@article{ShlapunovTarchanov2021,
  author    = {Shlapunov, Alexander and Tarchanov, Nikolaj Nikolaevič},
  title     = {An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n},
  series = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  volume    = {18},
  journal   = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  number    = {2},
  publisher = {Institut Matematiki Imeni S. L. Soboleva},
  address   = {Novosibirsk},
  issn      = {1813-3304},
  doi       = {10.33048/semi.2021.18.108},
  pages     = {1433 -- 1466},
  year      = {2021},
  abstract  = {We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations.},
  language  = {en}
}
@article{RoppLesurBaerenzungetal.2020,
  author    = {Ropp, Guillaume and Lesur, Vincent and B{\"a}renzung, Julien and Holschneider, Matthias},
  title     = {Sequential modelling of the Earth's core magnetic field},
  series = {Earth, Planets and Space},
  volume    = {72},
  journal   = {Earth, Planets and Space},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {1880-5981},
  doi       = {10.1186/s40623-020-01230-1},
  pages     = {15},
  year      = {2020},
  abstract  = {We describe a new, original approach to the modelling of the Earth's magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.},
  language  = {en}
}
@article{MazzonettoSalimova2020,
  author    = {Mazzonetto, Sara and Salimova, Diyora},
  title     = {Existence, uniqueness, and numerical approximations for stochastic burgers equations},
  series = {Stochastic analysis and applications},
  volume    = {38},
  journal   = {Stochastic analysis and applications},
  number    = {4},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {0736-2994},
  doi       = {10.1080/07362994.2019.1709503},
  pages     = {623 -- 646},
  year      = {2020},
  abstract  = {In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.},
  language  = {en}
}
@article{KellerPinchoverPogorzelski2020,
  author    = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
  title     = {From hardy to rellich inequalities on graphs},
  series = {Proceedings of the London Mathematical Society},
  volume    = {122},
  journal   = {Proceedings of the London Mathematical Society},
  number    = {3},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0024-6115},
  doi       = {10.1112/plms.12376},
  pages     = {458 -- 477},
  year      = {2020},
  abstract  = {We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.},
  language  = {en}
}
@article{KocJanuchtaHoefflerThomaetal.2017,
  author    = {Koc-Januchta, Marta and H{\"o}ffler, Tim and Thoma, Gun-Brit and Prechtl, Helmut and Leutner, Detlev},
  title     = {Visualizers versus verbalizers},
  series = {Computers in human behavior},
  volume    = {68},
  journal   = {Computers in human behavior},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0747-5632},
  doi       = {10.1016/j.chb.2016.11.028},
  pages     = {170 -- 179},
  year      = {2017},
  abstract  = {This study was conducted in order to examine the differences between visualizers and verbalizers in the way they gaze at pictures and texts while learning. Using a collection of questionnaires, college students were classified according to their visual or verbal cognitive style and were asked to learn about two different, in terms of subject and type of knowledge, topics by means of text-picture combinations. Eye-tracking was used to investigate their gaze behavior. The results show that visualizers spent significantly more time inspecting pictures than verbalizers, while verbalizers spent more time inspecting texts. Results also suggest that both visualizers' and verbalizers' way of learning is active but mostly within areas providing the source of information in line with their cognitive style (pictures or text). Verbalizers tended to enter non-informative, irrelevant areas of pictures sooner than visualizers. The comparison of learning outcomes showed that the group of visualizers achieved better results than the group of verbalizers on a comprehension test.},
  language  = {en}
}
@unpublished{BlanchardMathe2012,
  author    = {Blanchard, Gilles and Math{\´e}, Peter},
  title     = {Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57117},
