搜索结果：Journal of theoretical biology

Previous article Next article On the Construction and Comparison of Difference SchemesGilbert StrangGilbert Stranghttps://doi.org/10.1137/0705041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Barkley Rosser, A Runge-Kutta for all seasons, SIAM Rev., 9 (1967), 417–452 10.1137/1009069 MR0219242 0243.65041 LinkISIGoogle Scholar[2] Robert D. Richtmyer and , K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967xiv+405 MR0220455 0155.47502 Google Scholar[3] Peter D. Lax and , Burton Wendroff, Difference schemes for hyperbolic equations with high order of accuracy, Comm. Pure Appl. Math., 17 (1964), 381–398 MR0170484 0233.65050 CrossrefISIGoogle Scholar[4] Samuel Z. Burstein, Numerical methods in multidimensional shocked flows, AIAA J., 2 (1964), 2111–2117 MR0180067 CrossrefGoogle Scholar[5] S. Z. Burstein, Finite-difference calculations for hydrodynamic flows containing discontinuities, J. Comp. Phys., 2 (1967), 198–222 0166.22103 Google Scholar[6] C. Berger, On the numerical range of powers of an operator, to appear Google Scholar[7] W. P. Crowley, Second-order numerical advection, J. Comp. Phys., 1 (1967), 471–484 10.1016/0021-9991(67)90053-8 0149.44403 CrossrefGoogle Scholar[8] Gilbert Strang, Accurate partial difference methods. I. Linear Cauchy problems, Arch. Rational Mech. Anal., 12 (1963), 392–402 MR0146970 0113.32303 CrossrefISIGoogle Scholar[9] A. R. Gourlay and , J. Ll. Morris, A multistep formulation of the optimized Lax-Wendroff method for nonlinear hyperbolic systems in two space variables, Math. Comp., 22 (1968), 715–719 MR0251931 0172.19904 CrossrefISIGoogle Scholar[10] Peter Lax and , Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math., 13 (1960), 217–237 MR0120774 0152.44802 CrossrefISIGoogle Scholar[11] R. D. Richtmyer, A survey of difference methods for nonsteady fluid dynamics, Tech. Note, 63-2, National Center for Atmospheric Research, Boulder, Colorado, 1962 Google Scholar[12] Gilbert Strang, Accurate partial difference methods. II. Non-linear problems, Numer. Math., 6 (1964), 37–46 10.1007/BF01386051 MR0166942 0143.38204 CrossrefGoogle Scholar[13] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407 MR0135729 0112.34901 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Semiexplicit symplectic integrators for non-separable Hamiltonian systems23 September 2022 | Mathematics of Computation, Vol. 92, No. 339 Cross Ref A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemesJournal of Computational Physics, Vol. 472 Cross Ref Numerical computation for rogue waves in the coupled nonlinear Schrödinger equations with the coherent coupling effect29 April 2022 | International Journal of Computer Mathematics, Vol. 99, No. 12 Cross Ref A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systemsMathematics and Computers in Simulation, Vol. 202 Cross Ref Ultrafast laser matter interactions: modeling approaches, challenges, and prospects27 September 2022 | Modelling and Simulation in Materials Science and Engineering, Vol. 30, No. 8 Cross Ref An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gasesJournal of Computational Physics, Vol. 471 Cross Ref Implications of CO 2 mass transport dynamics for large-scale CCS in basalt formationsInternational Journal of Greenhouse Gas Control, Vol. 121 Cross Ref A charge-preserving compact splitting method for solving the coupled stochastic nonlinear Schrödinger equationsApplied Numerical Mathematics, Vol. 181 Cross Ref Local effects in vortex-flame interactions: Implications for turbulent premixed flame scaling and observablesCombustion and Flame, Vol. 245 Cross Ref Hamiltonian preserving nonlinear opticsPhysica D: Nonlinear Phenomena, Vol. 439 Cross Ref A fully coupled, fully implicit simulation method for unsteady flames using Jacobian approximation and clusteringCombustion and Flame, Vol. 245 Cross Ref Reactive Transport Modeling with a Coupled OpenFOAM®-PHREEQC Platform7 October 2022 | Transport in Porous Media, Vol. 145, No. 2 Cross Ref Multirate Exponential Rosenbrock MethodsVu Thai Luan, Rujeko Chinomona, and Daniel R. Reynolds13 October 2022 | SIAM Journal on Scientific Computing, Vol. 44, No. 5AbstractPDF (764 KB)Assessment of a new sub-grid model for magnetohydrodynamical turbulence. I. Magnetorotational instability10 October 2022 | Monthly Notices of the Royal Astronomical Society, Vol. 517, No. 3 Cross Ref Consistent submodel coupling in hybrid particle/finite volume algorithms for zone-adaptive modelling of turbulent reactive flows12 October 2022 | Combustion Theory and Modelling, Vol. 1 Cross Ref Real-time propagator eigenstates2 September 2022 | Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 55, No. 19 Cross Ref Operator splitting scheme based on barycentric Lagrange interpolation collocation method for the Allen-Cahn equation19 November 2021 | Journal of Applied Mathematics and Computing, Vol. 68, No. 5 Cross Ref Dynamics of Electron Pearcey– Gaussian Beams in a Constant Magnetic Field5 August 2022 | Annalen der Physik, Vol. 534, No. 10 Cross Ref Synergistic interactions of thermodiffusive instabilities and turbulence in lean hydrogen flamesCombustion and Flame, Vol. 244 Cross Ref General time-dependent configuration-interaction singles. II. Atomic case10 October 2022 | Physical Review A, Vol. 106, No. 4 Cross Ref A high order accurate numerical algorithm for the space-fractional Swift-Hohenberg equationComputers & Mathematics with Applications, Vol. 15 Cross Ref A self-adaptive theta scheme using discontinuity aware quadrature for solving conservation laws19 October 2021 | IMA Journal of Numerical Analysis, Vol. 42, No. 4 Cross Ref Isolating gasdynamic and chemical effects on the detonation cellular structure: A combined experimental and computational studyProceedings of the Combustion Institute, Vol. 9 Cross Ref Improved Uniform Error Bounds on Time-Splitting Methods for the Long-Time Dynamics of the Dirac Equation with Small Potentials Weizhu Bao , Yue Feng , and Jia Yin 27 September 2022 | Multiscale Modeling & Simulation, Vol. 20, No. 3AbstractPDF (16068 KB)Improving the Performance of Reactive Transport Simulations Using Artificial Neural Networks27 September 2022 | Transport in Porous Media, Vol. 513 Cross Ref Signatures of coherent vibronic exciton dynamics and conformational control in the two-dimensional electronic spectroscopy of conjugated polymers1 January 2022 | Faraday Discussions, Vol. 237 Cross Ref Robust estimation of charge carrier diffusivity using transient photoluminescence microscopyThe Journal of Chemical Physics, Vol. 157, No. 10 Cross Ref Electron Symmetric Pearcey Gaussian Vortex Beams5 August 2022 | Annalen der Physik, Vol. 534, No. 9 Cross Ref An enhanced semi-explicit particle finite element method for incompressible flows30 May 2022 | Computational Mechanics, Vol. 70, No. 3 Cross Ref A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo modelApplied Numerical Mathematics, Vol. 179 Cross Ref Far-field sonic boom prediction considering atmospheric turbulence effects: An improved approachChinese Journal of Aeronautics, Vol. 35, No. 9 Cross Ref An Improved Method for Coupling Hydrodynamics with Astrophysical Reaction Networks25 August 2022 | The Astrophysical Journal, Vol. 936, No. 1 Cross Ref High-order interpolatory Serendipity Virtual Element Method for semilinear parabolic problems14 June 2022 | Calcolo, Vol. 59, No. 3 Cross Ref Effects of wedge-angle change on the evolution of oblique detonation wave structurePhysics of Fluids, Vol. 34, No. 9 Cross Ref HPC-enabling technologies for high-fidelity combustion simulationsProceedings of the Combustion Institute, Vol. 33 Cross Ref A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational FormulationChun Liu, Cheng Wang, and Yiwei Wang2 August 2022 | SIAM Journal on Scientific Computing, Vol. 44, No. 4AbstractPDF (1148 KB)Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak NonlinearityWeizhu Bao, Yongyong Cai, and Yue Feng1 August 2022 | SIAM Journal on Numerical Analysis, Vol. 60, No. 4AbstractPDF (41582 KB)Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamics11 August 2022 | BIT Numerical Mathematics, Vol. 48 Cross Ref An effective operator splitting scheme for two-dimensional conservative nonlocal Allen–Cahn equationApplied Mathematics Letters, Vol. 130 Cross Ref A new accelerating technique for low speed flow: pseudo high speed methodChinese Journal of Aeronautics, Vol. 35, No. 8 Cross Ref The hydrodynamics of LERNAJournal of Computational Physics, Vol. 463 Cross Ref An asymptotic Green's function method for time-dependent Schrödinger equations with application to Kohn-Sham equationsJournal of Computational Physics, Vol. 463 Cross Ref Effects of differential diffusion on hydrogen flame kernel development under engine conditionsProceedings of the Combustion Institute, Vol. 14 Cross Ref Instability seeding mechanisms due to internal defects in inertial confinement fusion targetsPhysics of Plasmas, Vol. 29, No. 8 Cross Ref Investigation of droplet grouping in monodisperse streams by direct numerical simulationsPhysics of Fluids, Vol. 34, No. 8 Cross Ref The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven HohlraumsPhysics of Plasmas, Vol. 29, No. 8 Cross Ref Exponential Bhatnagar-Gross-Krook integrator for multiscale particle-based kinetic simulations4 August 2022 | Physical Review E, Vol. 106, No. 2 Cross Ref Casimir preserving spectrum of two-dimensional turbulence24 August 2022 | Physical Review Fluids, Vol. 7, No. 8 Cross Ref Learning PDE to Model Self-Organization of Matter9 August 2022 | Entropy, Vol. 24, No. 8 Cross Ref Numerical Estimation of Nozzle Throat Heat Flux in Oxygen-Methane Rocket Engines18 July 2022 | Journal of Propulsion and Power, Vol. 87 Cross Ref A sixth order entropy condition scheme for compressible flowComputers & Fluids, Vol. 243 Cross Ref Explore artificial neural networks for solving complex hydrocarbon chemistry in turbulent reactive flowsFundamental Research, Vol. 2, No. 4 Cross Ref High-order Scharfetter-Gummel-based schemes and applications to gas discharge modelingJournal of Computational Physics, Vol. 461 Cross Ref Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equationMathematics and Computers in Simulation, Vol. 197 Cross Ref Graphite Nozzle Erosion Trends in Paraffin/Oxygen Hybrid RocketsJournal of Propulsion and Power, Vol. 38, No. 4 Cross Ref A Massively Parallel Eulerian-Lagrangian Method for Advection-Dominated Transport in Viscous FluidsNils Kohl, Marcus Mohr, Sebastian Eibl, and Ulrich Rüde24 June 2022 | SIAM Journal on Scientific Computing, Vol. 44, No. 3AbstractPDF (52728 KB)Modeling of Wall Heat Flux in Oxygen-Methane Liquid Rocket Thrust Chambers20 June 2022 Cross Ref Verification and Validation of Immersed Boundary Solvers for Hypersonic Flows with Gas-Surface Interactions20 June 2022 Cross Ref Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump23 February 2022 | International Journal for Numerical Methods in Fluids, Vol. 94, No. 6 Cross Ref Second-order maximum principle preserving Strang’s splitting schemes for anisotropic fractional Allen-Cahn equations30 September 2021 | Numerical Algorithms, Vol. 90, No. 2 Cross Ref Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. Part 1 - Dispersion relations in the linear regimeCombustion and Flame, Vol. 240 Cross Ref Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn equationJournal of Computational Physics, Vol. 458 Cross Ref A dynamic relaxation method with operator splitting and random-choice strategy for SPHJournal of Computational Physics, Vol. 458 Cross Ref Numerical prediction of loudness metrics for N-waves and shaped sonic booms in kinematic turbulenceThe Journal of the Acoustical Society of America, Vol. 151, No. 6 Cross Ref Magneto-thermal instability in galaxy clusters – I. Theory and two-dimensional simulations9 