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1. Pairs Of Diagonal Quartic Forms: The Non-Singular Hasse Principle

   https://doi.org/10.1093/qmath/haac019  

   Brüdern, Jörg; Wooley, Trevor D. (July 2022, The Quarterly Journal of Mathematics)

   Abstract We establish the non-singular Hasse principle for pairs of diagonal quartic equations in 22 or more variables. 

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2. Similarity in spatial structure constrains ecosystem relationships: Building a macroscale understanding of lakes

   https://doi.org/10.1111/geb.12781  

   Lapierre, Jean‐Francois; Collins, Sarah_M; Seekell, David_A; Spence_Cheruvelil, Kendra; Tan, Pang‐Ning; Skaff, Nicholas_K; Taranu, Zofia_E; Fergus, C_Emi; Soranno, Patricia_A (September 2018, Global Ecology and Biogeography)

   Abstract AimWe aimed to measure the dominant spatial patterns in ecosystem properties (such as nutrients and measures of primary production) and the multi‐scaled geographical driver variables of these properties and to quantify how the spatial structure of pattern in all of these variables influences the strength of relationships among them. Location and time periodWe studied > 8,500 lakes in a 1.8 million km²area of Northeast U.S.A. Data comprised 10‐year medians (2002–2011) for measured ecosystem properties, long‐term climate averages and recent land use/land cover variables. Major taxa studiedWe focused on ecosystem properties at the base of aquatic food webs, including concentrations of nutrients and algal pigments that are proxies of primary productivity. MethodsWe quantified spatial structure in ecosystem properties and their geographical driver variables using distance‐based Moran eigenvector maps (dbMEMs). We then compared the similarity in spatial structure for all pairs of variables with the correlation between variables to illustrate how spatial structure constrains relationships among ecosystem properties. ResultsThe strength of spatial structure decreased in order for climate, land cover/use, lake ecosystem properties and lake and landscape morphometry. Having a comparable spatial structure is a necessary condition to observe a strong relationship between a pair of variables, but not a sufficient one; variables with very different spatial structure are never strongly correlated. Lake ecosystem properties tended to have an intermediary spatial structure compared with that of their main drivers, probably because climate and landscape variables with known ecological links induce spatial patterns. Main conclusionOur empirical results describe inherent spatial constraints that dictate the expected relationships between ecosystem properties and their geographical drivers at macroscales. Our results also suggest that understanding the spatial scales at which ecological processes operate is necessary to predict the effects of multi‐scaled environmental changes on ecosystem properties. 

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3. High spatial resolution global ocean metagenomes from Bio-GO-SHIP repeat hydrography transects

   https://doi.org/10.1038/s41597-021-00889-9  

   Larkin, Alyse A.; Garcia, Catherine A.; Garcia, Nathan; Brock, Melissa L.; Lee, Jenna A.; Ustick, Lucas J.; Barbero, Leticia; Carter, Brendan R.; Sonnerup, Rolf E.; Talley, Lynne D.; et al (April 2021, Scientific Data)

   Abstract Detailed descriptions of microbial communities have lagged far behind physical and chemical measurements in the marine environment. Here, we present 971 globally distributed surface ocean metagenomes collected at high spatio-temporal resolution. Our low-cost metagenomic sequencing protocol produced 3.65 terabases of data, where the median number of base pairs per sample was 3.41 billion. The median distance between sampling stations was 26 km. The metagenomic libraries described here were collected as a part of a biological initiative for the Global Ocean Ship-based Hydrographic Investigations Program, or “Bio-GO-SHIP.” One of the primary aims of GO-SHIP is to produce high spatial and vertical resolution measurements of key state variables to directly quantify climate change impacts on ocean environments. By similarly collecting marine metagenomes at high spatiotemporal resolution, we expect that this dataset will help answer questions about the link between microbial communities and biogeochemical fluxes in a changing ocean. 

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4. An Iterative Penalized Least Squares Approach to Sparse Canonical Correlation Analysis

   https://doi.org/10.1111/biom.13043  

   Mai, Qing; Zhang, Xin (February 2019, Biometrics)

   Abstract It is increasingly interesting to model the relationship between two sets of high-dimensional measurements with potentially high correlations. Canonical correlation analysis (CCA) is a classical tool that explores the dependency of two multivariate random variables and extracts canonical pairs of highly correlated linear combinations. Driven by applications in genomics, text mining, and imaging research, among others, many recent studies generalize CCA to high-dimensional settings. However, most of them either rely on strong assumptions on covariance matrices, or do not produce nested solutions. We propose a new sparse CCA (SCCA) method that recasts high-dimensional CCA as an iterative penalized least squares problem. Thanks to the new iterative penalized least squares formulation, our method directly estimates the sparse CCA directions with efficient algorithms. Therefore, in contrast to some existing methods, the new SCCA does not impose any sparsity assumptions on the covariance matrices. The proposed SCCA is also very flexible in the sense that it can be easily combined with properly chosen penalty functions to perform structured variable selection and incorporate prior information. Moreover, our proposal of SCCA produces nested solutions and thus provides great convenient in practice. Theoretical results show that SCCA can consistently estimate the true canonical pairs with an overwhelming probability in ultra-high dimensions. Numerical results also demonstrate the competitive performance of SCCA. 

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5. The performance of Cu-based friction material in dry clutch engagement

   https://doi.org/10.1177/1350650120944281  

   Koranteng, Kingsford; Shaahu, Joseph-Shaahu; Chengnan, Ma; Li, Heyan; Yi, Yun-Bo (July 2020, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology)

   An enhanced Cu-based friction material was prepared by the powder metallurgy techniques and proposed for use in the dry clutch system. The friction characteristics and wear rate of this friction material sliding against 65Mn steel are obtained using Universal Material Tester-5. The friction pairs were subjected to two operating variables, which are sliding speed and temperature. The effect of these variables during the engagement process of the friction pairs is investigated. Knowing the normal applied force and dimension of the clutch disc, the dynamic friction coefficient was translated to friction torque capacity with time. It was found that instability can be excited at low operational conditions when the resulting friction coefficient is high. At 25 ℃, the dynamic friction torque oscillates with time likewise at 400 ℃. Generally, a more stable friction torque is obtained when the sliding speed is varied compared to varying the temperatures. Moreover, the influence of the operating temperatures and sliding speeds on thermal buckling and thermoelastic instability of the friction disc is the second consideration in this work. The onset of thermoelastic instability occurs when the sliding speed exceeded 200 r/min and the results for the growth rate of hot spots were found to agree well with the critical speed of the system. Also, thermal buckling was highly dependent on the temperature difference between the inner and outer radius of the friction disc. 

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