@misc{HartmannBanischSarichetal., author = {Hartmann, Carsten and Banisch, Ralf and Sarich, Marco and Badowski, Tomasz and Sch{\"u}tte, Christof}, title = {Characterization of rare events in molecular dynamics}, series = {Entropy}, volume = {16}, journal = {Entropy}, number = {1}, issn = {1099-4300}, doi = {10.3390/e16010350}, pages = {350 -- 376}, language = {en} } @misc{HartmannSchuette, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Efficient rare event simulation by optimal nonequilibrium forcing}, series = {Journal of Statistical Mechanics: Theory and Experiment}, volume = {November}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, issn = {1742-5468}, doi = {10.1088/1742-5468/2012/11/P11004}, pages = {P 11004}, language = {en} } @misc{SarichBanischHartmannetal., author = {Sarich, Marco and Banisch, Ralf and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Markov state models for rare events in molecular dynamics}, series = {Entropy}, volume = {16}, journal = {Entropy}, number = {1}, issn = {1099-4300}, doi = {10.3390/e16010258}, pages = {258 -- 286}, language = {en} } @misc{ZhangWangHartmannetal., author = {Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Applications of the cross-entropy method to importance sampling and optimal control of diffusions}, series = {SIAM (Society for Industrial and Applied Mathematics)}, volume = {36}, journal = {SIAM (Society for Industrial and Applied Mathematics)}, number = {6}, issn = {1095-7197}, doi = {10.1137/14096493X}, pages = {A2654 -- A2672}, language = {en} } @misc{HartmannLatorreZhangetal., author = {Hartmann, Carsten and Latorre, Juan C. and Zhang, Wei and Pavliotis, Grigorios A.}, title = {Optimal control of multiscale systems using reduced-order models}, series = {Journal of Computational Dynamics (JCD)}, volume = {1}, journal = {Journal of Computational Dynamics (JCD)}, number = {2}, issn = {2158-2505}, doi = {10.3934/jcd.2014.1.279}, pages = {279 -- 306}, language = {en} } @misc{WangHartmannSchuette, author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Linear response theory and optimal control for a molecular system under non-equilibrium conditions}, series = {Molecular Physics: An International Journal at the Interface Between Chemistry and Physics}, volume = {111}, journal = {Molecular Physics: An International Journal at the Interface Between Chemistry and Physics}, number = {22-23}, issn = {1362-3028}, doi = {10.1080/00268976.2013.844370}, pages = {3555 -- 3564}, language = {en} } @misc{HartmannYanao, author = {Hartmann, Carsten and Yanao, Tomohiro}, title = {The falling cat problem and shape effects in small molecules in a random environment: a case study}, series = {Molecular Physics}, volume = {111}, journal = {Molecular Physics}, number = {22-23}, issn = {1362-3028}, doi = {10.1080/00268976.2013.831956}, pages = {3534 -- 3545}, language = {en} } @misc{HartmannSchaeferBungThoensZueva, author = {Hartmann, Carsten and Sch{\"a}fer-Bung, Boris and Th{\"o}ns-Zueva, Anastasia}, title = {Balanced averaging of bilinear systems with applications to stochastic control}, series = {SIAM Journal on Control and Optimization}, volume = {51}, journal = {SIAM Journal on Control and Optimization}, number = {3}, issn = {1095-7138}, doi = {10.1137/100796844}, pages = {2356 -- 2378}, language = {en} } @misc{WangHartmannSchuetteetal., author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Grand-Canonical-like Molecular-Dynamics Simulations by Using an Adaptive-Resolution Technique}, series = {PHYSICAL REVIEW X}, volume = {3}, journal = {PHYSICAL REVIEW X}, number = {1}, issn = {2160-3308}, doi = {10.1103/PhysRevX.3.011018}, pages = {011018}, language = {en} } @misc{SchaeferBungHartmannSchmidtetal., author = {Sch{\"a}fer-Bung, Boris and Hartmann, Carsten and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Dimension reduction by balanced truncation: Application to light-induced control of open quantum