

cond-mat.stat-mech↗
arXiv2026

Mutations of Local Floer Chain Complexes across Hamiltonian Bifurcations

We compute the chain-level change of local Floer complexes across the generic bifurcations of periodic orbits in four-dimensional Hamiltonian systems. Although local Floer homology is invariant across a bifurcation, the underlying chain complex mutates: periodic orbits and their Conley--Zehnder indices change discontinuously, and the Floer differential must change to compensate. Two tools make this mutation computable. First, we prove a Floer cascade counting theorem for Floer cylinders between multiply covered orbits of an autonomous system, which is not specific to the bifurcation analysis carried out here. Second, for each bifurcation type in Meyer's classification, and for two additional $\mathbb{Z}_2$-symmetric types, we construct a model Hamiltonian whose Floer cylinders are lifts of planar gradient trajectories, which we call the gradient revolutions, reducing the count to finite-dimensional Morse theory and cascade counting. We determine all seven mutations explicitly.

math.SG↗
arXiv2026

Bridging the Quantum Divide: A Learning-Centric Quantum Hackathon for Underrepresented Students (Extended Version)

This paper describes the design and implementation of a two-day quantum hackathon for underrepresented high school students in Nova Scotia, Canada. The first day of the hackathon is spent introducing students to quantum computing through hands-on activities, whereas the second day teaches students to apply this knowledge through guided challenges. Both days are informed by the theory of mastery learning and specification grading, with the full curriculum being crafted within the Integrated Course Design framework. This requires identifying situational factors unique to our target demographics, from which we develop learning outcomes, and then work backwards to a full curriculum with educative assessments. A novel aspect of our hackathon is that all circuit simulations are performed within Quirk: a decision based on best practices in computer science education. Based on feedback from students, we conclude that our hackathon successfully introduced students to the basics of quantum computing, and was able to reach most of our target demographics.

physics.ed-ph↗
arXiv2026

Diffusing diffusivity model with dichotomous noise

We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite interval. We derive analytical expressions for the short-time probability density function (PDF) of the particle displacement and analyse its asymptotic behaviour. While the PDF retains the characteristic logarithmic divergence at the origin, its tails differ from the Gaussian white-noise case: exponential tails are replaced by Gaussian ones modulated by a power-law with a switching-rate-dependent exponent. At long times, the dynamics converges to ordinary Gaussian diffusion. We determine the variance and covariance of the time-averaged stochastic diffusivity and show that it is self-averaging. The model provides a minimal analytically tractable framework for stochastic transport in environments with bounded or switching fluctuations.

cond-mat.stat-mech↗
arXiv2025

HERO-VQL: Hierarchical, Egocentric and Robust Visual Query Localization

In this work, we tackle the egocentric visual query localization (VQL), where a model should localize the query object in a long-form egocentric video. Frequent and abrupt viewpoint changes in egocentric videos cause significant object appearance variations and partial occlusions, making it difficult for existing methods to achieve accurate localization. To tackle these challenges, we introduce Hierarchical, Egocentric and RObust Visual Query Localization (HERO-VQL), a novel method inspired by human cognitive process in object recognition. We propose i) Top-down Attention Guidance (TAG) and ii) Egocentric Augmentation based Consistency Training (EgoACT). Top-down Attention Guidance refines the attention mechanism by leveraging the class token for high-level context and principal component score maps for fine-grained localization. To enhance learning in diverse and challenging matching scenarios, EgoAug enhances query diversity by replacing the query with a randomly selected corresponding object from groundtruth annotations and simulates extreme viewpoint changes by reordering video frames. Additionally, CT loss enforces stable object localization across different augmentation scenarios. Extensive experiments on VQ2D dataset validate that HERO-VQL effectively handles egocentric challenges, significantly outperforming baselines.

