@inproceedings{11814, abstract = {Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms maintain the solution to a problem (e.g., a matching) on an evolving input, i.e., a graph where nodes or edges are inserted or deleted over time. They output the value of the solution after each update operation, i.e., continuously. We study (event-level and user-level) differentially private algorithms for graph problems under continual observation, i.e., differentially private dynamic graph algorithms. We present event-level private algorithms for partially dynamic counting-based problems such as triangle count that improve the additive error by a polynomial factor (in the length T of the update sequence) on the state of the art, resulting in the first algorithms with additive error polylogarithmic in T. We also give ε-differentially private and partially dynamic algorithms for minimum spanning tree, minimum cut, densest subgraph, and maximum matching. The additive error of our improved MST algorithm is O(W log^{3/2}T / ε), where W is the maximum weight of any edge, which, as we show, is tight up to a (√{log T} / ε)-factor. For the other problems, we present a partially-dynamic algorithm with multiplicative error (1+β) for any constant β > 0 and additive error O(W log(nW) log(T) / (ε β)). Finally, we show that the additive error for a broad class of dynamic graph algorithms with user-level privacy must be linear in the value of the output solution’s range.}, author = {Fichtenberger, Hendrik and Henzinger, Monika H and Ost, Wolfgang}, booktitle = {29th Annual European Symposium on Algorithms}, isbn = {9783959772044}, issn = {1868-8969}, location = {Lisbon, Portual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Differentially private algorithms for graphs under continual observation}}, doi = {10.4230/LIPIcs.ESA.2021.42}, volume = {204}, year = {2021}, } @article{11886, abstract = {We present a deterministic (1+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the \sf CONGEST model); here 𝑛 is the number of nodes in the network, 𝐷 is its (hop) diameter, and edge weights are positive integers from 1 to poly(𝑛). This is the first nontrivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+𝑜(1))-approximation 𝑂̃ (𝑛√𝐷1/4+𝐷)-time algorithm of Nanongkai [in Proceedings of STOC, 2014, pp. 565--573] by a factor of as large as 𝑛1/8, and (ii) the 𝑂(𝜖−1log𝜖−1)-approximation factor of Lenzen and Patt-Shamir's 𝑂̃ (𝑛1/2+𝜖+𝐷)-time algorithm [in Proceedings of STOC, 2013, pp. 381--390] within the same running time. (Throughout, we use 𝑂̃ (⋅) to hide polylogarithmic factors in 𝑛.) Our running time matches the known time lower bound of Ω(𝑛/log𝑛‾‾‾‾‾‾‾√+𝐷) [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433--456], thus essentially settling the status of this problem which was raised at least a decade ago [M. Elkin, SIGACT News, 35 (2004), pp. 40--57]. It also implies a (2+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [in Proceedings of OPODIS, 2015, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2016, 6]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the “hitting set argument” commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic construction of an (𝑛𝑜(1),𝑜(1))-hop set of size 𝑛1+𝑜(1). We combine these techniques with many distributed algorithmic techniques, some of which are from problems that are not directly related to shortest paths, e.g., ruling sets [A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, SIAM J. Discrete Math., 1 (1988), pp. 434--446], source detection [C. Lenzen and D. Peleg, in Proceedings of PODC, 2013, pp. 375--382], and partial distance estimation [C. Lenzen and B. Patt-Shamir, in Proceedings of PODC, 2015, pp. 153--162]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+𝑜(1))-approximation 𝑛𝑜(1)-time algorithm on congested cliques, and (ii) a (1+𝑜(1))-approximation 𝑛𝑜(1)-pass 𝑛1+𝑜(1)-space streaming algorithm. The first result answers an open problem in [D. Nanongkai, in Proceedings of STOC, 2014, pp. 565--573]. The second result partially answers an open problem raised by McGregor in 2006 [List of Open Problems in Sublinear Algorithms: Problem 14].