@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} }