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In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces under random diffeomorphisms. 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Dr. Miller is a founder of and holds equity in AnatomyWorks. This arrangement has been reviewed and approved by the Johns Hopkins University in accordance with its conflict of interest policies.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The purpose of this work is to investigate a computational technique that is being used in the brain mapping community. The roles and responsibilities of the authors were discussed prior to the research. Efforts were made to make the work accessible by, for example, providing data used in the experiments, and maintaining an open-source repository of the code with extensive documentation.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Inclusion and Ethics Statement"}},{"value":"The mouse projection neuron traces came from the MouseLight project\u2019s NeuronBrowser website and the experimental protocols that generated this data can be found in Winnubst et al. ().","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Research Animals Statement"}},{"value":"The remaining authors have no conflicts of interest to declare.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}]}}