Miracle-dz/UniFAR-FTUs huggingface dataset:
A method for constructing asymmetric pair-copula and its application

ABSTRACT Pair-copula has become a hot spot in the research of both theory and application of statistics. Therefore, proper construction of pair-copula is an area worthy of study. Considering the asymmetry of variate dependence in practical applications and the disadvantages of the widely used asymmetric copulas, we propose a method to construct asymmetric pair-copula. In our method, we treat the asymmetric bivariate copula constructed by Liebscher's method as a generator, using this generator to construct asymmetric pair-copula. Also, on the basis of our method, we propose and prove a reference for selecting copula family in the construction. To verify the method, we construct asymmetric copulas and asymmetric pair-copulas using the daily runoff data collected at Yichang hydrological station to describe the extreme drought events of Yangtze River. After comparing the models in some aspects, we accept a model we construct, and the result displays the feasibility and practicality of the method we propose.
Statistical Methods for Analyzing Bivariate Mixed Outcomes

Multivariate outcomes are ubiquitous. Joint analysis of multivariate outcomes provides several benfits over separate analysis of each outcome. However, joint analysis of multivariate outcomes that are mixed, i.e., not on the same scale of measurement, can be challenging. This dissertation provides novel methods to analyze bivariate mixed outcomes, where we have exactly one continuous outcome and one binary outcome. A penalized generalized estimating equations framework to perform simultaneous estimation and variable selection for bivaraite mixed outcomes in the presence of a large number of covariates is provided. Next, fully Bayesian and empirical Bayes approaches to estimating the association between the two outcomes using a copula-based model are provided. Finally, methods for estimating and testing genomic effects in bivariate mixed secondary outcome models under case-control designs are presented. Statistical Methods for Analyzing Bivariate Mixed Outcomes
Numerical methods for deterministic and stochastic nonlocal problem in diffusion and mechanics

In this dissertation, the recently developed peridynamic nonlocal continuum model for solid mechanics is extensively studied, specifically, the numerical methods for the deterministic and stochastic steady-state peridynamics models. In contrast to the classical partial differential equation models, the peridynamic model is an integro-differential equation that does not involve spatial derivatives of the displacement field. As a result, the peridynamic model admits solutions having jump discontinuities so that it has been successfully applied to fracture problems. This dissentation consists of three major parts. The first part focuses on the onedimensional steady-state peridynamics model. Based on a variational formulation, continuous and discontinuous Galerkin finite element methods are developed for the peridynamic model. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. A strategy for identifying the discontinuities of the solution is developed and implemented. The convergence of the peridynamics model to the classical elasticity model is studied. Some relevant nonlocal problems are also considered. In the second part, we focus on the two-dimensional steady-state peridynamics model. Based on the numerical strategies and results from the one-dimensional peridynamics model, we developed and implemented the corresponding approaches for the two-dimensional case. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. In the third part, we study the stochastic peridynamics model. We focus on a version of the peridynamics model whose forcing terms are described by a finite-dimensional random vector, which is often called the finite-dimensional noise assumption. Monte Carlo methods, stochastic collocation with full tensor product and sparse grid methods based on this stochastic peridynamics model are implemented and compared.
Edgewise Outliers of Network Indexed Signals

We consider models for network-indexed multivariate data, also known as graph signals, involving a dependence between variables as well as across graph nodes. The dependence across nodes is typically established through the entries of the Laplacian matrix by imposing a distribution that relates the graph signal from one node to the next. Based on such distributional assumptions of the graph signal, we focus on outliers detection and introduce the new concept of edgewise outliers. For this purpose, we first derive the distribution of some sums of squares, in particular squared Mahalanobis distances that can be used to fix detection rules and thresholds for outlier detection. We then propose a robust version of the deterministic Minimum Covariance Determinant (MCD) algorithm that we call edgewise MCD. An application on simulated data shows the interest of taking the dependence structure into account. We also illustrate the utility of the proposed method with a real data set involving French departmental election data.
QDC: Quantum Diffusion Convolution Kernels on Graphs

Graph convolutional neural networks (GCNs) operate by aggregating messages over local neighborhoods given the prediction task under interest. Many GCNs can be understood as a form of generalized diffusion of input features on the graph, and significant work has been dedicated to improving predictive accuracy by altering the ways of message passing. In this work, we propose a new convolution kernel that effectively rewires the graph according to the occupation correlations of the vertices by trading on the generalized diffusion paradigm for the propagation of a quantum particle over the graph. We term this new convolution kernel the Quantum Diffusion Convolution (QDC) operator. In addition, we introduce a multiscale variant that combines messages from the QDC operator and the traditional combinatorial Laplacian. To understand our method, we explore the spectral dependence of homophily and the importance of quantum dynamics in the construction of a bandpass filter. Through these studies, as well as experiments on a range of datasets, we observe that QDC improves predictive performance on the widely used benchmark datasets when compared to similar methods.
SACReg: Scene-Agnostic Coordinate Regression for Visual Localization