cs.CV↗
arXiv2025

Conley-Zehnder Indices of Spatial Rotating Kepler Problem

We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits, using angular momentum and the Laplace-Runge-Lenz vector. We then compute the Conley-Zehnder indices of non-degenerate orbits and the Robbin-Salamon indices of degenerate families, establishing their contributions to symplectic homology via the Morse-Bott spectral sequence. To address coordinate degeneracies in the spatial setting, we introduce a new coordinate system based on the Laplace-Runge-Lenz vector. These results offer a full symplectic-topological profile of the three-dimensional rotating Kepler problem and connect it to generators of symplectic homology.

math.SG↗
arXiv2025

CA^2ST: Cross-Attention in Audio, Space, and Time for Holistic Video Recognition

We propose Cross-Attention in Audio, Space, and Time (CA^2ST), a transformer-based method for holistic video recognition. Recognizing actions in videos requires both spatial and temporal understanding, yet most existing models lack a balanced spatio-temporal understanding of videos. To address this, we propose a novel two-stream architecture, called Cross-Attention in Space and Time (CAST), using only RGB input. In each layer of CAST, Bottleneck Cross-Attention (B-CA) enables spatial and temporal experts to exchange information and make synergistic predictions. For holistic video understanding, we extend CAST by integrating an audio expert, forming Cross-Attention in Visual and Audio (CAVA). We validate the CAST on benchmarks with different characteristics, EPIC-KITCHENS-100, Something-Something-V2, and Kinetics-400, consistently showing balanced performance. We also validate the CAVA on audio-visual action recognition benchmarks, including UCF-101, VGG-Sound, KineticsSound, and EPIC-SOUNDS. With a favorable performance of CAVA across these datasets, we demonstrate the effective information exchange among multiple experts within the B-CA module. In summary, CA^2ST combines CAST and CAVA by employing spatial, temporal, and audio experts through cross-attention, achieving balanced and holistic video understanding.

cs.CV↗
arXiv2023

CAST: Cross-Attention in Space and Time for Video Action Recognition

Recognizing human actions in videos requires spatial and temporal understanding. Most existing action recognition models lack a balanced spatio-temporal understanding of videos. In this work, we propose a novel two-stream architecture, called Cross-Attention in Space and Time (CAST), that achieves a balanced spatio-temporal understanding of videos using only RGB input. Our proposed bottleneck cross-attention mechanism enables the spatial and temporal expert models to exchange information and make synergistic predictions, leading to improved performance. We validate the proposed method with extensive experiments on public benchmarks with different characteristics: EPIC-KITCHENS-100, Something-Something-V2, and Kinetics-400. Our method consistently shows favorable performance across these datasets, while the performance of existing methods fluctuates depending on the dataset characteristics.

cs.CV↗
arXiv2022

Formal Methods for Quantum Programs: A Survey

While recent progress in quantum hardware open the door for significant speedup in certain key areas (cryptography, biology, chemistry, optimization, machine learning, etc), quantum algorithms are still hard to implement right, and the validation of such quantum programs is achallenge. Moreover, importing the testing and debugging practices at use in classical programming is extremely difficult in the quantum case, due to the destructive aspect of quantum measurement. As an alternative strategy, formal methods are prone to play a decisive role in the emerging field of quantum software. Recent works initiate solutions for problems occurring at every stage of the development process: high-level program design, implementation, compilation, etc. We review the induced challenges for an efficient use of formal methods in quantum computing and the current most promising research directions.

cs.PL↗
arXiv2021

Concrete Categorical Model of a Quantum Circuit Description Language with Measurement

In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data -- qubits -- into classical data -- booleans -- . We propose a type system and an operational semantics for the language and we state safety properties. Next, we introduce a concrete categorical semantics for the proposed language, basing our approach on a recent model from Rios\&Selinger for Proto-Quipper-M. Our approach is to construct on top of a concrete category of circuits with measurements a Kleisli category, capturing as a side effect the action of retrieving classical content out of a quantum memory. We then show a soundness result for this semantics.

cs.LO↗