systems}, series = {The Journal of Chemical Physics}, volume = {135}, journal = {The Journal of Chemical Physics}, number = {1}, issn = {1089-7690}, doi = {10.1063/1.3605243}, pages = {014112}, language = {en} } @misc{Hartmann, author = {Hartmann, Carsten}, title = {Balanced model reduction of partially-observed Langevin equations: an averaging principle}, series = {Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences}, volume = {17}, journal = {Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences}, number = {5}, issn = {1744-5051}, doi = {10.1080/13873954.2011.576517}, pages = {463 -- 490}, language = {en} } @misc{HartmannLatorreCiccotti, author = {Hartmann, Carsten and Latorre, Juan C. and Ciccotti, Giovanni}, title = {On two possible definitions of the free energy for collective variables}, series = {The European Physical Journal Special Topics}, volume = {200}, journal = {The European Physical Journal Special Topics}, number = {1}, issn = {1951-6355}, doi = {10.1140/epjst/e2011-01519-7}, pages = {73 -- 89}, language = {en} } @misc{WalterHartmannMaddocks, author = {Walter, Jessika and Hartmann, Carsten and Maddocks, John H.}, title = {Ambient space formulations and statistical mechanics of holonomically constrained Langevin systems}, series = {The European Physical Journal Special Topics}, volume = {200}, journal = {The European Physical Journal Special Topics}, number = {1}, issn = {1951-6401}, doi = {10.1140/epjst/e2011-01523-y}, pages = {153 -- 181}, language = {en} } @misc{SchuetteWinkelmannHartmann, author = {Sch{\"u}tte, Christof and Winkelmann, Stefanie and Hartmann, Carsten}, title = {Optimal control of molecular dynamics using Markov state models}, series = {Mathematical Programming (Series B)}, volume = {134}, journal = {Mathematical Programming (Series B)}, number = {1}, issn = {0025-5610}, doi = {10.1007/s10107-012-0547-6}, pages = {259 -- 282}, language = {en} } @misc{LeyendeckerHartmannKoch, author = {Leyendecker, Sigrid and Hartmann, Carsten and Koch, Michael}, title = {Variational collision integrator for polymer chains}, series = {Journal of Computational Physics}, volume = {231}, journal = {Journal of Computational Physics}, number = {10}, issn = {0021-9991}, doi = {10.1016/j.jcp.2012.01.017}, pages = {3896 -- 3911}, language = {en} } @misc{LatorreMetznerHartmannetal., author = {Latorre, Juan C. and Metzner, Philipp and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Structure-preserving numerical discretization of reversible diffusions}, series = {Communications in Mathematical Sciences}, volume = {9}, journal = {Communications in Mathematical Sciences}, number = {4}, issn = {1945-0796}, pages = {1051 -- 1072}, language = {en} } @misc{HartmannVulcanovSchuette, author = {Hartmann, Carsten and Vulcanov, Valentina-Mira and Sch{\"u}tte, Christof}, title = {Balanced truncation of linear second-order systems: A Hamiltonian approach}, series = {Multiscale Modeling \& Simulation}, volume = {8}, journal = {Multiscale Modeling \& Simulation}, number = {4}, issn = {1540-3467}, doi = {10.1137/080732717}, pages = {1348 -- 1367}, language = {en} } @misc{SchuetteWalterHartmannetal., author = {Sch{\"u}tte, Christof and Walter, Jessika and Hartmann, Carsten and Huisinga, Wilhelm}, title = {An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations}, series = {Multiscale Modeling \& Simulation}, volume = {2}, journal = {Multiscale Modeling \& Simulation}, number = {3}, issn = {1540-3467}, doi = {10.1137/030600308}, pages = {501 -- 526}, language = {en} } @misc{HartmannDelleSite, author = {Hartmann, Carsten and Delle Site, Luigi}, title = {Editorial: Scale bridging in molecular simulation}, series = {The European Physical Journal Special Topics}, volume = {224}, journal = {The European Physical Journal Special Topics}, number = {12}, issn = {1951-6355}, doi = {10.1140/epjst/e2015-02406-y}, pages = {2173 -- 2176}, language = {en} } @misc{BittracherHartmannJungeetal., author = {Bittracher, Andreas and Hartmann, Carsten and Junge, Oliver and Koltai, P{\´e}ter}, title = {Pseudo generators for under-resolved molecular dynamics}, series = {The European Physical Journal Special Topics}, volume = {224}, journal = {The European Physical Journal Special Topics}, number = {12}, issn = {1951-6355}, doi = {10.1140/epjst/e2015-02422-y}, pages = {2463 -- 2490}, language = {en} } @misc{HartmannSchuetteWeberetal., author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Weber, Marcus and Zhang, Wei}, title = {Importance sampling in path space for diffusion processes with slow-fast variables}, series = {Probability Theory and Related Fields}, volume = {170}, journal = {Probability Theory and Related Fields}, number = {1-2}, issn = {0178-8051}, doi = {10.1007/s00440-017-0755-3}, pages = {177 -- 228}, language = {en} } @misc{ZhangHartmannSchuette, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective dynamics along given reaction coordinates, and reaction rate theory}, series = {Faraday Discussions}, volume = {195}, journal = {Faraday Discussions}, issn = {1359-6640}, doi = {10.1039/C6FD00147E}, pages = {365 -- 394}, language = {en} } @misc{BanischHartmann, author = {Banisch, Ralf and Hartmann, Carsten}, title = {A sparse Markov chain approximation of LQ-type stochastic control problems}, series = {Mathematical Control and Related Fields}, volume = {6}, journal = {Mathematical Control and Related Fields}, number = {3}, issn = {2156-8499}, doi = {10.3934/mcrf.2016007}, pages = {363 -- 389}, language = {en} } @misc{HartmannSchuetteZhang, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Model reduction algorithms for optimal control and importance sampling of diffusions}, series = {Nonlinearity}, volume = {29}, journal = {Nonlinearity}, number = {8}, issn = {1361-6544}, doi = {10.1088/0951-7715/29/8/2298}, pages = {2298 -- 2326}, language = {en} } @misc{AgarwalZhuHartmannetal., author = {Agarwal, Animesh and Zhu, Jinglong and Hartmann, Carsten and Wang, Han and Delle Site, Luigi}, title = {Molecular dynamics in a Grand Ensemble: Bergmann-Lebowitz model and adaptive resolution simulation}, series = {New Journal of Physics}, volume = {17}, journal = {New Journal of Physics}, issn = {1367-2630}, doi = {10.1088/1367-2630/17/8/083042}, pages = {18}, language = {en} } @misc{Hartmann, author = {Hartmann, Carsten}, title = {Leimkuhler, Ben ; Matthews, Charles: Molecular Dynamics. With Deterministic and Stochastic Numerical Methods. Cham : Springer, 2015}, series = {SIAM Review}, volume = {58}, journal = {SIAM Review}, number = {3}, issn = {1095-7200}, pages = {586 -- 588}, language = {en} } @misc{HartmannRichterSchuetteetal., author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, series = {Entropy}, volume = {19}, journal = {Entropy}, number = {11}, issn = {1099-4300}, doi = {10.3390/e19110626}, pages = {27}, language = {en} } @misc{SchmidtHartmann, author = {Schmidt, Burkhard and Hartmann, Carsten}, title = {WavePacket: A Matlab package for numerical quantum dynamics.II : Open quantum systems, optimal control, and model reduction}, series = {Computer Physics Communications}, volume = {228}, journal = {Computer Physics Communications}, issn = {0010-4655}, doi = {10.1016/j.cpc.2018.02.022}, pages = {229 -- 244}, language = {en} } @misc{DelleSiteCiccottiHartmann, author = {Delle Site, Luigi and Ciccotti, Giovanni and Hartmann, Carsten}, title = {Partitioning a macroscopic system into independent subsystems}, series = {Journal of Statistical Mechanics: Theory and Experiment}, volume = {August}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, issn = {1742-5468}, doi = {10.1088/1742-5468/aa75db}, pages = {13}, language = {en} } @misc{DonatiHartmannKeller, author = {Donati, Lorenzo and Hartmann, Carsten and Keller, Bettina G.