{"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/weber-s-law-based-perception-and-the","title":"Weber's law based perception and the stability of animal groups","arxiv_id":"1806.00716","date":"2019-04-18","proceeding":null,"authors":[],"abstract":"Group living animals form aggregations and flocks that remain cohesive in\nspite of internal movements of individuals. This is possible because individual\ngroup members repeatedly adjust their position and motion in response to the\nposition and motion of other group members. Here we develop a theoretical\napproach to address the question, what general features -- if any -- underlie\nthe interaction rules that mediate group stability in animals of all species?\nWe do so by considering how the spatial organisation of a group would change in\nthe complete absence of interactions. Without interactions, a group would\ndisperse in a way that can be easily characterised in terms of Fick's diffusion\nequations. We can hence address the inverse theoretical problem of finding the\nindividual-level interaction responses that are required to counterbalance\ndiffusion and to preserve group stability. We show that an individual-level\nresponse to neighbour densities in the form of Weber's law (a 'universal' law\ndescribing the functioning of the sensory systems of animals of all species)\nresults in an 'anti-diffusion' term at the group level. On short time scales,\nthis anti-diffusion restores the initial group configuration in a way which is\nreminiscent of methods for image deblurring in image processing. We also show\nthat any non-homogeneous, spatial density distribution can be preserved over\ntime if individual movement patterns have the form of a Weber's law response.\nWeber's law describes the fundamental functioning of perceptual systems. Our\nstudy indicates that it is also a necessary -- but not sufficient -- feature of\ncollective interactions in stable animal groups.","url_abs":"http://arxiv.org/abs/1806.00716v3","url_pdf":"http://arxiv.org/pdf/1806.00716v3.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":"weber-s-law-based-perception-and-the","repo_url":"https://github.com/pernafrost/weber_law_antidiffusion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"image-deblurring","task_name":"Image Deblurring"},{"task_slug":null,"task_name":"Position"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}