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Both the number of disasters in the U.S. and federal outlays following disasters are rising. FEMA's Public Assistance (PA) is a key program for rebuilding damaged public infrastructure and aiding local and state governments in recovery. It is the primary post-disaster source of recovery funds. Between 2000 and 2019, more than $125B (adjusted, 2020 dollars) was awarded through PA. While all who qualify for PA should have equal opportunity to receive aid, not all do, and the factors influencing how the program has been administered are complex and multifaceted. Lacking an understanding of the factors positively associated with historical receipt of aid, there is little way to objectively evaluate the efficacy of the PA program. In this work, we evaluate the salient features that contribute to the number of county-level PA applicants and projects following disasters. We use statistical learning theory applied to repetitive flooding events in the upper Midwest between 2003 and 2018 as a case study. The results suggest that many non-disaster related indicators are key predictors of PA outlays, including the state in which the disaster occurred, the county's prior experience with disasters, the county's median income, and the length of time between the end of the disaster and the date when a disaster is declared. Our work suggests that indicators of PA aid are tied to exposure, bureaucratic attributes, and human behavior. For equitable distribution of aid, policymakers should explore more disaster-relevant indicators for PA distribution. [ABSTRACT FROM AUTHOR]

Physics Informed Neural Networks (PINNs) have been achieving ever newer feats of solving complicated Partial Differential Equations (PDEs) numerically while offering an attractive trade-off between accuracy and speed of inference. A particularly challenging aspect of PDEs is that there exist simple PDEs which can evolve into singular solutions in finite time starting from smooth initial conditions. In recent times some striking experiments have suggested that PINNs might be good at even detecting such finite-time blow-ups. In this work, we embark on a program to investigate this stability of PINNs from a rigorous theoretical viewpoint. Firstly, we derive error bounds for PINNs for Burgers’ PDE, in arbitrary dimensions, under conditions that allow for a finite-time blow-up. Our bounds give a theoretical justification for the functional regularization terms that have been reported to be useful for training PINNs near finite-time blow-up. Then we demonstrate via experiments that our bounds are significantly correlated to the $\ell_2$ -distance of the neurally found surrogate from the true blow-up solution, when computed on sequences of PDEs that are getting increasingly close to a blow-up.

Legionella pneumophila (L. pneumophila) is a pathogenic bacterium primarily known for causing Legionnaires' Disease which is known for high mortality rates, particularly in the elderly. With caseloads continuing to increase, further research is needed to improve our understanding of optimized sampling schema and safe limits of L. pneumophila, in part to target improved treatment options and realistic population-level risk modeling. Particularly in healthcare and other high-risk locations these become crucial and time sensitive needs. Therefore, we conceptualized this research as a means of incorporating easily measured physiochemical water quality parameters and generalization of the unique ecology of building water systems to build a computational model that can allow for more rapid and accurate decision making. This research uses the specific machine learning (ML) method called statistical learning theory to incorporate concentration of host cells, such as native amoeba, and physiochemical water quality parameters to estimate the probability of observing ranges of Legionella gene copy concentrations. Using data from previously published research on Legionella prevalence in a large building, our ML method trains the model on the relative impacts of physiochemical parameters on likely amoeba host cell occurrences. The model is expanded to estimate host cell concentrations using correlations and regressions operated through LASSO algorithms. After categorization variables from these results are then used to inform a logistic regression to provide an estimate of the probability of Legionella gene copy concentration ranges. In summary, conventional results generated by logistic regression and multiple linear regression quantified the associations among ecological conditions in the water and ability to predict a likely range of Legionella concentration in a management focused way. Further, two ML methods, PCA and LASSO, demonstrated feasibility in accurate real-time monitoring of Legionella through physiochemical indicators as evidenced with good accuracy of predictions based for validation results. Furthermore results demonstrate the vital need to account for the impact of water quality on building on host cells, and via their quantified water microbial ecology, not just Legionella concentrations., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

For any K > 2 and the multiplicative cyclic group Ω K of order K , consider any function f : Ω K n → C and its Fourier expansion f (z) = ∑ α ∈ { 0 , 1 , ... , K − 1 } n a α z α , with d : = deg ⁡ (f) denoting its degree as a multivariate polynomial. We prove a Bohnenblust–Hille (BH) inequality in this setting: the ℓ 2 d / (d + 1) norm of the Fourier coefficients of f is bounded by C (d , K) ‖ f ‖ ∞ with C (d , K) independent of n. This is the interpolating case between the now well-understood BH inequalities for functions on the poly-torus (K = ∞) and the hypercube (K = 2) but those extreme cases of K have special properties whose absence for intermediate K prevent a proof by the standard BH framework. New techniques are developed exploiting the group structure of Ω K n. By known reductions, the cyclic group BH inequality also entails a noncommutative BH inequality for tensor products of the K × K complex matrix algebra (or in the language of quantum mechanics, systems of K -level qudits). These new BH inequalities generalize several applications in harmonic analysis and statistical learning theory to broader classes of functions and operators. [ABSTRACT FROM AUTHOR]