}, title = {Girsanov reweighting for path ensembles and Markov state models}, series = {The Journal of Chemical Physics}, volume = {146}, journal = {The Journal of Chemical Physics}, number = {124}, issn = {1089-7690}, doi = {10.1063/1.4989474}, pages = {244112-1 -- 244112-15}, language = {en} } @misc{DaraghmehQatananiHartmann, author = {Daraghmeh, Adnan and Qatanani, Naji and Hartmann, Carsten}, title = {Optimal control of linear systems with balanced reduced-order models: Perturbation approximations}, series = {Applied Mathematics and Computation}, volume = {337}, journal = {Applied Mathematics and Computation}, issn = {0096-3003}, doi = {10.1016/j.amc.2018.04.065}, pages = {119 -- 136}, language = {en} } @misc{KebiriNeureitherHartmann, author = {Kebiri, Omar and Neureither, Lara and Hartmann, Carsten}, title = {Singularly Perturbed Forward-Backward Stochastic Differential Equations: Application to the Optimal Control of Bilinear Systems}, series = {Computation}, volume = {6}, journal = {Computation}, number = {3}, issn = {2079-3197}, doi = {10.3390/computation6030041}, pages = {41 -- 41}, language = {en} } @misc{HartmannNeureitherSharma, author = {Hartmann, Carsten and Neureither, Lara and Sharma, Upanshu}, title = {Coarse-graining of non-reversible stochastic differential equations: quantitative results and connections to averaging}, series = {SIAM Journal on Mathematical Analysis}, volume = {52}, journal = {SIAM Journal on Mathematical Analysis}, number = {3}, issn = {1095-7154}, doi = {10.1137/19M1299852}, pages = {2689 -- 2733}, language = {en} } @misc{BennerBreitenHartmannetal., author = {Benner, Peter and Breiten, Tobias and Hartmann, Carsten and Schmidt, Burkhard}, title = {Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations}, series = {American Institute of Mathematical Sciences}, volume = {7}, journal = {American Institute of Mathematical Sciences}, number = {1}, issn = {2158-2491}, doi = {10.3934/jcd.2020001}, pages = {1 -- 33}, language = {en} } @misc{HartmannKebiriNeureitheretal., author = {Hartmann, Carsten and Kebiri, Omar and Neureither, Lara and Richter, Lorenz}, title = {Variational approach to rare event simulation using least-squares regression}, series = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {29}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, number = {6}, issn = {1089-7682}, doi = {10.1063/1.5090271}, pages = {16}, language = {en} } @misc{BeckerHartmann, author = {Becker, Simon and Hartmann, Carsten}, title = {Infinite-dimensional bilinear and stochastic balanced truncation with explicit error bounds}, series = {Mathematics of Control, Signals, and Systems}, volume = {31}, journal = {Mathematics of Control, Signals, and Systems}, number = {2}, issn = {1435-568X}, doi = {10.1007/s00498-019-0234-8}, pages = {37}, language = {en} } @misc{MezdoudHartmannRemitaetal., author = {Mezdoud, Zaineb and Hartmann, Carsten and Remita, Mohamed Riad and Kebiri, Omar}, title = {α-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs}, series = {Bulletin of the Institute of Mathematics Academia Sinica : New series}, volume = {16}, journal = {Bulletin of the Institute of Mathematics Academia Sinica : New series}, number = {3}, issn = {2304-7909}, doi = {10.21915/BIMAS.2021304}, pages = {263 -- 288}, language = {en} } @misc{RedjilGherbalKebiri, author = {Redjil, Amel and Gherbal, H. B. and Kebiri, Omar}, title = {Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps}, series = {Stochastic Analysis and Applications}, volume = {Vol. 41 (2023)}, journal = {Stochastic Analysis and Applications}, number = {1}, issn = {1532-9356}, doi = {10.1080/07362994.2021.1991809}, pages = {115 -- 133}, language = {en} } @misc{SkeelHartmann, author = {Skeel, Robert D. and Hartmann, Carsten}, title = {Choice of Damping Coefficient in Langevin Dynamics}, series = {The European Physical Journal. B}, volume = {94}, journal = {The European Physical Journal. B}, number = {9}, issn = {1434-6036}, doi = {10.1140/epjb/s10051-021-00182-z}, language = {en} } @misc{HartmannNeureitherStrehlau, author = {Hartmann, Carsten and Neureither, Lara and Strehlau, Markus}, title = {Reachability Analysis of Randomly Perturbed Hamiltonian Systems}, series = {IFAC PapersOnLine}, volume = {54}, journal = {IFAC PapersOnLine}, number = {19}, issn = {2405-8963}, doi = {10.1016/j.ifacol.2021.11.095}, pages = {307 -- 314}, language = {en} } @misc{NueskenRichter, author = {N{\"u}sken, Nikolas and Richter, Lorenz}, title = {Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space}, series = {Partial Differential Equations and Applications}, volume = {2}, journal = {Partial Differential Equations and Applications}, number = {4}, issn = {2662-2971}, doi = {10.1007/s42985-021-00102-x}, language = {en} } @misc{KebiriHafidaAbdeldjebbar, author = {Kebiri, Omar and Hafida, Bouanani and Abdeldjebbar, Kandouci}, title = {On the existence and uniqueness of solutions to forward backward stochastic differential equations driven by G-Brownian motion}, series = {Bulletin of the Institute of Mathematics Academia Sinica : New series}, volume = {15}, journal = {Bulletin of the Institute of Mathematics Academia Sinica : New series}, issn = {2304-7909}, pages = {217 -- 236}, language = {en} } @misc{RichterBoustatiNueskenetal., author = {Richter, Lorenz and Boustati, Ayman and N{\"u}sken, Nikolas and Ruiz, Francisco and Akyildiz, {\"O}mer Deniz}, title = {VarGrad: A Low-Variance Gradient Estimator for Variational Inference}, series = {34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada}, journal = {34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada}, doi = {10.48550/arXiv.2010.10436}, pages = {12}, language = {en} } @incollection{Hartmann, author = {Hartmann, Carsten}, title = {Gefangen in der Filterblase? Suchmaschinenergebnisse als Beispiel eines wissensbasierten Konsenses}, series = {Maschinen der Kommunikation. Interdisziplin{\"a}re Perspektiven auf Technik und Gesellschaft im digitalen Zeitalter}, booktitle = {Maschinen der Kommunikation. Interdisziplin{\"a}re Perspektiven auf Technik und Gesellschaft im digitalen Zeitalter}, editor = {Klimczak, Peter and Petersen, Christer and Schilling, Samuel}, publisher = {Springer}, address = {Wiesbaden}, isbn = {978-3-658-27851-9}, issn = {2662-5970}, doi = {10.1007/978-3-658-27852-6_3}, pages = {45 -- 62}, language = {de} } @misc{HartmannSchuetteZhang, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Jarzysnki equality, fluctuation theorems and variance reduction: Mathematical analysis and numerical algorithms}, series = {Journal of Statistical Physics}, volume = {175}, journal = {Journal of Statistical Physics}, number = {6}, issn = {1572-9613}, doi = {10.1007/s10955-019-02286-4}, pages = {1214 -- 1261}, language = {en} } @misc{DaraghmehHartmannQatanani, author = {Daraghmeh, Adnan and Hartmann, Carsten and Qatanani, Naji}, title = {Balanced model reduction of linear systems with nonzero initial conditions: singular perturbation approximation}, series = {Applied Mathematics and Computation}, volume = {353}, journal = {Applied Mathematics and Computation}, issn = {1873-5649}, doi = {10.1016/j.amc.2019.02.001}, pages = {295 -- 307}, language = {en} } @misc{EddahbiKebiriSene, author = {Eddahbi, Mhamed and Kebiri, Omar and Sene, Abou}, title = {Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients}, series = {Axioms}, volume = {12}, journal = {Axioms}, number = {12}, issn = {2075-1680}, doi = {10.3390/axioms12121068}, abstract = {In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a Zvonkin-type transformation in conjunction with the It{\^o}-Krylov's formula. We applied our findings to derive probabilistic representation of a particular set of Partial Differential Equations par have quadratic growth in the gradient (QPDEs) characterized by coefficients that are measurable and almost surely continuous. Additionally, we explored a stochastic control optimization problem related to an epidemic model, interpreting it as an infinite time horizon QBSDE with a measurable and integrable drifts.