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Recent discussions on the future of metropolitan cities underscore the pivotal role of (social) equity, driven by demographic and economic trends. More equal policies can foster and contribute to a city's economic success and social stability. In this work, we focus on identifying metropolitan areas with distinct economic and social levels in the greater Los Angeles area, one of the most diverse yet unequal areas in the United States. Utilizing American Community Survey data, we propose a Bayesian model for boundary detection based on income distributions. The model identifies areas with significant income disparities, offering actionable insights for policymakers to address social and economic inequalities. Our approach formalized as a Bayesian structural learning framework, models areal densities through finite mixture models. Efficient posterior computation is facilitated by a transdimensional Markov Chain Monte Carlo sampler. The methodology is validated via extensive simulations and applied to the income distributions in the greater Los Angeles area. We identify several boundaries in the income distributions which can be explained in light of other social dynamics such as crime rates and healthcare, showing the usefulness of such an analysis to policymakers.

Compositional data are contemporarily defined as positive vectors, the ratios among whose elements are of interest to the researcher. Financial statement analysis by means of accounting ratios fulfils this definition to the letter. Compositional data analysis solves the major problems in statistical analysis of standard financial ratios at industry level, such as skewness, non-normality, non-linearity and dependence of the results on the choice of which accounting figure goes to the numerator and to the denominator of the ratio. In spite of this, compositional applications to financial statement analysis are still rare. In this article, we present some transformations within compositional data analysis that are particularly useful for financial statement analysis. We show how to compute industry or sub-industry means of standard financial ratios from a compositional perspective. We show how to visualise firms in an industry with a compositional biplot, to classify them with compositional cluster analysis and to relate financial and non-financial indicators with compositional regression models. We show an application to the accounting statements of Spanish wineries using DuPont analysis, and a step-by-step tutorial to the compositional freeware CoDaPack.

Rational best approximations (in a Chebyshev sense) to real functions are characterized by an equioscillating approximation error. Similar results do not hold true for rational best approximations to complex functions in general. In the present work, we consider unitary rational approximations to the exponential function on the imaginary axis, which map the imaginary axis to the unit circle. In the class of unitary rational functions, best approximations are shown to exist, to be uniquely characterized by equioscillation of a phase error, and to possess a super-linear convergence rate. Furthermore, the best approximations have full degree (i.e., non-degenerate), achieve their maximum approximation error at points of equioscillation, and interpolate at intermediate points. Asymptotic properties of poles, interpolation nodes, and equioscillation points of these approximants are studied. Three algorithms, which are found very effective to compute unitary rational approximations including candidates for best approximations, are sketched briefly. Some consequences to numerical time-integration are discussed. In particular, time propagators based on unitary best approximants are unitary, symmetric and A-stable.

Reproduction numbers play a fundamental role in population dynamics. For age-structured models, these quantities are typically defined as spectral radius of operators acting on infinite dimensional spaces. As a result, their analytical computation is hardly achievable without additional assumptions on the model coefficients (e.g., separability of age-specific transmission rates) and numerical approximations are needed. In this paper we introduce a general numerical approach, based on pseudospectral collocation of the relevant operators, for approximating the reproduction numbers of a class of age-structured models with finite life span. To our knowledge, this is the first numerical method that allows complete flexibility in the choice of the ``birth'' and ``transition'' processes, which is made possible by working with an equivalent problem for the integrated state. We discuss applications to epidemic models with continuous rates, as well as models with piecewise continuous rates estimated from real data, illustrating how the method can compute different reproduction numbers-including the basic and the type reproduction number as special cases-by considering different interpretations of the age variable (e.g., chronological age, infection age, disease age) and the transmission terms (e.g., horizontal and vertical transmission).

Interactions between genes and environmental factors may play a key role in the etiology of many common disorders. Several regularized generalized linear models (GLMs) have been proposed for hierarchical selection of gene by environment interaction (GEI) effects, where a GEI effect is selected only if the corresponding genetic main effect is also selected in the model. However, none of these methods allow to include random effects to account for population structure, subject relatedness and shared environmental exposure. In this paper, we develop a unified approach based on regularized penalized quasi-likelihood (PQL) estimation to perform hierarchical selection of GEI effects in sparse regularized mixed models. We compare the selection and prediction accuracy of our proposed model with existing methods through simulations under the presence of population structure and shared environmental exposure. We show that for all simulation scenarios, compared to other penalized methods, our proposed method enforced sparsity by controlling the number of false positives in the model while having the best predictive performance. Finally, we apply our method to a real data application using the Orofacial Pain: Prospective Evaluation and Risk Assessment (OPPERA) study, and found that our method retrieves previously reported significant loci.

We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to \gamma\in (0,1)$. An estimator of the out-of-sample error of a robust M-estimator is analysed and proved to be consistent for a large family of loss functions that includes the Huber loss. As an application of this result, we propose an adaptive tuning procedure of the scale parameter $\lambda>0$ of a given loss function $\rho$: choosing$\hat \lambda$ in a given interval $I$ that minimizes the out-of-sample error estimate of the M-estimator constructed with loss $\rho_\lambda(\cdot) = \lambda^2 \rho(\cdot/\lambda)$ leads to the optimal out-of-sample error over $I$. The proof relies on a smoothing argument: the unregularized M-estimation objective function is perturbed, or smoothed, with a Ridge penalty that vanishes as $n\to+\infty$, and show that the unregularized M-estimator of interest inherits properties of its smoothed version.

The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell's equations also solves the wave equation which makes calculations very efficient. In this way our problem can be considered as a coupling problem for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.

Categorization is one of the basic tasks in machine learning and data analysis. Building on formal concept analysis (FCA), the starting point of the present work is that different ways to categorize a given set of objects exist, which depend on the choice of the sets of features used to classify them, and different such sets of features may yield better or worse categorizations, relative to the task at hand. In their turn, the (a priori) choice of a particular set of features over another might be subjective and express a certain epistemic stance (e.g. interests, relevance, preferences) of an agent or a group of agents, namely, their interrogative agenda. In the present paper, we represent interrogative agendas as sets of features, and explore and compare different ways to categorize objects w.r.t. different sets of features (agendas). We first develop a simple unsupervised FCA-based algorithm for outlier detection which uses categorizations arising from different agendas. We then present a supervised meta-learning algorithm to learn suitable (fuzzy) agendas for categorization as sets of features with different weights or masses. We combine this meta-learning algorithm with the unsupervised outlier detection algorithm to obtain a supervised outlier detection algorithm. We show that these algorithms perform at par with commonly used algorithms for outlier detection on commonly used datasets in outlier detection. These algorithms provide both local and global explanations of their results.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.

Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential future research directions.