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We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent advection velocity, diffusion coefficient, and reaction rates. We also examine a model with mass-dependent coefficients describing aggregation with sedimentation. For the simplified model, we obtain an exact solution for the stationary spatially dependent agglomerate densities. In the model describing aggregation with sedimentation, we report a new conservation law and develop a scaling theory for the densities. For numerical efficiency we exploit the low-rank approximation technique; this dramatically increases the computational speed and allows simulations of large systems. The numerical results are in excellent agreement with the predictions of our theory.

Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables ($p$) diverges as the number of serially dependent observations ($n$) increases. In this paper, we present a novel functional factor model for high-dimensional functional time series that maintains and makes use of the functional and dynamic structure to achieve great dimension reduction and find the latent factor structure. To estimate the number of functional factors and the factor loadings, we propose a fully functional estimation procedure based on an eigenanalysis for a nonnegative definite matrix. Our proposal involves a weight matrix to improve the estimation efficiency and tackle the issue of heterogeneity, the rationality of which is illustrated by formulating the estimation from a novel regression perspective. Asymptotic properties of the proposed method are studied when $p$ diverges at some polynomial rate as $n$ increases. To provide a parsimonious model and enhance interpretability for near-zero factor loadings, we impose sparsity assumptions on the factor loading space and then develop a regularized estimation procedure with theoretical guarantees when $p$ grows exponentially fast relative to $n.$ Finally, we demonstrate that our proposed estimators significantly outperform the competing methods through both simulations and applications to a U.K. temperature dataset and a Japanese mortality dataset.

In online experimentation, trigger-dilute analysis is an approach to obtain more precise estimates of intent-to-treat (ITT) effects when the intervention is only exposed, or "triggered", for a small subset of the population. Trigger-dilute analysis cannot be used for estimation when triggering is only partially observed. In this paper, we propose an unbiased ITT estimator with reduced variance for cases where triggering status is only observed in the treatment group. Our method is based on the efficiency augmentation idea of CUPED and draws upon identification frameworks from the principal stratification and instrumental variables literature. The unbiasedness of our estimation approach relies on a testable assumption that an augmentation term used for covariate adjustment equals zero in expectation. When this augmentation term fails a mean-zero test, we show how our estimator can incorporate in-experiment observations to reduce the augmentation's bias, by sacrificing the amount of variance reduced. This provides an explicit knob to trade off bias with variance. We demonstrate through simulations that our estimator can remain unbiased and achieve precision improvements as good as if triggering status were fully observed, and in some cases outperforms trigger-dilute analysis.

The use of mathematical models to make predictions about tumor growth and response to treatment has become increasingly more prevalent in the clinical setting. The level of complexity within these models ranges broadly, and the calibration of more complex models correspondingly requires more detailed clinical data. This raises questions about how much data should be collected and when, in order to minimize the total amount of data used and the time until a model can be calibrated accurately. To address these questions, we propose a Bayesian information-theoretic procedure, using a gradient-based score function to determine the optimal data collection times for model calibration. The novel score function introduced in this work eliminates the need for a weight parameter used in a previous study's score function, while still yielding accurate and efficient model calibration using even fewer scans on a sample set of synthetic data, simulating tumors of varying levels of radiosensitivity. We also conduct a robust analysis of the calibration accuracy and certainty, using both error and uncertainty metrics. Unlike the error analysis of the previous study, the inclusion of uncertainty analysis in this work|as a means for deciding when the algorithm can be terminated|provides a more realistic option for clinical decision-making, since it does not rely on data that will be collected later in time.

A key challenge in causal inference from observational studies is the identification of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel framework that leverages information in multiple parallel outcomes for causal identification with unmeasured confounding. Under a conditional independence structure among multiple parallel outcomes, we achieve nonparametric identification of causal effects with at least three parallel outcomes. Our identification results pave the road for causal effect estimation with multiple outcomes. In the Supplementary Material, we illustrate the promises of this framework by developing nonparametric estimating procedures in the discrete case, and evaluating their finite sample performance through numerical studies.