}, author = {Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {3}, pages = {STOC16--98--STOC16--137}, publisher = {Society for Industrial & Applied Mathematics}, title = {{A deterministic almost-tight distributed algorithm for approximating single-source shortest paths}}, doi = {10.1137/16m1097808}, volume = {50}, year = {2021}, } @inproceedings{11919, abstract = {Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse skeleton of the given graph that roughly preserves the shortest paths information. Spanners and emulators serve this purpose. Unfortunately, very little is known about dynamically maintaining sparse spanners and emulators as the graph is modified by a sequence of edge insertions and deletions. This paper develops fast dynamic algorithms for spanner and emulator maintenance and provides evidence from fine-grained complexity that these algorithms are tight. For unweighted undirected m-edge n-node graphs we obtain the following results. Under the popular OMv conjecture, there can be no decremental or incremental algorithm that maintains an n1+o(1) edge (purely additive) +nδ-emulator for any δ < 1/2 with arbitrary polynomial preprocessing time and total update time m1+o(1). Also, under the Combinatorial k-Clique hypothesis, any fully dynamic combinatorial algorithm that maintains an n1+o(1) edge (1 + ∊, no(1))-spanner or emulator for small ∊ must either have preprocessing time mn1–o(1) or amortized update time m1–o(1). Both of our conditional lower bounds are tight. As the above fully dynamic lower bound only applies to combinatorial algorithms, we also develop an algebraic spanner algorithm that improves over the m1–o(1) update time for dense graphs. For any constant ∊ ∊ (0, 1], there is a fully dynamic algorithm with worst-case update time O(n1.529) that whp maintains an n1+o(1) edge (1 + ∊, no(1))-spanner. Our new algebraic techniques allow us to also obtain a new fully dynamic algorithm for All-Pairs Shortest Paths (APSP) that can perform both edge updates and can report shortest paths in worst-case time O(n1.9), which are correct whp. This is the first path-reporting fully dynamic APSP algorithm with a truly subquadratic query time that beats O(n2.5) update time. It works against an oblivious adversary. Finally, we give two applications of our new dynamic spanner algorithms: (1) a fully dynamic (1 + ∊)-approximate APSP algorithm with update time O(n1.529) that can report approximate shortest paths in n1+o(1) time per query; previous subquadratic update/query algorithms could only report the distance, but not obtain the paths; (2) a fully dynamic algorithm for near-2-approximate Steiner tree maintenance with both terminal and edge updates.}, author = {Bergamaschi, Thiago and Henzinger, Monika H and Gutenberg, Maximilian Probst and Williams, Virginia Vassilevska and Wein, Nicole}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {1836--1855}, publisher = {Society for Industrial and Applied Mathematics}, title = {{New techniques and fine-grained hardness for dynamic near-additive spanners}}, doi = {10.1137/1.9781611976465.110}, year = {2021}, } @inproceedings{11920, abstract = {In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal min(O(log n), f) approximation factor. (Throughout, m, n, f, and C are parameters denoting the maximum number of sets, number of elements, frequency, and the cost range.) In the high-frequency range, when f = Ω(log n), this was achieved by a deterministic O(log n)-approximation algorithm with O(f log n) amortized update time [Gupta et al. STOC'17]. In the low-frequency range, the line of work by Gupta et al. [STOC'17], Abboud et al. [STOC'19], and Bhattacharya et al. [ICALP'15, IPCO'17, FOCS'19] led to a deterministic (1 + ∊) f-approximation algorithm with O(f log(Cn)/∊2) amortized update time. In this paper we improve the latter update time and provide the first bounds that subsume (and sometimes improve) the state-of-the-art dynamic vertex cover algorithms. We obtain: (1) (1 + ∊) f-approximation ratio in O(f log2(Cn)/∊3) worst-case update time: No non-trivial worst-case update time was previously known for dynamic set cover. Our bound subsumes and improves by a logarithmic factor the O(log3 n/poly(∊)) worst-case update time for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1) by Bhattacharya et al. [SODA'17]. (2) (1 + ∊) f-approximation ratio in O ((f2/∊3) + (f/∊2) log C) amortized update time: This result improves the previous O(f log (Cn)/∊2) update time bound for most values of f in the low-frequency range, i.e. whenever f = o(log n). It is the first that is independent of m and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [SODA'19] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). These results are achieved by leveraging the approximate complementary slackness and background schedulers techniques. These techniques were used in the local update scheme for dynamic vertex cover. Our main technical contribution is to adapt these techniques within the global update scheme of Bhattacharya et al. [FOCS'19] for the dynamic set cover problem.