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In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies.

In multiple changepoint analysis, assessing the uncertainty of detected changepoints is crucial for enhancing detection reliability -- a topic that has garnered significant attention. Despite advancements through selective p-values, current methodologies often rely on stringent assumptions tied to specific changepoint models and detection algorithms, potentially compromising the accuracy of post-detection statistical inference. We introduce TUNE (Thresholding Universally and Nullifying change Effect), a novel algorithm-agnostic approach that uniformly controls error probabilities across detected changepoints. TUNE sets a universal threshold for multiple test statistics, applicable across a wide range of algorithms, and directly controls the family-wise error rate without the need for selective p-values. Through extensive theoretical and numerical analyses, TUNE demonstrates versatility, robustness, and competitive power, offering a viable and reliable alternative for model-agnostic post-detection inference.

In this paper, we investigate alpha testing for high-dimensional linear factor pricing models. We propose a spatial sign-based max-type test to handle sparse alternative cases. Additionally, we prove that this test is asymptotically independent of the spatial-sign-based sum-type test proposed by Liu et al. (2023). Based on this result, we introduce a Cauchy Combination test procedure that combines both the max-type and sum-type tests. Simulation studies and real data applications demonstrate that the new proposed test procedure is robust not only for heavy-tailed distributions but also for the sparsity of the alternative hypothesis.

In recent years, there has been considerable research on testing alphas in high-dimensional linear factor pricing models. In our study, we introduce a novel max-type test procedure that performs well under sparse alternatives. Furthermore, we demonstrate that this new max-type test procedure is asymptotically independent from the sum-type test procedure proposed by Pesaran and Yamagata (2017). Building on this, we propose a Fisher combination test procedure that exhibits good performance for both dense and sparse alternatives.

Over the past decade, structured illumination microscopy (SIM) has found its niche in super-resolution (SR) microscopy due to its fast imaging speed and low excitation intensity. However, due to the significantly higher light dose compared to wide-field microscopy and the time-consuming post-processing procedures, long-term, real-time, super-resolution observation of living cells is still out of reach for most SIM setups, which inevitably limits its routine use by cell biologists. Here, we describe square lattice SIM (SL-SIM) for long-duration live cell imaging by using the square lattice optical field as illumination, which allows continuous super-resolved observation over long periods of time. In addition, by extending the previous joint spatial-frequency reconstruction concept to SL-SIM, a high-speed reconstruction strategy is validated in the GPU environment, whose reconstruction time is even shorter than image acquisition time, thus enabling real-time observation. We have demonstrated the potential of SL-SIM on various biological applications, ranging from microtubule cytoskeleton dynamics to the interactions of mitochondrial cristae and DNAs in COS7 cells. The inherent lower light dose and user-friendly workflow of the SL-SIM could help make long-duration, real-time and super-resolved observations accessible to biological laboratories.

In this study, we explore a robust testing procedure for the high-dimensional location parameters testing problem. Initially, we introduce a spatial-sign based max-type test statistic, which exhibits excellent performance for sparse alternatives. Subsequently, we demonstrate the asymptotic independence between this max-type test statistic and the spatial-sign based sum-type test statistic (Feng and Sun, 2016). Building on this, we propose a spatial-sign based max-sum type testing procedure, which shows remarkable performance under varying signal sparsity. Our simulation studies underscore the superior performance of the procedures we propose.

In this study, we introduce three distinct testing methods for testing alpha in high dimensional linear factor pricing model that deals with dependent data. The first method is a sum-type test procedure, which exhibits high performance when dealing with dense alternatives. The second method is a max-type test procedure, which is particularly effective for sparse alternatives. For a broader range of alternatives, we suggest a Cauchy combination test procedure. This is predicated on the asymptotic independence of the sum-type and max-type test statistics. Both simulation studies and practical data application demonstrate the effectiveness of our proposed methods when handling dependent observations.

Let $\mathfrak{g}$ be a simple complex Lie algebra of classical type. A generalized Verma module induced from a one-dimensional representation of a parabolic subalgebra of $\mathfrak{g}$ is called a scalar generalized Verma module of $\mathfrak{g}$. In this article, we use Gelfand-Kirillov dimension to determine the reducibility of scalar generalized Verma modules of $\mathfrak{g}$ associated to two-step nilpotent parabolic subalgebras of non-maximal type. Such a module exists only when $\mathfrak{g}=\mathfrak{sl}(n,\mathbb{C})$ or $\mathfrak{so}(2n,\mathbb{C})$ for classical types. We find that the reducible points of these modules can be drawn in a two-dimensional complex plane., Comment: 40pages. arXiv admin note: text overlap with arXiv:2306.01231 by other authors

This paper focuses on testing for the presence of alpha in time-varying factor pricing models, specifically when the number of securities N is larger than the time dimension of the return series T. We introduce a maximum-type test that performs well in scenarios where the alternative hypothesis is sparse. We establish the limit null distribution of the proposed maximum-type test statistic and demonstrate its asymptotic independence from the sum-type test statistics proposed by Ma et al.(2020).Additionally, we propose an adaptive test by combining the maximum-type test and sum-type test, and we show its advantages under various alternative hypotheses through simulation studies and two real data applications.

