Theory of fractional hybrid differential equations

AbstractIn this paper, we develop the theory of fractional hybrid differential equations involving Riemann–Liouville differential operators of order 0<q<1. An existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathéodory conditions. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions

Molecular and genetic effect of coding variants in human

Predicting the effect of missense variants is critically important in population and medical genetics. It is essential to interpret genetic variation in population screening and clinical diagnostic sequencing, to reach optimal statistical power of risk gene discovery in genetic studies of diseases and traits. A quantitative analysis of the fitness effect of all possible missense variants can provide a foundation for understanding how proteins evolve in humans and other species. In this thesis, I describe new methods to infer the effect of missense variants using various machine learning techniques. First, I worked on a ResNet-based supervised model to predict pathogenicity trained on curated databases. The curated clinical databases have uneven quality and uncertain bias across genes. To address this issue, I developed a new method, MisFit, to separately model the molecular effect and population fitness effect of missense variants, and to estimate them jointly using a probabilistic graphical model. The architecture of MisFit follows the biological causality of the variant effect, that is, for a missense variant, the protein sequence and structure context determine its molecular effect, which in turn determines its fitness effect given how the protein is involved in various conditions and traits. The latter is a latent factor encapsulated in a sigmoid-shaped function with gene-specific parameters. The fitness effect determines the expected allele counts in human populations. This model can be trained using large-scale population genome data without known pathogenicity labels. I investigated how informative allele counts are for inferring fitness effect using simulations with realistic demographic parameters. To take advantage of the latest deep learning techniques and large population genome data sets, I use a Poisson-Inverse-Gaussian distribution, which is differentiable, to approximate the probability of allele counts given fitness effect and sample size. We show that MisFit estimated heterozygous selection coefficient of missense variants is consistent with ratio of de novo mutations among observed variants in a population with child-parents trio data. Furthermore, de novo missense variants with selection coefficient >0.01 are significantly enriched in neurodevelopmental disorders cases, achieving the best performance in prioritization of de novos for new risk gene discovery compared to previous methods. We also show that the estimated molecular effect reached the state-of-the-art performance in the classification of damaging variants in deep mutational scanning assays, with improved consistency of the score scale across genes. Finally, I analyzed the transmission disequilibrium of inherited variants in autism using a new empirical Bayesian method to identify risk genes, which models relative risk as a continuous function of variant effect in each gene

Boosting Graph Foundation Model from Structural Perspective

Graph foundation models have recently attracted significant attention due to its strong generalizability. Although existing methods resort to language models to learn unified semantic representations across domains, they disregard the unique structural characteristics of graphs from different domains. To address the problem, in this paper, we boost graph foundation model from structural perspective and propose BooG. The model constructs virtual super nodes to unify structural characteristics of graph data from different domains. Specifically, the super nodes fuse the information of anchor nodes and class labels, where each anchor node captures the information of a node or a graph instance to be classified. Instead of using the raw graph structure, we connect super nodes to all nodes within their neighborhood by virtual edges. This new structure allows for effective information aggregation while unifying cross-domain structural characteristics. Additionally, we propose a novel pre-training objective based on contrastive learning, which learns more expressive representations for graph data and generalizes effectively to different domains and downstream tasks. Experimental results on various datasets and tasks demonstrate the superior performance of BooG. We provide our code and data here: https://anonymous.4open.science/r/BooG-EE42/

Center-to-face momentum interpolation and face-to-center flux reconstruction in Euler-Euler simulation of gas-solid flows

In order to resolve the pressure checkerboard field problem with collocated grid, it is essential to employ the momentum interpolation method when formulating the pressure equation, and the flux reconstruction method when updating the cell-centered velocity fields. In this study, we first derive a momentum interpolation method for Euler-Euler simulation of gas-solid flows, which is independent of the time step, the transient term discretization scheme, the under-relaxation factor and the shape of grid; a complete first-order flux reconstruction method is then proposed to update the cell-centered velocities. Their effectiveness are proved by simulating the hydrodynamics of solids settlement, gas-solid fixed bed, bubbling fluidized bed and circulating fluidized bed riser, and then comparing the simulation results to the theoretically known solutions. Their superiority over the standard solver of OpenFOAM in suppressing the high-frequency oscillations and enhancing the smoothness and accuracy is also proved. Finally, the difficulty in fully eliminating the high-frequency oscillations is attributed to the insufficiency of current methods in handling the situations where the independent variables undergo abrupt change

Think-then-Act: A Dual-Angle Evaluated Retrieval-Augmented Generation

Despite their impressive capabilities, large language models (LLMs) often face challenges such as temporal misalignment and generating hallucinatory content. Enhancing LLMs with retrieval mechanisms to fetch relevant information from external sources offers a promising solution. Inspired by the proverb "Think twice before you act," we propose a dual-angle evaluated retrieval-augmented generation framework \textit{Think-then-Act}. Unlike previous approaches that indiscriminately rewrite queries or perform retrieval regardless of necessity, or generate temporary responses before deciding on additional retrieval, which increases model generation costs, our framework employs a two-phase process: (i) assessing the input query for clarity and completeness to determine if rewriting is necessary; and (ii) evaluating the model's capability to answer the query and deciding if additional retrieval is needed. Experimental results on five datasets show that the \textit{Think-then-Act} framework significantly improves performance. Our framework demonstrates notable improvements in accuracy and efficiency compared to existing baselines and performs well in both English and non-English contexts. Ablation studies validate the optimal model confidence threshold, highlighting the resource optimization benefits of our approach.Comment: 12 pages, 8 figure