}, author = {Bhattacharya, Sayan and Henzinger, Monika H and Nanongkai, Danupon and Wu, Xiaowei}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {2537--2549}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Dynamic set cover: Improved amortized and worst-case update time}}, doi = {10.1137/1.9781611976465.150}, year = {2021}, } @inproceedings{11923, abstract = {We consider the following online optimization problem. We are given a graph G and each vertex of the graph is assigned to one of ℓ servers, where servers have capacity k and we assume that the graph has ℓ · k vertices. Initially, G does not contain any edges and then the edges of G are revealed one-by-one. The goal is to design an online algorithm ONL, which always places the connected components induced by the revealed edges on the same server and never exceeds the server capacities by more than ∊k for constant ∊ > 0. Whenever ONL learns about a new edge, the algorithm is allowed to move vertices from one server to another. Its objective is to minimize the number of vertex moves. More specifically, ONL should minimize the competitive ratio: the total cost ONL incurs compared to an optimal offline algorithm OPT. The problem was recently introduced by Henzinger et al. (SIGMETRICS'2019) and is related to classic online problems such as online paging and scheduling. It finds applications in the context of resource allocation in the cloud and for optimizing distributed data structures such as union–find data structures. Our main contribution is a polynomial-time randomized algorithm, that is asymptotically optimal: we derive an upper bound of O(log ℓ + log k) on its competitive ratio and show that no randomized online algorithm can achieve a competitive ratio of less than Ω(log ℓ + log k). We also settle the open problem of the achievable competitive ratio by deterministic online algorithms, by deriving a competitive ratio of Θ(ℓ log k); to this end, we present an improved lower bound as well as a deterministic polynomial-time online algorithm. Our algorithms rely on a novel technique which combines efficient integer programming with a combinatorial approach for maintaining ILP solutions. More precisely, we use an ILP to assign the connected components induced by the revealed edges to the servers; this is similar to existing approximation schemes for scheduling algorithms. However, we cannot obtain our competitive ratios if we run the ILP after each edge insertion. Instead, we identify certain types of edge insertions, after which we can manually obtain an optimal ILP solution at zero cost without resolving the ILP. We believe this technique is of independent interest and will find further applications in the future.}, author = {Henzinger, Monika H and Neumann, Stefan and Räcke, Harald and Schmid, Stefan}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {2799--2818}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Tight bounds for online graph partitioning}}, doi = {10.1137/1.9781611976465.166}, year = {2021}, } @inproceedings{11931, abstract = {Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications where data is constantly changing and evolving. Driven by this, we study the metric k-center clustering problem in the fully dynamic setting, where the goal is to efficiently maintain a clustering while supporting an intermixed sequence of insertions and deletions of points. This model also supports queries of the form (1) report whether a given point is a center or (2) determine the cluster a point is assigned to. We present a deterministic dynamic algorithm for the k-center clustering problem that provably achieves a (2 + ∊)-approximation in nearly logarithmic update and query time, if the underlying metric has bounded doubling dimension, its aspect ratio is bounded by a polynomial and ∊ is a constant. An important feature of our algorithm is that the update and query times are independent of k. We confirm the practical relevance of this feature via an extensive experimental study which shows that for large values of k, our algorithmic construction outperforms the state-of-the-art algorithm in terms of solution quality and running time.