en.wikipedia.org/wiki/Nonlocal_operator | Nonlocal operator - Wikipedia
arxiv.org/abs/2401.14651v1 | Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
www.semanticscholar.org/paper/Nonlocal-Models-in-Biology-and-Life-Sciences%3A-and-Pal-Melnik/0fddca01e001b0199c1c243d7feb1793d1a917a6 |Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
www.semanticscholar.org/paper/Aggregation-Diffusion-Equations%3A-Dynamics%2C-and-Carrillo-Craig/df8ebb70e27261ce04ee1b74b1b3032c15fc1e61 Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits
(not chess anytime soon, but hey i think i can share where i come from, or what I think is going to make sense to me when I get to put some reading energy into it).
www.semanticscholar.org/paper/Mathematics-of-Darwin%E2%80%99s-Diagram-Bessonov-Reinberg/8884cf25ed278df7896d894708fe15335ab1ed8c | [PDF] Mathematics of Darwin’s Diagram | Semantic Scholar
www.semanticscholar.org/paper/Nonlocal-Reaction%E2%80%93Diffusion-Model-of-Viral-of-Virus-Bessonov-Bocharov/da0823d58124fe2c4ad8a885df17d3eabdccf653?sort=pub-date |
Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains | Semantic Scholar
www.semanticscholar.org/paper/Nonlocal-Reaction%E2%80%93Diffusion-Equations-in-Biomedical-Banerjee-Kuznetsov/21323e23de269cb7c3c716c2c5b396afa8f8f72f |
Nonlocal Reaction–Diffusion Equations in Biomedical Applications | Semantic Scholar
pubmed.ncbi.nlm.nih.gov/35298702/link.springer.com/article/10.1007/s10441-022-09436-4 |
Nonlocal Reaction–Diffusion Equations in Biomedical Applications | Acta Biotheoretica
TODO: make sure nonlocal is what I think it is here. Because I think the phrasing is not specific. diffusion imply some non time arrow dependent variable domain, that I would not hesistate calling space, as it would serve its imagination support purpose to complete with math. linguistics later. We can think of diffusion, as the drop of milk cloud in ones coffer, looking at the initial transient could envelope evolution until thermal agitation loses all trace of that invading drop in pre-existing resting state of the whole cup content. Yes, intuition here, is definitely going to help.. cut on the pita of my ramblings. intuitoin is not flight of fancy in my usage. to be sure..
so start with a less limited proposition of intergral formulation with a function space a "parameter" domain, e.g. convolution kernels in the convolution integral formulation of the NN math. models before they get CPUed or prepared for that implementation. that can also be a more intense linguistic formulation to digest, as in all things transformed from their human concept is elegant mathematics, to the discrete versoins, needing more exectution precision, and extra overhead symbols from having to decide on grain size, and bounded values.. and keep following more indices of those, without the visual compressed, yet expresive symbolic version (which is usually critical to interpretation pass through, soit dit en passant).
but one can discussion different familiy "shapes" of such intergrant mutliplier of the state variables being followed. or flowed through time from appropriate initial condition domain, and invariant forward region or bounding region. things coming back of the various conditions that make those things well posed.. intution backbone helping find those back in verbal future sharing intent.
not dead yet that past blob. oh. it would be immunology, but also other evolutionary problems in physiological context like cancer, but also ecological contexts liek epidemiology, one can look at physicological tissue levels and bounder and well regulated ecosystem of many critters of cell types having an apparently cacophonic symphony of molecular exchanges across the ambient fluid.. good old hormonal signalling from tissue to tissue, but also locally within tissues.. Lots of cross-talks in all directions.. and yet it does some function .. stuff. (kidding, or using one of those words that remind me of certain chess theory words, not all but, how much one can struggle when not asking or not having the means to answer a question, so why even subconscious pop it out?
what is function in biology? I have not discussed that for some 15 years. But it is at the center, I think of the sought for understanding beyond the accumulation of data as knowledge expansion. I have been away from that keyboard for many years, but biological systems denomition seems to have survive in some lingo I might have seen on the webs.. it that sign of the return of physiology thinking into biolgoy (as a cloud of science fields, including the medical arts and techonololgies). Well, more the fundamental stuff. than the medical practice.. I mean research, and fundamental.. not very popular as i does not make a buck very fast for the investors.. yet. I would consider it part of the public necessary infrastructure, as much as roads or intentnet might be considered tangible. just that the time scale. are longer than Quarters horizon, and typical political or funding deciders horizon.
hormone concept, I was told or understood, was invented before any hormonal molecular evidence was ever found. It was induced hypothesis, imagined probably anthropomorphized in the thinking of the conceiving proponent, with no proof whatsover, to be a simple explanation that ought to make our whole body made of different and visibly so already segment of tissues.
how can any such thing work and function, through time.. in vivo? I don,t know the details. I was spoiler with knowledge already..
