@article{15275, abstract = {In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum integer n > 1 such that for any m-coloring of the edges of the complete graph Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings with bounded VC-dimension, that is, for m-colorings with the property that the set system induced by the neighborhoods of the vertices with respect to each color class has bounded VC-dimension.}, author = {Fox, Jacob and Pach, János and Suk, Andrew}, issn = {1439-6912}, journal = {Combinatorica}, keywords = {Computational Mathematics, Discrete Mathematics and Combinatorics}, number = {6}, pages = {803--813}, publisher = {Springer Nature}, title = {{Bounded VC-dimension implies the Schur-Erdős conjecture}}, doi = {10.1007/s00493-021-4530-9}, volume = {41}, year = {2021}, } @article{15276, abstract = {Biotrophic plant pathogens secrete effector proteins to manipulate the host physiology. Effectors suppress defenses and induce an environment favorable to disease development. Sequence-based prediction of effector function is impeded by their rapid evolution rate. In the maize pathogen Ustilago maydis, effector-coding genes frequently organize in clusters. Here we describe the functional characterization of the pleiades, a cluster of ten effector genes, by analyzing the micro- and macroscopic phenotype of the cluster deletion and expressing these proteins in planta. Deletion of the pleiades leads to strongly impaired virulence and accumulation of reactive oxygen species (ROS) in infected tissue. Eight of the Pleiades suppress the production of ROS upon perception of pathogen associated molecular patterns (PAMPs). Although functionally redundant, the Pleiades target different host components. The paralogs Taygeta1 and Merope1 suppress ROS production in either the cytoplasm or nucleus, respectively. Merope1 targets and promotes the auto-ubiquitination activity of RFI2, a conserved family of E3 ligases that regulates the production of PAMP-triggered ROS burst in plants.}, author = {Navarrete, Fernando and Grujic, Nenad and Stirnberg, Alexandra and Saado, Indira and Aleksza, David and Gallei, Michelle C and Adi, Hazem and Alcântara, André and Khan, Mamoona and Bindics, Janos and Trujillo, Marco and Djamei, Armin}, issn = {1553-7374}, journal = {PLOS Pathogens}, keywords = {Virology, Genetics, Molecular Biology, Immunology, Microbiology, Parasitology}, number = {6}, publisher = {Public Library of Science}, title = {{The Pleiades are a cluster of fungal effectors that inhibit host defenses}}, doi = {10.1371/journal.ppat.1009641}, volume = {17}, year = {2021}, } @article{15277, abstract = {Alternative splicing generates multiple transcript and protein isoforms from a single gene and controls transcript intracellular localization and stability by coupling to mRNA export and nonsense-mediated mRNA decay (NMD). RNA interference (RNAi) is a potent mechanism to modulate gene expression. However, its interactions with alternative splicing are poorly understood. We used artificial microRNAs (amiRNAs, also termed shRNAmiR) to knockdown all splice variants of selected target genes in Arabidopsis thaliana. We found that splice variants, which vary by their protein-coding capacity, subcellular localization and sensitivity to NMD, are affected differentially by an amiRNA, although all of them contain the target site. Particular transcript isoforms escape amiRNA-mediated degradation due to their nuclear localization. The nuclear and NMD-sensitive isoforms mask RNAi action in alternatively spliced genes. Interestingly, Arabidopsis SPL genes, which undergo alternative splicing and are targets of miR156, are regulated in the same manner. Moreover, similar results were obtained in mammalian cells using siRNAs, indicating cross-kingdom conservation of these interactions among RNAi and splicing isoforms. Furthermore, we report that amiRNA can trigger artificial alternative splicing, thus expanding the RNAi functional repertoire. Our findings unveil novel interactions between different post-transcriptional processes in defining transcript fates and regulating gene expression.