}, author = {Goranci, Gramoz and Henzinger, Monika H and Leniowski, Dariusz and Schulz, Christian and Svozil, Alexander}, booktitle = {2021 Proceedings of the Workshop on Algorithm Engineering and Experiments}, issn = {2164-0300}, location = {Alexandria, VA, United States}, pages = {143 --153}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Fully dynamic k-center clustering in low dimensional metrics}}, doi = {10.1137/1.9781611976472.11}, year = {2021}, } @article{11956, abstract = {Controlling the selectivity of a chemical reaction with external stimuli is common in thermal processes, but rare in visible-light photocatalysis. Here we show that the redox potential of a carbon nitride photocatalyst (CN-OA-m) can be tuned by changing the irradiation wavelength to generate electron holes with different oxidation potentials. This tuning was the key to realizing photo-chemo-enzymatic cascades that give either the (S)- or the (R)-enantiomer of phenylethanol. In combination with an unspecific peroxygenase from Agrocybe aegerita, green light irradiation of CN-OA-m led to the enantioselective hydroxylation of ethylbenzene to (R)-1-phenylethanol (99 % ee). In contrast, blue light irradiation triggered the photocatalytic oxidation of ethylbenzene to acetophenone, which in turn was enantioselectively reduced with an alcohol dehydrogenase from Rhodococcus ruber to form (S)-1-phenylethanol (93 % ee).}, author = {Schmermund, Luca and Reischauer, Susanne and Bierbaumer, Sarah and Winkler, Christoph K. and Diaz‐Rodriguez, Alba and Edwards, Lee J. and Kara, Selin and Mielke, Tamara and Cartwright, Jared and Grogan, Gideon and Pieber, Bartholomäus and Kroutil, Wolfgang}, issn = {1521-3773}, journal = {Angewandte Chemie International Edition}, number = {13}, pages = {6965--6969}, publisher = {Wiley}, title = {{Chromoselective photocatalysis enables stereocomplementary biocatalytic pathways}}, doi = {10.1002/anie.202100164}, volume = {60}, year = {2021}, } @article{11965, abstract = {Metallaphotocatalytic cross-coupling reactions are typically carried out by combining homogeneous or heterogeneous photocatalysts with a soluble nickel complex. Previous attempts to realize recyclable catalytic systems use immobilized iridium complexes to harvest light. We present bifunctional materials based on semiconductors for metallaphotocatalytic C−S cross-coupling reactions that can be reused without losing their catalytic activity. Key to the success is the permanent immobilization of a nickel complex on the surface of a heterogeneous semiconductor through phosphonic acid anchors. The optimized catalyst harvests a broad range of the visible light spectrum and requires a nickel loading of only ∼0.1 mol %.}, author = {Reischauer, Susanne and Pieber, Bartholomäus}, issn = {2367-0932}, journal = {ChemPhotoChem}, number = {8}, pages = {716--720}, publisher = {Wiley}, title = {{Recyclable, bifunctional metallaphotocatalysts for C−S cross‐coupling reactions}}, doi = {10.1002/cptc.202100062}, volume = {5}, year = {2021}, } @article{11972, abstract = {Carbon dots have been previosly immobilized on titanium dioxide to generate photocatalysts for pollutant degradation and water splitting. Here we demonstrate that these nanocomposites are valuable photocatalysts for metallaphotocatalytic carbon–heteroatom cross-couplings. These sustainable materials show a large applicability, high photostability, excellent reusability, and broadly absorb across the visible-light spectrum.}, author = {Zhao, Zhouxiang and Reischauer, Susanne and Pieber, Bartholomäus and Delbianco, Martina}, issn = {1463-9270}, journal = {Green Chemistry}, number = {12}, pages = {4524--4530}, publisher = {Royal Society of Chemistry}, title = {{Carbon dot/TiO₂ nanocomposites as photocatalysts for metallaphotocatalytic carbon-heteroatom cross-couplings}}, doi = {10.1039/d1gc01284c}, volume = {23}, year = {2021}, } @article{11974, abstract = {Visible light photocatalysis has become a powerful tool in organic synthesis that uses photons as traceless, sustainable reagents. Most of the activities in the field focus on the development of new reactions via common photoredox cycles, but recently a number of exciting new concepts and strategies entered less charted territories. We survey approaches that enable the use of longer wavelengths and show that the wavelength and intensity of photons are import parameters that enable tuning of the reactivity of a photocatalyst to control or change the selectivity of chemical reactions. In addition, we discuss recent efforts to substitute strong reductants, such as elemental lithium and sodium, by light and technological advances in the field.