@article{6762, abstract = {We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level of theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the doping profiles < system size.}, author = {Friesecke, Gero and Kniely, Michael}, issn = {15403467}, journal = {Multiscale Modeling and Simulation}, number = {3}, pages = {926--947}, publisher = {SIAM}, title = {{New optimal control problems in density functional theory motivated by photovoltaics}}, doi = {10.1137/18M1207272}, volume = {17}, year = {2019}, } @article{10874, abstract = {In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary octics to Siegel modular forms of genus 3. We use this connection to show that certain modular functions, when restricted to the hyperelliptic locus, assume values whose denominators are products of powers of primes of bad reduction for the associated hyperelliptic curves. We illustrate our theorem with explicit computations. This work is motivated by the study of the values of these modular functions at CM points of the Siegel upper half-space, which, if their denominators are known, can be used to effectively compute models of (hyperelliptic, in our case) curves with CM.}, author = {Ionica, Sorina and Kılıçer, Pınar and Lauter, Kristin and Lorenzo García, Elisa and Manzateanu, Maria-Adelina and Massierer, Maike and Vincent, Christelle}, issn = {2363-9555}, journal = {Research in Number Theory}, keywords = {Algebra and Number Theory}, publisher = {Springer Nature}, title = {{Modular invariants for genus 3 hyperelliptic curves}}, doi = {10.1007/s40993-018-0146-6}, volume = {5}, year = {2019}, } @article{7100, abstract = {We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.}, author = {Jeblick, Maximilian and Leopold, Nikolai K and Pickl, Peter}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, number = {1}, pages = {1--69}, publisher = {Springer Nature}, title = {{Derivation of the time dependent Gross–Pitaevskii equation in two dimensions}}, doi = {10.1007/s00220-019-03599-x}, volume = {372}, year = {2019}, } @article{7106, abstract = {PIN-FORMED (PIN) transporters mediate directional, intercellular movement of the phytohormone auxin in land plants. To elucidate the evolutionary origins of this developmentally crucial mechanism, we analysed the single PIN homologue of a simple green alga Klebsormidium flaccidum. KfPIN functions as a plasma membrane-localized auxin exporter in land plants and heterologous models. While its role in algae remains unclear, PIN-driven auxin export is probably an ancient and conserved trait within streptophytes.}, author = {Skokan, Roman and Medvecká, Eva and Viaene, Tom and Vosolsobě, Stanislav and Zwiewka, Marta and Müller, Karel and Skůpa, Petr and Karady, Michal and Zhang, Yuzhou and Janacek, Dorina P. and Hammes, Ulrich Z. and Ljung, Karin and Nodzyński, Tomasz and Petrášek, Jan and Friml, Jiří}, issn = {2055-0278}, journal = {Nature Plants}, number = {11}, pages = {1114--1119}, publisher = {Springer Nature}, title = {{PIN-driven auxin transport emerged early in streptophyte evolution}}, doi = {10.1038/s41477-019-0542-5}, volume = {5}, year = {2019}, } @article{7105, abstract = {Cell migration is hypothesized to involve a cycle of behaviours beginning with leading edge extension. However, recent evidence suggests that the leading edge may be dispensable for migration, raising the question of what actually controls cell directionality. Here, we exploit the embryonic migration of Drosophila macrophages to bridge the different temporal scales of the behaviours controlling motility. This approach reveals that edge fluctuations during random motility are not persistent and are weakly correlated with motion. In contrast, flow of the actin network behind the leading edge is highly persistent. Quantification of actin flow structure during migration reveals a stable organization and asymmetry in the cell-wide flowfield that strongly correlates with cell directionality. This organization is regulated by a gradient of actin network compression and destruction, which is controlled by myosin contraction and cofilin-mediated disassembly. It is this stable actin-flow polarity, which integrates rapid fluctuations of the leading edge, that controls inherent cellular persistence.}, author = {Yolland, Lawrence and Burki, Mubarik and Marcotti, Stefania and Luchici, Andrei and Kenny, Fiona N. and Davis, John Robert and Serna-Morales, Eduardo and Müller, Jan and Sixt, Michael K and Davidson, Andrew and Wood, Will and Schumacher, Linus J. and Endres, Robert G. and Miodownik, Mark and Stramer, Brian M.}, issn = {1476-4679}, journal = {Nature Cell Biology}, number = {11}, pages = {1370--1381}, publisher = {Springer Nature}, title = {{Persistent and polarized global actin flow is essential for directionality during cell migration}}, doi = {10.1038/s41556-019-0411-5}, volume = {21}, year = {2019}, } @article{7108, abstract = {We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes. Another simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-shellable.}, author = {Goaoc, Xavier and Patak, Pavel and Patakova, Zuzana and Tancer, Martin and Wagner, Uli}, issn = {0004-5411}, journal = {Journal of the ACM}, number = {3}, publisher = {ACM}, title = {{Shellability is NP-complete}}, doi = {10.1145/3314024}, volume = {66}, year = {2019}, } @inproceedings{7136, abstract = {It is well established that the notion of min-entropy fails to satisfy the \emph{chain rule} of the form H(X,Y)=H(X|Y)+H(Y), known for Shannon Entropy. Such a property would help to analyze how min-entropy is split among smaller blocks. Problems of this kind arise for example when constructing extractors and dispersers. We show that any sequence of variables exhibits a very strong strong block-source structure (conditional distributions of blocks are nearly flat) when we \emph{spoil few correlated bits}. This implies, conditioned on the spoiled bits, that \emph{splitting-recombination properties} hold. In particular, we have many nice properties that min-entropy doesn't obey in general, for example strong chain rules, "information can't hurt" inequalities, equivalences of average and worst-case conditional entropy definitions and others. Quantitatively, for any sequence X1,…,Xt of random variables over an alphabet X we prove that, when conditioned on m=t⋅O(loglog|X|+loglog(1/ϵ)+logt) bits of auxiliary information, all conditional distributions of the form Xi|X