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In this work, we introduce a three-step semiparametric methodology for the estimation of production frontiers. We consider a model inspired by the well-known Cobb-Douglas production function, wherein input factors operate multiplicatively within the model. Efficiency in the proposed model is assumed to follow a continuous univariate uniparametric distribution in $(0,1)$, referred to as Matsuoka's distribution, which is discussed in detail. Following model linearization, the first step is to semiparametrically estimate the regression function through a local linear smoother. The second step focuses on the estimation of the efficiency parameter. Finally, we estimate the production frontier through a plug-in methodology. We present a rigorous asymptotic theory related to the proposed three-step estimation, including consistency, and asymptotic normality, and derive rates for the convergences presented. Incidentally, we also study the Matsuoka's distribution, deriving its main properties. The Matsuoka's distribution exhibits a versatile array of shapes capable of effectively encapsulating the typical behavior of efficiency within production frontier models. To complement the large sample results obtained, a Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed three-step methodology. An empirical application using a dataset of Danish milk producers is also presented.

Abstract Like electoral systems, decision-making methods are also vulnerable to manipulation by decision-makers. The ability to effectively defend against such threats can only come from thoroughly understanding the manipulation mechanisms. In the presented article, we show two algorithms that can be used to launch a manipulation attack. They allow for equating the weights of two selected alternatives in the pairwise comparison method and, consequently, choosing a leader. The theoretical considerations are accompanied by a Monte Carlo simulation showing the relationship between the size of the PC matrix, the degree of inconsistency, and the ease of manipulation. This work is a continuation of our previous research published in the paper (Szybowski et al., 2023)

Entropy conditions play a crucial role in the extraction of a physically relevant solution for a system of conservation laws, thus motivating the construction of entropy stable schemes that satisfy a discrete analogue of such conditions. TeCNO schemes (Fjordholm et al. 2012) form a class of arbitrary high-order entropy stable finite difference solvers, which require specialized reconstruction algorithms satisfying the sign property at each cell interface. Recently, third-order WENO schemes called SP-WENO (Fjordholm and Ray, 2016) and SP-WENOc (Ray, 2018) have been designed to satisfy the sign property. However, these WENO algorithms can perform poorly near shocks, with the numerical solutions exhibiting large spurious oscillations. In the present work, we propose a variant of the SP-WENO, termed as Deep Sign-Preserving WENO (DSP-WENO), where a neural network is trained to learn the WENO weighting strategy. The sign property and third-order accuracy are strongly imposed in the algorithm, which constrains the WENO weight selection region to a convex polygon. Thereafter, a neural network is trained to select the WENO weights from this convex region with the goal of improving the shock-capturing capabilities without sacrificing the rate of convergence in smooth regions. The proposed synergistic approach retains the mathematical framework of the TeCNO scheme while integrating deep learning to remedy the computational issues of the WENO-based reconstruction. We present several numerical experiments to demonstrate the significant improvement with DSP-WENO over the existing variants of WENO satisfying the sign property.

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

The Linear Model of Co-regionalization (LMC) is a very general model of multitask gaussian process for regression or classification. While its expressivity and conceptual simplicity are appealing, naive implementations have cubic complexity in the number of datapoints and number of tasks, making approximations mandatory for most applications. However, recent work has shown that under some conditions the latent processes of the model can be decoupled, leading to a complexity that is only linear in the number of said processes. We here extend these results, showing from the most general assumptions that the only condition necessary to an efficient exact computation of the LMC is a mild hypothesis on the noise model. We introduce a full parametrization of the resulting \emph{projected LMC} model, and an expression of the marginal likelihood enabling efficient optimization. We perform a parametric study on synthetic data to show the excellent performance of our approach, compared to an unrestricted exact LMC and approximations of the latter. Overall, the projected LMC appears as a credible and simpler alternative to state-of-the art models, which greatly facilitates some computations such as leave-one-out cross-validation and fantasization.

We propose a material design method via gradient-based optimization on compositions, overcoming the limitations of traditional methods: exhaustive database searches and conditional generation models. It optimizes inputs via backpropagation, aligning the model's output closely with the target property and facilitating the discovery of unlisted materials and precise property determination. Our method is also capable of adaptive optimization under new conditions without retraining. Applying to exploring high-Tc superconductors, we identified potential compositions beyond existing databases and discovered new hydrogen superconductors via conditional optimization. This method is versatile and significantly advances material design by enabling efficient, extensive searches and adaptability to new constraints.

We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms Logistic Regression, Random Forest, and Support Vector Machine for this study. The input features are derived from the recurrence quantification of nonlinear time series and characteristic measures of the corresponding recurrence networks. For training and testing we generate synthetic data from standard nonlinear dynamical systems and evaluate the efficiency and performance of the machine learning algorithms in classifying time series into periodic, chaotic, hyper-chaotic, or noisy categories. Additionally, we explore the significance of input features in the classification scheme and find that the features quantifying the density of recurrence points are the most relevant. Furthermore, we illustrate how the trained algorithms can successfully predict the dynamical states of two variable stars, SX Her and AC Her from the data of their light curves.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

There is currently considerable excitement within government about the potential of artificial intelligence to improve public service productivity through the automation of complex but repetitive bureaucratic tasks, freeing up the time of skilled staff. Here, we explore the size of this opportunity, by mapping out the scale of citizen-facing bureaucratic decision-making procedures within UK central government, and measuring their potential for AI-driven automation. We estimate that UK central government conducts approximately one billion citizen-facing transactions per year in the provision of around 400 services, of which approximately 143 million are complex repetitive transactions. We estimate that 84% of these complex transactions are highly automatable, representing a huge potential opportunity: saving even an average of just one minute per complex transaction would save the equivalent of approximately 1,200 person-years of work every year. We also develop a model to estimate the volume of transactions a government service undertakes, providing a way for government to avoid conducting time consuming transaction volume measurements. Finally, we find that there is high turnover in the types of services government provide, meaning that automation efforts should focus on general procedures rather than services themselves which are likely to evolve over time. Overall, our work presents a novel perspective on the structure and functioning of modern government, and how it might evolve in the age of artificial intelligence.

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.