}, author = {Fuchs, Armin and Riegler, Stefan and Ayatollahi, Zahra and Cavallari, Nicola and Giono, Luciana E and Nimeth, Barbara A and Mutanwad, Krishna V and Schweighofer, Alois and Lucyshyn, Doris and Barta, Andrea and Petrillo, Ezequiel and Kalyna, Maria}, issn = {1362-4962}, journal = {Nucleic Acids Research}, keywords = {Genetics}, number = {2}, pages = {1133--1151}, publisher = {Oxford University Press}, title = {{Targeting alternative splicing by RNAi: From the differential impact on splice variants to triggering artificial pre-mRNA splicing}}, doi = {10.1093/nar/gkaa1260}, volume = {49}, year = {2021}, } @article{15278, abstract = {‘Dysbiosis’ of the adult gut microbiota, in response to challenges such as infection, altered diet, stress, and antibiotics treatment has been recently linked to pathological alteration of brain function and behavior. Moreover, gut microbiota composition constantly controls microglia maturation, as revealed by morphological observations and gene expression analysis. However, it is unclear whether microglia functional properties and crosstalk with neurons, known to shape and modulate synaptic development and function, are influenced by the gut microbiota. Here, we investigated how antibiotic-mediated alteration of the gut microbiota influences microglial and neuronal functions in adult mice hippocampus. Hippocampal microglia from adult mice treated with oral antibiotics exhibited increased microglia density, altered basal patrolling activity, and impaired process rearrangement in response to damage. Patch clamp recordings at CA3-CA1 synapses revealed that antibiotics treatment alters neuronal functions, reducing spontaneous postsynaptic glutamatergic currents and decreasing synaptic connectivity, without reducing dendritic spines density. Antibiotics treatment was unable to modulate synaptic function in CX3CR1-deficient mice, pointing to an involvement of microglia–neuron crosstalk through the CX3CL1/CX3CR1 axis in the effect of dysbiosis on neuronal functions. Together, our findings show that antibiotic alteration of gut microbiota impairs synaptic efficacy, suggesting that CX3CL1/CX3CR1 signaling supporting microglia is a major player in in the gut–brain axis, and in particular in the gut microbiota-to-neuron communication pathway.}, author = {Cordella, Federica and Sanchini, Caterina and Rosito, Maria and Ferrucci, Laura and Pediconi, Natalia and Cortese, Barbara and Guerrieri, Francesca and Pascucci, Giuseppe Rubens and Antonangeli, Fabrizio and Peruzzi, Giovanna and Giubettini, Maria and Basilico, Bernadette and Pagani, Francesca and Grimaldi, Alfonso and D’Alessandro, Giuseppina and Limatola, Cristina and Ragozzino, Davide and Di Angelantonio, Silvia}, issn = {2073-4409}, journal = {Cells}, keywords = {General Medicine}, number = {10}, publisher = {MDPI}, title = {{Antibiotics treatment modulates microglia–synapses interaction}}, doi = {10.3390/cells10102648}, volume = {10}, year = {2021}, } @article{15279, abstract = {We formulate and prove an analog of Poonen’s finite-field Bertini theorem with Taylor conditions that holds in the Grothendieck ring of varieties. This gives a broad generalization of the work of Vakil and Wood, who treated the case of smooth hypersurface sections, and is made possible by the use of motivic Euler products to write down candidate motivic probabilities. As applications, we give motivic analogs of many results in arithmetic statistics that have been proven using Poonen’s sieve, including work of Bucur and Kedlaya on complete intersections and Erman and Wood on semiample Bertini theorems.