  year      = {2012},
  abstract  = {The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.},
  language  = {en}
}
@unpublished{KellerRoellyValleriani2013,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {A quasi-random-walk to model a biological transport process},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63582},
  year      = {2013},
  abstract  = {Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.},
  language  = {en}
}
@unpublished{FradonRoelly2005,
  author    = {Fradon, Myriam and Roelly, Sylvie},
  title     = {Brownian Hard Balls submitted to an infinite rangeinteraction with slow decay},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49379},
  year      = {2005},
  abstract  = {We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a pair potential with infinite range and quasi polynomial decay. It is modelized by an infinite-dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with deterministic initial condition. We also show that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential.},
  language  = {en}
}
@incollection{Guenther2015,
  author    = {G{\"u}nther, Oliver},
  title     = {Zum Geleit},
  series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe},
  booktitle = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe},
  publisher = {Trafo},
  address   = {Berlin},
  isbn      = {978-3-86464-082-7},
  pages     = {7 -- 8},
  year      = {2015},
  language  = {de}
}
@book{GuentherPetscheFischeretal.2015,
  author    = {G{\"u}nther, Oliver and Petsche, Hans-Joachim and Fischer, Martin H. and Franz, Norbert P. and Steup, Martin and Sixtus, Elena and Heimann, Heinz-Dieter and Pr{\"o}ve, Ralf},
  title     = {Raum und Zahl im Fokus der Wissenschaften},
  series = {Studieren ++ : Konzepte, Perspektiven, Kompetenzen ; 1},
  journal   = {Studieren ++ : Konzepte, Perspektiven, Kompetenzen ; 1},
  editor    = {Petsche, Hans-Joachim},
  publisher = {Trafo},
  address   = {Berlin},
  isbn      = {978-3-86464-082-7},
  pages     = {168},
  year      = {2015},
  abstract  = {Die nun begonnene Reihe „studieren++" resultiert aus einer von der Universit{\"a}t Potsdam angebotenen Vorlesungsreihe. Das Besondere an dieser Vorlesungsreihe ist der multidisziplin{\"a}re Anspruch und die konsequent umgesetzte Zusammenarbeit {\"u}ber Disziplingrenzen hinweg. Die nicht nur {\"u}ber Instituts-, sondern {\"u}ber Fakult{\"a}tsgrenzen praktizierte Interdisziplinarit{\"a}t erlaubt die Betrachtung eines Problems oder Sachverhalts aus unterschiedlichen Blickwinkeln. Wissenschaftliche Fragestellungen sind komplex und nicht immer auf eine Disziplin beschr{\"a}nkt. Sie in ihrer G{\"a}nze erfassen und nachhaltige L{\"o}sungsstrategien oder Konzepte entwickeln zu k{\"o}nnen gelingt oft nur durch eine multidisziplin{\"a}re Kooperation. Eine Lehrveranstaltung wie die vorliegende ist nicht nur f{\"u}r die Studierenden einer Universit{\"a}t eine hervorragende M{\"o}glichkeit, um {\"u}ber die Grenzen der eigenen Disziplin hinaus zu blicken und die Zusammenarbeit mit Wissenschaftlerinnen und Wissenschaftlern aus anderen Bereichen zu pflegen. So lernt man, sich in andere Sichtweisen hineinzuversetzen und sich zwischen den Disziplinen zu bewegen - eine Kompetenz, die in der hochkomplexen Arbeitswelt von heute von hohem Nutzen ist. Der vorliegende erste Band der Reihe hat „Raum und Zahl" zum Thema und ist aus einer Ringvorlesung aus dem Wintersemester 2013/2014 entstanden. Drei der f{\"u}nf Fakult{\"a}ten, insgesamt neun Institute der Universit{\"a}t Potsdam, haben sich an der Vorlesung beteiligt und sich dieses spannenden Themas angenommen. Als jemand, der sich jahrelang wissenschaftlich mit algorithmischer Geometrie sowie mit raumbezogenen Datenbanken und Navigationssystemen besch{\"a}ftigt hat, kann ich nur bekr{\"a}ftigen, dass die Bez{\"u}ge zwischen Raum und Zahl, zwischen R{\"a}umen und Zahlen, noch viel st{\"a}rker im {\"o}ffentlichen Bewusstsein verankert geh{\"o}ren. R{\"a}ume auch quantitativ zu erfassen und zu verstehen ist eine Kulturtechnik, die an Wichtigkeit eher noch zunimmt, vor allem vor dem Hintergrund, dass wir genetisch nicht allzu gut auf derartige Herausforderungen vorbereitet sind. Denn viele unserer