Sustainable growth unveiled: exploring the nexus of green finance and high-quality economic development in China

Amidst global sustainability challenges, green finance emerges as a crucial instrument for advancing sustainable development, garnering increasing attention for its pivotal role in fostering high-quality economic development (HQED), particularly within the dynamic economic landscape of China. This study delves into the nexus between green finance and HQED across 30 Chinese provinces from 2012 to 2021. Employing the entropy method, indices for green finance and HQED index system are calculated, and their interaction is analyzed through a panel data model, incorporating tests for moderating effects of FinTech and green technological innovation, as well as assessing the heterogeneity across diverse regions. The findings highlight green finance’s significant role in enhancing HQED, with notable regional disparities. Specifically, the eastern region shows the strongest impact, followed by the central region, while the western and northeastern regions exhibit weaker influences. The study also identifies FinTech and green technological innovation as pivotal moderators, amplifying green finance’s positive effect on HQED. These insights underscore green finance’s importance in driving sustainable economic growth and highlight the necessity for region-specific strategies to optimize its impact. Policy recommendations based on these findings include prioritizing the development of green finance, formulating region-specific strategies, and leveraging the catalytic roles of FinTech and green technological innovation to enhance the efficacy of green finance in achieving HQED

Defending Large Language Models Against Jailbreak Attacks via Layer-specific Editing

Large language models (LLMs) are increasingly being adopted in a wide range of real-world applications. Despite their impressive performance, recent studies have shown that LLMs are vulnerable to deliberately crafted adversarial prompts even when aligned via Reinforcement Learning from Human Feedback or supervised fine-tuning. While existing defense methods focus on either detecting harmful prompts or reducing the likelihood of harmful responses through various means, defending LLMs against jailbreak attacks based on the inner mechanisms of LLMs remains largely unexplored. In this work, we investigate how LLMs response to harmful prompts and propose a novel defense method termed \textbf{L}ayer-specific \textbf{Ed}iting (LED) to enhance the resilience of LLMs against jailbreak attacks. Through LED, we reveal that several critical \textit{safety layers} exist among the early layers of LLMs. We then show that realigning these safety layers (and some selected additional layers) with the decoded safe response from selected target layers can significantly improve the alignment of LLMs against jailbreak attacks. Extensive experiments across various LLMs (e.g., Llama2, Mistral) show the effectiveness of LED, which effectively defends against jailbreak attacks while maintaining performance on benign prompts. Our code is available at \url{https://github.com/ledllm/ledllm}

Self-supervised Heterogeneous Graph Variational Autoencoders

Heterogeneous Information Networks (HINs), which consist of various types of nodes and edges, have recently demonstrated excellent performance in graph mining. However, most existing heterogeneous graph neural networks (HGNNs) ignore the problems of missing attributes, inaccurate attributes and scarce labels for nodes, which limits their expressiveness. In this paper, we propose a generative self-supervised model SHAVA to address these issues simultaneously. Specifically, SHAVA first initializes all the nodes in the graph with a low-dimensional representation matrix. After that, based on the variational graph autoencoder framework, SHAVA learns both node-level and attribute-level embeddings in the encoder, which can provide fine-grained semantic information to construct node attributes. In the decoder, SHAVA reconstructs both links and attributes. Instead of directly reconstructing raw features for attributed nodes, SHAVA generates the initial low-dimensional representation matrix for all the nodes, based on which raw features of attributed nodes are further reconstructed to leverage accurate attributes. In this way, SHAVA can not only complete informative features for non-attributed nodes, but rectify inaccurate ones for attributed nodes. Finally, we conduct extensive experiments to show the superiority of SHAVA in tackling HINs with missing and inaccurate attributes

A critical comparison of the implementation of granular pressure gradient term in Euler-Euler simulation of gas-solid flows

Numerical solution of Euler-Euler model using different in-house, open source and commercial software can generate significantly different results, even when the governing equations and the initial and boundary conditions are exactly same. Unfortunately, the underlying reasons have not been identified yet. In this article, three methods for calculating the granular pressure gradient term are presented for two-fluid model of gas-solid flows and implemented implicitly or explicitly into the solver in OpenFOAM: Method I assumes that the granular pressure gradient is equal to the elastic modulus plus the solid concentration gradient; Method II directly calculates the gradient using a difference scheme; Method III, which is proposed in this work, calculates the gradient as the sum of two partial derivatives: one related to the solid volume fraction and the other related to the granular energy. Obviously, only Methods II and III are consistent with kinetic theory of granular flow. It was found that the difference between all methods is small for bubbling fluidization. While for circulating fluidization, both methods II and III are capable of capturing non-uniform structures and producing superior results over Method I. The contradictory conclusions made from the simulation of different fluidization regimes is due to the different contribution of the term related to the granular energy gradient. Present study concludes that the implementation method of granular pressure gradient may have a significant impact on hydrodynamics and is probably a key factor contributing to the observed differences between different simulation software