Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling

We study the mixing time of the Metropolis-adjusted Langevin algorithm (MALA) for sampling from a log-smooth and strongly log-concave distribution. We establish its optimal minimax mixing time under a warm start. Our main contribution is two-fold. First, for a $d$-dimensional log-concave density with condition number $\kappa$, we show that MALA with a warm start mixes in $\tilde O(\kappa \sqrt{d})$ iterations up to logarithmic factors. This improves upon the previous work on the dependency of either the condition number $\kappa$ or the dimension $d$. Our proof relies on comparing the leapfrog integrator with the continuous Hamiltonian dynamics, where we establish a new concentration bound for the acceptance rate. Second, we prove a spectral gap based mixing time lower bound for reversible MCMC algorithms on general state spaces. We apply this lower bound result to construct a hard distribution for which MALA requires at least $\tilde \Omega (\kappa \sqrt{d})$ steps to mix. The lower bound for MALA matches our upper bound in terms of condition number and dimension. Finally, numerical experiments are included to validate our theoretical results.Comment: 63 pages, 2 figure

Insulin-Mimetic Action of Rhoifolin and Cosmosiin Isolated from Citrus grandis (L.) Osbeck Leaves: Enhanced Adiponectin Secretion and Insulin Receptor Phosphorylation in 3T3-L1 Cells

Citrus grandis (L.) Osbeck (red wendun) leaves have been used in traditional Chinese medicine to treat several illnesses including diabetes. However, there is no scientific evidence supporting these actions and its active compounds. Two flavone glycosides, rhoifolin and cosmosiin were isolated for the first time from red wendun leaves and, identified these leaves are rich source for rhoifolin (1.1%, w/w). In differentiated 3T3-L1 adipocytes, rhoifolin and cosmosiin showed dose-dependent response in concentration range of o.oo1–5 μM and 1–20 μM, respectively, in biological studies beneficial to diabetes. Particularly, rhoifolin and cosmosiin at 0.5 and 20 μM, respectively showed nearly similar response to that 10 nM of insulin, on adiponectin secretion level. Furthermore, 5 μM of rhoifolin and 20 μM of cosmosiin showed equal potential with 10 nM of insulin to increase the phosphorylation of insulin receptor-β, in addition to their positive effect on GLUT4 translocation. These findings indicate that rhoifolin and cosmosiin from red wendun leaves may be beneficial for diabetic complications through their enhanced adiponectin secretion, tyrosine phosphorylation of insulin receptor-β and GLUT4 translocation

Fourier Ptychographic Microscopy 10 Years on: A Review

Fourier ptychographic microscopy (FPM) emerged as a prominent imaging technique in 2013, attracting significant interest due to its remarkable features such as precise phase retrieval, expansive field of view (FOV), and superior resolution. Over the past decade, FPM has become an essential tool in microscopy, with applications in metrology, scientific research, biomedicine, and inspection. This achievement arises from its ability to effectively address the persistent challenge of achieving a trade-off between FOV and resolution in imaging systems. It has a wide range of applications, including label-free imaging, drug screening, and digital pathology. In this comprehensive review, we present a concise overview of the fundamental principles of FPM and compare it with similar imaging techniques. In addition, we present a study on achieving colorization of restored photographs and enhancing the speed of FPM. Subsequently, we showcase several FPM applications utilizing the previously described technologies, with a specific focus on digital pathology, drug screening, and three-dimensional imaging. We thoroughly examine the benefits and challenges associated with integrating deep learning and FPM. To summarize, we express our own viewpoints on the technological progress of FPM and explore prospective avenues for its future developments

Identifying Ways to Narrow Maize Yield Gaps Based on Plant Density Experiments

Exploring the maximum grain yields (GYs) and GY gaps in maize (Zea mays L.) can be beneficial for farmer to identify the GY-limiting factors and take adaptive management practices for a higher GY. The objective of this work was to identify the optimum maize plant density range and the ways to narrow maize GY gaps based on the variation of the GYs, dry matter (DM) accumulation and remobilization with changes in plant density. Field experiments were performed at the 71 Group and Qitai Farm in Xinjiang, China. Two modern cultivars, ZhengDan958 and ZhongDan909, were planted at 12 densities, ranging from 1.5 to 18 plants m−2. With increased plant density, single plant DM decreased exponentially, whereas population-level DM at the pre- (DMBS) and post- (DMAS) silking stages increased, and the amount of DM remobilization (ARDM) increased exponentially. Further analysis showed that plants were divided four density ranges: range I (<6.97 plants m−2), in which no DM remobilization occurred, DMBS and DMAS correlated significantly with GY; range II (6.97–9.54 plants m−2), in which the correlations of DMBS, DMAS, and ARDM with GY were significant; range III (9.54–10.67 plants m−2), in which GY and DMAS were not affected by density, DMBS increased significantly, and only the correlation of DMAS with GY was significant; and range IV (>10.67 plants m−2), in which the correlations of DMBS and ARDM with GY decreased significantly, while that of DMAS increased significantly. Therefore, ranges I and II were considered to be DM-dependent ranges, and a higher GY could be obtained by increasing the population-level DMAS, DMAS, and ARDM. Range III was considered the GY-stable range, increasing population-level DMBS, as well as preventing the loss of harvest index were the best way to enhance maize production. Range IV was interpreted as the GY-loss range, and a higher GY could be obtained by preventing the loss of HI and population-level DMAS