@article {ArndtBangerthFeder-2022-a, title = {The \textttdeal.II Library, Version 9.4}, journal = {Journal of Numerical Mathematics}, year = {2022}, author = {Daniel Arndt and Wolfgang Bangerth Marco Feder and Marc Fehling and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Simon Sticko and Bruno Turcksin and David Wells} } @article {ArndtBangerthBlais-2021-h, title = {The deal.II Library, Version 9.3}, journal = {Journal of Numerical Mathematics}, year = {2021}, url = {https://doi.org/10.1515/jnma-2021-0081}, author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Marc Fehling and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Uwe K{\"o}cher and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Sebastian Proell and Konrad Simon and Bruno Turcksin and David Wells and Jiaqi Zhang} } @article {ArndtBangerthDavydov-2020-a, title = {The deal.II finite element library: Design, features, and insights}, journal = {Computers and Mathematics with Applications}, year = {2020}, url = {https://doi.org/10.1016/j.camwa.2020.02.022}, author = {Daniel Arndt and Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {ArndtBangerthBlais-2020-a, title = {The deal.II library, Version 9.2}, journal = {Journal of Numerical Mathematics}, volume = {28}, number = {3}, year = {2020}, pages = {131{\textendash}146}, author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Thomas C. Clevenger and Marc Fehling and Alexander V. Grayver and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Reza Rastak and Ignacio Tomas and Bruno Turcksin and Zhuoran Wang and David Wells} } @article {ArndtBangerthClevenger-2019-a, title = {The deal.II Library, Version 9.1}, journal = {Journal of Numerical Mathematics}, year = {2019}, author = {Daniel Arndt and Wolfgang Bangerth and Thomas C. Clevenger and Denis Davydov and Marc Fehling and Garcia-Sanchez, Daniel and Harper, Graham and Timo Heister and Luca Heltai and Martin Kronbichler and Maguire Kynch, Ross and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {ArndtBangerthClevenger-2019-a, title = {The deal.II Library, Version 9.1}, journal = {Journal of Numerical Mathematics}, year = {2019}, abstract = {This paper provides an overview of the new features of the finite element library deal.II, version 9.1.}, issn = {15702820}, doi = {10.1515/jnma-2019-0064}, author = {Daniel Arndt and Wolfgang Bangerth and Thomas C. Clevenger and Denis Davydov and Marc Fehling and Garcia-Sanchez, Daniel and Harper, Graham and Timo Heister and Luca Heltai and Martin Kronbichler and Maguire Kynch, Ross and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {20.500.11767_81694, title = {The deal.II Library, Version 9.0}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, year = {2018}, doi = {10.1515/jnma-2018-0054}, url = {https://doi.org/10.1515/jnma-2018-0054}, author = {Giovanni Alzetta and Daniel Arndt and Wolfgang Bangerth and Boddu, Vishal and Brands, Benjamin and Denis Davydov and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Kormann, Katharina and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @conference {10.1007/978-3-319-91545-6_15, title = {On Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, year = {2018}, pages = {191{\textendash}203}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-91545-6}, doi = {10.1007/978-3-319-91545-6_15}, url = {https://link.springer.com/chapter/10.1007/978-3-319-91545-6_15}, author = {Paolo Bonicatto}, editor = {Klingenberg, Christian and Westdickenberg, Michael} } @article {20.500.11767_47950, title = {The deal.II Library, Version 8.5}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {25}, year = {2017}, pages = {137{\textendash}145}, doi = {10.1515/jnma-2017-0058}, url = {https://www.dealii.org/deal85-preprint.pdf}, author = {Daniel Arndt and Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {luzzatto_2017, title = {Integrability of dominated decompositions on three-dimensional manifolds}, journal = {Ergodic Theory and Dynamical Systems}, volume = {37}, number = {2}, year = {2017}, pages = {606{\textendash}620}, publisher = {Cambridge University Press}, abstract = {


We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.

