{"title":"[公式:见文本]类liouville量子重力表面下,通过费曼路径积分方法研究水流对鱼类洄游的影响。","authors":"Paramahansa Pramanik","doi":"10.1007/s12064-021-00345-7","DOIUrl":null,"url":null,"abstract":"<p><p>A stochastic differential game theoretic model has been proposed to determine optimal behavior of a fish while migrating against water currents both in rivers and oceans. Then, a dynamic objective function is maximized subject to two stochastic dynamics, one represents its location and another its relative velocity against water currents. In relative velocity stochastic dynamics, a Cucker-Smale type stochastic differential equation is introduced under white noise. As the information regarding hydrodynamic environment is incomplete and imperfect, a Feynman type path integral under <math>\n <msqrt>\n <mn>8</mn>\n <mrow>\n <mo>/</mo>\n </mrow>\n <mn>3</mn>\n </msqrt>\n</math> Liouville-like quantum gravity surface has been introduced to obtain a Wick-rotated Schrödinger type equation to determine an optimal strategy of a fish during its migration. The advantage of having Feynman type path integral is that, it can be used in more generalized nonlinear stochastic differential equations where constructing a Hamiltonian-Jacobi-Bellman (HJB) equation is impossible. The mathematical analytic results show exact expression of an optimal strategy of a fish under imperfect information and uncertainty.</p>","PeriodicalId":54428,"journal":{"name":"Theory in Biosciences","volume":"140 2","pages":"205-223"},"PeriodicalIF":1.3000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"<ArticleTitle xmlns:ns0=\\\"http://www.w3.org/1998/Math/MathML\\\">Effects of water currents on fish migration through a Feynman-type path integral approach under <ns0:math>\\n <ns0:msqrt>\\n <ns0:mn>8</ns0:mn>\\n <ns0:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <ns0:mo>/</ns0:mo>\\n </ns0:mrow>\\n <ns0:mn>3</ns0:mn>\\n </ns0:msqrt>\\n</ns0:math> Liouville-like quantum gravity surfaces.\",\"authors\":\"Paramahansa Pramanik\",\"doi\":\"10.1007/s12064-021-00345-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>A stochastic differential game theoretic model has been proposed to determine optimal behavior of a fish while migrating against water currents both in rivers and oceans. Then, a dynamic objective function is maximized subject to two stochastic dynamics, one represents its location and another its relative velocity against water currents. In relative velocity stochastic dynamics, a Cucker-Smale type stochastic differential equation is introduced under white noise. As the information regarding hydrodynamic environment is incomplete and imperfect, a Feynman type path integral under <math>\\n <msqrt>\\n <mn>8</mn>\\n <mrow>\\n <mo>/</mo>\\n </mrow>\\n <mn>3</mn>\\n </msqrt>\\n</math> Liouville-like quantum gravity surface has been introduced to obtain a Wick-rotated Schrödinger type equation to determine an optimal strategy of a fish during its migration. The advantage of having Feynman type path integral is that, it can be used in more generalized nonlinear stochastic differential equations where constructing a Hamiltonian-Jacobi-Bellman (HJB) equation is impossible. The mathematical analytic results show exact expression of an optimal strategy of a fish under imperfect information and uncertainty.</p>\",\"PeriodicalId\":54428,\"journal\":{\"name\":\"Theory in Biosciences\",\"volume\":\"140 2\",\"pages\":\"205-223\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory in Biosciences\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1007/s12064-021-00345-7\",\"RegionNum\":4,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2021/5/20 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory in Biosciences","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1007/s12064-021-00345-7","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/5/20 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"BIOLOGY","Score":null,"Total":0}
Effects of water currents on fish migration through a Feynman-type path integral approach under 8/3 Liouville-like quantum gravity surfaces.
A stochastic differential game theoretic model has been proposed to determine optimal behavior of a fish while migrating against water currents both in rivers and oceans. Then, a dynamic objective function is maximized subject to two stochastic dynamics, one represents its location and another its relative velocity against water currents. In relative velocity stochastic dynamics, a Cucker-Smale type stochastic differential equation is introduced under white noise. As the information regarding hydrodynamic environment is incomplete and imperfect, a Feynman type path integral under Liouville-like quantum gravity surface has been introduced to obtain a Wick-rotated Schrödinger type equation to determine an optimal strategy of a fish during its migration. The advantage of having Feynman type path integral is that, it can be used in more generalized nonlinear stochastic differential equations where constructing a Hamiltonian-Jacobi-Bellman (HJB) equation is impossible. The mathematical analytic results show exact expression of an optimal strategy of a fish under imperfect information and uncertainty.
期刊介绍:
Theory in Biosciences focuses on new concepts in theoretical biology. It also includes analytical and modelling approaches as well as philosophical and historical issues. Central topics are:
Artificial Life;
Bioinformatics with a focus on novel methods, phenomena, and interpretations;
Bioinspired Modeling;
Complexity, Robustness, and Resilience;
Embodied Cognition;
Evolutionary Biology;
Evo-Devo;
Game Theoretic Modeling;
Genetics;
History of Biology;
Language Evolution;
Mathematical Biology;
Origin of Life;
Philosophy of Biology;
Population Biology;
Systems Biology;
Theoretical Ecology;
Theoretical Molecular Biology;
Theoretical Neuroscience & Cognition.