Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales

The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strong convergent. A type of generalized martingales associated with $M$ are introduced and their convergence theorems are established. Some applications are also shown.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1504.0500

MOGAN: Morphologic-structure-aware Generative Learning from a Single Image

In most interactive image generation tasks, given regions of interest (ROI) by users, the generated results are expected to have adequate diversities in appearance while maintaining correct and reasonable structures in original images. Such tasks become more challenging if only limited data is available. Recently proposed generative models complete training based on only one image. They pay much attention to the monolithic feature of the sample while ignoring the actual semantic information of different objects inside the sample. As a result, for ROI-based generation tasks, they may produce inappropriate samples with excessive randomicity and without maintaining the related objects' correct structures. To address this issue, this work introduces a MOrphologic-structure-aware Generative Adversarial Network named MOGAN that produces random samples with diverse appearances and reliable structures based on only one image. For training for ROI, we propose to utilize the data coming from the original image being augmented and bring in a novel module to transform such augmented data into knowledge containing both structures and appearances, thus enhancing the model's comprehension of the sample. To learn the rest areas other than ROI, we employ binary masks to ensure the generation isolated from ROI. Finally, we set parallel and hierarchical branches of the mentioned learning process. Compared with other single image GAN schemes, our approach focuses on internal features including the maintenance of rational structures and variation on appearance. Experiments confirm a better capacity of our model on ROI-based image generation tasks than its competitive peers

FinSQL: Model-Agnostic LLMs-based Text-to-SQL Framework for Financial Analysis

Text-to-SQL, which provides zero-code interface for operating relational databases, has gained much attention in financial analysis; because, financial professionals may not well-skilled in SQL programming. However, until now, there is no practical Text-to-SQL benchmark dataset for financial analysis, and existing Text-to-SQL methods have not considered the unique characteristics of databases in financial applications, such as commonly existing wide tables. To address these issues, we collect a practical Text-to-SQL benchmark dataset and propose a model-agnostic Large Language Model (LLMs)-based Text-to-SQL framework for financial analysis. The benchmark dataset, BULL, is collected from the practical financial analysis business of Hundsun Technologies Inc., including databases for fund, stock, and macro economy. Besides, the proposed LLMs-based Text-to-SQL framework, FinSQL, provides a systematic treatment for financial Text-to-SQL from the perspectives of prompt construction, parameter-efficient fine-tuning and output calibration. Extensive experimental results on BULL demonstrate that FinSQL achieves the state-of-the-art Text-to-SQL performance at a small cost; furthermore, FinSQL can bring up to 36.64% performance improvement in scenarios requiring few-shot cross-database model transfer.Comment: 13 pages, 13 figure

C3: Zero-shot Text-to-SQL with ChatGPT

This paper proposes a ChatGPT-based zero-shot Text-to-SQL method, dubbed C3, which achieves 82.3\% in terms of execution accuracy on the holdout test set of Spider and becomes the state-of-the-art zero-shot Text-to-SQL method on the Spider Challenge. C3 consists of three key components: Clear Prompting (CP), Calibration with Hints (CH), and Consistent Output (CO), which are corresponding to the model input, model bias and model output respectively. It provides a systematic treatment for zero-shot Text-to-SQL. Extensive experiments have been conducted to verify the effectiveness and efficiency of our proposed method

Solventless autothermic production of energy-intensive furanic biofuels expedited by photothermal effect

Driving C-C coupling reactions to produce biofuels is usually energy-consuming and requires well-tailored catalysts. Herein, a novel photothermal catalytic strategy was developed to be highly efficient for cascade hydroxyalkylation-alkylation (HAA) of various biomass-derived aldehydes/ketones with 2-methylfuran or acetalization of different bioalcohols with furfural to exclusively afford furanic biofuel molecules (up to 94.8 % yield). The developed bio-based SO3H-functionalized graphene-like catalyst (GLB-SO3H-700) could complete the HAA and acetalization reactions in 10 min under solvent-free and room-temperature conditions. Infrared thermal imaging revealed that the local photothermal effect of interfacial solar heating could in-situ remove water co-product, thereby improving the reaction selectivity and rate as evidenced by kinetic study. Moreover, the GLB-SO3H-700 catalyst exhibited good stability and recyclability. The developed SO3H-functionalized graphene-like photothermal materials hold great potential for catalytic upgrading of biomass into high-quality biofuels under mild conditions.Peer reviewe

The biophysical climate mitigation potential of boreal peatlands during the growing season

Peatlands and forests cover large areas of the boreal biome and are critical for global climate regulation. They also regulate regional climate through heat and water vapour exchange with the atmosphere. Understanding how land-atmosphere interactions in peatlands differ from forests may therefore be crucial for modelling boreal climate system dynamics and for assessing climate benefits of peatland conservation and restoration. To assess the biophysical impacts of peatlands and forests on peak growing season air temperature and humidity, we analysed surface energy fluxes and albedo from 35 peatlands and 37 evergreen needleleaf forests-the dominant boreal forest type-and simulated air temperature and vapour pressure deficit (VPD) over hypothetical homogeneous peatland and forest landscapes. We ran an evapotranspiration model using land surface parameters derived from energy flux observations and coupled an analytical solution for the surface energy balance to an atmospheric boundary layer (ABL) model. We found that peatlands, compared to forests, are characterized by higher growing season albedo, lower aerodynamic conductance, and higher surface conductance for an equivalent VPD. This combination of peatland surface properties results in a similar to 20% decrease in afternoon ABL height, a cooling (from 1.7 to 2.5 degrees C) in afternoon air temperatures, and a decrease in afternoon VPD (from 0.4 to 0.7 kPa) for peatland landscapes compared to forest landscapes. These biophysical climate impacts of peatlands are most pronounced at lower latitudes (similar to 45 degrees N) and decrease toward the northern limit of the boreal biome (similar to 70 degrees N). Thus, boreal peatlands have the potential to mitigate the effect of regional climate warming during the growing season. The biophysical climate mitigation potential of peatlands needs to be accounted for when projecting the future climate of the boreal biome, when assessing the climate benefits of conserving pristine boreal peatlands, and when restoring peatlands that have experienced peatland drainage and mining.Peer reviewe

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data