}, author = {Bilu, Margaret and Howe, Sean}, issn = {1944-7833}, journal = {Algebra & Number Theory}, keywords = {Algebra and Number Theory}, number = {9}, pages = {2195--2259}, publisher = {Mathematical Sciences Publishers}, title = {{Motivic Euler products in motivic statistics}}, doi = {10.2140/ant.2021.15.2195}, volume = {15}, year = {2021}, } @article{15283, author = {Nicolas, William and Fäßler, Florian and Meyerowitz, Elliot and Jensen, Grant}, issn = {1435-8115}, journal = {Microscopy and Microanalysis}, keywords = {Instrumentation}, number = {S1}, pages = {3024--3026}, publisher = {Oxford University Press}, title = {{Peaking into the plant cell wall using cryo-FIB milling and electron cryo-tomography}}, doi = {10.1017/s1431927621010503}, volume = {27}, year = {2021}, } @misc{15284, abstract = {RevTerm is a static analysis tool for proving non-termination of integer C programs (possibly with non-determinism). RevTerm is an implementation of our method for non-termination proving presented in the paper “Proving Non-termination by Program Reversal”. }, author = {Chatterjee, Krishnendu and Goharshady, Ehsan Kafshdar and Novotný, Petr and Zikelic, Dorde}, publisher = {Association for Computing Machinery}, title = {{RevTerm}}, doi = {10.1145/3410304}, year = {2021}, } @article{15285, abstract = {Ever since the first publication of the standard communication protocol for computer-assisted electrocardiography (SCP-ECG), prENV 1064, in 1993, by the European Committee for Standardization (CEN), SCP-ECG has become a leading example in health informatics, enabling open, secure, and well-documented digital data exchange at a low cost, for quick and efficient cardiovascular disease detection and management. Based on the experiences gained, since the 1970s, in computerized electrocardiology, and on the results achieved by the pioneering, international cooperative research on common standards for quantitative electrocardiography (CSE), SCP-ECG was designed, from the beginning, to empower personalized medicine, thanks to serial ECG analysis. The fundamental concept behind SCP-ECG is to convey the necessary information for ECG re-analysis, serial comparison, and interpretation, and to structure the ECG data and metadata in sections that are mostly optional in order to fit all use cases. SCP-ECG is open to the storage of the ECG signal and ECG measurement data, whatever the ECG recording modality or computation method, and can store the over-reading trails and ECG annotations, as well as any computerized or medical interpretation reports. Only the encoding syntax and the semantics of the ECG descriptors and of the diagnosis codes are standardized. We present all of the landmarks in the development and publication of SCP-ECG, from the early 1990s to the 2009 International Organization for Standardization (ISO) SCP-ECG standards, including the latest version published by CEN in 2020, which now encompasses rest and stress ECGs, Holter recordings, and protocol-based trials.}, author = {Rubel, Paul and Fayn, Jocelyne and Macfarlane, Peter W. and Pani, Danilo and Schlögl, Alois and Värri, Alpo}, issn = {2673-3846}, journal = {Hearts}, keywords = {General Medicine}, number = {3}, pages = {384--409}, publisher = {MDPI}, title = {{The history and challenges of SCP-ECG: The standard communication protocol for computer-assisted electrocardiography}}, doi = {10.3390/hearts2030031}, volume = {2}, year = {2021}, } @article{19472, abstract = {The forebrain hemispheres are predominantly separated during embryogenesis by the interhemispheric fissure (IHF). Radial astroglia remodel the IHF to form a continuous substrate between the hemispheres for midline crossing of the corpus callosum (CC) and hippocampal commissure (HC). Deleted in colorectal carcinoma (DCC) and netrin 1 (NTN1) are molecules that have an evolutionarily conserved function in commissural axon guidance. The CC and HC are absent in Dcc and Ntn1 knockout mice, while other commissures are only partially affected, suggesting an additional aetiology in forebrain commissure formation. Here, we find that these molecules play a critical role in regulating astroglial development and IHF remodelling during CC and HC formation. Human subjects with DCC mutations display disrupted IHF remodelling associated with CC and HC malformations. Thus, axon guidance molecules such as DCC and NTN1 first regulate the formation of a midline substrate for dorsal commissures prior to their role in regulating axonal growth and guidance across it.