Benjamin Garcia de Figueiredo, Justin M. Calabrese, William F. Fagan, Ricardo Martinez-Garcia
{"title":"反应扩散过程中反应间时间的结构及其对计数统计的影响","authors":"Benjamin Garcia de Figueiredo, Justin M. Calabrese, William F. Fagan, Ricardo Martinez-Garcia","doi":"arxiv-2409.11433","DOIUrl":null,"url":null,"abstract":"Many natural phenomena are quantified by counts of observable events, from\nthe annihilation of quasiparticles in a lattice to predator-prey encounters on\na landscape to spikes in a neural network. These events are triggered at random\nintervals when an underlying dynamical system occupies a set of reactive states\nin its phase space. We derive a general expression for the distribution of\ntimes between events in such counting processes assuming the underlying\ntriggering dynamics is a stochastic process that converges to a stationary\ndistribution. Our results contribute to resolving a long-standing dichotomy in\nthe study of reaction-diffusion processes, showing the inter-reaction point\nprocess interpolates between a reaction- and a diffusion-limited regime. At low\nreaction rates, the inter-reaction process is Poisson with a rate depending on\nstationary properties of the event-triggering stochastic process. At high\nreaction rates, inter-reaction times are dominated by the hitting times to the\nreactive states. To further illustrate the power of this approach we apply our\nframework to obtain the counting statistics of two counting processes appearing\nin several biophysical scenarios. First, we study the common situation of\nestimating an animal's activity level by how often it crosses a detector,\nshowing that the mean number of crossing events can decrease monotonically with\nthe hitting rate, a seemingly 'paradoxical' result that could possibly lead to\nmisinterpretation of experimental count data. Second, we derive the ensemble\nstatistics for the detection of many particles, recovering and generalizing\nknown results in the biophysics of chemosensation. Overall, we develop a\nunifying theoretical framework to quantify inter-event time distributions in\nreaction-diffusion systems that clarifies existing debates in the literature\nand provide examples of application to real-world scenarios.","PeriodicalId":501040,"journal":{"name":"arXiv - PHYS - Biological Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The structure of inter-reaction times in reaction-diffusion processes and consequences for counting statistics\",\"authors\":\"Benjamin Garcia de Figueiredo, Justin M. Calabrese, William F. Fagan, Ricardo Martinez-Garcia\",\"doi\":\"arxiv-2409.11433\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many natural phenomena are quantified by counts of observable events, from\\nthe annihilation of quasiparticles in a lattice to predator-prey encounters on\\na landscape to spikes in a neural network. These events are triggered at random\\nintervals when an underlying dynamical system occupies a set of reactive states\\nin its phase space. We derive a general expression for the distribution of\\ntimes between events in such counting processes assuming the underlying\\ntriggering dynamics is a stochastic process that converges to a stationary\\ndistribution. Our results contribute to resolving a long-standing dichotomy in\\nthe study of reaction-diffusion processes, showing the inter-reaction point\\nprocess interpolates between a reaction- and a diffusion-limited regime. At low\\nreaction rates, the inter-reaction process is Poisson with a rate depending on\\nstationary properties of the event-triggering stochastic process. At high\\nreaction rates, inter-reaction times are dominated by the hitting times to the\\nreactive states. To further illustrate the power of this approach we apply our\\nframework to obtain the counting statistics of two counting processes appearing\\nin several biophysical scenarios. First, we study the common situation of\\nestimating an animal's activity level by how often it crosses a detector,\\nshowing that the mean number of crossing events can decrease monotonically with\\nthe hitting rate, a seemingly 'paradoxical' result that could possibly lead to\\nmisinterpretation of experimental count data. Second, we derive the ensemble\\nstatistics for the detection of many particles, recovering and generalizing\\nknown results in the biophysics of chemosensation. 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The structure of inter-reaction times in reaction-diffusion processes and consequences for counting statistics
Many natural phenomena are quantified by counts of observable events, from
the annihilation of quasiparticles in a lattice to predator-prey encounters on
a landscape to spikes in a neural network. These events are triggered at random
intervals when an underlying dynamical system occupies a set of reactive states
in its phase space. We derive a general expression for the distribution of
times between events in such counting processes assuming the underlying
triggering dynamics is a stochastic process that converges to a stationary
distribution. Our results contribute to resolving a long-standing dichotomy in
the study of reaction-diffusion processes, showing the inter-reaction point
process interpolates between a reaction- and a diffusion-limited regime. At low
reaction rates, the inter-reaction process is Poisson with a rate depending on
stationary properties of the event-triggering stochastic process. At high
reaction rates, inter-reaction times are dominated by the hitting times to the
reactive states. To further illustrate the power of this approach we apply our
framework to obtain the counting statistics of two counting processes appearing
in several biophysical scenarios. First, we study the common situation of
estimating an animal's activity level by how often it crosses a detector,
showing that the mean number of crossing events can decrease monotonically with
the hitting rate, a seemingly 'paradoxical' result that could possibly lead to
misinterpretation of experimental count data. Second, we derive the ensemble
statistics for the detection of many particles, recovering and generalizing
known results in the biophysics of chemosensation. Overall, we develop a
unifying theoretical framework to quantify inter-event time distributions in
reaction-diffusion systems that clarifies existing debates in the literature
and provide examples of application to real-world scenarios.