}, doi = {10.1017/etds.2015.64}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @inbook {ChinestaHuertaRozzaWillcox2017, title = {Model Reduction Methods}, booktitle = {Encyclopedia of Computational Mechanics Second Edition}, year = {2017}, pages = {1-36}, publisher = {John Wiley \& Sons}, organization = {John Wiley \& Sons}, chapter = {Model Reduction Methods}, abstract = {

This chapter presents an overview of model order reduction {\textendash} a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control {\textendash} critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1\&isAllowed=y

}, doi = {10.1002/9781119176817.ecm2110}, author = {Francisco Chinesta and Antonio Huerta and Gianluigi Rozza and Karen Willcox} } @article {20.500.11767_14498, title = {The deal.II library, Version 8.4}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {24}, year = {2016}, pages = {135{\textendash}141}, doi = {10.1515/jnma-2016-1045}, url = {https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf}, author = {Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and David Wells} } @article {doi:10.1142/S0129167X16500610, title = {A Frobenius theorem for corank-1 continuous distributions in dimensions two and three}, journal = {International Journal of Mathematics}, volume = {27}, number = {08}, year = {2016}, pages = {1650061}, abstract = {

We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive C1 distribution is uniquely integrable.

}, doi = {10.1142/S0129167X16500610}, url = {https://doi.org/10.1142/S0129167X16500610}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @article {doi:10.1080/14689367.2015.1057480, title = {Integrability of C1 invariant splittings}, journal = {Dynamical Systems}, volume = {31}, number = {1}, year = {2016}, pages = {79-88}, publisher = {Taylor \& Francis}, abstract = {

We derive some new conditions for integrability of dynamically defined C1 invariant splittings, formulated in terms of the singular values of the iterates of the derivative of the diffeomorphism which defines the splitting.

}, doi = {10.1080/14689367.2015.1057480}, url = {https://doi.org/10.1080/14689367.2015.1057480}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @mastersthesis {2016, title = {Integrability of continuous bundles and applications to dynamical systems}, year = {2016}, school = {SISSA}, abstract = {In this dissertation we study the problem of integrability of bundles with low regularities.}, author = {Khadim Mbacke War} } @inbook {2016, title = {Model Order Reduction: a survey}, booktitle = {Wiley Encyclopedia of Computational Mechanics, 2016}, year = {2016}, publisher = {Wiley}, organization = {Wiley}, url = {http://urania.sissa.it/xmlui/handle/1963/35194}, author = {Francisco Chinesta and Antonio Huerta and Gianluigi Rozza and Karen Willcox} } @article {2014, title = {Infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy}, number = {Advances in Mathematics;volume 255; pages 487-524;}, year = {2014}, publisher = {Elsevier}, abstract = {Following the approach of Carlet et al. (2011) [9], we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly higher-order poles at the origin and at infinity. We also show a connection between these infinite-dimensional Frobenius manifolds and the finite-dimensional Frobenius manifolds on the orbit space of extended affine Weyl groups of type A defined by Dubrovin and Zhang.}, doi = {10.1016/j.aim.2014.01.013}, url = {http://urania.sissa.it/xmlui/handle/1963/35026}, author = {Chaozhong Wu and Dafeng Zuo} } @article {2013, title = {Expanded degenerations and pairs}, journal = {Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386}, number = {arXiv:1110.2976v1;}, year = {2013}, note = {This article is composed of 41 pages and is recorded in PDF format}, publisher = {Taylor and Francis}, abstract = {Since Jun Li{\textquoteright}s original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas.}, keywords = {Expanded pairs}, doi = {10.1080/00927872.2012.658589}, url = {http://hdl.handle.net/1963/7383}, author = {Dan Abramovich and Charles Cadman and Barbara Fantechi and Jonathan Wise} } @article {2011, title = {D-branes, surface operators, and ADHM quiver representations}, number = {SISSA;01/2011/FM}, year = {2011}, note = {45 pages, v2: minor corrections}, institution = {SISSA}, abstract = {A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries.}, url = {http://hdl.handle.net/1963/4133}, author = {Ugo Bruzzo and Duiliu-Emanuel Diaconescu and M. Yardim and G. Pan and Yi Zhang and Chuang Wu-yen} } @conference {10.1007/978-1-4419-9554-4_10, title = {The Monge Problem in Geodesic Spaces}, booktitle = {Nonlinear Conservation Laws and Applications}, year = {2011}, pages = {217{\textendash}233}, publisher = {Springer US}, organization = {Springer US}, address = {Boston, MA}, abstract = {

