Conditional Testing based on Localized Conformal p-values

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.

Instant square lattice structured illumination microscopy: an optimal strategy towards photon-saving and real-time super-resolution observation

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.

An Automatic Design Framework of Swarm Pattern Formation based on Multi-objective Genetic Programming

Most existing swarm pattern formation methods depend on a predefined gene regulatory network (GRN) structure that requires designers' priori knowledge, which is difficult to adapt to complex and changeable environments. To dynamically adapt to the complex and changeable environments, we propose an automatic design framework of swarm pattern formation based on multi-objective genetic programming. The proposed framework does not need to define the structure of the GRN-based model in advance, and it applies some basic network motifs to automatically structure the GRN-based model. In addition, a multi-objective genetic programming (MOGP) combines with NSGA-II, namely MOGP-NSGA-II, to balance the complexity and accuracy of the GRN-based model. In evolutionary process, an MOGP-NSGA-II and differential evolution (DE) are applied to optimize the structures and parameters of the GRN-based model in parallel. Simulation results demonstrate that the proposed framework can effectively evolve some novel GRN-based models, and these GRN-based models not only have a simpler structure and a better performance, but also are robust to the complex and changeable environments.

Push and Pull Search Embedded in an M2M Framework for Solving Constrained Multi-objective Optimization Problems

In dealing with constrained multi-objective optimization problems (CMOPs), a key issue of multi-objective evolutionary algorithms (MOEAs) is to balance the convergence and diversity of working populations.

Embedding Push and Pull Search in the Framework of Differential Evolution for Solving Constrained Single-objective Optimization Problems

This paper proposes a push and pull search method in the framework of differential evolution (PPS-DE) to solve constrained single-objective optimization problems (CSOPs). More specifically, two sub-populations, including the top and bottom sub-populations, are collaborated with each other to search global optimal solutions efficiently. The top sub-population adopts the pull and pull search (PPS) mechanism to deal with constraints, while the bottom sub-population use the superiority of feasible solutions (SF) technique to deal with constraints. In the top sub-population, the search process is divided into two different stages --- push and pull stages.An adaptive DE variant with three trial vector generation strategies is employed in the proposed PPS-DE. In the top sub-population, all the three trial vector generation strategies are used to generate offsprings, just like in CoDE. In the bottom sub-population, a strategy adaptation, in which the trial vector generation strategies are periodically self-adapted by learning from their experiences in generating promising solutions in the top sub-population, is used to choose a suitable trial vector generation strategy to generate one offspring. Furthermore, a parameter adaptation strategy from LSHADE44 is employed in both sup-populations to generate scale factor $F$ and crossover rate $CR$ for each trial vector generation strategy. Twenty-eight CSOPs with 10-, 30-, and 50-dimensional decision variables provided in the CEC2018 competition on real parameter single objective optimization are optimized by the proposed PPS-DE. The experimental results demonstrate that the proposed PPS-DE has the best performance compared with the other seven state-of-the-art algorithms, including AGA-PPS, LSHADE44, LSHADE44+IDE, UDE, IUDE, $\epsilon$MAg-ES and C$^2$oDE.