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An additive Runge-Kutta method is used for the time stepping, which integrates the linear stiff terms by an explicit singly diagonally implicit Runge-Kutta (ESDIRK) method and the nonlinear terms by an explicit Runge-Kutta (ERK) method. In each time step, the implicit solve is performed by the recently developed Hierarchical Poincar\'e-Steklov (HPS) method. This is a fast direct solver for elliptic equations that decomposes the space domain into a hierarchical tree of subdomains and builds spectral collocation solvers locally on the subdomains. These ideas are naturally combined in the presented method since the singly diagonal coefficient in ESDIRK and a fixed time-step ensures that the coefficient matrix in the implicit solve of HPS remains the same for all time stages. This means that the precomputed inverse can be efficiently reused, leading to a scheme with complexity (in two dimensions) $\mathcal{O}(N^{1.5})$ for the precomputation where the solution operator to the elliptic problems is built, and then $\mathcal{O}(N \log N)$ for the solve in each time step. The stability of the method is proved for first order in time and any order in space, and numerical evidence substantiates a claim of stability for a much broader class of time discretization methods. Numerical experiments supporting the accuracy of efficiency of the method in one and two dimensions are presented.

Most studies in swarm robotics treat the swarm as an isolated system of interest. We argue that the prevailing view of swarms as self-sufficient, independent systems limits the scope of potential applications for swarm robotics. A robot swarm could act as a support in an heterogeneous system comprising other robots and/or human operators, in particular by quickly providing access to a large amount of data acquired in large unknown environments. Tasks such as target identification & tracking, scouting, or monitoring/surveillance could benefit from this approach.

Group testing, a method that screens subjects in pooled samples rather than individually, has been employed as a cost-effective strategy for chlamydia screening among Iowa residents. In efforts to deepen our understanding of chlamydia epidemiology in Iowa, several group testing regression models have been proposed. Different than previous approaches, we expand upon the varying coefficient model to capture potential age-varying associations with chlamydia infection risk. In general, our model operates within a Bayesian framework, allowing regression associations to vary with a covariate of key interest. We employ a stochastic search variable selection process for regularization in estimation. Additionally, our model can integrate random effects to consider potential geographical factors and estimate unknown assay accuracy probabilities. The performance of our model is assessed through comprehensive simulation studies. Upon application to the Iowa group testing dataset, we reveal a significant age-varying racial disparity in chlamydia infections. We believe this discovery has the potential to inform the enhancement of interventions and prevention strategies, leading to more effective chlamydia control and management, thereby promoting health equity across all populations.

We study the properties of a family of distances between functions of a single variable. These distances are examples of integral probability metrics, and have been used previously for comparing probability measures on the line; special cases include the Earth Mover's Distance and the Kolmogorov Metric. We examine their properties for general signals, proving that they are robust to a broad class of deformations. We also establish corresponding robustness results for the induced sliced distances between multivariate functions. Finally, we establish error bounds for approximating the univariate metrics from finite samples, and prove that these approximations are robust to additive Gaussian noise. The results are illustrated in numerical experiments, which include comparisons with Wasserstein distances.

The evaluation of text-generative vision-language models is a challenging yet crucial endeavor. By addressing the limitations of existing Visual Question Answering (VQA) benchmarks and proposing innovative evaluation methodologies, our research seeks to advance our understanding of these models' capabilities. We propose a novel VQA benchmark based on well-known visual classification datasets which allows a granular evaluation of text-generative vision-language models and their comparison with discriminative vision-language models. To improve the assessment of coarse answers on fine-grained classification tasks, we suggest using the semantic hierarchy of the label space to ask automatically generated follow-up questions about the ground-truth category. Finally, we compare traditional NLP and LLM-based metrics for the problem of evaluating model predictions given ground-truth answers. We perform a human evaluation study upon which we base our decision on the final metric. We apply our benchmark to a suite of vision-language models and show a detailed comparison of their abilities on object, action, and attribute classification. Our contributions aim to lay the foundation for more precise and meaningful assessments, facilitating targeted progress in the exciting field of vision-language modeling.