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

}, isbn = {978-1-4419-9554-4}, author = {Stefano Bianchini and Fabio Cavalletti}, editor = {Alberto Bressan and Chen, Gui-Qiang G. and Marta Lewicka and Wang, Dehua} } @article {2010, title = {Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.}, journal = {The European journal of neuroscience. 2010 Oct; 32(8):1364-79}, number = {PMID:20950280;}, year = {2010}, publisher = {Wiley}, abstract = {

We report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

}, doi = {10.1111/j.1460-9568.2010.07403.x}, url = {http://hdl.handle.net/1963/4480}, author = {Dario Motti and Caroline Le Duigou and Nicole Chemaly and Lucia Wittner and Dejan Lazarevic and Helena Krmac and Troels Torben Marstrand and Eivind Valen and Remo Sanges and Elia Stupka and Albin Sandelin and Enrico Cherubini and Stefano Gustincich and Richard Miles} } @article {mercuri2010global, title = {A global compactness result for the p-Laplacian involving critical nonlinearities}, journal = {Discrete \& Continuous Dynamical Systems-A}, volume = {28}, number = {2}, year = {2010}, pages = {469{\textendash}493}, abstract = {
We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

}, doi = {10.3934/dcds.2010.28.469}, url = {http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097}, author = {Mercuri, Carlo and Willem, Michel} } @article {2008, title = {Transition layer for the heterogeneous Allen-Cahn equation}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631}, number = {arXiv.org;math/0702878v1}, year = {2008}, abstract = {We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$.}, doi = {10.1016/j.anihpc.2007.03.008}, url = {http://hdl.handle.net/1963/2656}, author = {Fethi Mahmoudi and Andrea Malchiodi and Juncheng Wei} } @article {2007, title = {Boundary interface for the Allen-Cahn equation}, journal = {J. Fixed Point Theory Appl. 1 (2007) 305-336}, year = {2007}, doi = {10.1007/s11784-007-0016-7}, url = {http://hdl.handle.net/1963/2027}, author = {Andrea Malchiodi and Juncheng Wei} } @article {2007, title = {Boundary-clustered interfaces for the Allen{\textendash}Cahn equation}, journal = {Pacific Journal of Mathematics 229 (2007), No. 2, 447{\textendash}468}, year = {2007}, publisher = {Mathematical Sciences Publishers}, url = {http://hdl.handle.net/1963/5089}, author = {Andrea Malchiodi and Wei-Ming Ni and Juncheng Wei} } @article {2007, title = {Dirac operators on all Podles quantum spheres}, journal = {J. Noncomm. Geom. 1 (2007) 213-239}, number = {arXiv.org;math/0606480v2}, year = {2007}, abstract = {We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.}, doi = {10.4171/JNCG/5}, url = {http://hdl.handle.net/1963/2177}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi and Elmar Wagner} } @article {2005, title = {Multiple clustered layer solutions for semilinear Neumann problems on a ball}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163}, year = {2005}, publisher = {Elsevier}, doi = {10.1016/j.anihpc.2004.05.003}, url = {http://hdl.handle.net/1963/3532}, author = {Andrea Malchiodi and Wei-Ming Ni and Juncheng Wei} }