Lattice light-sheet microscopy (LLSM) is promising in long-term biological volumetric imaging due to its high spatiotemporal resolution and low phototoxicity. However, three-dimensional (3D) isotropic spatial resolution remains an unmet goal in LLSM because of its poorer axial resolution. Combing LLSM with fluorescence differential detection, namely LLSDM, has been proposed to improve the axial resolution of LLSM in simulation. It demonstrates the possibility of further enhancing the axial resolution in 3D volumetric imaging with LLSM by specifically discarding the off-focus photons captured using a complementary optical lattice (OL) profile generated with additional 0-π phase modulation at the objective pupil plane. The direct generation of the complementary lattice profile using the binary phase modulator conjugated to the sample plane for amplitude modulation, as used in LLSM, is also permittable. Nevertheless, the previously proposed configuration fails to provide a symmetric complementary lattice pattern along the axial axis, thus leading to the imbalanced off-focus photon suppression in the reconstructed images after subtraction [Opt. Lett. 45, 2854 (2020)10.1364/OL.393378]. Here, we modified the LLSDM theory which can produce an ideal complementary lattice pattern with central zero intensity and symmetrically distributed sidelobes. We also analyzed the impact of numerical aperture matching between the original and complementary lattice patterns and presented the consistency between the simulated and experimental results. As demonstrated by imaging the distribution of fluorescent beads and microtubules in fixed U2OS cells, as well as the dynamics of filopodia in live U2OS cells, LLSDM provides about 1.5 times improvement in axial resolution, and higher imaging contrast compared with traditional LLSM.

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We use Machine Learning (ML) to study firms’ joint pricing and ordering decisions for perishables in a dynamic loop. The research assumption is as follows: at the beginning of each period, the retailer prices both the new and old products and determines how many new products to order, while at the end of each period, the retailer decides how much remaining inventory should be carried over to the next period. The objective is to determine a joint pricing, ordering, and disposal strategy to maximize the total expected discounted profit. We establish a decision model based on Markov processes and use the Q-learning algorithm to obtain a near-optimal policy. From numerical analysis, we find that (i) the optimal number of old products carried over to the next period depends on the upper quantitative bound for old inventory; (ii) the optimal prices for new products are positively related to potential demand but negatively related to the decay rate, while the optimal prices for old products have a positive relationship with both; and (iii) ordering decisions are unrelated to the quantity of old products. When the decay rate is low or the variable ordering cost is high, the optimal orders exhibit a trapezoidal decline as the quantity of new products increases.

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