Scene coordinates regression (SCR), i.e., predicting 3D coordinates for every pixel of a given image, has recently shown promising potential. However, existing methods remain limited to small scenes memorized during training, and thus hardly scale to realistic datasets and scenarios. In this paper, we propose a generalized SCR model trained once to be deployed in new test scenes, regardless of their scale, without any finetuning. Instead of encoding the scene coordinates into the network weights, our model takes as input a database image with some sparse 2D pixel to 3D coordinate annotations, extracted from e.g. off-the-shelf Structure-from-Motion or RGB-D data, and a query image for which are predicted a dense 3D coordinate map and its confidence, based on cross-attention. At test time, we rely on existing off-the-shelf image retrieval systems and fuse the predictions from a shortlist of relevant database images w.r. t. the query. Afterwards camera pose is obtained using standard Perspective-n-Point (PnP). Starting from selfsupervised CroCo pretrained weights, we train our model on diverse datasets to ensure generalizabilty across various scenarios, and significantly outperform other scene regression approaches, including scene-specific models, on multiple visual localization benchmarks. Finally, we show that the database representation of images and their 2D-3D annotations can be highly compressed with negligible loss of localization performance.
Kernelized Offline Contextual Dueling Bandits

Preference-based feedback is important for many applications where direct evaluation of a reward function is not feasible. A notable recent example arises in reinforcement learning from human feedback on large language models. For many of these applications, the cost of acquiring the human feedback can be substantial or even prohibitive. In this work, we take advantage of the fact that often the agent can choose contexts at which to obtain human feedback in order to most efficiently identify a good policy, and introduce the offline contextual dueling bandit setting. We give an upper-confidence-bound style algorithm for this setting and prove a regret bound. We also give empirical confirmation that this method outperforms a similar strategy that uses uniformly sampled contexts.
Model Reporting for Certifiable AI: A Proposal from Merging EU Regulation into AI Development

Despite large progress in Explainable and Safe AI, practitioners suffer from a lack of regulation and standards for AI safety. In this work we merge recent regulation efforts by the European Union and first proposals for AI guidelines with recent trends in research: data and model cards. We propose the use of standardized cards to document AI applications throughout the development process. Our main contribution is the introduction of use-case and operation cards, along with updates for data and model cards to cope with regulatory requirements. We reference both recent research as well as the source of the regulation in our cards and provide references to additional support material and toolboxes whenever possible. The goal is to design cards that help practitioners develop safe AI systems throughout the development process, while enabling efficient third-party auditing of AI applications, being easy to understand, and building trust in the system. Our work incorporates insights from interviews with certification experts as well as developers and individuals working with the developed AI applications.
Longitudinal Data Clustering with a Copula Kernel Mixture Model

Many common clustering methods cannot be used for clustering multivariate longitudinal data in cases where variables exhibit high autocorrelations. In this article, a copula kernel mixture model (CKMM) is proposed for clustering data of this type. The CKMM is a finite mixture model which decomposes each mixture component's joint density function into its copula and marginal distribution functions. In this decomposition, the Gaussian copula is used due to its mathematical tractability and Gaussian kernel functions are used to estimate the marginal distributions. A generalized expectation-maximization algorithm is used to estimate the model parameters. The performance of the proposed model is assessed in a simulation study and on two real datasets. The proposed model is shown to have effective performance in comparison to standard methods, such as K-means with dynamic time warping clustering and latent growth models.
Neuromorphic Online Learning for Spatiotemporal Patterns with a Forward-only Timeline

Spiking neural networks (SNNs) are bio-plausible computing models with high energy efficiency. The temporal dynamics of neurons and synapses enable them to detect temporal patterns and generate sequences. While Backpropagation Through Time (BPTT) is traditionally used to train SNNs, it is not suitable for online learning of embedded applications due to its high computation and memory cost as well as extended latency. Previous works have proposed online learning algorithms, but they often utilize highly simplified spiking neuron models without synaptic dynamics and reset feedback, resulting in subpar performance. In this work, we present Spatiotemporal Online Learning for Synaptic Adaptation (SOLSA), specifically designed for online learning of SNNs composed of Leaky Integrate and Fire (LIF) neurons with exponentially decayed synapses and soft reset. The algorithm not only learns the synaptic weight but also adapts the temporal filters associated to the synapses. Compared to the BPTT algorithm, SOLSA has much lower memory requirement and achieves a more balanced temporal workload distribution. Moreover, SOLSA incorporates enhancement techniques such as scheduled weight update, early stop training and adaptive synapse filter, which speed up the convergence and enhance the learning performance. When compared to other non-BPTT based SNN learning, SOLSA demonstrates an average learning accuracy improvement of 14.2%. Furthermore, compared to BPTT, SOLSA achieves a 5% higher average learning accuracy with a 72% reduction in memory cost.
Formal Concept Lattice Representations and Algorithms for Hypergraphs

