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We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex polytope, a concentration phenomenon arises for this generalized relative entropy, and we quantify the concentration precisely. We also present a probabilistic formulation, and extend the concentration results to it. In addition, we provide a number of simplifications and improvements to our previous work, notably in dualizing the optimization problem, in the concentration with respect to $\ell_{\infty}$ distance, and in the relationship to generalized KL-divergence. A number of our results apply to general compact convex sets, not necessarily polyhedral.

Double robustness (DR) is a widely-used property of estimators that provides protection against model misspecification and slow convergence of nuisance functions. While DR is a global property on the probability distribution manifold, it often coincides with influence curves, which only ensure orthogonality to nuisance directions locally. This apparent discrepancy raises fundamental questions about the theoretical underpinnings of DR. In this short communication, we address two key questions: (1) Why do influence curves frequently imply DR "for free"? (2) Under what conditions do DR estimators exist for a given statistical model and parameterization? Using tools from semiparametric theory, we show that convexity is the crucial property that enables influence curves to imply DR. We then derive necessary and sufficient conditions for the existence of DR estimators under a mean squared differentiable path-connected parameterization. Our main contribution also lies in the novel geometric interpretation of DR using information geometry. By leveraging concepts such as parallel transport, m-flatness, and m-curvature freeness, we characterize DR in terms of invariance along submanifolds. This geometric perspective deepens the understanding of when and why DR estimators exist. The results not only resolve apparent mysteries surrounding DR but also have practical implications for the construction and analysis of DR estimators. The geometric insights open up new connections and directions for future research. Our findings aim to solidify the theoretical foundations of a fundamental concept and contribute to the broader understanding of robust estimation in statistics.

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first seeks a set of edges that leaves no disconnected nodes in the network; the second seeks a causal large connected component in the data. We tested these methods both for discrete synthetic and real data, and compared the results with those obtained for the PC algorithm, which we took as the benchmark. We show that this novel algorithm is generally faster and more accurate than the PC algorithm. The algorithm for determining the thresholds requires choosing a measure of causality. We tested our methods for Fisher Correlations, commonly used in PC algorithm (for instance in \cite{kalisch2005}), and further proposed a discrete and asymmetric measure of causality, that we called Net Influence, which provided very good results when inferring causal networks from discrete data. This metric allows for inferring directionality of the edges in the process of applying the thresholds, speeding up the inference of causal DAGs.

We give a simpler analysis of the ascending auction of Bikhchandani, de Vries, Schummer, and Vohra to sell a welfare-maximizing base of a matroid at Vickrey prices. The new proofs for economic efficiency and the charge of Vickrey prices only require a few matroid folklore theorems, therefore shortening the analysis of the design goals of the auction significantly.

The prevalence of digital media and evolving sociopolitical dynamics have significantly amplified the dissemination of hateful content. Existing studies mainly focus on classifying texts into binary categories, often overlooking the continuous spectrum of offensiveness and hatefulness inherent in the text. In this research, we present an extensive benchmark dataset for Amharic, comprising 8,258 tweets annotated for three distinct tasks: category classification, identification of hate targets, and rating offensiveness and hatefulness intensities. Our study highlights that a considerable majority of tweets belong to the less offensive and less hate intensity levels, underscoring the need for early interventions by stakeholders. The prevalence of ethnic and political hatred targets, with significant overlaps in our dataset, emphasizes the complex relationships within Ethiopia's sociopolitical landscape. We build classification and regression models and investigate the efficacy of models in handling these tasks. Our results reveal that hate and offensive speech can not be addressed by a simplistic binary classification, instead manifesting as variables across a continuous range of values. The Afro-XLMR-large model exhibits the best performances achieving F1-scores of 75.30%, 70.59%, and 29.42% for the category, target, and regression tasks, respectively. The 80.22% correlation coefficient of the Afro-XLMR-large model indicates strong alignments.

This work introduces a cooperative inspection system designed to efficiently control and coordinate a team of distributed heterogeneous UAV agents for the inspection of 3D structures in cluttered, unknown spaces. Our proposed approach employs a two-stage innovative methodology. Initially, it leverages the complementary sensing capabilities of the robots to cooperatively map the unknown environment. It then generates optimized, collision-free inspection paths, thereby ensuring comprehensive coverage of the structure's surface area. The effectiveness of our system is demonstrated through qualitative and quantitative results from extensive Gazebo-based simulations that closely replicate real-world inspection scenarios, highlighting its ability to thoroughly inspect real-world-like 3D structures.

Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the weights are appropriately constrained. This is to be contrasted with the ordinary ResNet architecture which, even if the spectral norms of the weights are constrained, has a Lipschitz constant that, in the worst case, grows exponentially with the depth of the network. Further analysis of the proposed architecture shows that the spectral norms of the weights can be further constrained to ensure that the network is an averaged operator, making it a natural candidate for a learned denoiser in Plug-and-Play algorithms. Using a novel adaptive way of enforcing the spectral norm constraints, we show that, even with these constraints, it is possible to train performant networks. The proposed architecture is applied to the problem of adversarially robust image classification, to image denoising, and finally to the inverse problem of deblurring.

This study introduces a new approach to optimize the geometrical parameters of pipe diffusers in centrifugal compressors for Micro Gas Turbines, tailored for a 100 kW unit. The methodology draws insights from optimized airfoil-type diffusers and addresses the unique topological challenges of pipe diffusers, using diffuser maps to enhance design precision. The effectiveness of this method is validated through 3D-RANS based steady CFD simulations, using the ANSYS CFX solver. Comparative performance assessments at 100 percent rotation speed show that the best-performing pipe diffuser slightly trails its airfoil counterpart in efficiency, achieving 82.2 percent total-to-total isentropic efficiency compared to 84.4 percent. However, it offers a reduced frontal area, enhancing compactness. The analysis also reveals a dualistic impact from the leading-edge geometry of the pipe diffuser, which generates two counter-rotating vortices. These vortices have beneficial effects in pseudo and semi-vaneless spaces while introducing destabilizing factors in channel spaces. This investigation highlights potential trade-offs and outlines conditions under which adverse effects dominate, leading to significant flow separation. These insights pave the way for refining diffuser designs to better balance performance with spatial efficiency, marking a critical step forward in compressor technology of micro gas turbine for decentralized power systems.

We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional set of global spatio-temporal modes, interpretable characterizations of the underlying spatial and temporal scales can be computed. Forecasting is also achieved with a linear model that uses a linear superposition of the dominant spatio-temporal features. The DMD method is demonstrated on three months of global chemistry dynamics data, showing its significant performance in computational speed and interpretability. We show that the presented decomposition method successfully extracts known major features of atmospheric chemistry, such as summertime surface pollution and biomass burning activities. Moreover, the DMD algorithm allows for rapid reconstruction of the underlying linear model, which can then easily accommodate non-stationary data and changes in the dynamics.