TY - GEN
AB - In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines.
AU - Derenthal, Ulrich
AU - Wilsch, Florian Alexander
ID - 10018
KW - Integral points
KW - del Pezzo surface
KW - universal torsor
KW - Manin’s conjecture
T2 - arXiv
TI - Integral points on singular del Pezzo surfaces
ER -
TY - THES
AB - 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.
AU - Hensel, Sebastian
ID - 10007
SN - 2663-337X
TI - Curvature driven interface evolution: Uniqueness properties of weak solution concepts
ER -
TY - GEN
AB - 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.
AU - Hensel, Sebastian
AU - Laux, Tim
ID - 10013
T2 - arXiv
TI - Weak-strong uniqueness for the mean curvature flow of double bubbles
ER -
TY - JOUR
AB - 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.
AU - Nikonorova, N
AU - Murphy, E
AU - Fonseca de Lima, CF
AU - Zhu, S
AU - van de Cotte, B
AU - Vu, LD
AU - Balcerowicz, D
AU - Li, Lanxin
AU - Kong, X
AU - De Rop, G
AU - Beeckman, T
AU - Friml, Jiří
AU - Vissenberg, K
AU - Morris, PC
AU - Ding, Z
AU - De Smet, I
ID - 10015
JF - Cells
KW - primary root
KW - (phospho)proteomics
KW - auxin
KW - (receptor) kinase
SN - 2073-4409
TI - The Arabidopsis root tip (phospho)proteomes at growth-promoting versus growth-repressing conditions reveal novel root growth regulators
VL - 10
ER -
TY - CONF
AB - 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 .
AU - Chatterjee, Krishnendu
AU - Dvorak, Wolfgang
AU - Henzinger, Monika
AU - Svozil, Alexander
ID - 10002
KW - Computer science
KW - Computational modeling
KW - Markov processes
KW - Probabilistic logic
KW - Formal verification
KW - Game Theory
SN - 1043-6871
T2 - Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Symbolic time and space tradeoffs for probabilistic verification
ER -
TY - JOUR
AB - Aprotic alkali metal–O2 batteries face two major obstacles to their chemistry occurring efficiently, the insulating nature of the formed alkali superoxides/peroxides and parasitic reactions that are caused by the highly reactive singlet oxygen (1O2). Redox mediators are recognized to be key for improving rechargeability. However, it is unclear how they affect 1O2 formation, which hinders strategies for their improvement. Here we clarify the mechanism of mediated peroxide and superoxide oxidation and thus explain how redox mediators either enhance or suppress 1O2 formation. We show that charging commences with peroxide oxidation to a superoxide intermediate and that redox potentials above ~3.5 V versus Li/Li+ drive 1O2 evolution from superoxide oxidation, while disproportionation always generates some 1O2. We find that 1O2 suppression requires oxidation to be faster than the generation of 1O2 from disproportionation. Oxidation rates decrease with growing driving force following Marcus inverted-region behaviour, establishing a region of maximum rate.
AU - Petit, Yann K.
AU - Mourad, Eléonore
AU - Prehal, Christian
AU - Leypold, Christian
AU - Windischbacher, Andreas
AU - Mijailovic, Daniel
AU - Slugovc, Christian
AU - Borisov, Sergey M.
AU - Zojer, Egbert
AU - Brutti, Sergio
AU - Fontaine, Olivier
AU - Freunberger, Stefan Alexander
ID - 9250
IS - 5
JF - Nature Chemistry
KW - General Chemistry
KW - General Chemical Engineering
SN - 1755-4330
TI - Mechanism of mediated alkali peroxide oxidation and triplet versus singlet oxygen formation
VL - 13
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 10004
KW - Computer science
KW - Heuristic algorithms
KW - Memory management
KW - Automata
KW - Markov processes
KW - Probability distribution
KW - Complexity theory
SN - 1043-6871
T2 - Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Stochastic processes with expected stopping time
ER -
TY - CONF
AB - In runtime verification, a monitor watches a trace of a system and, if possible, decides after observing each finite prefix whether or not the unknown infinite trace satisfies a given specification. We generalize the theory of runtime verification to monitors that attempt to estimate numerical values of quantitative trace properties (instead of attempting to conclude boolean values of trace specifications), such as maximal or average response time along a trace. Quantitative monitors are approximate: with every finite prefix, they can improve their estimate of the infinite trace's unknown property value. Consequently, quantitative monitors can be compared with regard to a precision-cost trade-off: better approximations of the property value require more monitor resources, such as states (in the case of finite-state monitors) or registers, and additional resources yield better approximations. We introduce a formal framework for quantitative and approximate monitoring, show how it conservatively generalizes the classical boolean setting for monitoring, and give several precision-cost trade-offs for monitors. For example, we prove that there are quantitative properties for which every additional register improves monitoring precision.
