Effects of water currents on fish migration through a Feynman-type path integral approach under \(\sqrt{8/3}\) Liouville-like quantum gravity surfaces

• Ahn SM, Ha SY (2010) Stochastic flocking dynamics of the cucker-smale model with multiplicative white noises. J Math Phys 51(10):103301

  Article  Google Scholar 

• Arai T, Hayano H, Asami H, Miyazaki N (2003) Coexistence of anadromous and lacustrine life histories of the shirauo, salangichthys microdon. Fish Oceanogr 12(2):134–139

  Article  Google Scholar 

• Arai T, Yang J, Miyazaki N (2006) Migration flexibility between freshwater and marine habitats of the pond smelt hypomesus nipponensis. J Fish Biol 68(5):1388–1398

  Article  Google Scholar 

• Baaquie BE (1997) A path integral approach to option pricing with stochastic volatility: some exact results. J de Phys I 7(12):1733–1753

  Google Scholar 

• Baaquie BE (2007) Quantum finance: path integrals and Hamiltonians for options and interest rates. Cambridge University Press, Cambridge

  Google Scholar 

• Bauer S, Klaassen M (2013) Mechanistic models of animal migration behaviour-their diversity, structure and use. J Anim Ecol 82(3):498–508

  Article  PubMed  PubMed Central  Google Scholar 

• Bochner S, Chandrasekharan K et al (1949) Fourier transforms. Princeton University Press, Princeton

  Google Scholar 

• Carrillo JA, Fornasier M, Rosado J, Toscani G (2010) Asymptotic flocking dynamics for the kinetic cucker-smale model. SIAM J Math Anal 42(1):218–236

  Article  Google Scholar 

• Dorst JP (2019) Migration. https://www.britannica.com/science/migration-animal, [Online; posted 06-August-2019]

• Duplantier B, Sheffield S (2011) Liouville quantum gravity and kpz. Inventiones mathematicae 185(2):333–393

  Article  Google Scholar 

• Feynman RP (1948) Space-time approach to non-relativistic quantum mechanics. Rev Mod Phys 20(2):367

  Article  Google Scholar 

• Fujiwara D (2017) Feynman’s idea. In rigorous time slicing approach to feynman path integrals. Springer, Berlin

  Book  Google Scholar 

• Guse B, Kail J, Radinger J, Schröder M, Kiesel J, Hering D, Wolter C, Fohrer N (2015) Eco-hydrologic model cascades: simulating land use and climate change impacts on hydrology, hydraulics and habitats for fish and macroinvertebrates. Sci Total Environ 533:542–556

  Article  CAS  PubMed  Google Scholar 

• Gwynne E, Miller J (2016) Metric gluing of brownian and \(\sqrt{8/3}\)-liouville quantum gravity surfaces. arXiv preprint arXiv:160800955

• Ha SY, Lee K, Levy D et al (2009) Emergence of time-asymptotic flocking in a stochastic cucker-smale system. Commun Math Sci 7(2):453–469

  Article  Google Scholar 

• Hebb DO (1949) The organization of behavior: a neuropsychological theory. Wiley, Chapman & Hall

  Google Scholar 

• Hellman Z, Levy YJ (2019) Measurable selection for purely atomic games. Econometrica 87(2):593–629

  Article  Google Scholar 

• Jonsson N, Jonsson B (2002) Migration of anadromous brown trout salmo trutta in a Norwegian river. Freshw Biol 47(8):1391–1401

  Article  Google Scholar 

• Kappen HJ (2005a) Linear theory for control of nonlinear stochastic systems. Phys Rev Lett 95(20):200201

  Article  PubMed  Google Scholar 

• Kappen HJ (2005b) Path integrals and symmetry breaking for optimal control theory. J Stat Mech Theor Exp 2005(11):P11011

  Article  Google Scholar 

• Kappen HJ (2007) An introduction to stochastic control theory, path integrals and reinforcement learning. AIP conference proceedings, American Institute of Physics 887:149–181

• Knizhnik VG, Polyakov AM, Zamolodchikov AB (1988) Fractal structure of 2d-quantum gravity. Modern Phys Lett A 3(08):819–826

  Article  CAS  Google Scholar 

• Lande R, Engen S, Saether BE et al (2003) Stochastic population dynamics in ecology and conservation. Oxford University Press, Oxford

  Book  Google Scholar 

• Larsson M (2012) Incidental sounds of locomotion in animal cognition. Anim Cognit 15(1):1–13

  Article  Google Scholar 

• Lemasson BH, Haefner JW, Bowen MD (2014) Schooling increases risk exposure for fish navigating past artificial barriers. PloS One 9(9):108220

  Article  Google Scholar 

• Marcet A, Marimon R (2019) Recursive contracts. Econometrica 87(5):1589–1631

  Article  Google Scholar 

• Mas-Colell A, Whinston MD, Green JR et al (1995) Microeconomic theory, vol 1. Oxford University Press, New York

  Google Scholar 

• Miller J (2018) Liouville quantum gravity as a metric space and a scaling limit. In: proceedings of the international congress of mathematicians: Rio de Janeiro 2018, World Scientific, pp 2945–2971

• Miller J, Sheffield S (2016a) Imaginary geometry i: interacting sles. Prob Theory Relat Fields 164(3–4):553–705

  Article  Google Scholar 

• Miller J, Sheffield S (2016b) Liouville quantum gravity and the brownian map iii: the conformal structure is determined. arXiv preprint arXiv:160805391