In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential nonlinear relationships among the variables. To address this limitation, we propose a partially linear structure that incorporates unspecified functions to capture nonlinear relationships. We establish the identifiability of the proposed model under mild conditions and introduce a practical estimation algorithm. We present the performance of our approach through numerical studies, including simulations and real data analysis.

In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on frequency estimation using Schnieper's framework for claim numbering. We demonstrate that Schnieper's model is consistent with a Poisson distribution for the total number of claims above a priority at each year of development, providing a robust basis for parameter estimation. Additionally, we explain how to build an alternative assumption based on a Negative binomial distribution, which yields similar results. The study includes a bootstrap procedure to manage uncertainty in parameter estimation and a case study comparing assumptions and evaluating the impact of the bootstrap approach.

In some causal inference scenarios, the treatment variable is measured inaccurately, for instance in epidemiology or econometrics. Failure to correct for the effect of this measurement error can lead to biased causal effect estimates. Previous research has not studied methods that address this issue from a causal viewpoint while allowing for complex nonlinear dependencies and without assuming access to side information. For such a scenario, this study proposes a model that assumes a continuous treatment variable that is inaccurately measured. Building on existing results for measurement error models, we prove that our model's causal effect estimates are identifiable, even without knowledge of the measurement error variance or other side information. Our method relies on a deep latent variable model in which Gaussian conditionals are parameterized by neural networks, and we develop an amortized importance-weighted variational objective for training the model. Empirical results demonstrate the method's good performance with unknown measurement error. More broadly, our work extends the range of applications in which reliable causal inference can be conducted.

Objective Hospitals register information in the electronic health records (EHR) continuously until discharge or death. As such, there is no censoring for in-hospital outcomes. We aimed to compare different dynamic regression modeling approaches to predict central line-associated bloodstream infections (CLABSI) in EHR while accounting for competing events precluding CLABSI. Materials and Methods We analyzed data from 30,862 catheter episodes at University Hospitals Leuven from 2012 and 2013 to predict 7-day risk of CLABSI. Competing events are discharge and death. Static models at catheter onset included logistic, multinomial logistic, Cox, cause-specific hazard, and Fine-Gray regression. Dynamic models updated predictions daily up to 30 days after catheter onset (i.e. landmarks 0 to 30 days), and included landmark supermodel extensions of the static models, separate Fine-Gray models per landmark time, and regularized multi-task learning (RMTL). Model performance was assessed using 100 random 2:1 train-test splits. Results The Cox model performed worst of all static models in terms of area under the receiver operating characteristic curve (AUC) and calibration. Dynamic landmark supermodels reached peak AUCs between 0.741-0.747 at landmark 5. The Cox landmark supermodel had the worst AUCs (<=0.731) and calibration up to landmark 7. Separate Fine-Gray models per landmark performed worst for later landmarks, when the number of patients at risk was low. Discussion and Conclusion Categorical and time-to-event approaches had similar performance in the static and dynamic settings, except Cox models. Ignoring competing risks caused problems for risk prediction in the time-to-event framework (Cox), but not in the categorical framework (logistic regression).

Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear measurements or subsampled isometries and has found many applications, including accelerated magnetic resonance imaging, which is modeled by the subsampled Fourier transform. In this work, we develop a general theory of infinite-dimensional compressed sensing for abstract inverse problems, possibly ill-posed, involving an arbitrary forward operator. This is achieved by considering a generalized restricted isometry property, and a quasi-diagonalization property of the forward map. As a notable application, for the first time, we obtain rigorous recovery estimates for the sparse Radon transform (i.e., with a finite number of angles $\theta_1,\dots,\theta_m$), which models computed tomography, in both the parallel-beam and the fan-beam settings. In the case when the unknown signal is $s$-sparse with respect to an orthonormal basis of compactly supported wavelets, we prove stable recovery under the condition \[ m\gtrsim s, \] up to logarithmic factors.