April 2022 | Monthly Notices of the Royal Astronomical Society, Vol. 513, No. 3 Cross Ref Computational Fluid Dynamics of Reacting Flows at Surfaces: Methodologies and Applications26 February 2022 | Chemie Ingenieur Technik, Vol. 94, No. 5 Cross Ref Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motionJournal of Computational and Applied Mathematics, Vol. 406 Cross Ref An improved finite integration method for nonlocal nonlinear Schrödinger equationsComputers & Mathematics with Applications, Vol. 113 Cross Ref Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithmComputer Physics Communications, Vol. 274 Cross Ref A high-order unified stochastic particle method based on the Bhatnagar-Gross-Krook model for multi-scale gas flowsComputer Physics Communications, Vol. 274 Cross Ref A new stabilised scheme for the Richards’ equation with evapotranspirationGroundwater for Sustainable Development, Vol. 17 Cross Ref Well-balanced discrete unified gas-kinetic scheme for two-phase systemsPhysics of Fluids, Vol. 34, No. 5 Cross Ref On the Physical Nature of “Anomalous” High Energy Electrons in Vacuum Diodes24 June 2022 | Russian Physics Journal, Vol. 64, No. 12 Cross Ref Stability and convergence of Strang splitting. Part II: Tensorial Allen-Cahn equationsJournal of Computational Physics, Vol. 454 Cross Ref A Model for Characteristic X-Ray Emission in Electron Probe Microanalysis Based on the (Filtered) Spherical Harmonic () Method for Electron Transport11 April 2022 | Microscopy and Microanalysis, Vol. 28, No. 2 Cross Ref Restoring the conservativity of characteristic-based segregated models: Application to the hybrid lattice Boltzmann methodPhysics of Fluids, Vol. 34, No. 4 Cross Ref An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system8 March 2022 | Journal of Plasma Physics, Vol. 88, No. 2 Cross Ref Atomistic simulation of ultra-short pulsed laser ablation of Al: an extension for non-thermalized electrons and ballistic transport29 December 2021 | Journal of Physics D: Applied Physics, Vol. 55, No. 13 Cross Ref Enhancing the Quantum Linear Systems Algorithm Using Richardson ExtrapolationACM Transactions on Quantum Computing, Vol. 3, No. 1 Cross Ref Reacting condensed phase explosives in direct contactJournal of Applied Physics, Vol. 131, No. 9 Cross Ref On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEs11 February 2022 | Journal of Scientific Computing, Vol. 90, No. 3 Cross Ref A three-dimensional Laguerre one-way wave equation solverApplied Numerical Mathematics, Vol. 173 Cross Ref Higher Order Auxiliary Field Quantum Monte Carlo MethodsJournal of Physics: Conference Series, Vol. 2207, No. 1 Cross Ref Numerical method for modeling photosynthesis of algae on pulsing soft corals31 March 2022 | Physical Review Fluids, Vol. 7, No. 3 Cross Ref Numerical Method for Approximate Solution of Fisher's Equation1 March 2022 | Journal of the Institute of Science and Technology Cross Ref Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber1 March 2022 | Fibers, Vol. 10, No. 3 Cross Ref CFD modeling of multiphase flows with detailed microkinetic description of the surface reactivityChemical Engineering Research and Design, Vol. 179 Cross Ref Nonlinear fourth order Taylor expansion of lattice Boltzmann schemesAsymptotic Analysis, Vol. 127, No. 4 Cross Ref Numerical scheme for solving a porous Saint-Venant type model for water flow on vegetated hillslopesApplied Numerical Mathematics, Vol. 172 Cross Ref A weak approximation method for irregular functionals of hypoelliptic diffusionsApplied Numerical Mathematics, Vol. 172 Cross Ref On pattern formation in reaction–diffusion systems containing self- and cross-diffusionCommunications in Nonlinear Science and Numerical Simulation, Vol. 105 Cross Ref Comparison of high-order Eulerian methods for electron hybrid modelJournal of Computational Physics, Vol. 451 Cross Ref Simulation of three-dimensional forced compressible isotropic turbulence by a redesigned discrete unified gas kinetic schemePhysics of Fluids, Vol. 34, No. 2 Cross Ref A coupled Lagrangian-Eulerian model for microplastics as vectors of contaminants applied to the Mediterranean Sea14 February 2022 | Environmental Research Letters, Vol. 17, No. 2 Cross Ref A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses22 December 2021 | Plasma Science and Technology, Vol. 24, No. 2 Cross Ref Burgers equation and convexification method: Propagation of wave packets and narrowband noiseThe Journal of the Acoustical Society of America, Vol. 151, No. 2 Cross Ref A Robust Reacting Flow Solver with Computational Diagnostics Based on OpenFOAM and Cantera14 February 2022 | Aerospace, Vol. 9, No. 2 Cross Ref Development of a Discontinuous Galerkin Ionosphere‐Plasmasphere Model3 February 2022 | Journal of Geophysical Research: Space Physics, Vol. 127, No. 2 Cross Ref Accurate and efficient simulations of Hamiltonian mechanical systems with discontinuous potentialsJournal of Computational Physics, Vol. 450 Cross Ref Stellar evolution and tidal dissipation in REBOUNDx10 January 2022 | Monthly Notices of the Royal Astronomical Society, Vol. 510, No. 4 Cross Ref Mechanisms for severe combustion instabilities induced by low-temperature fuel injection of an H 2 /O 2 rocket-type combustor29 December 2022 Cross Ref New Trends on Multiphase Flow Simulations Using Slug Capturing Approach2 April 2022 Cross Ref Modelling and Numerical Simulation of Binary Droplet Collisions Under Extreme Conditions31 August 2022 Cross Ref Investigation of the Behaviour of Supercooled Droplets Concerning Evaporation, Sublimation and Freezing Under Different Boundary Conditions31 August 2022 Cross Ref Symmetric Splitting Methods for Wave Equations: First Approaches24 September 2021 Cross Ref Efficient Experimental and Numerical Methods for Solving Vertical Distribution of Sediments in Dam-Break Flows19 May 2022 Cross Ref Aerosol–climate modeling Cross Ref Flame edge dynamics in counterflow nonpremixed flames of CH4/He versus air at low strain rates: An experimental and numerical studyCombustion and Flame, Vol. 235 Cross Ref Numerical modelling of turbulent geophysical flows using a hyperbolic shear shallow water model: Application to powder snow avalanchesComputers & Fluids, Vol. 233 Cross Ref Stochastic population balance methods for detailed modelling of flame-made aerosol particlesJournal of Aerosol Science, Vol. 159 Cross Ref Immersed boundary method for high-order flux reconstruction based on volume penalizationJournal of Computational Physics, Vol. 448 Cross Ref A unified formulation of splitting-based implicit time integration schemesJournal of Computational Physics, Vol. 448 Cross Ref Face-based in of Computational Physics, Vol. Cross Ref A hybrid method for problems with boundary in of Computational Physics, Vol. Cross Ref A computational for of of in the Vol. Cross Ref A discontinuous Galerkin in for and Vol. 17 Cross Ref Modeling of CO 2 in Reactive A January 2022 | Research, Vol. No. 1 Cross Ref for numerical simulation of January 2022 | Institute No. Cross Ref to Schemes for and January 2022 | Vol. No. 1 Cross Ref of discrete and Systems - Vol. No. 10 Cross Ref February 2022 | Vol. 5 Cross Ref numerical schemes for Hamiltonian dynamics Cross Ref Numerical Simulations on Nonlinear Quantum with the April 2022 | The Journal of computational Vol. 8 Cross Ref April 2022 Cross Ref of nonlocal and Systems - Vol. No. Cross Ref Local boundary for nonlinear Schrödinger equation with wave operator on August 2021 | Methods in the Applied Vol. 44, No. Cross Ref methods for in October 2021 | International Journal for Numerical and Methods in Vol. No. Cross Ref modeling of by a of change and December 2021 | Journal of Vol. No. Cross Ref Operator splitting and in Mathematics and Computation, Vol. Cross Ref of flow and equivalence on oblique detonation Science and Technology, Vol. Cross Ref combustion of droplet under and Flame, Vol. Cross Ref A high order operator splitting method based on for the nonlocal equationJournal of Computational Physics, Vol. Cross Ref reconstruction and schemes for volume of fluid method in of Computational Physics, Vol. Cross Ref A solver based on method for the February 2021 | Scientific Vol. No. 1 Cross Ref of of Schrödinger June 2021 | Scientific Vol. No. 1 Cross Ref and formation droplet a September 2021 | Scientific Vol. No. 1 Cross Ref of and on October 2021 | Scientific Vol. No. 1 Cross Ref Wave in of in MHD December 2021 | The Astrophysical Journal, Vol. No. 2 Cross Ref splitting methods with Journal of Chemical Physics, Vol. No. Cross Ref for simulations with Modelling & Vol. Cross Ref and Schrödinger equation with of Computational Physics, Vol. Cross Ref semilinear and the of Analysis, Vol. No. 10 Cross Ref A Numerical of Coupling Schemes for Atmospheric November 2021 | Journal of in Modeling Vol. No. Cross Ref Boundary variation conservative method for compressible and incompressible of Fluids, Vol. No. Cross Ref of Schemes in the of Vortex December 2021 | Computational Mathematics and Physics, Vol. No. Cross Ref method for the of and equations in September 2021 | Journal of Vol. No. 6 Cross Ref Conservative Schemes for Nonlinear Schrödinger Equations in a with of October 2021 | Mathematics, Vol. 9, No. Cross Ref in reactive August 2021 | Vol. No. Cross Ref Hamiltonian based approach for time in May 2021 | Molecular Physics, Vol. No. Cross Ref for Conservative Schemes for the of Nonlinear Pulse with a October 2021 | Nonlinear in Vol. 24, No. 3 Cross Ref Numerical and the for August 2021 | Journal of the Royal Society, Vol. No. Cross Ref A fully coupled two-dimensional model in August 2021 | Environmental Fluid Mechanics, Vol. No. 5 Cross Ref The formation and development of oblique detonation wave with different chemical Science and Technology, Vol. Cross Ref A improved numerical method for the simulation of rogue waves of nonlinear Schrödinger in Nonlinear Science and Numerical Simulation, Vol. Cross Ref Heat by in turbulent boundary at Journal of Heat and Vol. Cross Ref A Lagrangian-Eulerian method for of Computational Physics, Vol. Cross Ref in linear and nonlinear January 2021 | Journal of Applied Mathematics, Vol. No. 5 Cross Ref High-order geometric integrators for Journal of Chemical Physics, Vol. No. 12 Cross Ref of Flow in Gas with by Electron Cross Ref chemistry for and using flow of Applied Physics, Vol. No. Cross Ref modelling of premixed May 2021 | Combustion Theory and Modelling, Vol. No. 6 Cross Ref A numerical of control August 2021 | Vol. No. 1 Cross Ref A Conservative Semi-Lagrangian Transport Model on the July 2021 | in Atmospheric Vol. 38, No. 9 Cross Ref A Second-Order Method for Schrödinger Equations with July 2021 | Journal of Scientific Computing, Vol. 88, No. 3 Cross Ref Strang technique for the August 2021 | Vol. No. 3 Cross Ref splitting method for space-fractional Schrödinger equationApplied Numerical Mathematics, Vol. Cross Ref Numerical simulation of in the of Journal of Multiphase Vol. Cross Ref approximation of and numerical October 2021 | in Applied Vol. No. 3 Cross Ref electron dynamics in high Accurate prediction of September 2021 | Physical Review Vol. No. 10 Cross Ref On the of by the hydrogen in July 2021 | Monthly Notices of the Royal Astronomical Society, Vol. No. 2 Cross Ref Reaction Effects on Nozzle Erosion in Paraffin/Oxygen Hybrid July 2021 Cross Ref modeling in July 2021 Cross Ref A fast and efficient numerical algorithm for equation with a nonlocal Mathematics Letters, Vol. Cross Ref An particle hydrodynamics method for modeling Methods in Applied and Engineering, Vol. Cross Ref A model for droplet Journal of Heat and Vol. Cross Ref Numerical for high frequency equation efficient time for Schrödinger equationJournal of Computational Physics, Vol. Cross Ref and for and simulation of Magnetic Vol. Cross Ref Local wave