• Nguyen LTH, Ta VT, Yagi A (2016) Obstacle avoiding patterns and cohesiveness of fish school. J Theor Biol 406:116–123

  Article  PubMed  Google Scholar 

• Øksendal B (2003) Stochastic differential equations. In: stochastic differential equations. Springer, Berlin

  Book  Google Scholar 

• Øksendal B, Sulem A (2019) Applied Stochastic Control of Jump Diffusions. Springer. This a later edition of the original book published in 2007. Øksendal, B, & Sulem A. (2007). Applied Stochastic Control of Jump Diffusions (Vol. 498). Berlin: Springer. https://link.springer.com/content/pdf/10.1007/978-3-030-02781-0.pdf

• Pinti J, Celani A, Thygesen UH, Mariani P (2020) Optimal navigation and behavioural traits in oceanic migrations. Theor Ecol 13(4):583–593

  Article  Google Scholar 

• Pitici M (2018) The best writing on mathematics 2017. Princeton University Press, Princeton

  Book  Google Scholar 

• Polyakov AM (1981) Quantum geometry of bosonic strings. Phys Lett B 103(3):207–210

  Article  Google Scholar 

• Polyakov AM (1987) Quantum gravity in two dimensions. Modern Phys Lett A 2(11):893–898

  Article  CAS  Google Scholar 

• Polyakov AM (1996) Quantum geometry of fermionic strings. In: 30 Years Of The Landau Institute–Selected Papers, World Scientific, pp 602–604

• Pramanik P (2020) Optimization of market stochastic dynamics. SN Op Res Forum, Springer 1:1–17

  Google Scholar 

• Pramanik P, Polansky AM (2019) Semicooperation under curved strategy spacetime. arXiv preprint arXiv:191212146

• Pramanik P, Polansky AM (2020a) Motivation to run in one-day cricket. arXiv preprint arXiv:200111099

• Pramanik P, Polansky AM (2020b) Optimization of a dynamic profit function using euclidean path integral. arXiv preprint arXiv:200209394

• Radinger J, Wolter C (2015) Disentangling the effects of habitat suitability, dispersal, and fragmentation on the distribution of river fishes. Ecol Appl 25(4):914–927

  Article  PubMed  Google Scholar 

• Ross K (2008) Stochastic control in continuous time. Lecture Notes on Continuous Time Stochastic Control, Spring

• Schramm O (2000) Scaling limits of loop-erased random walks and uniform spanning trees. Israel J Math 118(1):221–288

  Article  Google Scholar 

• Shang Y, Bouffanais R (2014) Influence of the number of topologically interacting neighbors on swarm dynamics. Sci Rep 4:4184

  Article  CAS  PubMed  PubMed Central  Google Scholar 

• Sheffield S (2007) Gaussian free fields for mathematicians. Prob Theory Relat Fields 139(3–4):521–541

  Article  Google Scholar 

• Sheffield S et al (2016) Conformal weldings of random surfaces: Sle and the quantum gravity zipper. Ann Prob 44(5):3474–3545

  Article  Google Scholar 

• Simon B (1979) Functional integration and quantum physics. Academic press, Cambridge

  Google Scholar 

• Theodorou E, Buchli J, Schaal S (2010) Reinforcement learning of motor skills in high dimensions: a path integral approach. In: Robotics and Automation (ICRA), 2010 IEEE International Conference on, IEEE, pp 2397–2403

• Theodorou EA (2011) Iterative path integral stochastic optimal control: theory and applications to motor control. University of Southern California. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.418.8228&rep=rep1&type=pdf

• Ton TV, Linh NTH, Yagi A (2014) Flocking and non-flocking behavior in a stochastic cucker-smale system. Anal Appl 12(01):63–73

  Article  Google Scholar 

• Torney CJ, Lorenzi T, Couzin ID, Levin SA (2015) Social information use and the evolution of unresponsiveness in collective systems. J Royal Soc Interf 12(103):20140893

  Article  Google Scholar 

• Uchitane T, Ton TV, Yagi A (2012) An ordinary differential equation model for fish schooling. Sci Math Jpn 75(3):339–350

  Google Scholar 

• Van Den Broek B, Wiegerinck W, Kappen B (2008) Graphical model inference in optimal control of stochastic multi-agent systems. J Art Intell Res 32:95–122

  Google Scholar 

• Wang X, Pan Q, Kang Y, He M (2016) Predator group size distributions in predator-prey systems. Ecol complex 26:117–127

  Article  Google Scholar 

• Yang I, Morzfeld M, Tomlin CJ, Chorin AJ (2014) Path integral formulation of stochastic optimal control with generalized costs. IFAC proceedings volumes 47(3):6994–7000

• Yoshioka H (2017) A simple game-theoretic model for upstream fish migration. Theory Biosci 136(3–4):99–111

  Article  PubMed  Google Scholar 

• Yoshioka H (2019) A stochastic differential game approach toward animal migration. Theory Biosci 138(2):277–303

  Article  PubMed  Google Scholar 

• Yoshioka H, Yaegashi Y (2018) An optimal stopping approach for onset of fish migration. Theory Biosci 137(2):99–116

  Article  CAS  PubMed  Google Scholar 

• Yoshioka H, Shirai T, Tagami D (2019) A mixed optimal control approach for upstream fish migration. J Sustain Develop Energy W Environ Syst 7(1):101–121

  Article  Google Scholar 

Download references