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Women are at increased risk of bone loss during the menopausal transition; in fact, nearly 50\% of women's lifetime bone loss occurs during this time. The longitudinal relationships between estradiol (E2) and follicle-stimulating hormone (FSH), two hormones that change have characteristic changes during the menopausal transition, and bone health outcomes are complex. However, in addition to level and rate of change in E2 and FSH, variability in these hormones across the menopausal transition may be an important predictor of bone health, but this question has yet to be well explored. We introduce a joint model that characterizes individual mean estradiol (E2) trajectories and the individual residual variances and links these variances to bone health trajectories. In our application, we found that higher FSH variability was associated with declines in bone mineral density (BMD) before menopause, but this association was moderated over time after the menopausal transition. Additionally, higher mean E2, but not E2 variability, was associated with slower decreases in during the menopausal transition. We also include a simulation study that shows that naive two-stage methods often fail to propagate uncertainty in the individual-level variance estimates, resulting in estimation bias and invalid interval coverage

This work aims to explore the community structure of Santiago de Chile by analyzing the movement patterns of its residents. We use a dataset containing the approximate locations of home and work places for a subset of anonymized residents to construct a network that represents the movement patterns within the city. Through the analysis of this network, we aim to identify the communities or sub-cities that exist within Santiago de Chile and gain insights into the factors that drive the spatial organization of the city. We employ modularity optimization algorithms and clustering techniques to identify the communities within the network. Our results present that the novelty of combining community detection algorithms with segregation tools provides new insights to further the understanding of the complex geography of segregation during working hours.

There has been an increasingly widespread agreement among both academic circles and the general public that the Social Media Platforms (SMPs) play a central role in the dissemination of harmful and negative sentiment content in a coordinated manner. A substantial body of recent scholarly research has demonstrated the ways in which hateful content, political propaganda, and targeted messaging on SMPs have contributed to serious real-world consequences. Adopting inspirations from graph theory, in this paper we apply novel network and community finding algorithms over a representative Facebook dataset (n=608,417) which we have scrapped through 630 pages. By applying Girvan-Newman algorithm over the historical dataset our analysis finds five communities of coordinated networks of actors, within the contexts of Indian far-right Hindutva discourse. This work further paves the path for future potentials of applying such novel network analysis algorithms to SMPs, in order to automatically identify toxic coordinated communities and sub-communities, and to possibly resist real-world threats emerging from information dissemination in the SMPs.

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to compute the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption and capillarity.

In real life, success is often contingent upon multiple critical steps that are distant in time from each other and from the final reward. These critical steps are challenging to identify with traditional reinforcement learning (RL) methods that rely on the Bellman equation for credit assignment. Here, we present a new RL algorithm that uses offline contrastive learning to hone in on critical steps. This algorithm, which we call contrastive introspection (ConSpec), can be added to any existing RL algorithm. ConSpec learns a set of prototypes for the critical steps in a task by a novel contrastive loss and delivers an intrinsic reward when the current state matches one of these prototypes. The prototypes in ConSpec provide two key benefits for credit assignment: (1) They enable rapid identification of all the critical steps. (2) They do so in a readily interpretable manner, enabling out-of-distribution generalization when sensory features are altered. Distinct from other contemporary RL approaches to credit assignment, ConSpec takes advantage of the fact that it is easier to retrospectively identify the small set of steps that success is contingent upon than it is to prospectively predict reward at every step taken in the environment. Altogether, ConSpec improves learning in a diverse set of RL tasks, including both those with explicit, discrete critical steps and those with complex, continuous critical steps.

Condensed mathematics, developed by Clausen and Scholze over the last few years, is a new way of studying the interplay between algebra and geometry. It replaces the concept of a topological space by a more sophisticated but better-behaved idea, namely that of a condensed set. Central to the theory are solid abelian groups and liquid vector spaces, analogues of complete topological groups. N\"obeling's theorem, a surprising result from the 1960s about the structure of the abelian group of continuous maps from a profinite space to the integers, is a crucial ingredient in the theory of solid abelian groups; without it one cannot give any nonzero examples of solid abelian groups. We discuss a recently completed formalisation of this result in the Lean theorem prover, and give a more detailed proof than those previously available in the literature. The proof is somewhat unusual in that it requires induction over ordinals -- a technique which has not previously been used to a great extent in formalised mathematics.

The attention towards food products characteristics, such as nutritional properties and traceability, has risen substantially in the recent years. Consequently, we are witnessing an increased demand for the development of modern tools to monitor, analyse and assess food quality and authenticity. Within this framework, an essential set of data collection techniques is provided by vibrational spectroscopy. In fact, methods such as Fourier near infrared and mid infrared spectroscopy have been often exploited to analyze different foodstuffs. Nonetheless, existing statistical methods often struggle to deal with the challenges presented by spectral data, such as their high dimensionality, paired with strong relationships among the wavelengths. Therefore, the definition of proper statistical procedures accounting for the peculiarities of spectroscopy data is paramount. In this work, motivated by two dairy science applications, we propose an adaptive functional regression framework for spectroscopy data. The method stems from the trend filtering literature, allowing the definition of a highly flexible and adaptive estimator able to handle different degrees of smoothness. We provide a fast optimization procedure that is suitable for both Gaussian and non Gaussian scalar responses, and allows for the inclusion of scalar covariates. Moreover, we develop inferential procedures for both the functional and the scalar component thus enhancing not only the interpretability of the results, but also their usability in real world scenarios. The method is applied to two sets of MIR spectroscopy data, providing excellent results when predicting milk chemical composition and cows' dietary treatments. Moreover, the developed inferential routine provides relevant insights, potentially paving the way for a richer interpretation and a better understanding of the impact of specific wavelengths on milk features.

When students and users of statistical methods first learn about regression analysis there is an emphasis on the technical details of models and estimation methods that invariably runs ahead of the purposes for which these models might be used. More broadly, statistics is widely understood to provide a body of techniques for "modelling data", underpinned by what we describe as the "true model myth", according to which the task of the statistician/data analyst is to build a model that closely approximates the true data generating process. By way of our own historical examples and a brief review of mainstream clinical research journals, we describe how this perspective leads to a range of problems in the application of regression methods, including misguided "adjustment" for covariates, misinterpretation of regression coefficients and the widespread fitting of regression models without a clear purpose. We then outline an alternative approach to the teaching and application of regression methods, which begins by focussing on clear definition of the substantive research question within one of three distinct types: descriptive, predictive, or causal. The simple univariable regression model may be introduced as a tool for description, while the development and application of multivariable regression models should proceed differently according to the type of question. Regression methods will no doubt remain central to statistical practice as they provide a powerful tool for representing variation in a response or outcome variable as a function of "input" variables, but their conceptualisation and usage should follow from the purpose at hand.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.