einschl{\"a}gigen Gene entstammen noch aus der Zeit der Savanne, einer Zeit, zu der das Raumkonzept sich fast ausschließlich auf die unmittelbare r{\"a}umliche Umgebung bezog und Zahlen jenseits von 10 nur wenig Relevanz f{\"u}r das eigene {\"U}berleben hatten. Als Pr{\"a}sident der Universit{\"a}t Potsdam freut es mich ganz besonders, dass sich die hier vertretenen Wissenschaftler bereit erkl{\"a}rt haben, ihre {\"U}berlegungen mit den Studierenden und ihren Kolleginnen und Kollegen zu teilen. Herrn Kollegen Hans-Joachim Petsche m{\"o}chte ich f{\"u}r sein Engagement danken und ihm zu dieser gelungenen Reihe gratulieren. Der Geist der Wissenschaft, der nicht nur einsam im B{\"u}ro oder Labor gelebt wird, sondern gerade an einer Universit{\"a}t auch aktiv nach außen getragen werden sollte, wird hier in besonderer Weise sichtbar. Ich w{\"u}nsche Ihnen viel Freude bei der Lekt{\"u}re des Bandes und freue mich auf weitere Ver{\"o}ffentlichungen in dieser Reihe.},
  subject      = {Raum},
  language  = {de}
}
@misc{StraderSchneiderSchorlemmer2017,
  author    = {Strader, Anne and Schneider, Max and Schorlemmer, Danijel},
  title     = {Erratum zu: Strader, Anne; Schneider, Max; Schorlemmer, Danijel: Prospective and retrospective evaluation of five-year earthquake forecast models for California (Geophysical Journal International, 211 (2017) 1, S. 239 - 251, https://doi.org/10.1093/gji/ggx268)},
  series = {Geophysical journal international},
  volume    = {212},
  journal   = {Geophysical journal international},
  number    = {2},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggx496},
  pages     = {1314 -- 1314},
  year      = {2017},
  abstract  = {S-test results for the USGS and RELM forecasts. The differences between the simulated log-likelihoods and the observed log-likelihood are labelled on the horizontal axes, with scaling adjustments for the 40year.retro experiment. The horizontal lines represent the confidence intervals, within the 0.05 significance level, for each forecast and experiment. If this range contains a log-likelihood difference of zero, the forecasted log-likelihoods are consistent with the observed, and the forecast passes the S-test (denoted by thin lines). If the minimum difference within this range does not contain zero, the forecast fails the S-test for that particular experiment, denoted by thick lines. Colours distinguish between experiments (see Table 2 for explanation of experiment durations). Due to anomalously large likelihood differences, S-test results for Wiemer-Schorlemmer.ALM during the 10year.retro and 40year.retro experiments are not displayed. The range of log-likelihoods for the Holliday-et-al.PI forecast is lower than for the other forecasts due to relatively homogeneous forecasted seismicity rates and use of a small fraction of the RELM testing region.},
  language  = {en}
}
@article{BaerBandara2022,
  author    = {B{\"a}r, Christian and Bandara, Lashi},
  title     = {Boundary value problems for general first-order elliptic differential operators},
  series = {Journal of functional analysis},
  volume    = {282},
  journal   = {Journal of functional analysis},
  number    = {12},
  publisher = {Elsevier},
  address   = {Amsterdam [u.a.]},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2022.109445},
  pages     = {69},
  year      = {2022},
  abstract  = {We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.},
  language  = {en}
}
@article{MeraTarkhanov2022,
  author    = {Mera, Azal Jaafar Musa and Tarkhanov, Nikolai},
  title     = {An elliptic equation of finite index in a domain},
  series = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  volume    = {28},
  journal   = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  number    = {2},
  publisher = {Springer International},
  address   = {New York [u.a.]},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-022-00442-7},
  pages     = {10},
  year      = {2022},
  abstract  = {We give an example of first order elliptic equation for a complex-valued function in a plane domain which has a finite number of linearly independent solutions for any right-hand side. No boundary value conditions are thus required.},
  language  = {en}
