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1. Functional geometry and the Traité de Lutherie: functional pearl

   https://doi.org/10.1145/2544174.2500617  

   Mairson, Harry George ( November 2013 , ACM SIGPLAN Notices)

   We describe a functional programming approach to the design of outlines of eighteenth-century string instruments. The approach is based on the research described in François Denis's book, Traité de lutherie . The programming vernacular for Denis's instructions, which we call functional geometry , is meant to reiterate the historically justified language and techniques of this musical instrument design. The programming metaphor is entirely Euclidean, involving straightedge and compass constructions, with few (if any) numbers, and no Cartesian equations or grid. As such, it is also an interesting approach to teaching programming and mathematics without numerical calculation or equational reasoning. The advantage of this language-based, functional approach to lutherie is founded in the abstract characterization of common patterns in instrument design. These patterns include not only the abstraction of common straightedge and compass constructions, but of higher-order conceptualization of the instrument design process. We also discuss the role of arithmetic, geometric, harmonic, and subharmonic proportions, and the use of their rational approximants. 

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2. Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection

   https://doi.org/10.3390/e24020203  

   Naiman, Joseph ; Song, Peter Xuekun ( February 2022 , Entropy)

   Motivated by mobile devices that record data at a high frequency, we propose a new methodological framework for analyzing a semi-parametric regression model that allow us to study a nonlinear relationship between a scalar response and multiple functional predictors in the presence of scalar covariates. Utilizing functional principal component analysis (FPCA) and the least-squares kernel machine method (LSKM), we are able to substantially extend the framework of semi-parametric regression models of scalar responses on scalar predictors by allowing multiple functional predictors to enter the nonlinear model. Regularization is established for feature selection in the setting of reproducing kernel Hilbert spaces. Our method performs simultaneously model fitting and variable selection on functional features. For the implementation, we propose an effective algorithm to solve related optimization problems in that iterations take place between both linear mixed-effects models and a variable selection method (e.g., sparse group lasso). We show algorithmic convergence results and theoretical guarantees for the proposed methodology. We illustrate its performance through simulation experiments and an analysis of accelerometer data. 

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3. Dynamic Musculoskeletal Functional Morphology: Integrating diceCT and XROMM: DYNAMIC FUNCTIONAL MORPHOLOGY

   https://doi.org/10.1002/ar.23714  

   Orsbon, Courtney P. ; Gidmark, Nicholas J. ; Ross, Callum F. ( February 2018 , The Anatomical Record)
4. Common latitudinal gradients in functional richness and functional evenness across marine and terrestrial systems

   https://doi.org/10.1098/rspb.2019.0745  

   Schumm, M. ; Edie, S. M. ; Collins, K. S. ; Gómez-Bahamón, V. ; Supriya, K. ; White, A. E. ; Price, T. D. ; Jablonski, D. ( July 2019 , Proceedings of the Royal Society B: Biological Sciences)
5. Common latitudinal gradients in functional richness and functional evenness across marine and terrestrial systems.

   Schumm, M. ; Edie, S.M. ; Collins, K.S. ; Gómez-Bahamón, V. ; Supriya, K. ; White, A.E. ; Price, T.D. ; Jablonski, D. ( July 2019 , Proceedings - Royal Society. Biological Sciences)

   Functional diversity is an important aspect of biodiversity, but its relationship to species diversity in time and space is poorly understood. Here we compare spatial patterns of functional and taxonomic diversity across marine and terrestrial systems to identify commonalities in their respective ecological and evolutionary drivers. We placed species-level ecological traits into comparable multi-dimensional frameworks for two model systems, marine bivalves and terrestrial birds, and used global speciesoccurrence data to examine the distribution of functional diversity with latitude and longitude. In both systems, tropical faunas show high total functional richness (FR) but low functional evenness (FE) (i.e. the tropics contain a highly skewed distribution of species among functional groups). Functional groups that persist toward the poles become more uniform in species richness, such that FR declines and FE rises with latitude in both systems. Temperate assemblages are more functionally even than tropical assemblages subsampled to temperate levels of species richness, suggesting that high species richness in the tropics reflects a high degree of ecological specialization within a few functional groups and/or factors that favour high recent speciation or reduced extinction rates in those groups. 

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