Previous article Next article Fractional Brownian Motions, Fractional Noises and ApplicationsBenoit B. Mandelbrot and John W. Van NessBenoit B. Mandelbrot and John W. Van Nesshttps://doi.org/10.1137/1010093PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. Adelman, Long cycles—fact or artifact?, Amer. Economic Rev., 60 (1965), 444–463 Google Scholar[2] William Feller, The asymptotic distribution of the range of sums of independent random variables, Ann. Math. Statistics, 22 (1951), 427–432 MR0042626 0043.34201 CrossrefISIGoogle Scholar[3] I. M. Gel'fand and , N. Ya. Vilenkin, Generalized functions. Vol. 4, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1964 [1977]xiv+384 MR0435834 Google Scholar[4] C. W. J. Granger, The typical spectral shape of an economic variable, Econometrica, 34 (1966), 150–161 CrossrefISIGoogle Scholar[5] G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc., 71 (1951), 38–69 MR0051340 0043.30601 CrossrefISIGoogle Scholar[6] H. E. Hurst, , R. P. Black and , Y. M. Sinaika, Long Term Storage in Reservoirs. An Experimental Study, Constable, London, 1965 Google Scholar[7] A. N. Kolmogoroff, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, C. R. (Doklady) Acad. Sci. URSS (N.S.), 26 (1940), 115–118 MR0003441 0022.36001 Google Scholar[8] John Lamperti, Semi-stable stochastic processes, Trans. Amer. Math. Soc., 104 (1962), 62–78 MR0138128 0286.60017 CrossrefGoogle Scholar[9] Paul Lévy, Random functions: General theory with special reference to Laplacian random functions, Univ. California Publ. Statist., 1 (1953), 331–390 MR0055607 0052.14402 Google Scholar[10] Michel Loève, Probability theory, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960xvi+685 MR0123342 0095.12201 Google Scholar[11] Benoı⁁t Mandelbrot, Une classe processus stochastiques homothétiques à soi; application à la loi climatologique H. E. Hurst, C. R. Acad. Sci. Paris, 260 (1965), 3274–3277 MR0176521 0127.09501 Google Scholar[12] B. Mandelbrot, Self-similar error-clusters in communication systems and the concept of conditional stationarity, IEEE Trans. Comet. Tech., COM-13 (1965), 71–90 10.1109/TCOM.1965.1089090 CrossrefISIGoogle Scholar[13] B. Mandelbrot, Noises with an $l/f$ spectrum, a bridge between direct current and white noise, IEEE Trans. Information Theory, IT-13 (1967), 289–298 10.1109/TIT.1967.1053992 0148.40507 CrossrefISIGoogle Scholar[14] Benoit Mandelbrot, Sporadic random functions and conditional spectral analysis: Self-similar examples and limitsProc. Fifth Berkeley Sympos. Mathematical Statistics and Probability (Berkeley, Calif., 1965/66), Vol. III: Physical Sciences, Univ. California Press, Berkeley, Calif., 1967, 155–179 MR0224243 0189.18302 Google Scholar[15] B. Mandelbrot and , J. R. Wallis, Noah, Joseph and operational hydrology, Water Resources Research, to appear Google Scholar[16] B. Mandelbrot and , J. R. Wallis, Computer experiments with fractional Gaussian noise, Water Resources Research, to appear Google Scholar[17] B. Mandelbrot and , J. R. Wallis, Some long run properties of geophysical records, Water Resources Research, to appear. Google Scholar[18] G. Maruyama, The harmonic analysis of stationary stochastic processes, Mem. Fac. Sci. Kyusyu Univ. A., 4 (1949), 45–106 MR0032127 0045.40602 CrossrefGoogle Scholar[19] M. Rosenblatt, Independence and dependenceProc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, 431–443 MR0133863 0105.11802 Google Scholar[20] G. I. Taylor, Statistical theory of turbulence, Proc. Roy. Sac. Ser. A, 151 (1935), 421–478 CrossrefGoogle Scholar[21] H. Weyl, Bemerkungen zum Begriff der Differential-Quotenten gebrochener Ordnung, Vierteljschr. Naturforsch. Ges. Zürich, 62 (1967), 296–302 Google Scholar[22] A. M. Yaglom, Correlation theory of processes with random stationary nth increments, Amer. Math. Soc. Transl. (2), 8 (1958), 87–141 MR0091554 0080.34903 CrossrefGoogle Scholar[23] A. M. Yaglom, L. M. LeCam and , J. Neyman, Stationary Gaussian processes satisfying the strong mixing condition and best predictable functionalsBernoulli-Bayes-Laplace Anniversary Volume, Springer-Verlag, New York, 1965, 241–252 0142.13904 CrossrefGoogle Scholar[24] A. M. Yaglom, Outline of some topics in linear extrapolation of stationary random processesProc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II:Contributions to Probability Theory, Part 1, Univ. California Press, Berkeley, Calif., 1967, 259–278 MR0215358 0189.18401 Google Scholar[25] Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952vi+329, 2nd ed. MR0076084 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motionJournal of Computational and Applied Mathematics, Vol. 420 | 1 Mar 2023 Cross Ref ARMA–GARCH model with fractional generalized hyperbolic innovationsFinancial Innovation, Vol. 8, No. 1 | 15 May 2022 Cross Ref Fokker–Planck equation of the fractional Brownian motionInternational Journal of Non-Linear Mechanics, Vol. 147 | 1 Dec 2022 Cross Ref A generative model for fBm with deep ReLU neural networksJournal of Complexity, Vol. 73 | 1 Dec 2022 Cross Ref Emergence of non-Fickian transport in truncated pluri-Gaussian permeability fieldsGEM - International Journal on Geomathematics, Vol. 13, No. 1 | 1 October 2022 Cross Ref A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary frameworkCommunications in Nonlinear Science and Numerical Simulation, Vol. 114 | 1 Nov 2022 Cross Ref Multiscaling and rough volatility: An empirical investigationInternational Review of Financial Analysis, Vol. 84 | 1 Nov 2022 Cross Ref Multivariate claim processes with rough intensities: Properties and estimationInsurance: Mathematics and Economics, Vol. 107 | 1 Nov 2022 Cross Ref Exploring the dynamic nonlinear relationship between crude oil price and implied volatility indices: A new perspective from MMV-MFDFAPhysica A: Statistical Mechanics and its Applications, Vol. 603 | 1 Oct 2022 Cross Ref On the model of random walk with multiple memory structurePhysica A: Statistical Mechanics and its Applications, Vol. 603 | 1 Oct 2022 Cross Ref Self-similarity and response of fractional differential equations under white noise inputProbabilistic Engineering Mechanics, Vol. 70 | 1 Oct 2022 Cross Ref The truncated Euler–Maruyama method for CIR model driven by fractional Brownian motionStatistics & Probability Letters, Vol. 189 | 1 Oct 2022 Cross Ref Discrete scaling and criticality in a chain of adaptive excitable integratorsChaos, Solitons & Fractals, Vol. 163 | 1 Oct 2022 Cross Ref Novel Neuron-like Procedure of Weak Signal Detection against the Non-Stationary Noise Background with Application to Underwater SoundRemote Sensing, Vol. 14, No. 19 | 29 September 2022 Cross Ref Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series DynamicsNonlinear Systems - Recent Developments and Advances [Working Title] | 22 September 2022 Cross Ref Asymptotic of the running maximum distribution of a Gaussian BridgeStochastic Analysis and Applications, Vol. 28 | 19 September 2022 Cross Ref Wavelet eigenvalue regression in high dimensionsStatistical Inference for Stochastic Processes, Vol. 1 | 18 September 2022 Cross Ref Data-Driven Modeling of Non-Markovian Noise in Semiconductor Lasers2022 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) | 12 Sep 2022 Cross Ref Continuous wavelet estimation for multivariate fractional Brownian motionPakistan Journal of Statistics and Operation Research | 10 September 2022 Cross Ref Persistence in daily returns of stocks with highest market capitalization in the Indian marketDigital Finance, Vol. 503 | 9 September 2022 Cross Ref Bayesian semiparametric long memory models for discretized event dataThe Annals of Applied Statistics, Vol. 16, No. 3 | 1 Sep 2022 Cross Ref Scale invariance in fNIRS as a measurement of cognitive loadCortex, Vol. 154 | 1 Sep 2022 Cross Ref Efficient calculation of fractal properties via the Higuchi methodNonlinear Dynamics, Vol. 109, No. 4 | 23 June 2022 Cross Ref N-Fold Compound Option Fuzzy Pricing Based on the Fractional Brownian MotionInternational Journal of Fuzzy Systems, Vol. 24, No. 6 | 9 May 2022 Cross Ref On the nature and propagation of errors in roughness parameters obtained from spectral analysis of atomic force microscopy topographic imagesJournal of Vacuum Science & Technology A, Vol. 40, No. 5 | 1 Sep 2022 Cross Ref Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processesChaos, Solitons & Fractals, Vol. 162 | 1 Sep 2022 Cross Ref Study on the Effect of Judgment Excitation Mode to Relieve Driving Fatigue Based on MF-DFABrain Sciences, Vol. 12, No. 9 | 6 September 2022 Cross Ref Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitionsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, No. 9 | 1 Sep 2022 Cross Ref How critical is brain criticality?Trends in Neurosciences, Vol. 21 | 1 Sep 2022 Cross Ref Estimation of hurst exponent for sequential monitoring of clinical trials with covariate adaptive randomizationContemporary Clinical Trials, Vol. 120 | 1 Sep 2022 Cross Ref A GMM approach to estimate the roughness of stochastic volatilityJournal of Econometrics, Vol. 57 | 1 Sep 2022 Cross Ref Frequency–frequency correlations of single-trajectory spectral densities of Gaussian processesNew Journal of Physics, Vol. 24, No. 9 | 27 September 2022 Cross Ref Dispersion heterogeneous recurrence analysis and its use on fault detectionCommunications in Nonlinear Science and Numerical Simulation, Vol. 3 | 1 Sep 2022 Cross Ref UNIFORM CONTINUITY OF FRACTIONAL ORDER INTEGRAL OF FRACTAL INTERPOLATION FUNCTIONFractals, Vol. 30, No. 06 | 6 June 2022 Cross Ref Order pattern recurrence for the analysis of complex systemsPhysica A: Statistical Mechanics and its Applications, Vol. 65 | 1 Sep 2022 Cross Ref Multifractal detrended cross-correlation analysis of radioactivity borne radon, thoron and meteorological time seriesPhysica A: Statistical Mechanics and its Applications, Vol. 10 | 1 Sep 2022 Cross Ref Recovering mixtures of fast-diffusing states from short single-particle trajectorieseLife, Vol. 11 | 30 August 2022 Cross Ref Shadow Price Approximation for the Fractional Black Scholes ModelInternational Journal of Mathematics and Mathematical Sciences, Vol. 2022 | 29 Aug 2022 Cross Ref Roughness and intermittency within metropolitan regions - Application in three French conurbationsEnvironment and Planning B: Urban Analytics and City Science, Vol. 215 | 27 August 2022 Cross Ref Understanding the structure of cognitive noisePLOS Computational Biology, Vol. 18, No. 8 | 17 August 2022 Cross Ref Edgeworth expansion of the t-statistic of the whittle MLE for linear regression processes with long-memory disturbancesCommunications in Statistics - Theory and Methods, Vol. 3 | 16 August 2022 Cross Ref Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and modelsPhysical Chemistry Chemical Physics, Vol. 24, No. 31 | 1 January 2022 Cross Ref UV Slopes at All Redshifts Are Consistent with H = 1 Stochastic Star Formation HistoriesResearch Notes of the AAS, Vol. 6, No. 8 | 10 August 2022 Cross Ref A stochastic model to reproduce the star formation history of individual galaxies in hydrodynamic simulationsMonthly Notices of the Royal Astronomical Society, Vol. 515, No. 3 | 13 July 2022 Cross Ref Forecasting with fractional Brownian motion: a financial perspectiveQuantitative Finance, Vol. 22, No. 8 | 20 May 2022 Cross Ref Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferentialInternational Journal of Nonlinear Sciences and Numerical Simulation, Vol. 0, No. 0 | 3 August 2022 Cross Ref Pairs trading