Miracle-dz/UniFAR-FTUs huggingface dataset:
Fundamental solutions and critical Lane-Emden exponents for nonlinear integral operators in cones

In this article we study the fundamental solutions or ``$\alpha$-harmonic functions"for some nonlinear positive homogeneous nonlocal elliptic problems in conical domains, such as $$ \begin{eqnarray*}\label{ecbir1a1} {\mathcal F }(u)=0\ \ \hbox{in} \ \ \mathcal{C}_\omega,\quad u=0\ \ \hbox{in} \ \ \mathbb{R}^n\setminus \mathcal{C}_\omega ,\ \ \end{eqnarray*} $$ where $\omega$ is a proper $C^2$ domain in $S^{N-1}$ for $ N\geq 2$, $\mathcal{C}_\omega:=\{x\,|\,x\neq 0, {|x|^{-1}}x\in \omega\}$ is the cone-like domain related to $\omega$, and ${\mathcal F }$ is an extremal fully nonlinear integral operator. We prove the existence of two fundamental solutions that are homogeneous and do not change signs in the cone; one is bounded at the origin and the other at infinity. As an application, we use the fundamental solutions obtained to prove a Liouville type theorem in cones for supersolutions of Lane-Emden-Fowler equation of the form $$ \begin{eqnarray*}\label{eq 0.2} {\mathcal F }(u)+u^p = 0\ \ \hbox{in} \ \ \mathcal{C}_\omega, \quad u=0\ \ \hbox{in} \ \ \mathbb{R}^n\setminus \mathcal{C}_\omega. \end{eqnarray*} $$ We also prove a generalized Hopf type lemma in domains with corners. Most of our results are new even when ${\mathcal F }$ is the fractional Laplacian operator.
Zero-Shot Batch-Level Anomaly Detection

Anomaly detection (AD) plays a crucial role in many safety-critical application domains. The challenge of adapting an anomaly detector to drift in the normal data distribution, especially when no training data is available for the"new normal", has led to the development of zero-shot AD techniques. In this paper, we propose a simple yet effective method called Adaptive Centered Representations (ACR) for zero-shot batch-level AD. Our approach trains off-the-shelf deep anomaly detectors (such as deep SVDD) to adapt to a set of inter-related training data distributions in combination with batch normalization, enabling automatic zero-shot generalization for unseen AD tasks. This simple recipe, batch normalization plus meta-training, is a highly effective and versatile tool. Our results demonstrate the first zero-shot AD results for tabular data and outperform existing methods in zero-shot anomaly detection and segmentation on image data from specialized domains.
Attributable and Scalable Opinion Summarization

We propose a method for unsupervised opinion summarization that encodes sentences from customer reviews into a hierarchical discrete latent space, then identifies common opinions based on the frequency of their encodings. We are able to generate both abstractive summaries by decoding these frequent encodings, and extractive summaries by selecting the sentences assigned to the same frequent encodings. Our method is attributable, because the model identifies sentences used to generate the summary as part of the summarization process. It scales easily to many hundreds of input reviews, because aggregation is performed in the latent space rather than over long sequences of tokens. We also demonstrate that our appraoch enables a degree of control, generating aspect-specific summaries by restricting the model to parts of the encoding space that correspond to desired aspects (e.g., location or food). Automatic and human evaluation on two datasets from different domains demonstrates that our method generates summaries that are more informative than prior work and better grounded in the input reviews.
pTSE: A Multi-model Ensemble Method for Probabilistic Time Series Forecasting