A spatial-sign based test procedure is proposed for high dimensional white noise test in this paper. We establish the limit null distribution and give the asymptotical relative efficient of our test with respect to the test proposed by Feng et al. (2022) under some special alternative hypothesis. Simulation studies also demonstrate the efficiency and robustness of our test for heavy-tailed distributions.

The composition and structure of interstellar dust are important and complex for the study of the evolution of stars and the \textbf{interstellar medium} (ISM). However, there is a lack of corresponding experimental data and model theories. By theoretical calculations based on ab-initio method, we have predicted and geometry optimized the structures of Carbon-rich (C-rich) dusts, carbon ($^{12}$C), iron carbide (FeC), silicon carbide (SiC), even silicon ($^{28}$Si), iron ($^{56}$Fe), and investigated the optical absorption coefficients and emission coefficients of these materials in 0D (zero$-$dimensional), 1D, and 2D nanostructures. Comparing the \textbf{nebular spectra} of the supernovae (SN) with the coefficient of dust, we find that the optical absorption coefficient of the 2D $^{12}$C, $^{28}$Si, $^{56}$Fe, SiC and FeC structure corresponds to the absorption peak displayed in the infrared band (5$-$8) $\mu$$m$ of the spectrum at 7554 days after the SN1987A explosion. And it also corresponds to the spectrum of 535 days after the explosion of SN2018bsz, when the wavelength in the range of (0.2$-$0.8) and (3$-$10) $\mu$$m$. Nevertheless, 2D SiC and FeC corresponds to the spectrum of 844 days after the explosion of SN2010jl, when the wavelength is within (0.08$-$10) $\mu$$m$. Therefore, FeC and SiC may be the second type of dust in SN1987A corresponding to infrared band (5$-$8) $\mu$$m$ of dust and may be in the ejecta of SN2010jl and SN2018bsz.

The unwanted zero-order diffraction is still an issue in beam shaping using pixelated spatial light modulators. In this paper, we report a new approach for zero-order free beam shaping by designing an asymmetric triangle reflector and introducing a digital blazed grating and a digital lens to the phase hologram addressed onto the spatial light modulator. By adding the digital lens phase to the previously reported complex-amplitude coding algorithms, we realized the generation of complex beams without the burden of zero-order diffraction. We comparatively investigated the produced complex light fields using the modified complex-amplitude coding algorithms to validate the proposed method., Comment: 6 pages, 4 figures

The Ballast Water Management Convention can decrease the introduction risk of harmful aquatic organisms and pathogens, yet the Convention increases shipping costs and causes subsequent economic impacts. This paper examines whether the Convention generates disproportionate invasion risk reduction results and economic impacts on Small Island Developing States (SIDS) and Least Developed Countries (LDCs). Risk reduction is estimated with an invasion risk assessment model based on a higher-order network, and the effects of the regulation on national economies and trade are estimated with an integrated shipping cost and computable general equilibrium modeling framework. Then we use the Lorenz curve to examine if the regulation generates risk or economic inequality among regions. Risk reduction ratios of all regions (except Singapore) are above 99%, which proves the effectiveness of the Convention. The Gini coefficient of 0.66 shows the inequality in risk changes relative to income levels among regions, but risk reductions across all nations vary without particularly high risks for SIDS and LDCs than for large economies. Similarly, we reveal inequality in economic impacts relative to income levels (the Gini coefficient is 0.58), but there is no evidence that SIDS and LDCs are disproportionately impacted compared to more developed regions. Most changes in GDP, real exports, and real imports of studied regions are minor (smaller than 0.1%). However, there are more noteworthy changes for select sectors and trade partners including Togo, Bangladesh, and Dominican Republic, whose exports may decrease for textiles and metal and chemicals. We conclude the Convention decreases biological invasion risk and does not generate disproportionate negative impacts on SIDS and LDCs.

The Mediterranean Sea is one of the most heavily invaded marine regions. This work focuses on the dynamics and potential policy options for ballast water-mediated nonindigenous species to the Mediterranean. Specifically, we (1) estimated port risks in years 2012, 2015, and 2018, (2) identified hub ports that connect many clusters, and (3) evaluated four regulatory scenarios. The risk results show that Gibraltar, Suez, and Istanbul remained high-risk ports from 2012-2018, and they served as hub ports that connected several spread clusters. With policy scenario analysis, we found that regulating the high-risk hub ports can disproportionately reduce the overall risk to the Mediterranean: the average risk to all ports was reduced by 5-10% by regulating one high-risk hub port, while the average risk to all ports was only reduced by 0.2% by regulating one average-risk Mediterranean port. We also found that only regulating high-risk ports cannot reduce their risks effectively.