}, author = {Reischauer, Susanne and Pieber, Bartholomäus}, issn = {2589-0042}, journal = {iScience}, number = {3}, publisher = {Elsevier}, title = {{Emerging concepts in photocatalytic organic synthesis}}, doi = {10.1016/j.isci.2021.102209}, volume = {24}, year = {2021}, } @article{11981, abstract = {The cleavage of benzyl ethers by catalytic hydrogenolysis or Birch reduction suffers from poor functional group compatibility and limits their use as a protecting group. The visible-light-mediated debenzylation disclosed here renders benzyl ethers temporary protective groups, enabling new orthogonal protection strategies. Using 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) as a stoichiometric or catalytic photooxidant, benzyl ethers can be cleaved in the presence of azides, alkenes, and alkynes. The reaction time can be reduced from hours to minutes in continuous flow.}, author = {Cavedon, Cristian and Sletten, Eric T. and Madani, Amiera and Niemeyer, Olaf and Seeberger, Peter H. and Pieber, Bartholomäus}, issn = {1523-7052}, journal = {Organic Letters}, number = {2}, pages = {514--518}, publisher = {American Chemical Society}, title = {{Visible-light-mediated oxidative debenzylation enables the use of benzyl ethers as temporary protecting groups}}, doi = {10.1021/acs.orglett.0c04026}, volume = {23}, year = {2021}, } @unpublished{12068, abstract = {Metallaphotocatalysis typically requires a photocatalyst to harness the energy of visible-light and transfer it to a transition metal catalyst to trigger chemical reactions. The most prominent example is the merger of photo- and nickel catalysis that unlocked various cross-couplings. However, the high reactivity of excited photocatalyst can lead to unwanted side reactions thus limiting this approach. Here we show that a bipyridine ligand that is subtly decorated with two carbazole groups forms a nickel complex that absorbs visible-light and promotes several carbon–heteroatom cross-couplings in the absence of an exogenous photocatalysts. The ligand can be polymerized in a simple one-step procedure to afford a porous organic polymer that can be used for heterogeneous nickel catalysis in the same reactions. The material can be easily recovered and reused multiple times maintaining high catalytic activity and selectivity.}, author = {Cavedon, Cristian and Gisbertz, Sebastian and Vogl, Sarah and Richter, Noah and Schrottke, Stefanie and Teutloff, Christian and Seeberger, Peter H. and Thomas, Arne and Pieber, Bartholomäus}, publisher = {ChemRxiv}, title = {{Photocatalyst-free, visible-light-mediated nickel catalyzed carbon–heteroatom cross-couplings}}, doi = {10.26434/chemrxiv-2021-kt2wr}, year = {2021}, } @unpublished{12070, abstract = {Controlling the selectivity of a chemical reaction with external stimuli is common in thermal processes, but rare in visible-light photocatalysis. Here we show that the redox potential of a carbon nitride photocatalyst (CN-OA-m) can be tuned by changing the irradiation wavelength to generate electron holes with different oxidation potentials. This tuning was the key to realizing photo-chemo-enzymatic cascades that give either the (S)- or the (R)-enantiomer of phenylethanol. In combination with an unspecific peroxygenase from Agrocybe aegerita, green light irradiation of CN-OA-m led to the enantioselective hydroxylation of ethylbenzene to (R)-1-phenylethanol (99% ee). In contrast, blue light irradiation triggered the photocatalytic oxidation of ethylbenzene to acetophenone, which in turn was enantioselectively reduced with an alcohol dehydrogenase from Rhodococcus ruber to form (S)-1-phenylethanol (93% ee).}, author = {Schmermund, Luca and Reischauer, Susanne and Bierbaumer, Sarah and Winkler, Christoph and Diaz-Rodriguez, Alba and Edwards, Lee J. and Kara, Selin and Mielke, Tamara and Cartwright, Jared and Grogan, Gideon and Pieber, Bartholomäus and Kroutil, Wolfgang}, publisher = {ChemRxiv}, title = {{Switching between enantiomers by combining chromoselective photocatalysis and biocatalysis}}, doi = {10.26434/chemrxiv.13521527}, year = {2021}, } @article{12071, abstract = {Despite many efforts to rationalize the strongly correlated electronic ground states in doped Mott insulators, the nature of the doping-induced insulator-to-metal transition is still a subject under intensive