Various probabilistic time series forecasting models have sprung up and shown remarkably good performance. However, the choice of model highly relies on the characteristics of the input time series and the fixed distribution that model is based on. Due to the fact that the probability distributions cannot be averaged over different models straightforwardly, the current time series model ensemble methods cannot be directly applied to improve the robustness and accuracy of forecasting. To address this issue, we propose pTSE, a multi-model distribution ensemble method for probabilistic forecasting based on Hidden Markov Model (HMM). pTSE only takes off-the-shelf outputs from member models without requiring further information about each model. Besides, we provide a complete theoretical analysis of pTSE to prove that the empirical distribution of time series subject to an HMM will converge to the stationary distribution almost surely. Experiments on benchmarks show the superiority of pTSE over all member models and competitive ensemble methods.
Appraising the Potential Uses and Harms of LLMs for Medical Systematic Reviews

Medical systematic reviews play a vital role in healthcare decision making and policy. However, their production is time-consuming, limiting the availability of high-quality and up-to-date evidence summaries. Recent advancements in large language models (LLMs) offer the potential to automatically generate literature reviews on demand, addressing this issue. However, LLMs sometimes generate inaccurate (and potentially misleading) texts by hallucination or omission. In healthcare, this can make LLMs unusable at best and dangerous at worst. We conducted 16 interviews with international systematic review experts to characterize the perceived utility and risks of LLMs in the specific context of medical evidence reviews. Experts indicated that LLMs can assist in the writing process by drafting summaries, generating templates, distilling information, and crosschecking information. They also raised concerns regarding confidently composed but inaccurate LLM outputs and other potential downstream harms, including decreased accountability and proliferation of low-quality reviews. Informed by this qualitative analysis, we identify criteria for rigorous evaluation of biomedical LLMs aligned with domain expert views.
DRL meets DSA Networks: Convergence Analysis and Its Application to System Design

In dynamic spectrum access (DSA) networks, secondary users (SUs) need to opportunistically access primary users' (PUs) radio spectrum without causing significant interference. Since the interaction between the SU and the PU systems are limited, deep reinforcement learning (DRL) has been introduced to help SUs to conduct spectrum access. Specifically, deep recurrent Q network (DRQN) has been utilized in DSA networks for SUs to aggregate the information from the recent experiences to make spectrum access decisions. DRQN is notorious for its sample efficiency in the sense that it needs a rather large number of training data samples to tune its parameters which is a computationally demanding task. In our recent work, deep echo state network (DEQN) has been introduced to DSA networks to address the sample efficiency issue of DRQN. In this paper, we analytically show that DEQN comparatively requires less amount of training samples than DRQN to converge to the best policy. Furthermore, we introduce a method to determine the right hyperparameters for the DEQN providing system design guidance for DEQN-based DSA networks. Extensive performance evaluation confirms that DEQN-based DSA strategy is the superior choice with regard to computational power while outperforming DRQN-based DSA strategies.
Toward More Transparent and Accurate Cancer Diagnosis With an Unsupervised CAE Approach

According to the Global Cancer Observatory, 2020, breast cancer is the most prevalent cancer type in both genders (11.7%), while prostate cancer is the second most common cancer type in men (14.1%). In digital pathology, Content-Based Medical Image Retrieval (CBMIR) is a powerful tool for improving cancer diagnosis by searching for similar histopathological Whole Slide Images (WSIs). CBMIR empowers pathologists to explore similar patches to their query, enhancing diagnostic reliability and accuracy. In this paper, a customized unsupervised Convolutional Auto Encoder (CAE) was developed in the proposed Unsupervised CBMIR (UCBMIR) to replicate the traditional cancer diagnosis workflow, offering the potential to enhance diagnostic accuracy and efficiency by reducing pathologists’ workload. Furthermore, it provides a more transparent supporting tool for pathologists in cancer diagnosis. UCBMIR was evaluated using two widely used numerical techniques in CBMIR, visual techniques, and compared with a classifier. Validation encompassed three data sets, including an external evaluation to demonstrate its effectiveness. UCBMIR achieved 99% and 80% top 5 recalls on BreaKHis and SICAPv2 with the first evaluation technique while using the second technique, it reached 91% and 70% precision for BreaKHis and SICAPv2, respectively. Moreover, UCBMIR displayed a strong capability to identify diverse patterns, yielding 81% accuracy in the top 5 predictions on an external image from Arvaniti. The proposed unsupervised CBMIR tool delivered 83% accuracy in retrieving images with the same cancer type.
Radicalized by Thinness: Using a Model of Radicalization to Understand Pro-Anorexia Communities on Twitter