}, language = {en} } @article{GridAgramKebirietal., author = {Grid, Maroua and Agram, Nacira and Kebiri, Omar and {\O}ksendal, Bernt}, title = {Deep learning for solving initial path optimization of mean-field systems with memory}, series = {Stochastics}, journal = {Stochastics}, publisher = {Informa UK Limited}, issn = {1744-2508}, doi = {10.1080/17442508.2024.2402741}, pages = {1 -- 22}, language = {en} } @article{BouguetofMezdoudKebirietal., author = {Bouguetof, Khaoula and Mezdoud, Zaineb and Kebiri, Omar and Hartmann, Carsten}, title = {On the existence and uniqueness of the solution to multifractional stochastic delay differential equation}, series = {Fractional Calculus and Applied Analysis}, volume = {27}, journal = {Fractional Calculus and Applied Analysis}, number = {5}, publisher = {Springer Science and Business Media LLC}, issn = {1311-0454}, doi = {10.1007/s13540-024-00314-z}, pages = {2284 -- 2304}, abstract = {AbstractIn this paper we study existence and uniqueness of solution stochastic differential equations involving fractional integrals driven by Riemann-Liouville multifractional Brownian motion and a standard Brownian. Then, we obtain approximate numerical solution of our problem and colon cancer chemotherapy effect model are presented to confirm our results. We show that considering time dependent Hurst parameters play an important role to get more realistic results.}, language = {en} } @article{BouananiKebiriHartmannetal., author = {Bouanani, Hafida and Kebiri, Omar and Hartmann, Carsten and Redjil, Amel}, title = {Optimal Relaxed Control for a Decoupled G-FBSDE}, series = {Journal of Optimization Theory and Applications}, volume = {202}, journal = {Journal of Optimization Theory and Applications}, number = {3}, publisher = {Springer Science and Business Media LLC}, issn = {0022-3239}, doi = {10.1007/s10957-024-02495-2}, pages = {1027 -- 1059}, abstract = {AbstractIn this paper we study a system of decoupled forward-backward stochastic differential equations driven by a G-Brownian motion (G-FBSDEs) with non-degenerate diffusion. Our objective is to establish the existence of a relaxed optimal control for a non-smooth stochastic optimal control problem. The latter is given in terms of a decoupled G-FBSDE. The cost functional is the solution of the backward stochastic differential equation at the initial time. The key idea to establish existence of a relaxed optimal control is to replace the original control problem by a suitably regularised problem with mollified coefficients, prove the existence of a relaxed control, and then pass to the limit.}, language = {en} } @article{BoumezbeurBoutabiaRedjiletal., author = {Boumezbeur, Zakaria and Boutabia, Hac{\`e}ne and Redjil, Amel and Kebiri, Omar}, title = {Differentiability of G-neutral stochastic differential equations with respect to parameter}, series = {Random Operators and Stochastic Equations}, volume = {32}, journal = {Random Operators and Stochastic Equations}, number = {2}, publisher = {Walter de Gruyter GmbH}, issn = {0926-6364}, doi = {/10.1515/rose-2024-2005}, pages = {159 -- 173}, abstract = {In this paper, we study the differentiability of solutions of neutral stochastic differential equations driven by G-Brownian motion with respect to parameter. Under suitable assumptions, we show that solutions are differentiable with respect to the parameter which appears in the initial data. In addition, the stochastic differential equation of the derivative is given and the existence-uniqueness of solution is proved. Moreover, an example to illustrate the theoretically obtained results is presented.