}, author = {Morcom, Laura and Gobius, Ilan and Marsh, Ashley PL and Suárez, Rodrigo and Lim, Jonathan WC and Bridges, Caitlin and Ye, Yunan and Fenlon, Laura R and Zagar, Yvrick and Douglass, Amelia May Barnett and Donahoo, Amber-Lee S and Fothergill, Thomas and Shaikh, Samreen and Kozulin, Peter and Edwards, Timothy J and Cooper, Helen M and Sherr, Elliott H and Chédotal, Alain and Leventer, Richard J and Lockhart, Paul J and Richards, Linda J}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{DCC regulates astroglial development essential for telencephalic morphogenesis and corpus callosum formation}}, doi = {10.7554/elife.61769}, volume = {10}, year = {2021}, } @article{19489, abstract = {Let K be a cyclic number field of odd degree over 𝑄 with odd narrow class number, such that 2 is inert in 𝐾/𝑄. We define a family of number fields {𝐾(𝑝)}𝑝, depending on K and indexed by the rational primes p that split completely in 𝐾/𝑄, in which p is always ramified of degree 2. Conditional on a standard conjecture on short character sums, the density of such rational primes p that exhibit one of two possible ramified factorizations in 𝐾(𝑝)/𝑄 is strictly between 0 and 1 and is given explicitly as a formula in terms of the degree of the extension 𝐾/𝑄. Our results are unconditional in the cubic case. Our proof relies on a detailed study of the joint distribution of spins of prime ideals.}, author = {Chan, Yik Tung and McMeekin, Christine and Milovic, Djordjo}, issn = {2363-9555}, journal = {Research in Number Theory}, publisher = {Springer Nature}, title = {{A density of ramified primes}}, doi = {10.1007/s40993-021-00295-5}, volume = {8}, year = {2021}, } @article{19492, abstract = {Kuroda’s formula relates the class number of a multiquadratic number field K to the class numbers of its quadratic subfields ki. A key component in this formula is the unit group index (math formular). We study how Q(K) behaves on average in certain natural families of totally real biquadratic fields K parametrized by prime numbers.}, author = {Chan, Yik Tung and Milovic, Djordjo}, issn = {1432-1823}, journal = {Mathematische Zeitschrift}, number = {2}, pages = {1509--1527}, publisher = {Springer Nature}, title = {{Kuroda’s formula and arithmetic statistics}}, doi = {10.1007/s00209-021-02823-6}, volume = {300}, year = {2021}, } @article{19909, abstract = {Most water in the Universe may be superionic, and its thermodynamic and transport properties are crucial for planetary science but difficult to probe experimentally or theoretically. We use machine learning and free-energy methods to overcome the limitations of quantum mechanical simulations and characterize hydrogen diffusion, superionic transitions and phase behaviours of water at extreme conditions. We predict that close-packed superionic phases, which have a fraction of mixed stacking for finite systems, are stable over a wide temperature and pressure range, whereas a body-centred cubic superionic phase is only thermodynamically stable in a small window but is kinetically favoured. Our phase boundaries, which are consistent with existing—albeit scarce—experimental observations, help resolve the fractions of insulating ice, different superionic phases and liquid water inside ice giants.}, author = {Cheng, Bingqing and Bethkenhagen, Mandy and Pickard, Chris J. and Hamel, Sebastien}, issn = {1745-2481}, journal = {Nature Physics}, number = {11}, pages = {1228--1232}, publisher = {Springer Nature}, title = {{Phase behaviours of superionic water at planetary conditions}}, doi = {10.1038/s41567-021-01334-9}, volume = {17}, year = {2021}, } @article{20619, abstract = {The first author’s previous work established Solomon’s WDVV-type relations for Welschinger’s invariant curve counts in real symplectic fourfolds by lifting geometric relations over possibly unorientable morphisms. We apply her framework to obtain WDVV-style relations for the disk invariants of real symplectic sixfolds with some symmetry, in particular confirming Alcolado’s prediction for P^3 and extending it to other spaces. These relations reduce the computation of Welschinger’s invariants of many real symplectic sixfolds to invariants in small degrees and provide lower bounds for counts of real rational curves with positive-dimensional insertions in some cases. In the case of P^3, our lower bounds fit perfectly with Kollár’s vanishing results.