with fractional Ornstein–Uhlenbeck spread modelApplied Economics, Vol. 10 | 3 August 2022 Cross Ref Stochastic particle unbinding modulates growth dynamics and size of transcription factor condensates in living cellsProceedings of the National Academy of Sciences, Vol. 119, No. 31 | 26 July 2022 Cross Ref Option pricing based on a type of fuzzy processJournal of Ambient Intelligence and Humanized Computing, Vol. 13, No. 8 | 26 June 2021 Cross Ref Entropic Compressibility of Lévy ProcessesIEEE Transactions on Information Theory, Vol. 68, No. 8 | 1 Aug 2022 Cross Ref Comment on “A computational technique to classify several fractional Brownian motion processes” [Chaos Solitons and Fractals 150(2021) 111152]Chaos, Solitons & Fractals, Vol. 161 | 1 Aug 2022 Cross Ref Fractional Gaussian fields on the Sierpiński Gasket and related fractalsJournal d'Analyse Mathématique, Vol. 146, No. 2 | 11 July 2022 Cross Ref Multifractal Characterization and Modeling of Blood Pressure SignalsAlgorithms, Vol. 15, No. 8 | 26 July 2022 Cross Ref Robustness of Detrended Cross-correlation Analysis Method Under Outliers ObservationsFluctuation and Noise Letters, Vol. 21, No. 04 | 21 April 2022 Cross Ref Entropy fluctuation and correlation transfer in tunable discrete-time quantum walk with fractional Gaussian noisePhysical Review E, Vol. 106, No. 2 | 15 August 2022 Cross Ref Poincaré Plot Nonextensive Distribution Entropy: A New Method for Electroencephalography (EEG) Time SeriesSensors, Vol. 22, No. 16 | 21 August 2022 Cross Ref A Model Based on Fractional Brownian Motion for Temperature Fluctuation in the Campi Flegrei CalderaFractal and Fractional, Vol. 6, No. 8 | 30 July 2022 Cross Ref Acceleration scaling and stochastic dynamics of a fluid particle in turbulencePhysical Review Fluids, Vol. 7, No. 8 | 24 August 2022 Cross Ref Multifractional Brownian motion characterization based on Hurst exponent estimation and statistical learningChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, No. 8 | 1 Aug 2022 Cross Ref Stability analysis of the Iraqi GNSS stationsJournal of Applied Geodesy, Vol. 16, No. 3 | 31 March 2022 Cross Ref Multifractal test for nonlinearity of interactions across scales in time seriesBehavior Research Methods, Vol. 61 | 19 July 2022 Cross Ref Rolling Bearing Fault Diagnosis Based on MFDFA-SPS and ELMMathematical Problems in Engineering, Vol. 2022 | 18 Jul 2022 Cross Ref Encoding Protest Duration In An Agent-Based Model As Characteristic Phase Transitions2022 Annual Modeling and Simulation Conference (ANNSIM) | 18 Jul 2022 Cross Ref Decomposing the effect of anomalous diffusion enables direct calculation of the Hurst exponent and model classification for single random pathsJournal of Physics A: Mathematical and Theoretical, Vol. 55, No. 27 | 13 June 2022 Cross Ref Classification of stochastic processes by convolutional neural networksJournal of Physics A: Mathematical and Theoretical, Vol. 55, No. 27 | 24 June 2022 Cross Ref A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophesJournal of Forecasting, Vol. 4 | 6 July 2022 Cross Ref The first exit time of fractional Brownian motion from the minimum and maximum parabolic domainsStatistics & Probability Letters, Vol. 186 | 1 Jul 2022 Cross Ref Fractional stochastic Loewner evolution and scaling curvesPhysica A: Statistical Mechanics and its Applications, Vol. 597 | 1 Jul 2022 Cross Ref Stochastic pursuit-evasion curves for foraging dynamicsPhysica A: Statistical Mechanics and its Applications, Vol. 597 | 1 Jul 2022 Cross Ref Power‐type derivatives for rough volatility with jumpsJournal of Futures Markets, Vol. 42, No. 7 | 13 May 2022 Cross Ref Simultaneous Identification of Volatility and Mean-Reverting Parameter for European Option under Fractional CKLS ModelFractal and Fractional, Vol. 6, No. 7 | 21 June 2022 Cross Ref Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentialsNew Journal of Physics, Vol. 24, No. 7 | 7 July 2022 Cross Ref Sublinear diffusion in the generalized triangle mapPhysical Review E, Vol. 106, No. 1 | 11 July 2022 Cross Ref Multivariate long memory structure in the cryptocurrency market: The impact of COVID-19International Review of Financial Analysis, Vol. 82 | 1 Jul 2022 Cross Ref Unravelling the origins of anomalous diffusion: From molecules to migrating storksPhysical Review Research, Vol. 4, No. 3 | 18 July 2022 Cross Ref Fractality of Borsa Istanbul during the COVID-19 PandemicMathematics, Vol. 10, No. 14 | 18 July 2022 Cross Ref Probing local chromatin dynamics by tracking telomeresBiophysical Journal, Vol. 121, No. 14 | 1 Jul 2022 Cross Ref Are the top six cryptocurrencies efficient? Evidence from time‐varying long memoryInternational Journal of Finance & Economics, Vol. 27, No. 3 | 7 December 2020 Cross Ref The anomalous process in singlet fission kinetic model with time-dependent coefficientPhysica B: Condensed Matter, Vol. 117 | 1 Jul 2022 Cross Ref A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$Daxin Nie and Weihua DengSIAM Journal on Numerical Analysis, Vol. 60, No. 3 | 28 June 2022AbstractPDF (498 KB)Elimination of Image Saturation Effects on Multifractal Statistics Using the 2D WTMM in Vol. 13 | 28 June 2022 Cross Ref the relationship between processes with fractional Brownian motion errors of Statistical and Simulation, Vol. 8 | 28 June 2022 Cross Ref under a fractional Brownian motion with Stochastic in and Vol. 2 | 27 June 2022 Cross Ref of rough stochastic volatility models on Journal, Vol. 19 | June 2022 Cross Ref the of anomalous diffusion with the of of Physics A: Mathematical and Theoretical, Vol. 55, No. 24 | 26 May 2022 Cross Ref impact on Evidence from a Hurst A: Statistical Mechanics and its Applications, Vol. | 1 2022 Cross Ref method to the of in fractal and Vol. 10, No. 2 | 18 May 2022 Cross Ref of Using and Statistical in Journal of Science and Transactions of Engineering, Vol. No. 3 | 26 September 2021 Cross Ref The of fractional Brownian Annals of Applied Vol. 32, No. 3 | 1 2022 Cross Ref behavior during the a comparison between and European based on Economic Vol. 12, No. 2 | 20 September 2021 Cross Ref On fractional Lévy motion: and in Applied Vol. No. 2 | 6 June 2022 Cross Ref Time and Persistence in An Using Fractional Journal of Research, Vol. 16, No. 3 | 7 April 2022 Cross Ref A for time fractional with Vol. No. | 2 2021 Cross Ref and Vol. No. 2 | 13 June 2022 Cross Ref Long short time the rough and in and Finance, Vol. No. 1 | 8 2021 Cross Ref properties for a fractional and Applied Analysis, Vol. No. 3 | 13 May 2022 Cross Ref Fractional Lévy motion with for and analysis of Vol. | 1 2022 Cross Ref random in Review E, Vol. No. 6 | 27 June 2022 Cross Ref of of fractional Brownian Review E, Vol. No. 6 | 30 June 2022 Cross Ref of for fractional impulsive differential equations driven by fractional Brownian and Stochastic Vol. 0, No. 0 | 31 May 2022 Cross Ref of fractional stochastic differential equation with and fractional Brownian Vol. | 30 May 2022 Cross Ref the of scales in and Planning B: Urban Analytics and City Science, Vol. 11 | May 2022 Cross Ref the of on of International Conference on and | 23 May 2022 Cross Ref the of in Multivariate by in the Wavelet 2022 - 2022 IEEE International Conference on and Signal | 23 May 2022 Cross Ref estimation for the model driven by the complex fractional Brownian Vol. No. 4 | 28 July 2021 Cross Ref Anomalous diffusion and memory in Computational Biology, Vol. 18, No. 5 | 18 May 2022 Cross Ref OF OF A | 13 May 2022 Cross Ref On the of Vol. 10, No. 9 | 22 April 2022 Cross Ref Convergence of for for with of Computing, Vol. No. 2 | 21 March 2022 Cross Ref Entropy of in a Review E, Vol. No. 5 | 2 May 2022 Cross Ref Analysis of during 26 August Vol. 24, No. 5 | 14 May 2022 Cross Ref stability of stochastic A and Dynamics, Vol. 22, No. | 18 April 2022 Cross Ref behavior in a model with A, Vol. | 1 May 2022 Cross Ref Asymptotic for driven by fractional Brownian motion in the of Mathematical Analysis and Applications, Vol. No. 1 | 1 May 2022 Cross Ref Generalized and rough Ornstein–Uhlenbeck Vol. | 30 April 2022 Cross Ref The the distribution of processes for the estimation of the Sciences Journal, Vol. No. 6 | 12 April 2022 Cross Ref and Application of Some Fractional Driven by Fractional Economics, Vol. 2 | April 2022 Cross Ref for processes and to Vol. No. 4 | 1 March 2022 Cross Ref Stochastic with to fractional processes in of Analysis, Vol. No. 8 | 1 2022 Cross Ref of and in Hurst exponents from spectral analysis of atomic force microscopy topographic Science, Vol. | 1 2022 Cross Ref in Distribution to Stochastic Driven by a Fractional Brownian Journal of Mathematics, Vol. No. 2 | 21 2022 Cross Ref a Under Random and Stochastic and Transactions on Science and Engineering, Vol. No. 2 | 1 2022 Cross Ref A new fractional based on nonlinear structure to systems with and of and Vol. No. | 30 January 2021 Cross Ref and The Transactions on and Systems, Vol. No. 2 | 1 2022 Cross Ref Analysis on with of and Fractional, Vol. 6, No. 4 | 14 April 2022 Cross Ref The of the Fractional and Fractional, Vol. 6, No. 4 | 15 April 2022 Cross Ref A and for complex Review E, Vol. No. 4 | 18 April 2022 Cross Ref of under in Review E, Vol. No. 4 | April 2022 Cross Ref theory of of an Review A, Vol. No. 4 | 26 April 2022 Cross Ref method for model in fractal Solitons & Fractals, Vol. | 1 2022 Cross Ref Time fractional equation with a based fractional Solitons & Fractals, Vol. | 1 2022 Cross Ref stochastic and of with complex in Applied Mechanics and Engineering, Vol. | 1 2022 Cross Ref OF Journal, Vol. No. 2 | 18 August 2022 Cross Ref The of of Fractional by in Vol. 2 | 24 March 2022 Cross Ref Bayesian of scaled fractional Brownian motionJournal of Physics A: Mathematical and | 24 March 2022 Cross Ref Anomalous diffusion: fractional Brownian motion fractional motionJournal of Physics A: Mathematical and Theoretical, Vol. 55, No. 11 | 23 2022 Cross Ref process with noise as a anomalous diffusion of Physics A: Mathematical and | 8 March 2022 Cross Ref by and Analysis and Vol. | 4 March 2022 Cross Ref Stochastic for the stochastic differential equations with & Probability Letters, Vol. | 1 Mar 2022 Cross Ref Multivariate range A: Statistical Mechanics and its Applications, Vol. | 1 Mar 2022 Cross Ref the memory for and time with Vol. No. 3 | 31 January 2022 Cross Ref for the Fractional Ornstein–Uhlenbeck of Vol. No. 1 | 22 October 2020 Cross Ref Properties of a Generalized Fractional Brownian of Vol. No. 1 | 9 January 2021 Cross Ref The for Time of Stochastic Vol. 10, No. 3 | 23 2022 Cross Ref A for Long in Higher Vol. 10, No. 5 | 24 2022 Cross Ref The of time Journal of Statistics, Vol. No. 1 | 14 August 2021 Cross Ref Estimation on of time generalized Dynamics, Vol. No. 4 | 12 January 2022 Cross Ref of the in the of fields by the of the Vol. | 1 Mar 2022 Cross Ref Statistical of nonlinear time and application to Review Research, Vol. 4, No. 1 | 17 March 2022 Cross Ref Price Modeling of under for Vol. 13, No. 3 | 18 March 2022 Cross Ref and in Advances of Physical Sciences, Vol. 06 | 27 April 2022 Cross Ref of of under fractional Brownian motionStatistics & Probability Letters, Vol. | 1 Mar 2022 Cross Ref Fractional and Statistical An of the Indian of Science, Vol. 29 | 24 2022 Cross Ref diffusion with stochastic of Physics A: Mathematical and Theoretical, Vol. 55, No. 7 | 28 January 2022 Cross Ref On the fractional stochastic for random Analysis and Applications, Vol. | 2 2022 Cross Ref of and Systems to

