More Like this

1. Functional Autoencoders for Functional Data Representation Learning

   https://doi.org/10.1137/1.9781611976700.75  

   Hsieh, Tsung-Yu ; Wang, Suhang ; Honavar, Vasant ( January 2021 , Proceedings of the SIAM International Conference on Data Mining)

   In many real-world applications, e.g., monitoring of individual health, climate, brain activity, environmental exposures, among others, the data of interest change smoothly over a continuum, e.g., time, yielding multi-dimensional functional data. Solving clustering, classification, and regression problems with functional data calls for effective methods for learning compact representations of functional data. Existing methods for representation learning from functional data, e.g., functional principal component analysis, are generally limited to learning linear mappings from the data space to the representation space. However, in many applications, such linear methods do not suffice. Hence, we study the novel problem of learning non-linear representations of functional data. Specifically, we propose functional autoencoders, which generalize neural network autoencoders so as to learn non-linear representations of functional data. We derive from first principles, a functional gradient based algorithm for training functional autoencoders. We present results of experiments which demonstrate that the functional autoencoders outperform the state-of-the-art baseline methods. 

   more » « less
2. HasChor: Functional Choreographic Programming for All (Functional Pearl)

   https://doi.org/10.1145/3607849  

   Shen, Gan ; Kashiwa, Shun ; Kuper, Lindsey ( August 2023 , Proceedings of the ACM on Programming Languages)

   Choreographic programming is an emerging paradigm for programming distributed systems. In choreographic programming, the programmer describes the behavior of the entire system as a single, unified program -- a choreography-- which is then compiled to individual programs that run on each node, via a compilation step called endpoint projection. We present a new model for functional choreographic programming where choreographies are expressed as computations in a monad. Our model supports cutting-edge choreographic programming features that enable modularity and code reuse: in particular, it supports higher-order choreographies, in which a choreography may be passed as an argument to another choreography, and location-polymorphic choreographies, in which a choreography can abstract over nodes. Our model is implemented in a Haskell library, HasChor, which lets programmers write choreographic programs while using the rich Haskell ecosystem at no cost, bringing choreographic programming within reach of everyday Haskellers. Moreover, thanks to Haskell's abstractions, the implementation of the HasChor library itself is concise and understandable, boiling down endpoint projection to its short and simple essence.

    

   more » « less
3. Functional Frogs

   https://doi.org/10.1525/abt.2023.85.8.448  

   Flud, Gabrielle ; Angle, Julie ; Simon, Monique N ; Moen, Daniel S ( October 2023 , The American Biology Teacher)

   Evolution by natural selection and adaptation are core concepts in biology that students must see and correctly understand their meaning. However, using these concepts in evidence-based learning strategies in the classroom is a difficult task. Here, we present a 5E lesson plan to address the Next Generation Science Standards performance expectation HS-LS4-4, to “construct an explanation based on evidence for how natural selection leads to adaptation of populations.” The Functional Frogs lesson provides multiple hands-on activities to engage students in the development of hypotheses, collection and analysis of empirical data on frog swimming, presentation of results, and construction of explanations supported by evidence for the results. The lesson’s central idea is for students to understand the trait values that provide an advantage in the aquatic environment, increasing a frog’s survival. The link between morphological changes and survival is used to explain how natural selection acts on populations, leading to adaptive evolution.

    

   more » « less
4. FMEM: Functional Mixed Effects Models for Longitudinal Functional Responses

   https://doi.org/10.5705/ss.202017.0505  

   Zhu, Hongtu ; Chen, Kehui ; Luo, Xinchao ; Yuan, Ying ; Wang, Jane-Ling ( January 2019 , Statistica Sinica)
5. 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. 

   more » « less