The rise in eating disorders, a condition with serious health complications, has been linked to the proliferation of idealized body images on social media platforms. However, the relationship between social media and eating disorders is more complex, with online platforms potentially enabling harmful behaviors by linking people to ``pro-ana'' communities that promote eating disorders. We conceptualize the growth of harmful pro-ana communities as a process of online radicalization. We show that a model of radicalization explains how individuals are driven to conversations about extreme behaviors, like fasting, to achieve the ``thin body'' goal, and how these conversations are validated by pro-ana communities. By facilitating social connections to like-minded others, a shared group identity and emotional support, social media platforms can trap individuals within toxic echo chambers that normalize extreme disordered eating behaviors and other forms of self-harm. Characterizing and quantifying the role of online communities in amplifying harmful conversations will support the development of strategies to mitigate their impact and promote better mental health.
InstructIE: A Bilingual Instruction-based Information Extraction Dataset

Traditional information extraction (IE) methodologies, constrained by pre-defined classes and static training paradigms, often falter in adaptability, especially in the dynamic world. To bridge this gap, we explore an instruction-based IE paradigm in this paper, leveraging the substantial cross-task generalization capabilities of Large Language Models (LLMs). We observe that most existing IE datasets tend to be overly redundant in their label sets, which leads to the inclusion of numerous labels not directly relevant to the extraction content when constructing instructions. To tackle this issue, we introduce a bilingual theme-centric IE instruction dataset (Chinese and English), InstructIE, and for the first time, incorporate a theme scheme design that effectively simplifies the label structure. Furthermore, we develop an innovative framework named KG2Instruction, which is specifically designed for the automatic generation of such datasets. Experimental evaluations based on InstructIE reveal that while current models show promise in Instruction-based IE tasks, opportunities for their potential optimization also emerge. The dataset is available at https://huggingface.co/datasets/zjunlp/InstructIE.
Visualizing Linguistic Diversity of Text Datasets Synthesized by Large Language Models

Large language models (LLMs) can be used to generate smaller, more refined datasets via few-shot prompting for benchmarking, fine-tuning or other use cases. However, understanding and evaluating these datasets is difficult, and the failure modes of LLM-generated data are still not well understood. Specifically, the data can be repetitive in surprising ways, not only semantically but also syntactically and lexically. We present LinguisticLens, a novel interactive visualization tool for making sense of and analyzing syntactic diversity of LLM-generated datasets. LinguisticLens clusters text along syntactic, lexical, and semantic axes. It supports hierarchical visualization of a text dataset, allowing users to quickly scan for an overview and inspect individual examples. The live demo is available at https://shorturl.at/zHOUV.
Proving Almost-Sure Innermost Termination of Probabilistic Term Rewriting Using Dependency Pairs

Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems (TRSs) automatically. We adapt the dependency pair framework to the probabilistic setting in order to prove almost-sure innermost termination of probabilistic TRSs. To evaluate its power, we implemented the new framework in our tool AProVE.
Unsupervised Scientific Abstract Segmentation with Normalized Mutual Information

The abstracts of scientific papers consist of premises and conclusions. Structured abstracts explicitly highlight the conclusion sentences, whereas non-structured abstracts may have conclusion sentences at uncertain positions. This implicit nature of conclusion positions makes the automatic segmentation of scientific abstracts into premises and conclusions a challenging task. In this work, we empirically explore using Normalized Mutual Information (NMI) for abstract segmentation. We consider each abstract as a recurrent cycle of sentences and place segmentation boundaries by greedily optimizing the NMI score between premises and conclusions. On non-structured abstracts, our proposed unsupervised approach GreedyCAS achieves the best performance across all evaluation metrics; on structured abstracts, GreedyCAS outperforms all baseline methods measured by $P_k$. The strong correlation of NMI to our evaluation metrics reveals the effectiveness of NMI for abstract segmentation.
Project-Based Learning for Robot Control Theory: A Robot Operating System (ROS) Based Approach

