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Abstract Thek-dimensional functional order property ($$\operatorname {FOP}_k$$ ${FOP}_k$) is a combinatorial property of a$$(k+1)$$ $(k+1)$-partitioned formula. This notion arose in work of Terry and Wolf [59, 60], which identified$$\operatorname {NFOP}_2$$ ${NFOP}_2$as a ternary analogue of stability in the context of two finitary combinatorial problems related to hypergraph regularity and arithmetic regularity. In this paper we show$$\operatorname {NFOP}_k$$ ${NFOP}_k$has equally strong implications in model-theoretic classification theory, where its behavior as a$$(k+1)$$ $(k+1)$-ary version of stability is in close analogy to the behavior ofk-dependence as a$$(k+1)$$ $(k+1)$-ary version of$$\operatorname {NIP}$$ $NIP$. Our results include several new characterizations of$$\operatorname {NFOP}_k$$ ${NFOP}_k$, including a characterization in terms of collapsing indiscernibles, combinatorial recharacterizations, and a characterization in terms of type-counting when$$k=2$$ $k=2$. As a corollary of our collapsing theorem, we show$$\operatorname {NFOP}_k$$ ${NFOP}_k$is closed under Boolean combinations, and that$$\operatorname {FOP}_k$$ ${FOP}_k$can always be witnessed by a formula where all but one variable have length 1. When$$k=2$$ $k=2$, we prove a composition lemma analogous to that of Chernikov and Hempel from the setting of 2-dependence. Using this, we provide a new class of algebraic examples of$$\operatorname {NFOP}_2$$ ${NFOP}_2$theories. Specifically, we show that ifTis the theory of an infinite dimensional vector space over a fieldK, equipped with a bilinear form satisfying certain properties, thenTis$$\operatorname {NFOP}_2$$ ${NFOP}_2$if and only ifKis stable. Along the way we provide a corrected and reorganized proof of Granger’s quantifier elimination and completeness results for these theories. 

Applications of Copper (Cu) range from small scale applications such as microelectronics interconnects to very large high-powered applications such as railguns. In all these applications, Cu conductivity and ampacity play vital roles. In some applications such as railguns, where Cu also plays a structural role, not only is high conductivity needed, but high strength, high ductility, and high wear resistance are also critical. Current technologies have achieved their full potential for producing better materials. New approaches and technologies are needed to develop superior properties. This research examines a new fabrication approach that is expected to produce Cu with superior mechanical strength, enhanced wear resistance, and increased electrical conductivity. Materials with refined grain structures were obtained by breaking down the coarse-grained Cu particles via cryogenic ball milling, followed by the consolidation of powders using cold isostatic pressing (CIP) and subsequent Continuous Equal Channel Angular Pressing (C-ECAP). The mixture of fine and ultrafine grains, with sizes between 200 nm to 2.5 µm and an average of 500 nm, was formed after ball milling at cryogenic temperatures. Further processing via C-ECAP produced nanostructured Cu with average grain sizes below 50 nm and excellent homogenous equiaxed grain shapes and random orientations. The hardness and tensile strength of the final Cu were approximately 158% and 95% higher than the traditional coarse-grained Cu bar, respectively. This material also displayed a good electrical conductivity rate of 74% International Annealed Copper Standard (IACS), which is comparable to the current Cu materials used in railgun applications. 

Community assembly describes how different ecological processes shape microbial community composition and structure. How environmental factors impact community assembly remains elusive. Here we sampled microbial communities and >200 biogeochemical variables in groundwater at the Oak Ridge Field Research Center, a former nuclear waste disposal site, and developed a theoretical framework to conceptualize the relationships between community assembly processes and environmental stresses. We found that stochastic assembly processes were critical (>60% on average) in shaping community structure, but their relative importance decreased as stress increased. Dispersal limitation and ‘drift’ related to random birth and death had negative correlations with stresses, whereas the selection processes leading to dissimilar communities increased with stresses, primarily related to pH, cobalt and molybdenum. Assembly mechanisms also varied greatly among different phylogenetic groups. Our findings highlight the importance of microbial dispersal limitation and environmental heterogeneity in ecosystem restoration and management. 

ABSTRACT Unconventional oil and gas (UOG) extraction is increasing exponentially around the world, as new technological advances have provided cost-effective methods to extract hard-to-reach hydrocarbons. While UOG has increased the energy output of some countries, past research indicates potential impacts in nearby stream ecosystems as measured by geochemical and microbial markers. Here, we utilized a robust data set that combines 16S rRNA gene amplicon sequencing (DNA), metatranscriptomics (RNA), geochemistry, and trace element analyses to establish the impact of UOG activity in 21 sites in northern Pennsylvania. These data were also used to design predictive machine learning models to determine the UOG impact on streams. We identified multiple biomarkers of UOG activity and contributors of antimicrobial resistance within the order Burkholderiales . Furthermore, we identified expressed antimicrobial resistance genes, land coverage, geochemistry, and specific microbes as strong predictors of UOG status. Of the predictive models constructed ( n  = 30), 15 had accuracies higher than expected by chance and area under the curve values above 0.70. The supervised random forest models with the highest accuracy were constructed with 16S rRNA gene profiles, metatranscriptomics active microbial composition, metatranscriptomics active antimicrobial resistance genes, land coverage, and geochemistry ( n  = 23). The models identified the most important features within those data sets for classifying UOG status. These findings identified specific shifts in gene presence and expression, as well as geochemical measures, that can be used to build robust models to identify impacts of UOG development. IMPORTANCE The environmental implications of unconventional oil and gas extraction are only recently starting to be systematically recorded. Our research shows the utility of microbial communities paired with geochemical markers to build strong predictive random forest models of unconventional oil and gas activity and the identification of key biomarkers. Microbial communities, their transcribed genes, and key biomarkers can be used as sentinels of environmental changes. Slight changes in microbial function and composition can be detected before chemical markers of contamination. Potential contamination, specifically from biocides, is especially concerning due to its potential to promote antibiotic resistance in the environment. Additionally, as microbial communities facilitate the bulk of nutrient cycling in the environment, small changes may have long-term repercussions. Supervised random forest models can be used to identify changes in those communities, greatly enhance our understanding of what such impacts entail, and inform environmental management decisions. 

In the follow-up treatment of high-grade gliomas (HGGs), differentiating true tumor progression from treatment-related effects, such as pseudoprogression and radiation necrosis, presents an ongoing clinical challenge. Conventional MRI with and without intravenous contrast serves as the clinical benchmark for the posttreatment surveillance imaging of HGG. However, many advanced imaging techniques have shown promise in helping better delineate the findings in indeterminate scenarios, as posttreatment effects can often mimic true tumor progression on conventional imaging. These challenges are further confounded by the histologic admixture that can commonly occur between tumor growth and treatment-related effects within the posttreatment bed. This review discusses the current practices in the surveillance imaging of HGG and the role of advanced imaging techniques, including perfusion MRI and metabolic MRI.