investigation. Here, we probe the nanoscale electronic structure of the Mott insulator Sr₂IrO₄δ with low-temperature scanning tunneling microscopy and find an enhanced local density of states (LDOS) inside the Mott gap at the location of individual defects which we interpret as defects at apical oxygen sites. A chiral behavior in the topography for those defects has been observed. We also visualize the local enhanced conductance arising from the overlapping of defect states which induces finite LDOS inside of the Mott gap. By combining these findings with the typical spatial extension of isolated defects of about 2 nm, our results indicate that the insulator-to-metal transition in Sr₂IrO₄−δ could be percolative in nature.}, author = {Sun, Zhixiang and Guevara, Jose M. and Sykora, Steffen and Paerschke, Ekaterina and Manna, Kaustuv and Maljuk, Andrey and Wurmehl, Sabine and van den Brink, Jeroen and Büchner, Bernd and Hess, Christian}, issn = {2643-1564}, journal = {Physical Review Research}, number = {2}, publisher = {American Physical Society}, title = {{Evidence for a percolative Mott insulator-metal transition in doped Sr₂IrO₄}}, doi = {10.1103/physrevresearch.3.023075}, volume = {3}, year = {2021}, } @unpublished{12076, abstract = {We find an asymptotic formula for the number of primitive vectors $(z_1,\ldots,z_4)\in (\mathbb{Z}_{\neq 0})^4$ such that $z_1,\ldots, z_4$ are all squareful and bounded by $B$, and $z_1+\cdots + z_4 = 0$. Our result agrees in the power of $B$ and $\log B$ with the Campana-Manin conjecture of Pieropan, Smeets, Tanimoto and V\'{a}rilly-Alvarado.}, author = {Shute, Alec L}, booktitle = {arXiv}, title = {{Sums of four squareful numbers}}, doi = {10.48550/arXiv.2104.06966}, year = {2021}, } @unpublished{12077, abstract = {We compare the Manin-type conjecture for Campana points recently formulated by Pieropan, Smeets, Tanimoto and V\'{a}rilly-Alvarado with an alternative prediction of Browning and Van Valckenborgh in the special case of the orbifold $(\mathbb{P}^1,D)$, where $D =\frac{1}{2}[0]+\frac{1}{2}[1]+\frac{1}{2}[\infty]$. We find that the two predicted leading constants do not agree, and we discuss whether thin sets could explain this discrepancy. Motivated by this, we provide a counterexample to the Manin-type conjecture for Campana points, by considering orbifolds corresponding to squareful values of binary quadratic forms.}, author = {Shute, Alec L}, booktitle = {arXiv}, title = {{On the leading constant in the Manin-type conjecture for Campana points}}, doi = {10.48550/arXiv.2104.14946}, year = {2021}, } @article{12188, abstract = {Molecular mechanisms enabling the switching and maintenance of epigenetic states are not fully understood. Distinct histone modifications are often associated with ON/OFF epigenetic states, but how these states are stably maintained through DNA replication, yet in certain situations switch from one to another remains unclear. Here, we address this problem through identification of Arabidopsis INCURVATA11 (ICU11) as a Polycomb Repressive Complex 2 accessory protein. ICU11 robustly immunoprecipitated in vivo with PRC2 core components and the accessory proteins, EMBRYONIC FLOWER 1 (EMF1), LIKE HETEROCHROMATIN PROTEIN1 (LHP1), and TELOMERE_REPEAT_BINDING FACTORS (TRBs). ICU11 encodes a 2-oxoglutarate-dependent dioxygenase, an activity associated with histone demethylation in other organisms, and mutant plants show defects in multiple aspects of the Arabidopsis epigenome. To investigate its primary molecular function we identified the Arabidopsis FLOWERING LOCUS C (FLC) as a direct target and found icu11 disrupted the cold-induced, Polycomb-mediated silencing underlying vernalization. icu11 prevented reduction in H3K36me3 levels normally seen during the early cold phase, supporting a role for ICU11 in H3K36me3 demethylation. This was coincident with an attenuation of H3K27me3 at the internal nucleation site in FLC, and reduction in H3K27me3 levels across the body of the gene after plants were returned to the warm. Thus, ICU11 is required for the cold-induced epigenetic switching between the mutually exclusive chromatin states at FLC, from the active H3K36me3 state to the silenced H3K27me3 state. These data support the importance of physical coupling of histone modification activities to promote epigenetic switching between opposing chromatin states.