Previous article Next article Approximate Integration of Stochastic Differential EquationsG. N. Mil'shtejnG. N. Mil'shtejnhttps://doi.org/10.1137/1119062PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. I. Gikhman and , A. V. Skorokhod, Introduction to the Theory of Random Processes, Izd-vo "Nauka", Moscow, 1965, (In Russian.) Google Scholar[2] I. I. Gikhman and , A. V. Skorokhod, Stochastic Differential Equations, Springer, New York, 1972 0242.60003 CrossrefGoogle Scholar[3] R. Z. Khas'minskii, Stability of Systems of Differential Equations under Random Perturbations of their Parameters, Izd-vo "Nauka", Moscow, 1969, (In Russian.) Google Scholar[4] E. Hills and , R. Phillips, Functional Analysis and Semigroups, American Mathematical Society, Providence, RI., 1957 0078.10004 Google Scholar[5] R. L. Stratonovich, Conditional Markov processes and their application to the theory of optimal control, Translated from the Russian by R. N. and N. B. McDonough for Scripta Technica, Inc. Modern Analytic and Computational Methods in Science and Mathematics, No. 7, American Elsevier Publishing Co., Inc., New York, 1968xvii+350 MR0221860 (36:4912) 0159.46804 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein schemeAIMS Mathematics, Vol. 8, No. 2 Cross Ref Impact of flow field resolution on produced water transport in Lagrangian and Eulerian modelsMarine Pollution Bulletin, Vol. 182 Cross Ref Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models19 April 2022 | Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 84, No. 4 Cross Ref Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry12 August 2022 | Entropy, Vol. 24, No. 8 Cross Ref Planktos: An Agent-Based Modeling Framework for Small Organism Movement and Dispersal in a Fluid Environment with Immersed Structures10 June 2022 | Bulletin of Mathematical Biology, Vol. 84, No. 7 Cross Ref Pricing path-dependent exotic options with flow-based generative networksApplied Soft Computing, Vol. 124 Cross Ref Estimation of drift and diffusion functions from unevenly sampled time-series data27 July 2022 | Physical Review E, Vol. 106, No. 1 Cross Ref The Generalized Gamma Distribution as a Useful RND under Heston's Stochastic Volatility Model26 May 2022 | Journal of Risk and Financial Management, Vol. 15, No. 6 Cross Ref On the approximation and simulation of iterated stochastic integrals and the corresponding Lévy areas in terms of a multidimensional Brownian motion26 May 2021 | Stochastic Analysis and Applications, Vol. 40, No. 3 Cross Ref Brownian particles driven by spatially periodic noise1 March 2022 | The European Physical Journal E, Vol. 45, No. 3 Cross Ref The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations23 February 2022 | Risks, Vol. 10, No. 3 Cross Ref 1 January 2022 Cross Ref Learning Stochastic Optimal Policies via Gradient DescentIEEE Control Systems Letters, Vol. 6 Cross Ref A Closed Form Solution for Pricing Variance Swaps Under the Rescaled Double Heston Model27 November 2021 | Computational Economics, Vol. 11 Cross Ref Cell-cell communication through FGF4 generates and maintains robust proportions of differentiated cell types in embryonic stem cells5 November 2021 | Development, Vol. 148, No. 21 Cross Ref On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model17 November 2021 | Mathematics, Vol. 9, No. 22 Cross Ref Mathematical modelling of the second wave of COVID-19 infections using deterministic and stochastic SIDR models7 July 2021 | Nonlinear Dynamics, Vol. 106, No. 2 Cross Ref A Local and Time Resolution of the COVID-19 Propagation—A Two-Dimensional Approach for Germany Including Diffusion Phenomena to Describe the Spatial Spread of the COVID-19 Pandemic7 July 2021 | Physics, Vol. 3, No. 3 Cross Ref Deep learning-based least squares forward-backward stochastic differential equation solver for high-dimensional derivative pricing26 March 2021 | Quantitative Finance, Vol. 21, No. 8 Cross Ref Information Transmission in Delay-Coupled Neuronal Circuits in the Presence of a Relay Population29 July 2021 | Frontiers in Systems Neuroscience, Vol. 15 Cross Ref Efficient simulation methods for the Quasi-Gaussian term-structure model with volatility smiles: practical applications of the KLNV-scheme4 February 2021 | Quantitative Finance, Vol. 21, No. 7 Cross Ref Convergence, non-negativity and stability of a new Lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model18 September 2020 | Japan Journal of Industrial and Applied Mathematics, Vol. 38, No. 2 Cross Ref Active noise-driven particles under space-dependent friction in one dimension4 May 2021 | Physical Review E, Vol. 103, No. 5 Cross Ref Transmission delays and frequency detuning can regulate information flow between brain regions15 April 2021 | PLOS Computational Biology, Vol. 17, No. 4 Cross Ref On the MS-stability of predictor–corrector schemes for stochastic differential equationsMathematics and Computers in Simulation, Vol. 180 Cross Ref Deep Splitting Method for Parabolic PDEsChristian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, and Ariel Neufeld13 September 2021 | SIAM Journal on Scientific Computing, Vol. 43, No. 5AbstractPDF (580 KB)A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line FailureJacob Roth, David A. Barajas-Solano, Panos Stinis, Jonathan Weare, and Mihai Anitescu25 January 2021 | Multiscale Modeling & Simulation, Vol. 19, No. 1AbstractPDF (39676 KB)Computing the finite time Lyapunov exponent for flows with uncertaintiesJournal of Computational Physics, Vol. 425 Cross Ref On the RND under Heston's Stochastic Volatility ModelSSRN Electronic Journal, Vol. 79 Cross Ref How Does Noise Help Robustness? Explanation and Exploration under the Neural SDE Framework Cross Ref Building a path-integral calculus: a covariant discretization approach18 November 2019 | Journal of Physics A: Mathematical and Theoretical, Vol. 52, No. 50 Cross Ref Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing17 July 2019 | Applied Mathematical Finance, Vol. 26, No. 3 Cross Ref A new delta expansion for multivariate diffusions via the Itô-Taylor expansionJournal of Econometrics, Vol. 209, No. 2 Cross Ref Variance swaps with double exponential Ornstein-Uhlenbeck stochastic volatilityThe North American Journal of Economics and Finance, Vol. 48 Cross Ref Stochastic simulation of anharmonic dissipation. II. Harmonic bath potentials with quadratic couplingsThe Journal of Chemical Physics, Vol. 150, No. 7 Cross Ref Gliotransmitter Exocytosis and Its Consequences on Synaptic Transmission22 January 2019 Cross Ref Modeling Neuron–Glia Interactions with the Brian 2 Simulator22 January 2019 Cross Ref Wave pinning in competition-diffusion models in variable environmentsJournal of Theoretical Biology, Vol. 461 Cross Ref Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative PricingSSRN Electronic Journal Cross Ref Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEsApplied Mathematics and Computation, Vol. 339 Cross Ref Preventing plunder: Military technology, capital accumulation, and economic growthJournal of Macroeconomics, Vol. 58 Cross Ref Numerical methods for simulation of stochastic differential equations15 January 2018 | Advances in Difference Equations, Vol. 2018, No. 1 Cross Ref Stationary moments, diffusion limits, and extinction times for logistic growth with random catastrophesJournal of Theoretical Biology, Vol. 454 Cross Ref Gaussian process approximations for fast inference from infectious disease dataMathematical Biosciences, Vol. 301 Cross Ref Phase drift on networks of coupled crystal oscillators for precision timing5 July 2018 | Physical Review E, Vol. 98, No. 1 Cross Ref Continuous-time smooth ambiguity preferencesJournal of Economic Dynamics and Control, Vol. 90 Cross Ref Generalized Green's function molecular dynamics for canonical ensemble simulations29 May 2018 | Physical Review E, Vol. 97, No. 5 Cross Ref Recursive marginal quantization of higher-order schemes19 January 2018 | Quantitative Finance, Vol. 18, No. 4 Cross Ref Diffusion Monte Carlo simulations of gas phase and adsorbed D 2 -(H 2 ) n clustersThe Journal of Chemical Physics, Vol. 148, No. 10 Cross Ref Application of Legendre spectral-collocation method to delay differential and stochastic delay differential equationAIP Advances, Vol. 8, No. 3 Cross Ref Finite variance unbiased estimation of stochastic differential equations Cross Ref A stochastic SIS epidemic model with vaccinationPhysica A: Statistical Mechanics and its Applications, Vol. 486 Cross Ref Forward, backward, and weighted stochastic bridges12 October 2017 | Physical Review E, Vol. 96, No. 4 Cross Ref Heat-Assisted Multiferroic Solid-State Memory25 August 2017 | Materials, Vol. 10, No. 9 Cross Ref Effects of correlations and fees in random multiplicative environments: Implications for portfolio management7 August 2017 | Physical Review E, Vol. 96, No. 2 Cross Ref Stochastic C-Stability and B-Consistency of Explicit and Implicit Milstein-Type Schemes19 September 2016 | Journal of Scientific Computing, Vol. 70, No. 3 Cross Ref Algorithms for integration of stochastic differential equations using parallel optimized sampling in the Stratonovich calculusComputer Physics Communications, Vol. 212 Cross Ref Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential EquationsM. Navarro Jimenez, O. P. Le Maître, and O. M. Knio18 April 2017 | SIAM/ASA Journal on Uncertainty Quantification, Vol. 5, No. 1AbstractPDF (1572 KB)Milstein-Type Procedures for Numerical Solutions of Stochastic Differential Equations with Markovian SwitchingSon L. Nguyen, Tuan A. Hoang, Dung T. Nguyen, and George Yin18 April 2017 | SIAM Journal on Numerical Analysis, Vol. 55, No. 2AbstractPDF (467 KB)Modeling Tools for Financial Options19 August 2017 Cross Ref Generating Random Numbers with Specified Distributions19 August 2017 Cross Ref Monte Carlo Simulation with Stochastic Differential Equations19 August 2017 Cross Ref Standard Methods for Standard Options19 August 2017 Cross Ref Finite-Element Methods19 August 2017 Cross Ref Pricing of Exotic Options19 August 2017 Cross Ref Beyond Black and Scholes19 August 2017 Cross Ref Preventing Plunder: Military Technology, Capital Accumulation, and Economic GrowthSSRN Electronic Journal Cross Ref Density Approximations for Multivariate Diffusions via an Itô-Taylor Expansion ApproachSSRN Electronic Journal Cross Ref A high-order discontinuous Galerkin method for Itô stochastic ordinary differential equationsJournal of Computational and Applied Mathematics, Vol. 308 Cross Ref Double-implicit and split two-step Milstein schemes for stochastic differential equations2 September 2015 | International Journal of Computer Mathematics, Vol. 93, No. 12 Cross Ref Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle26 October 2016 | Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 46 Cross Ref Synchronization detection in networks of coupled oscillators for pattern recognition Cross Ref Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds6 November 2015 | Annalen der Physik, Vol. 528, No. 5 Cross Ref Stochastic simplified modelling of abrasive waterjet footprints1 February 2016 | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, No. 2186 Cross Ref Parallel Optimized Sampling for Stochastic EquationsBogdan Opanchuk, Simon Kiesewetter, and Peter D. Drummond20 December 2016 | SIAM Journal on Scientific Computing, Vol. 38, No. 6AbstractPDF (1075 KB)Chebyshev spectral collocation method for stochastic delay differential equations8 April 2015 | Advances in Difference Equations, Vol. 2015, No. 1 Cross Ref An improved Milstein method for stiff stochastic differential equations1 December 2015 | Advances in Difference Equations, Vol. 2015, No. 1 Cross Ref Adaptive outer synchronization of delay-coupled nonidentical complex networks in the presence of intrinsic time delay and circumstance noise19 December 2014 | Nonlinear Dynamics, Vol. 80, No. 1-2 Cross Ref On the convergence of diffusion Monte Carlo in non-Euclidean spaces. I. Free diffusionThe Journal of Chemical Physics, Vol. 142, No. 11 Cross Ref On the convergence of diffusion Monte Carlo in non-Euclidean spaces. II. Diffusion with sources and sinksThe Journal of Chemical Physics, Vol. 142, No. 11 Cross Ref PC analysis of stochastic differential equations driven by Wiener noiseReliability Engineering & System Safety, Vol. 135 Cross Ref Modelling of Langevin Equations by the Method of Multiple ScalesIFAC-PapersOnLine, Vol. 48, No. 1 Cross Ref Computational solution of stochastic differential equations20 August 2013 | WIREs Computational Statistics, Vol. 5, No. 5 Cross Ref Stochastic modeling of the full cycle of one-product macroeconomy of growth27 March 2013 | Cybernetics and Systems Analysis, Vol. 49, No. 2 Cross Ref The Langevin and Fokker–Planck Equations in Polymer Rheology Cross Ref Time-Step Considerations in Particle Simulation Algorithms for Coulomb Collisions in PlasmasIEEE Transactions on Plasma Science, Vol. 38, No. 9 Cross Ref Ergodicity of the Stochastic Nosé–Hoover Heat BathJournal of the Physical Society of Japan, Vol. 79, No. 7 Cross Ref The foundations of a unified approach to mathematical modelling of angiogenesis31 October 2009 | International Journal of Advances in Engineering Sciences and Applied Mathematics, Vol. 1, No. 1 Cross Ref Weak forms of the locally transversal linearization (LTL) technique for stochastically driven nonlinear oscillatorsApplied Mathematical Modelling, Vol. 32, No. 9 Cross Ref Evolution of Compact Binary Populations in Globular Clusters: A Boltzmann Study. II. Introducing StochasticityThe Astrophysical Journal, Vol. 680, No. 2 Cross Ref Approximation Schemes for Stochastic Differential Equations in Hilbert SpaceYu. S. Mishura and G. M. Shevchenko28 August 2007 | Theory of Probability & Its Applications, Vol. 51, No. 3AbstractPDF (195 KB)Accurate Integration of Stochastic Climate Models with Application to El NiñoMonthly Weather Review, Vol. 132, No. 1 Cross Ref Quiet direct simulation of coulomb collisionsIEEE Transactions on Plasma Science, Vol. 31, No. 1 Cross Ref Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motionsThe Annals of Applied Probability, Vol. 11, No. 2 Cross Ref A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate VolatilitySSRN Electronic Journal Cross Ref A Nonparametric Analysis of the Forward Rate VolatilitiesSSRN Electronic Journal Cross Ref Statistical-mechanically exact simulation of polymer conformation in an external fieldThe Journal of Chemical Physics, Vol. 107, No. 15 Cross Ref Stability Analysis of Numerical Schemes for Stochastic Differential EquationsYoshihiro Saito and Taketomo Mitsui1 August 2006 | SIAM Journal on Numerical Analysis, Vol. 33, No. 6AbstractPDF (1444 KB)Approximation of Lyapunov Exponents of Nonlinear Stochastic Differential EquationsAxel Grorud and Denis Talay5 July 2006 | SIAM Journal on Applied Mathematics, Vol. 56, No. 2AbstractPDF (2423 KB)Approximation of the Zakai Equation for Nonlinear FilteringKazufumi Ito1 August 2006 | SIAM Journal on Control and Optimization, Vol. 34, No. 2AbstractPDF (1181 KB)Effects of distributed delays on the stability of structures under seismic excitation and multiplicative noiseSadhana, Vol. 20, No. 2-4 Cross Ref Numerical procedures for sample structures on stochastic differential equationsJournal of Mathematical Physics, Vol. 31, No. 8 Cross Ref Models of Chemical Gradient Sensing by Cells Cross Ref A Theorem on the Order of Convergence of Mean-Square Approximations of Solutions of Systems of Stochastic Differential EquationsG. N. Mil–shtein17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 4AbstractPDF (412 KB)Weak Approximation of Solutions of Systems of Stochastic Differential EquationsG. N. Mil'shtein28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 4AbstractPDF (1203 KB)Piecewise Constant Approximation for the Monte-Carlo Calculation of Wiener IntegralsA. D. Vent-Tsel', S. A. Gladyshev, and G. N. Mil'shteyn17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 4AbstractPDF (700 KB)Numerical Treatment of Stochastic Differential EquationsW. Rüemelin31 July 2006 | SIAM Journal on Numerical Analysis, Vol. 19, No. 3AbstractPDF (835 KB)A Method of Second-Order Accuracy Integration of Stochastic Differential EquationsG. N. Mil'shtein17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 2AbstractPDF (451 KB)Brownian dynamics study of transitions in a polymer chain of bistable oscillatorsThe Journal of Chemical Physics, Vol. 69, No. 3 Cross Ref Computational field theory and pattern formation Cross Ref Volume 19, Issue 3| 1975Theory of Probability & Its Applications History Submitted:23 September 1973Published online:28 July 2006 InformationCopyright © 1975 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119062Article page range:pp. 557-562ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

