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As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method for data valuation. However, a limitation of Data Shapley is its assumption of a fixed dataset, contrasting with the dynamic nature of real-world applications where data constantly evolves and expands. This paper establishes the relationship between Data Shapley and infinite-order U-statistics and addresses this limitation by quantifying the uncertainty of Data Shapley with changes in data distribution from the perspective of U-statistics. We make statistical inferences on data valuation to obtain confidence intervals for the estimations. We construct two different algorithms to estimate this uncertainty and provide recommendations for their applicable situations. We also conduct a series of experiments on various datasets to verify asymptotic normality and propose a practical trading scenario enabled by this method.

Polarization engineering has been proven to enhance the capabilities of light manipulation and thus facilitate the development of integrated photonic devices. In this study, we introduce a polarization rotator based on gradiently-twisted $\alpha$-MoO$_3$ thin film, that works for the mid infrared range and functions in a transmission mode. To be specific, the proposed device is constructed by gradiently-twisted $\alpha$-MoO$_3$ multilayers with a subwavelength thickness of only 5 microns, namely, one-third of the working wavelength. Our analytical calculation demonstrates the efficacy of this subwavelength thin film rotator in converting a linearly polarized wave into its orthogonal counterpart, thanks to its chiral nature. The twisted $\alpha$-MoO$_3$ multilayers exhibit the capability to significantly manipulate dispersion characteristics while maintaining low optical losses, thereby enabling a wide bandwidth exceeding 2.5 THz with a polarization ratio surpassing 17 dB. Moreover, the operational frequency can be adjusted across a 3.4 THz range by altering the incident angle of the incident waves. This adaptable design, characterized by its polarization versatility, can be customized to suit practical applications within wireless communication, radar systems, optical switching, and imaging technologies., Comment: Accepted by Applied Physics Letters

Tunable optical filter at the chip scale plays a crucial role in fulfilling the need for the reconfigurability in channel routing, optical switching, and wavelength division multiplexing systems. In this letter, we propose a tunable double notch filter on thin-film lithium niobate using dual micro-ring architecture. This unique integrated filter is essential for complex photonic integrated circuits, along with multiple channels and various frequency spacing. With only one loaded voltage, the device demonstrates a wide frequency spacing tunability from 16.1 GHz to 89.9 GHz by reversely tunning the resonances of the two micro-rings while the center wavelength between the two resonances remains unaltered. Moreover, by utilizing the pronounced electro-optic properties of lithium niobate, associated with the tight light confinement nanophotonic waveguides, the device demonstrates a spacing tunability of 0.82 GHz/V and a contrast of 10~16 dB. In addition, the device has an ultracompact footprint of 0.0248 mm2., Comment: accepted by Optics Letters

We explore correlations harvesting by two static detectors locally interacting with vacuum massless scalar fields in the presence of an infinite perfectly reflecting boundary. We study the phenomena of mutual information harvesting and entanglement harvesting for two detector-boundary alignments, i.e., parallel-to-boundary and vertical-to-boundary alignments. Our results show that the presence of the boundary generally inhibits mutual information harvesting relative to that in flat spacetime without any boundaries. In contrast, the boundary may play a doubled-edged role in entanglement harvesting, i.e., inhibiting entanglement harvesting in the near zone of the boundary while assisting it in the far zone of the boundary. Moreover, there exists an optimal detector energy gap difference between two nonidentical detectors that makes such detectors advantageous in correlations harvesting as long as the interdetector separation is large enough. The value of the optimal detector energy gap difference depends on both the interdetector separation and the detector-to-boundary distance. A comparison of the correlations harvesting in two different alignments shows that although correlations harvesting share qualitatively the same properties, they also display quantitative differences in that the detectors in vertical-to-boundary alignment always harvest comparatively more mutual information than the parallel-to-boundary ones, while they harvest comparatively more entanglement only near the boundary., Comment: 32 pages, 14 figures