Control theory is an important cornerstone of the robotics field and is considered a fundamental subject in an undergraduate and postgraduate robotics curriculum. Furthermore, project-based learning has shown significant benefits in engineering domains, specifically in interdisciplinary fields such as robotics which require hands-on experience to master the discipline adequately. However, designing a project-based learning experience to teach control theory in a hands-on setting can be challenging, due to the rigor of mathematical concepts involved in the subject. Moreover, access to reliable hardware required for a robotics control lab, including the robots, sensors, interfaces, and measurement instruments, may not be feasible in developing countries and even many academic institutions in the US. The current paper presents a set of six project-based assignments for an advanced postgraduate Robot Control course. The assignments leverage the Robot Operating System (ROS), an open-source set of tools, libraries, and software, which is a de facto standard for the development of robotics applications. The use of ROS, along with its physics engine simulation framework, Gazebo, provides a hands-on robotics experience equivalent to working with real hardware. Learning outcomes include: i) theoretical analysis of linear and nonlinear dynamical systems, ii) formulation and implementation of advanced model-based robot control algorithms using classical and modern control theory, and iii) programming and performance evaluation of robotic systems on physics engine robot simulators. Course evaluations and student surveys demonstrate that the proposed project-based assignments successfully bridge the gap between theory and practice, and facilitate learning of control theory concepts and state-of-the-art robotics techniques through a hands-on approach.
Region of Attraction Estimation Using Union Theorem in Sum-of-Squares Optimization

Appropriate estimation of Region of Attraction for a nonlinear dynamical system plays a key role in system analysis and control design. Sum-of-Squares optimization is a powerful tool enabling Region of Attraction estimation for polynomial dynamical systems. Employment of a positive definite function called shape function within the Sum-of-Squares procedure helps to find a richer representation of the Lyapunov function and a larger corresponding Region of Attraction estimation. However, existing Sum-of-Squares optimization techniques demonstrate very conservative results. The main novelty of this paper is the Union theorem which enables the use of multiple shape functions to create a polynomial Lyapunov function encompassing all the areas generated by the shape functions. The main contribution of this paper is a novel computationally-efficient numerical method for Region of Attraction estimation, which remarkably improves estimation performance and overcomes limitations of existing methods, while maintaining the resultant Lyapunov function polynomial, thus facilitating control system design and construction of control Lyapunov function with enhanced Region of Attraction using conventional Sum-of-Squares tools. A mathematical proof of the Union theorem along with its application to the numerical algorithm of Region of Attraction estimation is provided. The method yields significantly enlarged Region of Attraction estimations even for systems with non-symmetric or unbounded Region of Attraction, which is demonstrated via simulations of several benchmark examples.
PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Prediction

In this paper, we investigate the challenge of spatio-temporal video prediction, which involves generating future videos based on historical data streams. Existing approaches typically utilize external information such as semantic maps to enhance video prediction, which often neglect the inherent physical knowledge embedded within videos. Furthermore, their high computational demands could impede their applications for high-resolution videos. To address these constraints, we introduce a novel approach called Physics-assisted Spatio-temporal Network (PastNet) for generating high-quality video predictions. The core of our PastNet lies in incorporating a spectral convolution operator in the Fourier domain, which efficiently introduces inductive biases from the underlying physical laws. Additionally, we employ a memory bank with the estimated intrinsic dimensionality to discretize local features during the processing of complex spatio-temporal signals, thereby reducing computational costs and facilitating efficient high-resolution video prediction. Extensive experiments on various widely-used datasets demonstrate the effectiveness and efficiency of the proposed PastNet compared with state-of-the-art methods, particularly in high-resolution scenarios. Our code is available at https://github.com/easylearningscores/PastNet.
Universal defects statistics with strong long-range interactions