A general division of labor has an arbitrary number of subtasks, and asymmetric interactions among players in the subtask-holder upstream groups and the downstream groups. Cooperation among the subtask-holders is essential in division of labor. We construct a general division of labor network model with a single output, where subtask-holder groups are located, and the process never stops for a defection. We consider that cooperators and defectors exist in each subtask-holder group initially; cooperators in a group pay a cost of cooperation to upgrade the product or service quality, defectors do not pay any cost, reducing the quality. More cooperator groups can upgrade the quality more, thus all the players in all groups can obtain a better reputation defined as a bonus. We found that the division of labor with a bonus meets the social dilemma condition, and our model can be studied from the viewpoint of evolution of cooperation. Our analysis of replicator equations shows the benefits are canceled out in the equations; thus, benefits never influence the evolution of cooperation. As a result, the network structure of the division of labor never influences the dynamics. We also show that sanction on the defectors induces the evolution of cooperation and co-existences of cooperator groups and defector groups, and that the bonus functions determine whether the number of the subtask-holder groups in the division of labor influences on the evolution of cooperation. Our results will contribute to the theoretical understanding of division of labor on the network structure.

Chronic inflammation is a key factor in the degenerative changes of osteoarthritic joints. Obesity significantly raises the risk of osteoarthritis (OA), since excess body fat (adipose tissue) not only systemically increases the level of inflammation but also locally stimulates the inflammatory responses within osteoarthritic joints. In this context, physical activity is a practical approach in OA prevention and intervention, whereas current therapeutic strategies remain empirical and lack patient-specific tailoring. This makes it challenging to determine the appropriate dose and timing of physical activity therapy for diverse individuals. Building on our previous work of an adipokine-mediated inflammation model, this study aimed to analyse the effects of obesity and physical activity on OA inflammation by parameterising the inflammatory activities. In this model, five key mediator groups (pro- and anti-inflammatory cytokines, matrix metalloproteinases, adipokines and fibronectin fragments) were included. A global sensitivity analysis was conducted in the estimated parametric space and revealed the critical role of adiposity-associated factors in regulating inflammation. In addition, the inflammatory activities were simulated by tuning two adiposity-associated parameters, body mass index (BMI) and physical activity level (PAL), factoring in a simulated injury. The effectiveness of three physical activity intervention strategies was assessed by examining the inflammatory responses of the representative cases with four BMI profiles. A marked sensitivity to the timing (window period) of physical activity implementation was found. Results underscored the importance of accounting for both the adiposity level and the extent of tissue damage when designing intervention strategies of physical activity and optimising their timing for managing OA inflammation. This novel computational study analyses the adiposity-associated effects of physical activity on OA inflammation, illustrating that the effective window period of physical activity interventions varies from 0 to 15 months, depending on the level of adiposity and mechanical damage. Outcomes from the evaluation of the time window can strategically contribute to optimising physical activity interventions for the management of OA risk at an early stage.