}, language = {en} } @article{LalaouiBenCherifBalatifKebiri, author = {Lalaoui Ben Cherif, Sidi Mohamed and Balatif, Omar and Kebiri, Omar}, title = {Analysis and optimal control of a vaccinated pandemic COVID-19 model}, series = {Journal of Mathematical Sciences}, volume = {280}, journal = {Journal of Mathematical Sciences}, number = {4}, publisher = {Springer Science and Business Media LLC}, issn = {1072-3374}, doi = {10.1007/s10958-024-06992-7}, pages = {582 -- 604}, language = {en} } @misc{SiddiquiEddahbiKebiri, author = {Siddiqui, Maryam and Eddahbi, Mhamed and Kebiri, Omar}, title = {Numerical solutions of stochastic differential equations with jumps and measurable drifts}, series = {Mathematics}, volume = {11}, journal = {Mathematics}, number = {17}, publisher = {MDPI AG}, issn = {2227-7390}, doi = {10.3390/math11173755}, pages = {1 -- 14}, abstract = {This paper deals with numerical analysis of solutions to stochastic differential equations with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic real-valued function that satisfies a second-order differential equation. The Euler-Maruyama scheme is used to approximate the solution to the equations. It is shown that the rate of convergence is 12. Numerically, two different methods are used to approximate solutions for this class of SDEJs. The first method is the direct approximation of the original equation using the Euler-Maruyama scheme with specific tests for the evaluation of the singular part at simulated values of the solution. The second method consists of taking the inverse of the Euler-Maruyama approximation for Zvonkin's transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical methods is carried out. Theoretical results are illustrated and proved by means of an example.}, language = {en} } @misc{BeliliSahariKebirietal., author = {Belili, Mohamed Cherif and Sahari, Mohamed Lamine and Kebiri, Omar and Zeghdoudi, Halim}, title = {Analyzing bifurcations and optimal control strategies in SIRS epidemic models: insights from theory and COVID-19 data}, series = {Mathematical and Computational Applications}, volume = {29}, journal = {Mathematical and Computational Applications}, number = {4}, publisher = {MDPI}, issn = {2297-8747}, doi = {10.3390/mca29040069}, pages = {22}, abstract = {This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin's maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic's spread.}, language = {en} } @incollection{HartmannRichter, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness}, series = {Artificial Intelligence - Limits and Prospects}, booktitle = {Artificial Intelligence - Limits and Prospects}, editor = {Klimczak, Peter and Petersen, Christer}, publisher = {transcript Verlag}, address = {Bielefeld}, isbn = {978-3-8376-5732-6}, doi = {10.14361/9783839457320-004}, pages = {43 -- 82}, language = {en} } @misc{SchuetteKlusHartmann, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, series = {Acta Numerica}, volume = {Vol. 32}, journal = {Acta Numerica}, issn = {1474-0508}, doi = {10.1017/S0962492923000016}, pages = {517 -- 673}, language = {en} } @misc{SaciRedjilBoutabiaetal., author = {Saci, Akram and Redjil, Amel and Boutabia, Hacene and Kebiri, Omar}, title = {Fractional stochastic differential equations driven by G-Brownian motion with delays}, series = {Probability and Mathematical Statistics}, volume = {43}, journal = {Probability and Mathematical Statistics}, number = {1}, issn = {0208-4147}, doi = {10.37190/0208-4147.00092}, pages = {1 -- 21}, language = {en} } @misc{BenGherbalRedjilKebiri, author = {Ben Gherbal, Hanane and Redjil, Amel and Kebiri, Omar}, title = {The relaxed maximum principle for G-stochastic control systems with controlled jumps}, series = {Advances in Mathematics: Scientific Journal}, volume = {11}, journal = {Advances in Mathematics: Scientific Journal}, number = {12}, issn = {1857-8365}, doi = {10.37418/amsj.11.12.11}, pages = {1313 -- 1343}, language = {en} } @misc{HuberLieblRosenowRoemeretal., author = {Huber-Liebl, Markus and Rosenow, Tillmann and R{\"o}mer, Ronald and Wirsching, G{\"u}nther and Wolff, Matthias}, title = {It all starts with a little difference : tensors as data and code.