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only in the intersection relationships of the hyperedges, and so forming the"intersection complex"of a hypergraph is quite valuable. This identifies a valuable isomorphism between the intersection complex and the"concept lattice"formed from taking the hypergraph's incidence matrix as a"formal context": hypergraphs also generalize graphs in that their incidence matrices are arbitrary Boolean matrices. This isomorphism allows connecting discrete algorithms for lattices and hypergraphs, in particular s-walks or s-paths on hypergraphs can be mapped to order theoretical operations on the concept lattice. We give new algorithms for formal concept lattices and hypergraph s-walks on concept lattices. We apply this to a large real-world dataset and find deep lattices implying high interconnectivity and complex geometry of hyperedges.
Pseudorandomness of the Sticky Random Walk

We extend the pseudorandomness of random walks on expander graphs using the sticky random walk. Building on prior works, it was recently shown that expander random walks can fool all symmetric functions in total variation distance (TVD) upto an $O(\lambda(\frac{p}{\min f})^{O(p)})$ error, where $\lambda$ is the second largest eigenvalue of the expander, $p$ is the size of the arbitrary alphabet used to label the vertices, and $\min f = \min_{b\in[p]} f_b$, where $f_b$ is the fraction of vertices labeled $b$ in the graph. Golowich and Vadhan conjecture that the dependency on the $(\frac{p}{\min f})^{O(p)}$ term is not tight. In this paper, we resolve the conjecture in the affirmative for a family of expanders. We present a generalization of the sticky random walk for which Golowich and Vadhan predict a TVD upper bound of $O(\lambda p^{O(p)})$ using a Fourier-analytic approach. For this family of graphs, we use a combinatorial approach involving the Krawtchouk functions to derive a strengthened TVD of $O(\lambda)$. Furthermore, we present equivalencies between the generalized sticky random walk, and, using linear-algebraic techniques, show that the generalized sticky random walk parameterizes an infinite family of expander graphs.
Analyzing time series of unequal durations using Multidimensional Recurrence Quantification Analysis (MdRQA): validation and implementation using Python

In recent years, recurrent quantification analysis (RQA) and its multi-dimensional version (MdRQA) have emerged as a popular tool for assessing interpersonal behavioral or physiological synchrony in groups of two or more individuals. While experimental data in such studies are typically collected for a fixed, pre-determined duration, naturally occurring phenomena may often reach a state of transition after an unpredictable or varying duration of time. The resulting recurrence plots (RPs) across samples cannot be compared directly via linear scaling because the sensitivity of RQA variables to local dynamics would vary. We propose to address this by using the sliding window technique on individual RPs and using the summary statistics of the different RQA variable distributions computed across the sliding windows to differentiate the dynamics of the original time series of unequal durations. We first tested our approach in two simulated models: 1) the Rossler attractor and 2) the Kuramoto model. We compared the ability of different summary statistics of RQA variable distributions to accurately predict the dynamic states of the system across varying levels of noise, unequal lengths of time series, and, in the case of the Kuramoto model, different numbers of oscillators across samples. We found that the mode was the most robust to the degree of noise in the signals. We further tested and validated it on open access data from a recent study comparing spontaneously generated interpersonal movement synchrony in a dyad. To our knowledge, this is the first systematic attempt to validate the use of MdRQA in computing and comparing synchrony between systems of non-uniform composition and unequal time series data, paving the way for future work that examines interpersonal synchrony in more naturalistic, ecologically valid contexts.
Solving differential equations with deep learning: a beginner’s guide

The research in artificial intelligence methods with potential applications in science has become an essential task in the scientific community in recent years. Physics-informed neural networks (PINNs) is one of these methods and represents a contemporary technique based on neural network fundamentals to solve differential equations. These networks can potentially improve or complement classical numerical methods in computational physics, making them an exciting area of study. In this paper, we introduce PINNs at an elementary level, mainly oriented to physics education, making them suitable for educational purposes at both undergraduate and graduate levels. PINNs can be used to create virtual simulations and educational tools that aid in understating complex physical concepts and processes involving differential equations. By combining the power of neural networks with physics principles, PINNs can provide an interactive and engaging learning experience that can improve students’ understanding and retention of physics concepts in higher education.
Multiparameter Water Quality Monitoring System for Continuous Monitoring of Fresh Waters