}, author = {Chen, Xujia and Zinger, Aleksey}, issn = {1432-1807}, journal = {Mathematische Annalen}, number = {3-4}, pages = {1231--1313}, publisher = {Springer Nature}, title = {{WDVV-type relations for disk Gromov–Witten invariants in dimension 6}}, doi = {10.1007/s00208-020-02130-1}, volume = {379}, year = {2021}, } @article{20622, abstract = {We first recall Solomon’s relations for Welschinger invariants counting real curves in real symplectic fourfolds and the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV)-style relations for Welschinger invariants counting real curves in real symplectic sixfolds with some symmetry. We then explicitly demonstrate that, in some important cases (projective spaces with standard conjugations, real blowups of the projective plane, and two- and threefold products of the one-dimensional projective space with two involutions each), these relations provide complete recursions determining all Welschinger invariants from basic input. We include extensive tables of Welschinger invariants in low degrees obtained from these recursions with Mathematica. These invariants provide lower bounds for counts of real rational curves, including with curve insertions in smooth algebraic threefolds.}, author = {Chen, Xujia and Zinger, Aleksey}, issn = {2154-3321}, journal = {Kyoto Journal of Mathematics}, number = {2}, pages = {339--376}, publisher = {Duke University Press}, title = {{WDVV-type relations for Welschinger's invariants: Applications}}, doi = {10.1215/21562261-2021-0005}, volume = {61}, year = {2021}, } @article{20765, abstract = {

A cascade Suzuki–Miyaura cross-coupling between two non-symmetrical coupling partners gave rise to 9,10-dihydrophenanthrenes with full site-selectivity. The choice of base was critical to facilitate the challenging coupling of the secondary boronate group.

}, author = {Willems, Suzanne and Toupalas, Georgios and Reisenbauer, Julia and Morandi, Bill}, issn = {1364-548X}, journal = {Chemical Communications}, number = {32}, pages = {3909--3912}, publisher = {Royal Society of Chemistry}, title = {{A site-selective and stereospecific cascade Suzuki–Miyaura annulation of alkyl 1,2-bisboronic esters and 2,2′-dihalo 1,1′-biaryls}}, doi = {10.1039/d1cc00648g}, volume = {57}, year = {2021}, } @article{10000, abstract = {Inhibition or targeted deletion of histone deacetylase 3 (HDAC3) is neuroprotective in a variety neurodegenerative conditions, including retinal ganglion cells (RGCs) after acute optic nerve damage. Consistent with this, induced HDAC3 expression in cultured cells shows selective toxicity to neurons. Despite an established role for HDAC3 in neuronal pathology, little is known regarding the mechanism of this pathology.}, author = {Schmitt, Heather M. and Fehrman, Rachel L. and Maes, Margaret E and Yang, Huan and Guo, Lian Wang and Schlamp, Cassandra L. and Pelzel, Heather R. and Nickells, Robert W.}, issn = {1552-5783}, journal = {Investigative Ophthalmology and Visual Science}, number = {10}, publisher = {Association for Research in Vision and Ophthalmology}, title = {{Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression}}, doi = {10.1167/IOVS.62.10.14}, volume = {62}, 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 H 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}, } @article{10005, abstract = {We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.}, author = {Bulíček, Miroslav and Maringová, Erika and Málek, Josef}, issn = {1793-6314}, journal = {Mathematical Models and Methods in Applied Sciences}, keywords = {Nonlinear parabolic systems, implicit constitutive theory, weak solutions, existence, uniqueness}, number = {09}, publisher = {World Scientific Publishing}, title = {{On nonlinear problems of parabolic type with implicit constitutive equations involving flux}}, doi = {10.1142/S0218202521500457}, volume = {31}, year = {2021}, } @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 = {Institute of Science and Technology Austria}, title = {{Curvature driven interface evolution: Uniqueness properties of weak solution concepts}}, doi = {10.15479/at:ista:10007}, year = {2021}, }