}, series = {Elektronische Sprachsignalverarbeitung 2025 : Tagungsband der 36. Konferenz Halle/Saale, 5.-7. M{\"a}rz 2025}, journal = {Elektronische Sprachsignalverarbeitung 2025 : Tagungsband der 36. Konferenz Halle/Saale, 5.-7. M{\"a}rz 2025}, editor = {Grawunder, Sven}, publisher = {TUDpress}, address = {Dresden}, isbn = {978-3-95908-803-9}, issn = {0940-6832}, pages = {170 -- 179}, abstract = {We further promote the idea of quantum inspiration and propose to equip cognitive systems not only with tensors for data representation but also for operation representation. We argue that these are two sides of the same coin. For experimental symbolic algorithms we introduce a suitable testbed and give its proper specification. We formalize our method of behavioural control with tensor algebra and discuss its implementation for our physical testbed realization.}, language = {en} } @misc{MaierRosenowTuurietal., author = {Maier, Isidor Konrad and Rosenow, Tillmann and Tuuri, Okko and Wolff, Matthias}, title = {Frequency-magnitude relation of numeral words based on search-engine results}, series = {Elektronische Sprachsignalverarbeitung, Tagungsband der 36. Konferenz, 05.-07.03.2025, Halle/Saale}, journal = {Elektronische Sprachsignalverarbeitung, Tagungsband der 36. Konferenz, 05.-07.03.2025, Halle/Saale}, editor = {Grawunder, Sven}, publisher = {TUDpress}, address = {Dresden}, isbn = {978-3-95908-803-9}, issn = {0940-6832}, pages = {51 -- 60}, abstract = {We googled various numeral words from 28 languages. Different approaches for the description of the data were investigated. In all of the 28 languages, the found frequency-magnitude dependence fits better to a power law than to an exponential law. The result can be used to distinguish grammatically correct from incorrect numerals based on the prediction of search results.}, language = {en} } @misc{DelleSiteHartmann, author = {Delle Site, Luigi and Hartmann, Carsten}, title = {Computationally feasible bounds for the free energy of nonequilibrium steady states, applied to simple models of heat conduction}, series = {Molecular Physics}, journal = {Molecular Physics}, publisher = {Informa UK Limited}, issn = {0026-8976}, doi = {10.1080/00268976.2024.2391484}, pages = {15}, language = {en} } @article{HartmannRichter, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Nonasymptotic Bounds for Suboptimal Importance Sampling}, series = {SIAM/ASA Journal on Uncertainty Quantification}, volume = {12}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, number = {2}, publisher = {Society for Industrial \& Applied Mathematics (SIAM)}, issn = {2166-2525}, doi = {10.1137/21M1427760}, pages = {309 -- 346}, language = {en} } @article{DelleSiteHartmann, author = {Delle Site, Luigi and Hartmann, Carsten}, title = {Scaling law for the size dependence of a finite-range quantum gas}, series = {Physical Review A}, volume = {109}, journal = {Physical Review A}, number = {2}, publisher = {American Physical Society (APS)}, issn = {2469-9926}, doi = {10.1103/PhysRevA.109.022209}, pages = {9}, language = {en} } @misc{ReibleHilleHartmannetal., author = {Reible, Benedikt and Hille, Julian F. and Hartmann, Carsten and Delle Site, Luigi}, title = {Finite size effects and thermodynamic accuracy in many-particle systems}, series = {Physical Review Research}, volume = {5}, journal = {Physical Review Research}, number = {2}, issn = {2643-1564}, doi = {10.1103/PhysRevResearch.5.023156}, pages = {023156-1 -- 023156-8}, language = {en} } @misc{ReibleHartmannDelleSite, author = {Reible, Benedikt and Hartmann, Carsten and Delle Site, Luigi}, title = {Two-sided Bogoliubov inequality to estimate finite-size effects in quantum molecular simulations}, series = {Letters in Mathematical Physics}, volume = {112}, journal = {Letters in Mathematical Physics}, number = {5}, issn = {1573-0530}, doi = {10.1007/s11005-022-01586-3}, pages = {1 -- 17}, language = {en} }