{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/10100605","title":"Stochastic Continuous Time Neurite Branching Models with Tree and Segment Dependent Rates","arxiv_id":"1010.0605","date":"2010-10-04","proceeding":null,"authors":["Ronald A. J. van Elburg"],"abstract":"In this paper we introduce a continuous time stochastic neurite branching\nmodel closely related to the discrete time stochastic BES-model. The discrete\ntime BES-model is underlying current attempts to simulate cortical development,\nbut is difficult to analyze. The new continuous time formulation facilitates\nanalytical treatment thus allowing us to examine the structure of the model\nmore closely. We derive explicit expressions for the time dependent\nprobabilities p(\\gamma, t) for finding a tree \\gamma at time t, valid for\narbitrary continuous time branching models with tree and segment dependent\nbranching rates. We show, for the specific case of the continuous time\nBES-model, that as expected from our model formulation, the sums needed to\nevaluate expectation values of functions of the terminal segment number\n\\mu(f(n),t) do not depend on the distribution of the total branching\nprobability over the terminal segments. In addition, we derive a system of\ndifferential equations for the probabilities p(n,t) of finding n terminal\nsegments at time t. For the continuous BES-model, this system of differential\nequations gives direct numerical access to functions only depending on the\nnumber of terminal segments, and we use this to evaluate the development of the\nmean and standard deviation of the number of terminal segments at a time t. For\ncomparison we discuss two cases where mean and variance of the number of\nterminal segments are exactly solvable. Then we discuss the numerical\nevaluation of the S-dependence of the solutions for the continuous time\nBES-model. The numerical results show clearly that higher S values, i.e. values\nsuch that more proximal terminal segments have higher branching rates than more\ndistal terminal segments, lead to more symmetrical trees as measured by three\ntree symmetry indicators.","url_abs":"http://arxiv.org/abs/1010.0605v2","url_pdf":"http://arxiv.org/pdf/1010.0605v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"10100605","repo_url":"https://github.com/ModelDBRepository/129071","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}