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How can citizens moderate hate, toxicity, and extremism in online discourse? We analyze a large corpus of more than 130,000 discussions on German Twitter over the turbulent four years marked by the migrant crisis and political upheavals. With the help of human annotators, language models and machine learning classifiers, we identify different dimensions of discourse. We use a matching approach and longitudinal statistical analyses to discern the effectiveness of different counter speech strategies on the micro-level (individual tweet pairs), meso-level (discussion trees) and macro-level (days) of discourse. We find that expressing simple opinions, not necessarily supported by facts, but also without insults, relates to the least hate, toxicity, and extremity of speech and speakers in subsequent discussions. Sarcasm also helps in achieving those outcomes, in particular in the presence of organized extreme groups on the meso-level. Constructive comments such as providing facts or exposing contradictions can backfire and attract more extremity. Mentioning either outgroups or ingroups is typically related to a deterioration of discourse. A pronounced emotional tone, either negative such as anger or fear, or positive such as enthusiasm and pride, also leads to worse outcomes. Going beyond one-shot analyses on smaller samples of discourse, our findings have implications for the successful management of online commons through collective civic moderation.

We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local H\"older continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Finally, we present the results of some numerical experiments.

We develop new matching estimators for estimating causal quantile exposure-response functions and quantile exposure effects with continuous treatments. We provide identification results for the parameters of interest and establish the asymptotic properties of the derived estimators. We introduce a two-step estimation procedure. In the first step, we construct a matched data set via generalized propensity score matching, adjusting for measured confounding. In the second step, we fit a kernel quantile regression to the matched set. We also derive a consistent estimator of the variance of the matching estimators. Using simulation studies, we compare the introduced approach with existing alternatives in various settings. We apply the proposed method to Medicare claims data for the period 2012-2014, and we estimate the causal effect of exposure to PM$_{2.5}$ on the length of hospital stay for each zip code of the contiguous United States.

We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the correspondence-interleaving distance, a metric for hierarchical clusterings that we introduce. Taking certain one-parameter slices of degree-Rips recovers well-known methods for density-based clustering, but we show that these methods are unstable. However, we prove that degree-Rips, as a multiparameter object, is stable, and we propose an alternative approach for taking slices of degree-Rips, which yields a one-parameter hierarchical clustering algorithm with better stability properties. We prove that this algorithm is consistent, using the correspondence-interleaving distance. We provide an algorithm for extracting a single clustering from one-parameter hierarchical clusterings, which is stable with respect to the correspondence-interleaving distance. And, we integrate these methods into a pipeline for density-based clustering, which we call Persistable. Adapting tools from multiparameter persistent homology, we propose visualization tools that guide the selection of all parameters of the pipeline. We demonstrate Persistable on benchmark datasets, showing that it identifies multi-scale cluster structure in data.

Training robust speaker verification systems without speaker labels has long been a challenging task. Previous studies observed a large performance gap between self-supervised and fully supervised methods. In this paper, we apply a non-contrastive self-supervised learning framework called DIstillation with NO labels (DINO) and propose two regularization terms applied to embeddings in DINO. One regularization term guarantees the diversity of the embeddings, while the other regularization term decorrelates the variables of each embedding. The effectiveness of various data augmentation techniques are explored, on both time and frequency domain. A range of experiments conducted on the VoxCeleb datasets demonstrate the superiority of the regularized DINO framework in speaker verification. Our method achieves the state-of-the-art speaker verification performance under a single-stage self-supervised setting on VoxCeleb. Code has been made publicly available at //github.com/alibaba-damo-academy/3D-Speaker.

The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the solution to the problem at hand. The numerical method employed in the study combines a standard Backward Differentiation Formula (BDF)-type time-stepping procedure with a geometrically unfitted finite element discretization technique. Additionally, Nitsche's method is utilized to enforce the boundary conditions. The paper presents a convergence estimate for several velocity--pressure elements that are inf-sup stable. The estimate demonstrates optimal order convergence in the energy norm for the velocity component and a scaled $L^2(H^1)$-type norm for the pressure component.

Algorithms for solving the linear classification problem have a long history, dating back at least to 1936 with linear discriminant analysis. For linearly separable data, many algorithms can obtain the exact solution to the corresponding 0-1 loss classification problem efficiently, but for data which is not linearly separable, it has been shown that this problem, in full generality, is NP-hard. Alternative approaches all involve approximations of some kind, including the use of surrogates for the 0-1 loss (for example, the hinge or logistic loss) or approximate combinatorial search, none of which can be guaranteed to solve the problem exactly. Finding efficient algorithms to obtain an exact i.e. globally optimal solution for the 0-1 loss linear classification problem with fixed dimension, remains an open problem. In research we report here, we detail the rigorous construction of a new algorithm, incremental cell enumeration (ICE), that can solve the 0-1 loss classification problem exactly in polynomial time. We prove correctness using concepts from the theory of hyperplane arrangements and oriented matroids. We demonstrate the effectiveness of this algorithm on synthetic and real-world datasets, showing optimal accuracy both in and out-of-sample, in practical computational time. We also empirically demonstrate how the use of approximate upper bound leads to polynomial time run-time improvements to the algorithm whilst retaining exactness. To our knowledge, this is the first, rigorously-proven polynomial time, practical algorithm for this long-standing problem.

We present Surjective Sequential Neural Likelihood (SSNL) estimation, a novel method for simulation-based inference in models where the evaluation of the likelihood function is not tractable and only a simulator that can generate synthetic data is available. SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function which allows for conventional Bayesian inference using either Markov chain Monte Carlo methods or variational inference. By embedding the data in a low-dimensional space, SSNL solves several issues previous likelihood-based methods had when applied to high-dimensional data sets that, for instance, contain non-informative data dimensions or lie along a lower-dimensional manifold. We evaluate SSNL on a wide variety of experiments and show that it generally outperforms contemporary methods used in simulation-based inference, for instance, on a challenging real-world example from astrophysics which models the magnetic field strength of the sun using a solar dynamo model.

Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric CFD application solved with the Discontinuous Galerkin method.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.