@phdthesis{10007,
abstract = {The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis.},
author = {Hensel, Sebastian},
issn = {2663-337X},
pages = {300},
publisher = {IST Austria},
title = {{Curvature driven interface evolution: Uniqueness properties of weak solution concepts}},
doi = {10.15479/at:ista:10007},
year = {2021},
}
@unpublished{10013,
abstract = {We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.},
author = {Hensel, Sebastian and Laux, Tim},
booktitle = {arXiv},
title = {{Weak-strong uniqueness for the mean curvature flow of double bubbles}},
year = {2021},
}
@article{10015,
abstract = {Auxin plays a dual role in growth regulation and, depending on the tissue and concentration of the hormone, it can either promote or inhibit division and expansion processes in plants. Recent studies have revealed that, beyond transcriptional reprogramming, alternative auxincontrolled mechanisms regulate root growth. Here, we explored the impact of different concentrations of the synthetic auxin NAA that establish growth-promoting and -repressing conditions on the root tip proteome and phosphoproteome, generating a unique resource. From the phosphoproteome data, we pinpointed (novel) growth regulators, such as the RALF34-THE1 module. Our results, together with previously published studies, suggest that auxin, H+-ATPases, cell wall modifications and cell wall sensing receptor-like kinases are tightly embedded in a pathway regulating cell elongation. Furthermore, our study assigned a novel role to MKK2 as a regulator of primary root growth and a (potential) regulator of auxin biosynthesis and signalling, and suggests the importance of the MKK2
Thr31 phosphorylation site for growth regulation in the Arabidopsis root tip.},
author = {Nikonorova, N and Murphy, E and Fonseca de Lima, CF and Zhu, S and van de Cotte, B and Vu, LD and Balcerowicz, D and Li, Lanxin and Kong, X and De Rop, G and Beeckman, T and Friml, Jiří and Vissenberg, K and Morris, PC and Ding, Z and De Smet, I},
issn = {2073-4409},
journal = {Cells},
keywords = {primary root, (phospho)proteomics, auxin, (receptor) kinase},
publisher = {Molecular Diversity Preservation International},
title = {{The Arabidopsis root tip (phospho)proteomes at growth-promoting versus growth-repressing conditions reveal novel root growth regulators}},
doi = {10.3390/cells10071665},
volume = {10},
year = {2021},
}
@inproceedings{10002,
abstract = {We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with n vertices and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires O(n2) symbolic operations and O(1) symbolic space. The only other symbolic algorithm for the MEC decomposition requires O(nm−−√) symbolic operations and O(m−−√) symbolic space. A main open question is whether the worst-case O(n2) bound for symbolic operations can be beaten. We present a symbolic algorithm that requires O˜(n1.5) symbolic operations and O˜(n−−√) symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and symbolic space: for all 0<ϵ≤1/2 the symbolic algorithm requires O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space ( O˜ hides poly-logarithmic factors). Using our techniques we present faster algorithms for computing the almost-sure winning regions of ω -regular objectives for MDPs. We consider the canonical parity objectives for ω -regular objectives, and for parity objectives with d -priorities we present an algorithm that computes the almost-sure winning region with O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space, for all 0<ϵ≤1/2 .},
author = {Chatterjee, Krishnendu and Dvorak, Wolfgang and Henzinger, Monika and Svozil, Alexander},
booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science},
isbn = {978-1-6654-4896-3},
issn = {1043-6871},
keywords = {Computer science, Computational modeling, Markov processes, Probabilistic logic, Formal verification, Game Theory},
location = {Rome, Italy},
pages = {1--13},
publisher = {Institute of Electrical and Electronics Engineers},
title = {{Symbolic time and space tradeoffs for probabilistic verification}},
doi = {10.1109/LICS52264.2021.9470739},
year = {2021},
}
@inproceedings{10004,
abstract = {Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science},
isbn = {978-1-6654-4896-3},
issn = {1043-6871},
keywords = {Computer science, Heuristic algorithms, Memory management, Automata, Markov processes, Probability distribution, Complexity theory},
location = {Rome, Italy},
pages = {1--13},
publisher = {Institute of Electrical and Electronics Engineers},
title = {{Stochastic processes with expected stopping time}},
doi = {10.1109/LICS52264.2021.9470595},
year = {2021},
}