Data valuation -- quantifying the contribution of individual data sources to certain predictive behaviors of a model -- is of great importance to enhancing the transparency of machine learning and designing incentive systems for data sharing. Existing work has focused on evaluating data sources with the shared feature or sample space. How to valuate fragmented data sources of which each only contains partial features and samples remains an open question. We start by presenting a method to calculate the counterfactual of removing a fragment from the aggregated data matrix. Based on the counterfactual calculation, we further propose 2D-Shapley, a theoretical framework for fragmented data valuation that uniquely satisfies some appealing axioms in the fragmented data context. 2D-Shapley empowers a range of new use cases, such as selecting useful data fragments, providing interpretation for sample-wise data values, and fine-grained data issue diagnosis., Comment: 25 pages, 13 figures, ICML 2023

We make a detailed comparison between entanglement harvesting for uniformly accelerated detectors in vacuum and static ones in a thermal bath at the Unruh temperature and find that, for a small energy gap relative to the Heisenberg energy of the detectors, static detectors in the thermal bath can harvest more entanglement and possess a comparatively larger harvesting-achievable range than the uniformly accelerated ones; however, as the energy gap grows sufficiently large, the uniformly accelerated detectors are instead likely to harvest more entanglement and possess a relatively larger harvesting-achievable range than inertial ones in the thermal bath. In comparison with static detectors in vacuum, there exist phenomena of acceleration-assisted entanglement harvesting but never that of thermal-noise-assisted one. A notably interesting feature is that, although both the amount of entanglement harvested and the harvesting-achievable interdetector separation for static detectors in a thermal bath are always a decreasing function of temperature, they are not always so for uniformly accelerated detectors as acceleration (Unruh temperature) varies, suggesting the existence of the anti-Unruh effect in the entanglement harvesting phenomena of the accelerated detectors., Comment: 18 pages, 5 figures

Tissue segmentation is the mainstay of pathological examination, whereas the manual delineation is unduly burdensome. To assist this time-consuming and subjective manual step, researchers have devised methods to automatically segment structures in pathological images. Recently, automated machine and deep learning based methods dominate tissue segmentation research studies. However, most machine and deep learning based approaches are supervised and developed using a large number of training samples, in which the pixelwise annotations are expensive and sometimes can be impossible to obtain. This paper introduces a novel unsupervised learning paradigm by integrating an end-to-end deep mixture model with a constrained indicator to acquire accurate semantic tissue segmentation. This constraint aims to centralise the components of deep mixture models during the calculation of the optimisation function. In so doing, the redundant or empty class issues, which are common in current unsupervised learning methods, can be greatly reduced. By validation on both public and in-house datasets, the proposed deep constrained Gaussian network achieves significantly (Wilcoxon signed-rank test) better performance (with the average Dice scores of 0.737 and 0.735, respectively) on tissue segmentation with improved stability and robustness, compared to other existing unsupervised segmentation approaches. Furthermore, the proposed method presents a similar performance (p-value > 0.05) compared to the fully supervised U-Net., Comment: 13 pages, 8 figures, accepted by IEEE TMI

Recognition of glomeruli lesions is the key for diagnosis and treatment planning in kidney pathology; however, the coexisting glomerular structures such as mesangial regions exacerbate the difficulties of this task. In this paper, we introduce a scheme to recognize fine-grained glomeruli lesions from whole slide images. First, a focal instance structural similarity loss is proposed to drive the model to locate all types of glomeruli precisely. Then an Uncertainty Aided Apportionment Network is designed to carry out the fine-grained visual classification without bounding-box annotations. This double branch-shaped structure extracts common features of the child class from the parent class and produces the uncertainty factor for reconstituting the training dataset. Results of slide-wise evaluation illustrate the effectiveness of the entire scheme, with an 8-22% improvement of the mean Average Precision compared with remarkable detection methods. The comprehensive results clearly demonstrate the effectiveness of the proposed method., Comment: 33 pages, 6 figures, accepted by the Pattern Recognition journal