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The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently utilized time-discretization numerical schemes for solving the Allen-Cahn equation, with focuses on the Backward Euler, Crank-Nicolson (CN), convex splitting of modified CN, and Diagonally Implicit Runge-Kutta (DIRK) methods. Our stability analysis reveals that the Convex Splitting of the Modified CN scheme exhibits unconditional stability, allowing greater flexibility in time step selection, while the other schemes are conditionally stable. Additionally, our robustness analysis highlights that the Backward Euler method converges to correct physical solutions regardless of initial conditions. In contrast, the other methods studied in this work show sensitivity to initial conditions and may converge to incorrect physical solutions if the initial conditions are not carefully chosen. This study introduces a comprehensive approach to assessing stability and robustness in numerical methods for solving the Allen-Cahn equation, providing a new perspective for evaluating numerical techniques for general nonlinear differential equations.

Recent studies have demonstrated that ultrahigh-$Q$ resonances, which are robust to fabrication imperfections, can be realized by merging multiple bound states in the continuum (BICs) in momentum space. The merging of multiple BICs holds significant promise for practical applications, providing a robust means to attain ultrahigh-$Q$ resonances that greatly enhance light-matter interactions. In this study, we introduce a novel approach to achieve the merging of BICs at the edges of the fourth stop band, which opens at the third-order $\Gamma$ point, in one-dimensional leaky-mode photonic lattices. Photonic band gaps and BICs arise from periodic modulations in lattice parameters. However, near the third-order $\Gamma$ point, out-of-plane radiation arises by the first and second Fourier harmonic components in the lattice parameters. Accidental BICs can emerge at specific $k$ points where an optimal balance exists between these two Fourier harmonic components. We demonstrate that these accidental BICs are topologically stable, and their positions in momentum space can be precisely controlled by adjusting a specific lattice parameter that influences the strength of the first and second Fourier harmonic components. Furthermore, we show that accidental BICs can be merged at the third-order $\Gamma$ point, with or without a symmetry-protected BIC, by finely adjusting this specific lattice parameter while keeping other parameters constant.

Unidirectional light emission from planar photonic structures is highly advantageous for a wide range of optoelectronic applications. Recently, it has been demonstrated that unidirectional guided resonances (UGRs) can be realized by utilizing topological polarization singularities in momentum space. However, the practical application of these topological unidirectional emitters has been limited due to their intricate geometric configurations, requiring special efforts with high-cost fabrication processes. In this study, we show that unidirectional light emission can be achieved in conventional one-dimensional zero-contrast gratings (ZCGs), which can be easily fabricated using current nanofabrication technologies. In ZCGs, the interband coupling between even-like and odd-like waveguide modes leads to the formation of quasi-UGRs, characterized by significantly higher decay rates in either the upward or downward direction compared to the opposite direction. We demonstrate that these quasi-UGRs evolve into genuine UGRs with an gradual increase in grating thickness. Moreover, the emission direction of UGRs can be selectively steered either upward or downward by adjusting the lattice parameters. In addition to quasi-UGRs and UGRs, our study also reveals additional topological phenomena in ZCGs, including exceptional points and quasi-BICs.

Quantum interferometry based on induced-coherence phenomena has demonstrated the possibility of undetected-photon measurements. Perturbation in the optical path of probe photons can be detected by interference signals generated by quantum mechanically correlated twin photons propagating through a different path, possibly at a different wavelength. To the best of our knowledge, this work demonstrates for the first time a hybrid-type induced-coherence interferometer that incorporates a Mach-Zehnder-type interferometer for visible photons and a Michelson-type interferometer for infrared photons, based on double-pass pumped spontaneous parametric down-conversion. This configuration enables infrared optical measurements via the detection of near-visible photons and provides methods for characterizing the quality of measurements by identifying photon pairs of different origins. The results verify that the induced-coherence interference visibility is approximately the same as the heralding efficiencies between twin photons along the relevant spatial modes. Applications to both time-domain and frequency-domain quantum-optical induced-coherence tomography for three-dimensional test structures are demonstrated. The results prove the feasibility of practical undetected-photon sensing and imaging techniques based on the presented structure.

While many FSCIL studies have been undertaken, achieving satisfactory performance, especially during incremental sessions, has remained challenging. One prominent challenge is that the encoder, trained with an ample base session training set, often underperforms in incremental sessions. In this study, we introduce a novel training framework for FSCIL, capitalizing on the generalizability of the Contrastive Language-Image Pre-training (CLIP) model to unseen classes. We achieve this by formulating image-object-specific (IOS) classifiers for the input images. Here, an IOS classifier refers to one that targets specific attributes (like wings or wheels) of class objects rather than the image's background. To create these IOS classifiers, we encode a bias prompt into the classifiers using our specially designed module, which harnesses key-prompt pairs to pinpoint the IOS features of classes in each session. From an FSCIL standpoint, our framework is structured to retain previous knowledge and swiftly adapt to new sessions without forgetting or overfitting. This considers the updatability of modules in each session and some tricks empirically found for fast convergence. Our approach consistently demonstrates superior performance compared to state-of-the-art methods across the miniImageNet, CIFAR100, and CUB200 datasets. Further, we provide additional experiments to validate our learned model's ability to achieve IOS classifiers. We also conduct ablation studies to analyze the impact of each module within the architecture., Comment: 8 pages, 4 figures, 4 tables

This paper proposes a system capable of recognizing a speaker's utterance-level emotion through multimodal cues in a video. The system seamlessly integrates multiple AI models to first extract and pre-process multimodal information from the raw video input. Next, an end-to-end MER model sequentially predicts the speaker's emotions at the utterance level. Additionally, users can interactively demonstrate the system through the implemented interface., Comment: Interspeech 2023

Bound states in the continuum (BICs) theoretically have the ability to confine electromagnetic waves in limited regions with infinite radiative quality ($Q$) factors. However, in practical experiments, resonances can only exhibit finite $Q$ factors due to unwanted scattering losses caused by fabrication imperfections. Recently, it has been shown that ultrahigh-$Q$ guided-mode resonances (GMRs), which are robust to fabrication imperfections, can be realized by merging multiple BICs in momentum space. In this study, we analytically and numerically investigate the merging and band transition of accidental BICs in planar photonic lattices. Accidental BICs can merge at the edges of the second stop band, either with or without a symmetry-protected BIC. We show that as the thickness of the photonic lattice gradually increases, the merged state of BICs transitions from the upper to the lower band edge. Using coupled-mode analysis, we present the analytical merging thickness at which multiple accidental BICs merge at the second-order $\Gamma$ point. Our coupled-mode analysis could be beneficial for achieving ultrahigh-$Q$ GMRs in various photonic lattices composed of materials with different dielectric constants.

The use of nonlinear PDEs has led to significant advancements in various fields, such as physics, biology, ecology, and quantum mechanics. However, finding multiple solutions for nonlinear PDEs can be a challenging task, especially when suitable initial guesses are difficult to obtain. In this paper, we introduce a novel approach called the Companion-Based Multilevel finite element method (CBMFEM), which can efficiently and accurately generate multiple initial guesses for solving nonlinear elliptic semi-linear equations with polynomial nonlinear terms using finite element methods with conforming elements. We provide a theoretical analysis of the error estimate of finite element methods using an appropriate notion of isolated solutions, for the nonlinear elliptic equation with multiple solutions and present numerical results obtained using CBMFEM which are consistent with the theoretical analysis.