The spread and control of antibiotic resistance is a major public health issue and challenge to address. This has driven a growing interest in bacteriophages, used alone or in combination with antibiotics to treat antibiotic-resistant biofilms. Evaluating the potential of phage therapy requires a detailed understanding of phages-microbes interactions, from their lytic activity to their capacity for transducing resistance genes. Mathematical models are a powerful tool to investigate specific aspects of these complex mechanisms, where a great number of biotic and abiotic interactions are involved. We present here a mathematical model exploring the role of phages in biofilm ecosystems and the potential of phage therapy to eliminate resistant bacterial populations. The model is formulated as a system of non-local partial differential equations in a one-dimensional, free-boundary domain. It incorporates all major routes of horizontal gene transfer - conjugation, natural transformation, and generalised transduction - along with selective pressure from metals and antibiotics, within a spatially structured, growing biofilm. Numerical simulations investigate the contribution of vertical and horizontal gene transfer, including generalised transduction, to the spread of plasmid-mediated resistance. We assess the potential of phage therapy, both as a stand-alone treatment and in combination with antibiotics, highlighting how phage-antibiotic synergy can substantially reduce the antibiotic concentration required to eradicate even resistant biofilms. The simulations reveal how phage predation contributes to selective pressure and shapes biofilm ecology.

We introduce a time-delayed human-malaria interaction model to examine the dynamics of malaria transmission and to evaluate the impact of awareness-based interventions. In this study, we incorporate two time delays: one representing the incubation period of malaria during transmission and the other accounting for the time required to organize and implement awareness programs. The delayed and non-delayed models are calibrated using observed malaria case data from India, the Democratic Republic of the Congo, and Uganda, and their predictive performance is assessed using relevant evaluation metrics to determine their accuracy and reliability. In the non-delayed model, variance-based MeFAST and correlation-based LHS-PRCC global sensitivity analyses are conducted to determine the key parameters that significantly influence the model dynamics. Based on the convergence test and statistical analyses, the two methods yield nearly the same number of significant parameters for the infected compartments. The existence of periodic oscillations emerging with a stable limit cycle is established by analyzing a supercritical Hopf bifurcation associated with the decay rate of awareness. Subsequently, in the delayed system, the direction and stability of the delay-induced Hopf bifurcation have been demonstrated using the normal form and the center manifold theorem, revealing the supercritical Hopf bifurcation and highlighting the challenges in controlling disease spread. Compared to a single delay, the presence of multiple delays destabilizes the system earlier and lowers the delay threshold for periodic behavior. Chaotic dynamics has been observed due to the high value of time delay in reported cases of infectives which reflects the importance of low delay value in awareness to control the spread of the disease. Despite chaotic behavior, the high availability of treatment and the extensive use of insecticides have been found to effectively control the dynamics.The delayed optimal control results indicate that the combination of insecticide measures and treatment is the most effective in controlling infections.

I derive a novel stochastic equation for the evolution of the additive genetic variance-covariance matrix G in response to mutation, selection, drift, and fluctuating population size. Common wisdom holds that the effect of drift on G is simply to reduce each of its entries by a common proportional amount while preserving its orientation. In contrast, I find that drift causes significant and directional shifts in the orientation of G by driving genetic correlations to their extremes. Biologically, this is a consequence of linkage build-up introduced by drift. I compare these theoretical results to empirical observations based on experiments conducted by Phillips et al. (2001). Additionally, to derive the model of G-matrix evolution, I developed a novel synthetic framework for modelling ecological and evolutionary dynamics of populations carrying multivariate traits. This framework is optimized for deriving new models across a wide range of topics in population biology. Foundations of the framework are formalized by the theory of measure-valued processes, but application of the framework only requires multivariate calculus, and heuristics are presented in the main text for making additional calculations involving stochastic processes. Collectively, this work establishes a powerful framework enabling efficient formal analysis of integrated population processes across evolution and ecology, and its potential for making new discoveries is illustrated by novel findings on fundamental aspects of G-matrix evolution.

Individuals experience varying selective pressures as they pass through different classes, defined by developmental stage, age, physiological condition, or spatial location. Adaptive Dynamics models predict the long-term evolutionary dynamics of class-structured populations, but there is a trade-off when using the two forms of the selection gradient. The determinant-form - defined by the derivative of the determinant of the class transition rate matrix - has an explicit formula but lacks a biological interpretation. Alternatively, the reproductive-value-weighted-form (RVW-form) has a clear biological interpretation, but the reproductive values do not have explicit formulas outside of special cases. In this study, I show that the determinant-form is a sum of class-mediated indirect effects of selection, where for each indirect effect, selection alters the transition rate for a particular class and changes in that rate propagate through the population and indirectly affect the density of that class. I also show how to compute the reproductive values from minors of the population's transition rate matrix. Those minors represent the total effects between classes and can be visualized as pathways through a population's life cycle graph, mirroring classical results for discrete-time stage-structured models. To illustrate the utility of these results, I analyze a model of virulence evolution in an environmentally transmitted parasite, yielding novel predictions about how density-dependent host mortality and trait-dependent decay rates affect predictions related to the Curse of the Pharaoh hypothesis. I also analyze a model of the evolution of lysis and lysogeny, which helps clarify how host density and parasite life-history traits affect viral evolution.

This commentary highlights the influenza model of Arino et al. (2008), emphasizing its analytical framework for evaluating vaccination, antiviral treatment, and behavioral withdrawal. Its simplicity and tractability illustrate the lasting value of deterministic compartmental models in understanding epidemic control.

Size is an important trait among marine phytoplankton as it influences a vast range of physiological, ecological, and evolutionary processes. For Trichodesmium, a cyanobacterial diazotroph important for the global nitrogen cycle, size is a flexible trait that can change because of its ability to form colonies. Trichodesmium colonies can persist from 10 µm to greater than 1 mm in the natural environment. Despite this known ability, we still do not know whether a maximum size limit exists for Trichodesmium colonies and, more importantly, whether any mechanisms regulate this limit. In this paper, we use a theoretical metabolic model to investigate the role of two factors known to influence Trichodesmium colony size: carbon dioxide and light availability. The greater the availability of carbon dioxide or the average light availability, the greater the potential colony size of Trichodesmium. Carbon limitations have a much stronger effect on colony sizes than light limitations. Higher respiratory costs, perhaps due to higher water temperatures, do not appear to limit maximum colony sizes unless they consume nearly all the carbon that is fixed. Our theoretical model highlights several scenarios that likely assert some control over the ecology of Trichodesmium in the global ocean. It also implies that natural colonies must have mechanisms to escape from carbon limitations. To achieve sizes like 1 mm, Trichodesmium colonies must be highly porous (>91%) or live in environments with a nutrient flux 12 times greater than what molecular diffusion can provide.

Remote digital symptom monitoring systems (rSMS) have been increasingly used in recent years to monitor symptoms, health-related quality of life, and other patient-reported outcomes in lung cancer. Previous studies have demonstrated variability in study design, types of rSMS, and outcomes used to assess benefits for patients and health care systems. However, there remains a lack of synthesized evidence pertaining to the similarities and differences among rSMS, including their theoretical underpinnings, key functional components, and reported benefits and limitations. This review aims to identify and synthesize existing research to map the current landscape of rSMS in lung cancer, including the theoretical foundations for its development and implementation, as well as its types, applications, and outcomes. This scoping review followed the Joanna Briggs Institute scoping review framework and adhered to the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews) guidelines. A comprehensive literature search was conducted from database inception to October 16, 2025, across 7 English-language databases and 3 Chinese-language databases (CNKI, WanFang, and SinoMed). Eligible studies were peer-reviewed original research articles examining rSMS among adults with lung cancer. Data were independently screened and extracted by 2 reviewers, with discrepancies resolved by a third reviewer. Quantitative data were extracted using a standardized form and synthesized descriptively. Content analysis was performed to analyze the qualitative data. A total of 41 studies involving 11,765 patients and 85 health care providers were included. Twelve studies focused exclusively on advanced-stage lung cancer. Participants were generally middle-aged to older adults (mean ages 51-74 y), with male participants typically comprising 30% to 50% across studies. Most studies were conducted in the United States (n=19). We identified 32 patient-reported outcome measures that were used either as core rSMS components or as study outcomes. Four common functional modules were observed across rSMS: data collection, data analysis, response systems, and patient education. Qualitative evidence was limited; the most frequently reported benefit was the promotion of patient-centered care. Health care providers raised concerns about uncertain effectiveness and increased workload. This scoping review highlights the promising role of rSMS in lung cancer care and provides a structured map of current evidence. It adds to prior literature in 3 ways. First, it summarizes how and how often theoretical frameworks are reported and applied in rSMS development and implementation. Second, it synthesizes and categorizes four common functional modules across systems. Third, it differentiates measures embedded as rSMS components from those used as evaluation outcomes. These contributions clarify current practices and methodological gaps and underscore the importance of theory-informed design, functional clarity, and stakeholder engagement in the development of patient-centered, clinically meaningful, and sustainable rSMS platforms.