AU - Henzinger, Thomas A
AU - Sarac, Naci E
ID - 10003
KW - Computer science
KW - Runtime
KW - Registers
KW - Time factors
KW - Monitoring
SN - 1043-6871
T2 - Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Quantitative and approximate monitoring
ER -
TY - THES
AB - Blood – this is what animals use to heal wounds fast and efficient. Plants do not have blood circulation and their cells cannot move. However, plants have evolved remarkable capacities to regenerate tissues and organs preventing further damage. In my PhD research, I studied the wound healing in the Arabidopsis root. I used a UV laser to ablate single cells in the root tip and observed the consequent wound healing. Interestingly, the inner adjacent cells induced a
division plane switch and subsequently adopted the cell type of the killed cell to replace it. We termed this form of wound healing “restorative divisions”. This initial observation triggered the questions of my PhD studies: How and why do cells orient their division planes, how do they feel the wound and why does this happen only in inner adjacent cells.
For answering these questions, I used a quite simple experimental setup: 5 day - old seedlings were stained with propidium iodide to visualize cell walls and dead cells; ablation was carried out using a special laser cutter and a confocal microscope. Adaptation of the novel vertical microscope system made it possible to observe wounds in real time. This revealed that restorative divisions occur at increased frequency compared to normal divisions. Additionally,
the major plant hormone auxin accumulates in wound adjacent cells and drives the expression of the wound-stress responsive transcription factor ERF115. Using this as a marker gene for wound responses, we found that an important part of wound signalling is the sensing of the collapse of the ablated cell. The collapse causes a radical pressure drop, which results in strong tissue deformations. These deformations manifest in an invasion of the now free spot specifically by the inner adjacent cells within seconds, probably because of higher pressure of the inner tissues. Long-term imaging revealed that those deformed cells continuously expand towards the wound hole and that this is crucial for the restorative division. These wound-expanding cells exhibit an abnormal, biphasic polarity of microtubule arrays
before the division. Experiments inhibiting cell expansion suggest that it is the biphasic stretching that induces those MT arrays. Adapting the micromanipulator aspiration system from animal scientists at our institute confirmed the hypothesis that stretching influences microtubule stability. In conclusion, this shows that microtubules react to tissue deformation
and this facilitates the observed division plane switch. This puts mechanical cues and tensions at the most prominent position for explaining the growth and wound healing properties of plants. Hence, it shines light onto the importance of understanding mechanical signal transduction.
AU - Hörmayer, Lukas
ID - 9992
SN - 2663-337X
TI - Wound healing in the Arabidopsis root meristem
ER -
TY - JOUR
AB - When short-range attractions are combined with long-range repulsions in colloidal particle systems, complex microphases can emerge. Here, we study a system of isotropic particles, which can form lamellar structures or a disordered fluid phase when temperature is varied. We show that, at equilibrium, the lamellar structure crystallizes, while out of equilibrium, the system forms a variety of structures at different shear rates and temperatures above melting. The shear-induced ordering is analyzed by means of principal component analysis and artificial neural networks, which are applied to data of reduced dimensionality. Our results reveal the possibility of inducing ordering by shear, potentially providing a feasible route to the fabrication of ordered lamellar structures from isotropic particles.
AU - Pȩkalski, J.
AU - Rzadkowski, Wojciech
AU - Panagiotopoulos, A. Z.
ID - 7956
IS - 20
JF - The Journal of chemical physics
TI - Shear-induced ordering in systems with competing interactions: A machine learning study
VL - 152
ER -