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Housing and household characteristics are key determinants of social and economic well-being, yet our understanding of their interrelationships remains limited. This study addresses this knowledge gap by developing a deep contrastive learning (DCL) model to infer housing-household relationships using the American Community Survey (ACS) Public Use Microdata Sample (PUMS). More broadly, the proposed model is suitable for a class of problems where the goal is to learn joint relationships between two distinct entities without explicitly labeled ground truth data. Our proposed dual-encoder DCL approach leverages co-occurrence patterns in PUMS and introduces a bisect K-means clustering method to overcome the absence of ground truth labels. The dual-encoder DCL architecture is designed to handle the semantic differences between housing (building) and household (people) features while mitigating noise introduced by clustering. To validate the model, we generate a synthetic ground truth dataset and conduct comprehensive evaluations. The model further demonstrates its superior performance in capturing housing-household relationships in Delaware compared to state-of-the-art methods. A transferability test in North Carolina confirms its generalizability across diverse sociodemographic and geographic contexts. Finally, the post-hoc explainable AI analysis using SHAP values reveals that tenure status and mortgage information play a more significant role in housing-household matching than traditionally emphasized factors such as the number of persons and rooms. 

We present a systematic framework to quantify the interplay between coherence and wave-particle duality in generic two-path interference systems. Our analysis reveals a closed-form duality ellipse (DE) equality, that rigorously unifies visibility (a traditional waveness measure) and predictability (a particleness measure) with degree of coherence, providing a complete mathematical embodiment of Bohr's complementarity principle. Extending this framework to quantum imaging with undetected photons (QIUP), where both path information and photon interference are inherently linked to spatial object reconstruction, we establish an imaging duality ellipse (IDE) that directly connects wave-particle duality to the object's transmittance profile. This relation enables object characterization through duality measurements alone and remains robust against experimental imperfections such as decoherence and misalignment. Our results advance the fundamental understanding of quantum duality while offering a practical toolkit for optimizing coherence-driven quantum technologies, from imaging to sensing. 

Abstract Wave‐particle duality, intertwining two inherently contradictory properties of quantum systems, remains one of the most conceptually profound aspects of quantum mechanics. By using the concept of energy capacity, the ability of a quantum system to store and extract energy, a device‐independent uncertainty relation is derived for wave‐particle duality. This relation is shown to be independent of both the representation space and the measurement basis of the quantum system. Furthermore, it is experimentally validated that this wave‐particle duality relation using a photon‐based platform. 

We demonstrate super-resolved localization of three point sources with the assistance of a machine learning model that is based on the decomposition of the source signal into Hermite Gaussian modes. High fidelity of over 80% is achieved. 

We explore the equivalence between paraxial optical beam propagation and 2D harmonic oscillator evolution. The phenomenon of quantum state revival of harmonic oscillator is shown to be simulated with the propagation of a focusing beam. 

We experimentally investigate polarization, entanglement, and complementary behavior of a light beam, and the center of mass and moment of inertia of a two-mass system, confirming an unexpected quantitative link between wave optics and mechanics. 

We investigate superresolution of two general point sources using continuous rotation of the observation basis. Optimal superresolution with maximum estimation accuracy is achieved when measurements are performed in the Schmidt basis. 

We investigate super-resolution of two spatially separated practical point sources using machine learning. High fidelity of over 90% is achieved for separations that are 16 times smaller than the conventional resolution limit.