Quasi-static transformations, or slow quenches, of many-body quantum systems across quantum critical points create topological defects. The Kibble-Zurek mechanism regulates the appearance of defects in a local quantum system through a classical combinatorial process. However, long-range interactions disrupt the conventional Kibble-Zurek scaling and lead to a density of defects that is independent of the rate of the transformation. In this study, we analytically determine the complete full counting statistics of defects generated by slow annealing a strong long-range system across its quantum critical point. We demonstrate that the mechanism of defect generation in long-range systems is a purely quantum process with no classical equivalent. Furthermore, universality is not only observed in the defect density but also in all the moments of the distribution. Our findings can be tested on various experimental platforms, including Rydberg gases and trapped ions.
Linear $\chi$-binding functions for $\{P_3\cup P_2, gem\}$-free graphs

Finding families that admit a linear $\chi$-binding function is a problem that has interested researchers for a long time. Recently, the question of finding linear subfamilies of $2K_2$-free graphs has garnered much attention. In this paper, we are interested in finding a linear subfamily of a specific superclass of $2K_2$-free graphs, namely $(P_3\cup P_2)$-free graphs. We show that the class of $\{P_3\cup P_2,gem\}$-free graphs admits $f=2\omega$ as a linear $\chi$-binding function. Furthermore, we give examples to show that the optimal $\chi$-binding function $f^*\geq \left\lceil\frac{5\omega(G)}{4}\right\rceil$ for the class of $\{P_3\cup P_2, gem\}$-free graphs and that the $\chi$-binding function $f=2\omega$ is tight when $\omega=2$ and $3$.
Hierarchical screening with retesting in a low prevalence population

This article develops the effect of imperfect inspection on screening acceptance-sampling procedure with retesting in a low prevalence population. The procedure is based on pooling samples and testing the pool as a whole for presence or absence of infected samples, then retesting the pools that test positive on the first test, and proceeding to individual testing only if such presence is also indicated on retest. If sampling is perfect, the procedure can reduce the expected cost, and accuracy is attained especially if the proportion of infection is low. Modifications on the procedure to hierarchical screening, which are aimed at further reduction in expected number of tests, are discussed.
Electroproduction of baryonic excitation studied via the Omega-Meson decay channel

The differential cross-section for p(e, eω)p has been studied at Q ∼ 5.5 (GeV/c). Here Q represents the four momentum squared of the virtual photon in the excitation of baryonic resonances by an electron projectile. The excitation cross-section for the baryonic resonances and their de-excitation rates and channels provides information on the underlying structure of QCD. The selection of the ω decay channel constrains the particular baryonic resonances that contribute to the measured cross-section. A significant aspect of the data presented from W = 1.72 GeV to W = 1.92 GeV is that the Q falls in the region where the transition from non-pertubative processes characterised by constituent quarks dominate to the regime where the hard processes are expected to play an increasing important role. This is therefore an interesting region to acquire further data. In order to extract the ω-meson differential cross section from the JLAB data, the data was compared to a full Monte Carlo simulation of the detector based on events generated for omega production in a way that the production cross section was varied to achieve a match to the data. The binning selected for this procedure takes into account the measure of robustness of the stripping of the ω peak from the multi-pion background as well as the statistics in the measured data and the Monte Carlo simulation of the signal and background physics [1]. An error estimation technique for the cross section was based on determining the dependence via the Monte Carlo simulation of the extracted cross section parameters on the experimental set-up (including parameters for the spectrometer, target beam geometries and performance). We compare our results with a Regge-based model for hadronic content in the t-channel exchange of a photon in Q region of overlap. There is an extension of this data into a completely new region, which is the highest yet measured. The result from the study of baryonic excitation via the ω channel gives a good correlation between theory and experiment in the overlapped kinematic regime of the used theoretical simulation.