Due to the global water crisis there is a strong need for real-time water quality monitoring with high temporal and spatial resolution. This paper presents an economical multiparameter water quality monitoring system for continuous monitoring of fresh waters. It is based on a sensor node that integrates turbidity, temperature, and conductivity sensors, a miniature eighteen-channel spectrophotometer, and a sensor for the detection of thermotolerant coliforms, which is a major novelty of the system. Due to the influence of water impurities on the measurement of thermotolerant coliforms, a heuristic method has been developed to mitigate this effect. Moreover, the sensor is low power and with an integrated Long Range Wide Area Network module, it comprises a system that is wireless sensor network ready and can send data to a dedicated server. In addition, the system is submersible, capable of long-term field operation, and significantly cheaper in comparison to existing solutions. The purpose of the system is to give early warning of incidental pollution situations, thus enabling authorities to take action regarding further prevention of such occasions.
Rotating Kiselev Black Holes in $f(R,T)$ Gravity

Exact solutions describing rotating black holes can provide significant opportunities for testing modified theories of gravity, which are motivated by the challenges posed by dark energy and dark matter. Starting with a spherical Kiselev black hole as a seed metric, we construct rotating Kiselev black holes within the $f(R,T)$ gravity framework using the revised Newman-Janis algorithm - the $f(R,T)$ gravity-motivated rotating Kiselev black holes (FRKBH), which encompasses, as exceptional cases, Kerr ($K=0$) and Kerr-Newman ($K=Q^2$) black holes. These solutions give rise to distinct classes of black holes surrounded by fluids while considering specific values of the equation-of-state parameter, $w$, for viable choices for the $f(R,T)$ function. From the parameter space or domain of existence of black holes defined by $a$ and $\gamma$ for FKRBH, we discover that when $a_1a_2$), we encounter two distinct critical values $\gamma=\gamma_{E1}, \; \gamma_{E2}$ with $\gamma_{E1}>\gamma_{E2}$ (or $\gamma=\gamma_{E3},\; \gamma_{E4}$ with $\gamma_{E3}>\gamma_{E4}$. We delve into the horizon and global structure of FKRBH spacetimes and examine their dependence on parameters $w$ and $\gamma$. This exploration is motivated by the remarkable effects of $f(R,T)$ gravity, which gives rise to diverse and intricate spacetime structures within the domain where black holes exist.
Semantically-Enhanced Deep Collision Prediction for Autonomous Navigation Using Aerial Robots

This paper contributes a novel and modularized learning-based method for aerial robots navigating cluttered environments containing hard-to-perceive thin obstacles without assuming access to a map or the full pose estimation of the robot. The proposed solution builds upon a semantically-enhanced Variational Autoencoder that is trained with both real-world and simulated depth images to compress the input data, while preserving semantically-labeled thin obstacles and handling invalid pixels in the depth sensor's output. This compressed representation, in addition to the robot's partial state involving its linear/angular velocities and its attitude are then utilized to train an uncertainty-aware 3D Collision Prediction Network in simulation to predict collision scores for candidate action sequences in a predefined motion primitives library. A set of simulation and experimental studies in cluttered environments with various sizes and types of obstacles, including multiple hard-to-perceive thin objects, were conducted to evaluate the performance of the proposed method and compare against an end-to-end trained baseline. The results demonstrate the benefits of the proposed semantically-enhanced deep collision prediction for learning-based autonomous navigation.
Towards practical reinforcement learning for tokamak magnetic control

Reinforcement learning (RL) has shown promising results for real-time control systems, including the domain of plasma magnetic control. However, there are still significant drawbacks compared to traditional feedback control approaches for magnetic confinement. In this work, we address key drawbacks of the RL method; achieving higher control accuracy for desired plasma properties, reducing the steady-state error, and decreasing the required time to learn new tasks. We build on top of \cite{degrave2022magnetic}, and present algorithmic improvements to the agent architecture and training procedure. We present simulation results that show up to 65\% improvement in shape accuracy, achieve substantial reduction in the long-term bias of the plasma current, and additionally reduce the training time required to learn new tasks by a factor of 3 or more. We present new experiments using the upgraded RL-based controllers on the TCV tokamak, which validate the simulation results achieved, and point the way towards routinely achieving accurate discharges using the RL approach.