}
@article{HinzSchwarz2022,
  author    = {Hinz, Michael and Schwarz, Michael},
  title     = {A note on Neumann problems on graphs},
  series = {Positivity},
  volume    = {26},
  journal   = {Positivity},
  number    = {4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1385-1292},
  doi       = {10.1007/s11117-022-00930-0},
  pages     = {23},
  year      = {2022},
  abstract  = {We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.},
  language  = {en}
}
@article{CapałaPadashChechkinetal.2020,
  author    = {Capała, Karol and Padash, Amin and Chechkin, Aleksei V. and Shokri, Babak and Metzler, Ralf and Dybiec, Bartłomiej},
  title     = {Levy noise-driven escape from arctangent potential wells},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {30},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {12},
  publisher = {American Institute of Physics},
  address   = {Woodbury, NY},
  issn      = {1054-1500},
  doi       = {10.1063/5.0021795},
  pages     = {15},
  year      = {2020},
  abstract  = {The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Levy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Levy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Levy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.},
  language  = {en}
}
@article{ReichWeissmann2021,
  author    = {Reich, Sebastian and Weissmann, Simon},
  title     = {Fokker-Planck particle systems for Bayesian inference: computational approaches},
  series = {SIAM ASA journal on uncertainty quantification},
  volume    = {9},
  journal   = {SIAM ASA journal on uncertainty quantification},
  number    = {2},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {2166-2525},
  doi       = {10.1137/19M1303162},
  pages     = {446 -- 482},
  year      = {2021},
  abstract  = {Bayesian inference can be embedded into an appropriately defined dynamics in the space of probability measures. In this paper, we take Brownian motion and its associated Fokker-Planck equation as a starting point for such embeddings and explore several interacting particle approximations. More specifically, we consider both deterministic and stochastic interacting particle systems and combine them with the idea of preconditioning by the empirical covariance matrix. In addition to leading to affine invariant formulations which asymptotically speed up convergence, preconditioning allows for gradient-free implementations in the spirit of the ensemble Kalman filter. While such gradient-free implementations have been demonstrated to work well for posterior measures that are nearly Gaussian, we extend their scope of applicability to multimodal measures by introducing localized gradient-free approximations. Numerical results demonstrate the effectiveness of the considered methodologies.},
  language  = {en}
}
@article{KuckelkornStueblerTextorisTaubeetal.2019,
  author    = {Kuckelkorn, Ulrike and St{\"u}bler, Sabine and Textoris-Taube, Kathrin and Kilian, Christiane and Niewienda, Agathe and Henklein, Petra and Janek, Katharina and Stumpf, Michael P. H. and Mishto, Michele and Liepe, Juliane},
  title     = {Proteolytic dynamics of human 20S thymoproteasome},
  series = {The journal of biological chemistry},
  volume    = {294},
  journal   = {The journal of biological chemistry},
  number    = {19},
  publisher = {American Society for Biochemistry and Molecular Biology},
  address   = {Bethesda},
  issn      = {1083-351X},
  doi       = {10.1074/jbc.RA118.007347},
  pages     = {7740 -- 7754},
  year      = {2019},
  abstract  = {An efficient immunosurveillance of CD8(+) T cells in the periphery depends on positive/negative selection of thymocytes and thus on the dynamics of antigen degradation and epitope production by thymoproteasome and immunoproteasome in the thymus. Although studies in mouse systems have shown how thymoproteasome activity differs from that of immunoproteasome and strongly impacts the T cell repertoire, the proteolytic dynamics and the regulation of human thymoproteasome are unknown. By combining biochemical and computational modeling approaches, we show here that human 20S thymoproteasome and immunoproteasome differ not only in the proteolytic activity of the catalytic sites but also in the peptide transport. These differences impinge upon the quantity of peptide products rather than where the substrates are cleaved. The comparison of the two human 20S proteasome isoforms depicts different processing of antigens that are associated to tumors and autoimmune diseases.},
