On Explicit Probability Densities Associated with Fuss-Catalan Numbers

In this note we give explicitly a family of probability densities, the moments of which are Fuss-Catalan numbers. The densities appear naturally in random matrices, free probability and other contexts.Comment: 4 page

Improvement of peptide identification with considering the abundance of mRNA and peptide

Scripts used for data analysis in this study. (DOCX 35 kb

Cramer-Rao Bounds for Near-Field Sensing: A Generic Modular Architecture

A generic modular array architecture is proposed, featuring uniform/non-uniform subarray layouts that allows for flexible deployment. The bistatic near-field sensing system is considered, where the target is located in the near-field of the whole modular array and the far-field of each subarray. Then, the closed-form expressions of Cramer-Rao bounds (CRBs) for range and angle estimations are derived based on the hybrid spherical and planar wave model (HSPM). Simulation results validate the accuracy of the derived closed-form CRBs and demonstrate that: i) The HSPM with varying angles of arrival (AoAs) between subarrays can reduce the CRB for range estimation compared to the traditional HSPM with shared AoA; and ii) The proposed generic modular architecture with subarrays positioned closer to the edges can significantly reduce the CRBs compared to the traditional modular architecture with uniform subarray layout, when the array aperture is fixed

Characterization of pore systems in fine-grained carbonate rocks using digital core technology

The characterization of pore systems in fine-grained carbonate rocks faces numerous challenges due to the significant complexity of microscopic features, including a variation of micro- and nanoscale pore sizes and the complex pore-throat distribution. In this work, digital core technology was adopted to characterize the pore systems of lacustrine fine-grained carbonate rocks in the Yingxi area of Qaidam Basin. The simulated results indicated that the pore types predominantly contain intercrystalline and dissolution pores. The former exhibit high porosity but extremely low permeability and are primarily developed in bedded dolostones. Conversely, the latter show relatively higher permeability, predominantly developed in bedded calcareous dolostones. The elevated dolomite content provides the material basis for the development of intercrystalline pores, while the extremely small throat radius constrains the fluidity of this pore system. In addition, the dissolution has a great impact on improving the permeable capability of intercrystalline pore system via increasing the radius and specific surface area of pores and throats.Document Type: Research highlightCited as: Hu, C., Zhao, Z., Gao, S., Liu, C., Wu, K., Pang, P. Characterization of pore systems in fine-grained carbonate rocks using digital core technology. Advances in Geo-Energy Research, 2024, 12(1): 77-80. https://doi.org/10.46690/ager.2024.04.0

MDCR: A Dataset for Multi-Document Conditional Reasoning

The same real-life questions posed to different individuals may lead to different answers based on their unique situations. For instance, whether a student is eligible for a scholarship depends on eligibility conditions, such as major or degree required. ConditionalQA was proposed to evaluate models' capability of reading a document and answering eligibility questions, considering unmentioned conditions. However, it is limited to questions on single documents, neglecting harder cases that may require cross-document reasoning and optimization, for example, "What is the maximum number of scholarships attainable?" Such questions over multiple documents are not only more challenging due to more context having to understand, but also because the model has to (1) explore all possible combinations of unmentioned conditions and (2) understand the relationship between conditions across documents, to reason about the optimal outcome. To evaluate models' capability of answering such questions, we propose a new dataset MDCR, which can reflect real-world challenges and serve as a new test bed for complex conditional reasoning that requires optimization. We evaluate this dataset using the most recent LLMs and demonstrate their limitations in solving this task. We believe this dataset will facilitate future research in answering optimization questions with unknown conditions

metaX: a flexible and comprehensive software for processing metabolomics data

BACKGROUND: Non-targeted metabolomics based on mass spectrometry enables high-throughput profiling of the metabolites in a biological sample. The large amount of data generated from mass spectrometry requires intensive computational processing for annotation of mass spectra and identification of metabolites. Computational analysis tools that are fully integrated with multiple functions and are easily operated by users who lack extensive knowledge in programing are needed in this research field. RESULTS: We herein developed an R package, metaX, that is capable of end-to-end metabolomics data analysis through a set of interchangeable modules. Specifically, metaX provides several functions, such as peak picking and annotation, data quality assessment, missing value imputation, data normalization, univariate and multivariate statistics, power analysis and sample size estimation, receiver operating characteristic analysis, biomarker selection, pathway annotation, correlation network analysis, and metabolite identification. In addition, metaX offers a web-based interface (http://metax.genomics.cn) for data quality assessment and normalization method evaluation, and it generates an HTML-based report with a visualized interface. The metaX utilities were demonstrated with a published metabolomics dataset on a large scale. The software is available for operation as either a web-based graphical user interface (GUI) or in the form of command line functions. The package and the example reports are available at http://metax.genomics.cn/. CONCLUSIONS: The pipeline of metaX is platform-independent and is easy to use for analysis of metabolomics data generated from mass spectrometry. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12859-017-1579-y) contains supplementary material, which is available to authorized users

From Summary to Action: Enhancing Large Language Models for Complex Tasks with Open World APIs

The distinction between humans and animals lies in the unique ability of humans to use and create tools. Tools empower humans to overcome physiological limitations, fostering the creation of magnificent civilizations. Similarly, enabling foundational models like Large Language Models (LLMs) with the capacity to learn external tool usage may serve as a pivotal step toward realizing artificial general intelligence. Previous studies in this field have predominantly pursued two distinct approaches to augment the tool invocation capabilities of LLMs. The first approach emphasizes the construction of relevant datasets for model fine-tuning. The second approach, in contrast, aims to fully exploit the inherent reasoning abilities of LLMs through in-context learning strategies. In this work, we introduce a novel tool invocation pipeline designed to control massive real-world APIs. This pipeline mirrors the human task-solving process, addressing complicated real-life user queries. At each step, we guide LLMs to summarize the achieved results and determine the next course of action. We term this pipeline `from Summary to action', Sum2Act for short. Empirical evaluations of our Sum2Act pipeline on the ToolBench benchmark show significant performance improvements, outperforming established methods like ReAct and DFSDT. This highlights Sum2Act's effectiveness in enhancing LLMs for complex real-world tasks