A note on maximal operators for the Schr\"{o}dinger equation on T1.\mathbb{T}^1.

Motivated by the study of the maximal operator for the Schr\"{o}dinger equation on the one-dimensional torus $\mathbb{T}^1$, it is conjectured that for any complex sequence $\{b_n\}_{n=1}^N$, $$\left\| \sup_{t\in [0,N^2]} \left|\sum_{n=1}^N b_n e \left(x\frac{n}{N} + t\frac{n^2}{N^2} \right) \right| \right\|_{L^4([0,N])} \leq C_\epsilon N^{\epsilon} N^{\frac{1}{2}} \|b_n\|_{\ell^2}$$ In this note, we show that if we replace the sequence $\{\frac{n^2}{N^2}\}_{n=1}^N$ by an arbitrary sequence $\{a_n\}_{n=1}^N$ with only some convex properties, then $$\left\| \sup_{t\in [0,N^2]} \left|\sum_{n=1}^N b_n e \left(x\frac{n}{N} + ta_n \right) \right| \right\|_{L^4([0,N])} \leq C_\epsilon N^\epsilon N^{\frac{7}{12}} \|b_n\|_{\ell^2}.$$ We further show that this bound is sharp up to a $C_\epsilon N^\epsilon$ factor.Comment: 13 page

Study on Solution-Processable Polypyrrole-Based Conducting Polymers

Due to the adjustable conductivity, cost-effective synthesis, and easy device fabrication, conducting polymers have wide-ranging applications in numerous areas, including sensors, solar cells, supercapacitors, and electrodes. Among conducting polymers, polypyrrole (PPy) has attracted lots of attention because of its high conductivity, biocompatibility, and mass producibility. However, PPy is insoluble in most solvents, which lowers its processability and limits its application. In the past few decades, many works by researchers around the world have been done to improve the solubility of PPy. Unfortunately, the two major strategies, including doping with large contour ions and introducing an alkyl sidechain to the PPy backbone, were found to significantly decrease the conductivity of PPy by several orders of magnitude. For the doping method, the restricted dopant options limit the conductivity of PPy, whereas the alkyl sidechains twist the polymer structure thus influencing the conductivity. As a result, new methods need to be explored to improve the solubility of PPy without sacrificing its electrical properties. In this work, two strategies were applied to address this problem. The first is to introduce an alkyl carbamate sidechain to the PPy backbone; the carbamate sidechain can solubilize the polymer, while allowing thermal removal at mild temperatures. Thus, after solution processing, the obtained polymer film can be thermally annealed to remove the sidechain, thereby recovering the PPy structure and conductivity. The second one is to introduce an alkoxy sidechain at the N position of the PPy backbone. This sidechain has less steric hindrance than the alkyl sidechain. Therefore, the PPy with the alkoxy sidechain was expected to have a more planar backbone compared to the alkyl chain-substituted counterpart and as such was expected to have higher conductivity. We first designed, synthesized, and characterized poly(2-ethylhexyl 1H-pyrrole-1-carboxylate) (PEPC), with a 2-ethylhexyl carbamate chain substituted at the N position of PPy. Different synthetic routes were explored and optimized, including organometallic polymerization and oxidative polymerization. The desired polymer was successfully synthesized and was soluble in various organic solvents, including acetone, dichloromethane, and chloroform. Polymer films in a thickness of 50-60 nm could be deposited from the PEPC chloroform solution on a SiO2/Si substrate, which satisfies requirements for sensor applications. 1 However, the 2-ethylhexyl carbamate sidechain could not be completely removed by thermal annealing and acid cleavage due to the primary structure of ethylhexyl aliphatic chain of the carbamate being reluctant to undergo decomposition. This led to a low conductivity of the PEPC thin films. In the future, a carbamate sidechain with a different secondary or tertiary structure may be applied, allowing easy removal of the sidechain and restoration of the PPy structure. Poly[1-((2-ethylhexyl)oxy)-1H-pyrrole] (PEOP) with a 2-(ethylhexyl)oxy sidechain at the N position of PPy was designed, and its synthesis was explored. Due to the difficulties in the synthesizing and purifying the monomer, 1-((2-ethylhexyl)oxy)-1H-pyrrole, the desired PEOP was not obtained. However, it was found that the 2-(ethylhexyl)oxy sidechain can undergo a thermolysis process under milder temperatures than the alkyl carbamate sidechain, as evidenced by FTIR and TGA results. Therefore, the thermal instability of 2-(ethylhexyl)oxy and other alkoxy sidechains on nitrogen may allow the development of other polymers that require the sidechains to be thermally removable at mild temperatures. In addition, new synthetic approaches can be explored in the future to obtain a more structurally defined PEOP

iMetricGAN: Intelligibility Enhancement for Speech-in-Noise using Generative Adversarial Network-based Metric Learning

The intelligibility of natural speech is seriously degraded when exposed to adverse noisy environments. In this work, we propose a deep learning-based speech modification method to compensate for the intelligibility loss, with the constraint that the root mean square (RMS) level and duration of the speech signal are maintained before and after modifications. Specifically, we utilize an iMetricGAN approach to optimize the speech intelligibility metrics with generative adversarial networks (GANs). Experimental results show that the proposed iMetricGAN outperforms conventional state-of-the-art algorithms in terms of objective measures, i.e., speech intelligibility in bits (SIIB) and extended short-time objective intelligibility (ESTOI), under a Cafeteria noise condition. In addition, formal listening tests reveal significant intelligibility gains when both noise and reverberation exist.Comment: 5 pages, Submitted to INTERSPEECH 202

YOLOv8-Peas: a lightweight drought tolerance method for peas based on seed germination vigor

IntroductionDrought stress has become an important factor affecting global food production. Screening and breeding new varieties of peas (Pisum sativum L.) for drought-tolerant is of critical importance to ensure sustainable agricultural production and global food security. Germination rate and germination index are important indicators of seed germination vigor, and the level of germination vigor of pea seeds directly affects their yield and quality. The traditional manual germination detection can hardly meet the demand of full-time sequence nondestructive detection. We propose YOLOv8-Peas, an improved YOLOv8-n based method for the detection of pea germination vigor.MethodsWe constructed a pea germination dataset and used multiple data augmentation methods to improve the robustness of the model in real-world scenarios. By introducing the C2f-Ghost structure and depth-separable convolution, the model computational complexity is reduced and the model size is compressed. In addition, the original detector head is replaced by the self-designed PDetect detector head, which significantly improves the computational efficiency of the model. The Coordinate Attention (CA) mechanism is added to the backbone network to enhance the model's ability to localize and extract features from critical regions. The neck used a lightweight Content-Aware ReAssembly of FEatures (CARAFE) upsampling operator to capture and retain detailed features at low levels. The Adam optimizer is used to improve the model's learning ability in complex parameter spaces, thus improving the model's detection performance.ResultsThe experimental results showed that the Params, FLOPs, and Weight Size of YOLOv8-Peas were 1.17M, 3.2G, and 2.7MB, respectively, which decreased by 61.2%, 61%, and 56.5% compared with the original YOLOv8-n. The mAP of YOLOv8-Peas was on par with that of YOLOv8-n, reaching 98.7%, and achieved a detection speed of 116.2FPS. We used PEG6000 to simulate different drought environments and YOLOv8-Peas to analyze and quantify the germination vigor of different genotypes of peas, and screened for the best drought-resistant pea varieties.DiscussionOur model effectively reduces deployment costs, improves detection efficiency, and provides a scientific theoretical basis for drought-resistant genotype screening in pea