  language  = {en}
}
@article{CozzoniMaibaumHamm2021,
  author    = {Cozzoni, Barbara and Maibaum, Michael and Hamm, Maximilian},
  title     = {Thermal analysis and constraints for the MASCOT landing site selection on the asteroid Ryugu},
  series = {Planetary and space science},
  volume    = {205},
  journal   = {Planetary and space science},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0032-0633},
  doi       = {10.1016/j.pss.2021.105286},
  pages     = {11},
  year      = {2021},
  abstract  = {In June 2018, after 4 years of cruise, the Japanese space probe Hayabusa2 [1-Watanabe S. et al.: Hayabusa2 Mission Overview. (2017)] reached the Near-Earth Asteroid (162173) Ryugu. Hayabusa2 carried a small Lander named MASCOT (Mobile Asteroid Surface Scout) [2-Ho T. M. et al.: MASCOT-The Mobile Asteroid Surface Scout onboard the Hayabusa2 mission. (2017)], jointly developed by the German Aerospace Center (DLR) and the French Space Agency (CNES), to investigate Ryugu's surface structure, composition and physical properties including its thermal behaviour and magnetization in-situ. The Microgravity User Support Centre (DLR-MUSC) in Cologne was in charge of providing all thermal conditions and constraints necessary for the selection of the final landing site and for the final operations of the Lander MASCOT on the surface of the asteroid Ryugu. This article provides a comprehensive assessment of these thermal conditions and constraints, based on predictions performed with the Thermal Mathematical Model (TMM) of MASCOT using different asteroid surface thermal models, ephemeris data for approach as well as descent and hopping trajectories, the related operation sequences and scenarios and the possible environmental conditions driven by the Hayabusa2 spacecraft. A comparison with the real telemetry data confirms the analysis and provides further information about the asteroid characteristics.},
  language  = {en}
}
@article{BaerHanke2022,
  author    = {B{\"a}r, Christian and Hanke, Bernhard},
  title     = {Local flexibility for open partial differential relations},
  series = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.},
  volume    = {75},
  journal   = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.},
  number    = {6},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0010-3640},
  doi       = {10.1002/cpa.21982},
  pages     = {1377 -- 1415},
  year      = {2022},
  abstract  = {We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry. The main application is a general approximation result by sections that have very restrictive local properties on open dense subsets. This shows, for instance, that given any K is an element of Double-struck capital R every manifold of dimension at least 2 carries a complete C-1,C- 1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course, this is impossible for C-2-metrics in general.},
  language  = {en}
}
@article{ClavierGuoPaychaetal.2020,
  author    = {Clavier, Pierre and Guo, Li and Paycha, Sylvie and Zhang, Bin},
  title     = {Locality and renormalization: universal properties and integrals on trees},
  series = {Journal of mathematical physics},
  volume    = {61},
  journal   = {Journal of mathematical physics},
  number    = {2},
  publisher = {American Institute of Physics},
  address   = {College Park, Md.},
  issn      = {0022-2488},
  doi       = {10.1063/1.5116381},
  pages     = {19},
  year      = {2020},
  abstract  = {The purpose of this paper is to build an algebraic framework suited to regularize branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the locality framework of properly decorated rooted forests. These universal properties are then applied to derive the multivariate regularization of integrals indexed by rooted forests. We study their renormalization, along the lines of Kreimer's toy model for Feynman integrals.},
  language  = {en}
}