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Recent extended reality headsets and field robots have adopted covers to protect the front-facing cameras from environmental hazards and falls. The surface irregularities on the cover can lead to optical aberrations like blurring and non-parametric distortions. Novel view synthesis methods like NeRF and 3D Gaussian Splatting are ill-equipped to synthesize from sequences with optical aberrations. To address this challenge, we introduce SynthCover to enable novel view synthesis through protective covers for downstream extended reality applications. SynthCover employs a Refractive Field that estimates the cover's geometry, enabling precise analytical calculation of refracted rays. Experiments on synthetic and real-world scenes demonstrate our method's ability to accurately model scenes viewed through protective covers, achieving a significant improvement in rendering quality compared to prior methods. We also show that the model can adjust well to various cover geometries with synthetic sequences captured with covers of different surface curvatures. To motivate further studies on this problem, we provide the benchmarked dataset containing real and synthetic walkable scenes captured with protective cover optical aberrations., Comment: WACV 2025

In this paper, we introduce a novel estimator for vision-aided inertial navigation systems (VINS), the Preconditioned Cholesky-based Square Root Information Filter (PC-SRIF). When solving linear systems, employing Cholesky decomposition offers superior efficiency but can compromise numerical stability. Due to this, existing VINS utilizing (Square Root) Information Filters often opt for QR decomposition on platforms where single precision is preferred, avoiding the numerical challenges associated with Cholesky decomposition. While these issues are often attributed to the ill-conditioned information matrix in VINS, our analysis reveals that this is not an inherent property of VINS but rather a consequence of specific parameterizations. We identify several factors that contribute to an ill-conditioned information matrix and propose a preconditioning technique to mitigate these conditioning issues. Building on this analysis, we present PC-SRIF, which exhibits remarkable stability in performing Cholesky decomposition in single precision when solving linear systems in VINS. Consequently, PC-SRIF achieves superior theoretical efficiency compared to alternative estimators. To validate the efficiency advantages and numerical stability of PC-SRIF based VINS, we have conducted well controlled experiments, which provide empirical evidence in support of our theoretical findings. Remarkably, in our VINS implementation, PC-SRIF's runtime is 41% faster than QR-based SRIF., Comment: This work has been submitted to the IEEE for possible publication

3-dB couplers, which are commonly used in photonic integrated circuits for on-chip information processing, precision measurement, and quantum computing, face challenges in achieving robust performance due to their limited 3-dB bandwidths and sensitivity to fabrication errors. To address this, we introduce topological physics to nanophotonics, developing a framework for topological 3-dB couplers. These couplers exhibit broad working wavelength range and robustness against fabrication dimensional errors. By leveraging valley-Hall topology and mirror symmetry, the photonic-crystal-slab couplers achieve ideal 3-dB splitting characterized by a wavelength-insensitive scattering matrix. Tolerance analysis confirms the superiority on broad bandwidth of 48 nm and robust splitting against dimensional errors of 20 nm. We further propose a topological interferometer for on-chip distance measurement, which also exhibits robustness against dimensional errors. This extension of topological principles to the fields of interferometers, may open up new possibilities for constructing robust wavelength division multiplexing, temperature-drift-insensitive sensing, and optical coherence tomography applications., Comment: 20 pages, 4 figures

Achieving efficient and consistent localization a prior map remains challenging in robotics. Conventional keyframe-based approaches often suffers from sub-optimal viewpoints due to limited field of view (FOV) and/or constrained motion, thus degrading the localization performance. To address this issue, we design a real-time tightly-coupled Neural Radiance Fields (NeRF)-aided visual-inertial navigation system (VINS). In particular, by effectively leveraging the NeRF's potential to synthesize novel views, the proposed NeRF-VINS overcomes the limitations of traditional keyframe-based maps (with limited views) and optimally fuses IMU, monocular images, and synthetically rendered images within an efficient filter-based framework. This tightly-coupled fusion enables efficient 3D motion tracking with bounded errors. We extensively compare the proposed NeRF-VINS against the state-of-the-art methods that use prior map information and demonstrate its ability to perform real-time localization, at over 10 Hz, on a resource-constrained Jetson AGX Orin embedded platform., Comment: 6 pages, 7 figures

By means of the data sets of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS), we investigate the relationship between the variability amplitude and luminosity at 5100 \AA, black hole mass, Eddington ratio, $ R_{\rm Fe \, II}$ ( the ratio of the flux of Fe II line within 4435-4685 \AA ~to the broad proportion of $\rm H\beta$ line) as well as $ R_{5007}$ (the ratio of the flux [O III] line to the total $\rm H\beta$ line) of the broad line Seyfert 1 (BLS1) and narrow line Seyfert 1 (NLS1) galaxies sample in g,r,i,z and y bands, respectively. We also analyze the similarities and differences of the variability characteristics between the BLS1 galaxies and NLS1 galaxies. The results are listed as follows. (1). The cumulative probability distribution of the variability amplitude shows that NLS1 galaxies are lower than that in BLS1 galaxies. (2). We analyze the dependence of the variability amplitude with the luminosity at 5100 \AA, black hole mass, Eddington ratio, $ R_{\rm Fe \,II}$ and $ R_{5007}$, respectively. We find significantly negative correlations between the variability amplitude and Eddington ratio, insignificant correlations with the luminosity at 5100 \AA. The results also show significantly positive correlations with the black hole mass and $ R_{5007}$, significantly negative correlations with $ R_{\rm Fe\, II}$ which are consistent with Rakshit and Stalin(2017) in low redshift bins (z<0.4) and Ai et al.(2010). (3). The relationship between the variability amplitude and the radio loudness is investigated for 155 BLS1 galaxies and 188 NLS1 galaxies. No significant correlations are found in our results., Comment: 10 pages, 5 figures, accepted by Astrophysics and Space Science, in Press

Hamiltonian approach in quantum theory provides a new thinking for option pricing with stochastic interest rates. For barrier options, the option price changing process is similar to the infinite high barrier scattering problem in quantum mechanics; for double barrier options, the option price changing process is analogous to a particle moving in a infinite square potential well. Using Hamiltonian approach, the expressions of pricing kernels and option prices under Vasicek stochastic interest rate model could be derived. Numerical results of options price as functions of underlying prices are also shown., Comment: 18 pages,5 figures

Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional double-barrier step (PDBS) options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well. We have derived the pricing kernel of PDBS options with time dependent interest rate and volatility. Numerical results of option price as a function of underlying asset price are shown as well. Path integral method can be easily generalized to the pricing of PDBS options with curved boundaries., Comment: 18 pages, 3 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:2209.12542

Hamiltonian approach in quantum mechanics provides a new thinking for barrier option pricing. For proportional floating barrier step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem in quantum mechanics; for floating double-barrier step options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well. Using Hamiltonian methodology, the analytical expressions of pricing kernel and option price could be derived. Numerical results of option price as a function of underlying price, floating rate, interest rate and exercise price are shown, which are consistent with the results given by mathematical calculations., Comment: 26 pages, 5 figures

This is the technical report of the 9th place in the final result of PARSE2022 Challenge. We solve the segmentation problem of the pulmonary artery by using a two-stage method based on a 3D CNN network. The coarse model is used to locate the ROI, and the fine model is used to refine the segmentation result. In addition, in order to improve the segmentation performance, we adopt multi-view and multi-window level method, at the same time we employ a fine-tune strategy to mitigate the impact of inconsistent labeling.