Bayesian methods for modelling and inference are being increasingly used in the cryospheric sciences, and glaciology in particular. Here, we present a review of recent works in glaciology that adopt a Bayesian approach when conducting an analysis. We organise the chapter into three categories: i) Gaussian-Gaussian models, ii) Bayesian hierarchical models, and iii) Bayesian calibration approaches. In addition, we present two detailed case studies that involve the application of Bayesian hierarchical models in glaciology. The first case study is on the spatial prediction of surface mass balance across the Icelandic mountain glacier Langj\"okull, and the second is on the prediction of sea-level rise contributions from the Antactcic ice sheet. This chapter is presented in such a way that it is accessible to both statisticians as well as earth scientists.

Feature attribution is often loosely presented as the process of selecting a subset of relevant features as a rationale of a prediction. This lack of clarity stems from the fact that we usually do not have access to any notion of ground-truth attribution and from a more general debate on what good interpretations are. In this paper we propose to formalise feature selection/attribution based on the concept of relaxed functional dependence. In particular, we extend our notions to the instance-wise setting and derive necessary properties for candidate selection solutions, while leaving room for task-dependence. By computing ground-truth attributions on synthetic datasets, we evaluate many state-of-the-art attribution methods and show that, even when optimised, some fail to verify the proposed properties and provide wrong solutions.

We study the use of the Wave-U-Net architecture for speech enhancement, a model introduced by Stoller et al for the separation of music vocals and accompaniment. This end-to-end learning method for audio source separation operates directly in the time domain, permitting the integrated modelling of phase information and being able to take large temporal contexts into account. Our experiments show that the proposed method improves several metrics, namely PESQ, CSIG, CBAK, COVL and SSNR, over the state-of-the-art with respect to the speech enhancement task on the Voice Bank corpus (VCTK) dataset. We find that a reduced number of hidden layers is sufficient for speech enhancement in comparison to the original system designed for singing voice separation in music. We see this initial result as an encouraging signal to further explore speech enhancement in the time-domain, both as an end in itself and as a pre-processing step to speech recognition systems.

Rankings of people and items are at the heart of selection-making, match-making, and recommender systems, ranging from employment sites to sharing economy platforms. As ranking positions influence the amount of attention the ranked subjects receive, biases in rankings can lead to unfair distribution of opportunities and resources, such as jobs or income. This paper proposes new measures and mechanisms to quantify and mitigate unfairness from a bias inherent to all rankings, namely, the position bias, which leads to disproportionately less attention being paid to low-ranked subjects. Our approach differs from recent fair ranking approaches in two important ways. First, existing works measure unfairness at the level of subject groups while our measures capture unfairness at the level of individual subjects, and as such subsume group unfairness. Second, as no single ranking can achieve individual attention fairness, we propose a novel mechanism that achieves amortized fairness, where attention accumulated across a series of rankings is proportional to accumulated relevance. We formulate the challenge of achieving amortized individual fairness subject to constraints on ranking quality as an online optimization problem and show that it can be solved as an integer linear program. Our experimental evaluation reveals that unfair attention distribution in rankings can be substantial, and demonstrates that our method can improve individual fairness while retaining high ranking quality.

There is a need for systems to dynamically interact with ageing populations to gather information, monitor health condition and provide support, especially after hospital discharge or at-home settings. Several smart devices have been delivered by digital health, bundled with telemedicine systems, smartphone and other digital services. While such solutions offer personalised data and suggestions, the real disruptive step comes from the interaction of new digital ecosystem, represented by chatbots. Chatbots will play a leading role by embodying the function of a virtual assistant and bridging the gap between patients and clinicians. Powered by AI and machine learning algorithms, chatbots are forecasted to save healthcare costs when used in place of a human or assist them as a preliminary step of helping to assess a condition and providing self-care recommendations. This paper describes integrating chatbots into telemedicine systems intended for elderly patient after their hospital discharge. The paper discusses possible ways to utilise chatbots to assist healthcare providers and support patients with their condition.