The high heterogeneity of lung adenocarcinoma (LUAD) is largely due to its complex tumor immune microenvironment (TIME). Cancer-associated fibroblasts (CAFs) are a core matrix component of TIME. However, their functional heterogeneity and the specific molecular mechanisms driving tumor progression have not been fully elucidated. In addition, the role of nuclear receptor NR2F2 in tumor development is still controversial. This study integrated scRNA-seq data from the GEO database with RNA-seq data from TCGA and GEO and then performed multiple levels of validation through in vitro experiments. We adopted a systematic computational biology strategy and analyzed the cellular composition, interaction networks and functional states of cancer-associated fibroblasts (CAFs) in lung adenocarcinoma using Seurat, CellChat, and AUCell. According to the marker genes of key CAF subgroup, prognostic risk models were constructed through LASSO-Cox regression and validated in an independent cohort (GSE72094). Afterwards, we carried out in vitro experiments and validated the biological role of NR2F2 through a coculture system. Functional validation was conducted through siRNA knockdown, plasmid overexpression, CCK-8 assay, EdU labeling, and Transwell experiments. We noticed the CAF - 2 subgroup, characterized by the highest level of TGF - β signaling activation, sends various signals to different cell types. We constructed and verified a consistent prognostic signature made of 16 genes using the LASSO-Cox method. This model can effectively assess the risk of LUAD patients. The prognosis in high-risk group is worse. And we also do some analysis to find out that risk score is highly associated with immunosuppressive TME and high expressions of PD - L1. We have found in our further study that the expression of NR2F2 in CAF is associated with the promoting of matrix remodeling and metabolic reprogramming. From the coculture system and in vitro functional experiments, overexpression of NR2F2 in CAFs enhanced tumor cell proliferation and invasion, whereas knockdown of NR2F2 attenuated these malignant phenotypes. Using single-cell RNA sequencing data, we identified a CAF subgroup with the most active TGF-β signaling. Based on the marker genes of the subgroup, we constructed and validated an effective prognostic model, then we further screened and confirmed NR2F2 as a major pro-tumorigenic regulator from this feature gene set through single cell and transcriptome data as well as in vitro experiments. NR2F2 promotes malignant remodeling of TIME by synergistically enhancing TGF-β signaling and EMT processes. Our study provides not only a solid theoretical foundation but also a therapeutic target to explore new therapeutic options targeting the CAFs-TGF-β-EMT axis.

Subaerial biofilms (SABs) are microbial communities that colonize exposed surfaces, playing a role in biogeochemical cycles and the deterioration of built heritage. Their functioning is tightly coupled to environmental conditions, particularly moisture and carbon availability. This work presents a predictive framework to assess the long-term stability of SABs in response to future environmental changes - specifically, variations in temperature (T), air relative humidity (RH), and atmospheric CO2 partial pressure. The approach is based on a system of ordinary differential equations that describe the dynamics of key SAB components such as cyanobacteria, heterotrophs and polysaccharides. Using daily environmental profiles representative of summer and winter conditions, the model explores both the individual and combined impacts of T, RH and CO2 on microbial metabolism, productivity, and ecosystem composition. Results suggest that while temperature increases negatively affect inorganic carbon availability, they do not cause substantial shifts in SAB structure - consistent with the wide thermal tolerance typical of these communities. In contrast, elevated atmospheric CO2 may enhance carbon fixation and overall productivity. However, air relative humidity emerges as the primary regulator of microbial viability: even small fluctuations significantly alter the duration of metabolically active periods, with declines potentially leading to ecosystem collapse. Notably, the interaction between CO2 and water activity is synergistic: increases in atmospheric CO2 together with temperature-driven changes in relative humidity - either upward or downward - can in combination significantly influence SAB dynamics. These findings highlight the central role of water activity in maintaining SAB viability and suggest that even moderate shifts in microclimatic moisture availability could have profound impacts on these microbial communities.

The problem of estimating the growth rate of a birth and death processes based on the coalescence times of a sample of n individuals has been considered by several authors (Stadler in Journal of Theoretical Biology 261(1):58-66, 2009: Williams et al in Nature 602 (7895):162-168, 2022: Mitchell et al in Nature 606(7913):343-350, 2022: Johnson et al in Bioinformatics 39(9):btad561, 2023). This problem has applications, for example, to cancer research, when one is interested in determining the growth rate of a clone. Recently, Johnson et al Bioinformatics 39(9):btad561, 2023) proposed an analytical method for estimating the growth rate using the theory of coalescent point processes, which has comparable accuracy to more computationally intensive methods when the sample size n is large. We use a similar approach to obtain an estimate of the growth rate that is not based on the assumption that n is large. We demonstrate, through simulations using the R package cloneRate, that our estimator of the growth rate performs well in comparison with previous approaches when n is small.

Habitat fragmentation is one of the most immediate and substantial threats to biodiversity, generating isolated populations with reduced genetic diversity. Genetic monitoring has become essential for detecting fragmentation and tracking its progress. However, the coherent interpretation of genetic monitoring data and understanding the genetic consequences of fragmentation require frameworks that accurately represent real-world complexity. Existing theoretical frameworks typically rely on simplified spatial structures and do not adequately capture the heterogeneous migration patterns of natural populations. Here, we integrate network theory and mathematical population genetics to develop a framework for studying the genetic consequences of fragmentation processes, explicitly accounting for heterogeneous connectivity and temporal dynamics. We apply this framework to examine how different fragmentation processes affect genetic measures commonly used in genetic monitoring. Through analysis of simulated and empirical networks, we find that different fragmentation scenarios produce substantially distinct trajectories in key genetic measures, sometimes exhibiting rapid transitional dynamics. Furthermore, fragmentation can cause deviations from classical theoretical expectations, such as the expected correlation between genetic and geographic distance (isolation-by-distance) or between genetic diversity and connectivity. Finally, we propose and demonstrate detectable early warning signals in genetic monitoring data that precede rapid transitional phases. Our framework thus provides a practical interpretation of genetic monitoring data, and a proof-of-concept that bridges the gap between idealized theoretical models and real-world connectivity dynamics.

In temperate regions, respiratory virus epidemics recur on a yearly basis, primarily during the winter season. This is believed to be induced by seasonal forcing, where the rate at which the virus can be transmitted varies cyclically across the course of each year. Seasonal epidemics can place substantial burden upon the healthcare system, with large numbers of infections and hospitalisations occurring across a short time period. However, the interactions between seasonal forcing and the factors necessary for epidemic resurgence - such as waning immunity, antigenic variation or demography - remain poorly understood. In this manuscript, we examine how the dynamics of antibody waning and antigenic variation can shape the seasonal recurrence of epidemics. We develop a novel susceptible-infectious-susceptible (SIS) immuno-epidemiological model of respiratory virus spread, where the susceptible population is stratified by their antibody level against the currently circulating strain of the virus, with this decaying as both antibody waning and antigenic drift occur. In the absence of seasonal forcing, we demonstrate the existence of two Hopf bifurcations over the effective antibody decay rate, with associated periodic model solutions. When seasonal forcing is introduced, we identify complex interactions between the strength of forcing and the effective antibody decay rate, yielding myriad dynamics including multi-year periodicity, quasiperiodicity and chaos. The timing and magnitude of seasonal epidemics is highly sensitive to this interaction, with the distribution of infection timing (by time of year) varying substantially across the parameter space. Finally, we show that seasonal forcing can produce resonant damping resulting in a cumulative infection incidence that is less than would otherwise be observed.

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by the accumulation of toxic protein plaques in the brain. Abundant evidence indicates that &#x3b2;-amyloid (A&#x3b2;) serves as an important pathological hallmark in AD, with A&#x3b2; oligomers (A&#x3b2;o) exhibiting critical neurotoxicity. The imbalance of Ca2+ homeostasis has also been demonstrated to exhibit complex interplay with abnormal A&#x3b2; accumulation. Several A&#x3b2;-targeting drugs are currently employed in the treatment of AD. However, the multifactorial mechanisms driving AD contribute to the suboptimal efficacy of existing clinical therapies. Motivated by these factors, multi-target combination therapies emerge as the prominent trend in AD research. In this paper, we propose an optimal control model to describe A&#x3b2;o dynamics under multi-target combined therapy. Also, the basic reproduction number R0 is derived as a threshold parameter to characterize the AD process. We find that A&#x3b2;o can be maintained at a low steady state when R0&#x202f;<&#x202f; 1, indicating the potential for disease control. The results of parameter sensitivity analysis based on R0 further confirm the significant impact of control variables on the system evolution. Subsequently, we investigate the theoretical results of the optimality system, proving the existence and uniqueness of the optimal solution. Numerical simulations are conducted to demonstrate the control efficacy of different strategies, revealing that drug combination therapy exhibits superior control over A&#x3b2;o steady-state compared to mono therapy. Moreover, cost-effectiveness analysis is employed to compare different control strategies, with the objective of identifying the optimal approach that balances drug costs with therapeutic efficacy. Notably, appropriately lowering the drug dosage in triple therapy retains the potential for maintaining therapeutic effects, thereby improving drug cost control. In summary, this work provides important insights into multi-target combination therapy for early treatment of AD.

Understanding the spatiotemporal dependencies between different protein species, as observed through fluorescent confocal laser microscopy, is crucial for gaining insight into their biological functions. We introduce an estimator of their bulk movement patterns between time points on a space, &#x3a8;, using the earth mover's distance. We propose a test statistic that combines these bulk movement patterns over a partition, &#x3a8;w, of &#x3a8; into w subregions and compares them between two samples. At the core of our approach lies a novel null hypothesis framework, consisting of statements regarding between- and within-sample independence of bulk movement patterns, alongside a statement of distributional invariance under the operation of a geometrically defined subgroup of permutations acting on &#x3a8;w. This framework yields a geometrically informed permutation (GIP) test designed to quantify the significance of dependencies between bulk movement patterns. We validate the approach using synthetic data spanning a range of independent and dependent scenarios with varying geometrical properties. Finally, we apply the GIP test to experiments involving the microtubule-associated proteins EB3 and TACC3, obtaining evidence that reinforces previous biological findings on the colocalisation of these proteins. More broadly, our proposed methodology is applicable to a wide range of spatiotemporal molecular data problems in which geometric structure is fundamental, particularly when the surrounding cellular or tissue environment informs the dynamics.