}, author = {Bloomer, Rebecca H. and Hutchison, Claire E. and Bäurle, Isabel and Walker, James and Fang, Xiaofeng and Perera, Pumi and Velanis, Christos N. and Gümüs, Serin and Spanos, Christos and Rappsilber, Juri and Feng, Xiaoqi and Goodrich, Justin and Dean, Caroline}, issn = {0027-8424}, journal = {Proceedings of the National Academy of Sciences}, keywords = {Multidisciplinary}, number = {28}, pages = {16660--16666}, publisher = {Proceedings of the National Academy of Sciences}, title = {{The Arabidopsis epigenetic regulator ICU11 as an accessory protein of polycomb repressive complex 2}}, doi = {10.1073/pnas.1920621117}, volume = {117}, year = {2020}, } @article{12189, abstract = {Meiotic crossovers (COs) are important for reshuffling genetic information between homologous chromosomes and they are essential for their correct segregation. COs are unevenly distributed along chromosomes and the underlying mechanisms controlling CO localization are not well understood. We previously showed that meiotic COs are mis-localized in the absence of AXR1, an enzyme involved in the neddylation/rubylation protein modification pathway in Arabidopsis thaliana. Here, we report that in axr1-/-, male meiocytes show a strong defect in chromosome pairing whereas the formation of the telomere bouquet is not affected. COs are also redistributed towards subtelomeric chromosomal ends where they frequently form clusters, in contrast to large central regions depleted in recombination. The CO suppressed regions correlate with DNA hypermethylation of transposable elements (TEs) in the CHH context in axr1-/- meiocytes. Through examining somatic methylomes, we found axr1-/- affects DNA methylation in a plant, causing hypermethylation in all sequence contexts (CG, CHG and CHH) in TEs. Impairment of the main pathways involved in DNA methylation is epistatic over axr1-/- for DNA methylation in somatic cells but does not restore regular chromosome segregation during meiosis. Collectively, our findings reveal that the neddylation pathway not only regulates hormonal perception and CO distribution but is also, directly or indirectly, a major limiting pathway of TE DNA methylation in somatic cells.}, author = {Christophorou, Nicolas and She, Wenjing and Long, Jincheng and Hurel, Aurélie and Beaubiat, Sébastien and Idir, Yassir and Tagliaro-Jahns, Marina and Chambon, Aurélie and Solier, Victor and Vezon, Daniel and Grelon, Mathilde and Feng, Xiaoqi and Bouché, Nicolas and Mézard, Christine}, issn = {1553-7404}, journal = {PLOS Genetics}, keywords = {Cancer Research, Genetics (clinical), Genetics, Molecular Biology, Ecology, Evolution, Behavior and Systematics}, number = {6}, publisher = {Public Library of Science (PLoS)}, title = {{AXR1 affects DNA methylation independently of its role in regulating meiotic crossover localization}}, doi = {10.1371/journal.pgen.1008894}, volume = {16}, year = {2020}, } @article{12310, abstract = {Let be a sequence of points on an elliptic curve defined over a number field K. In this paper, we study the denominators of the x-coordinates of this sequence. We prove that, if Q is a torsion point of prime order, then for n large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and a Lang-Trotter conjecture. Indeed, given two points P and Q on the elliptic curve, we prove a lower bound for the number of primes p such that P is in the orbit of Q modulo p.}, author = {Verzobio, Matteo}, issn = {0022-314X}, journal = {Journal of Number Theory}, keywords = {Algebra and Number Theory}, number = {4}, pages = {378--390}, publisher = {Elsevier}, title = {{Primitive divisors of sequences associated to elliptic curves}}, doi = {10.1016/j.jnt.2019.09.003}, volume = {209}, year = {2020}, } @article{12594, abstract = {Information about end-of-winter spatial distribution of snow depth is important for seasonal forecasts of spring/summer streamflow in high-mountain regions. Nevertheless, such information typically relies upon extrapolation from a sparse network of observations at low elevations. Here, we test the potential of high-resolution snow depth data derived from optical stereophotogrammetry of Pléiades satellites for improving the representation of snow depth initial conditions (SDICs) in a glacio-hydrological model and assess potential improvements in the skill of snowmelt and streamflow simulations in a high-elevation Andean catchment. We calibrate model parameters controlling glacier mass balance and snow cover evolution using ground-based and satellite observations, and consider the relative importance of accurate estimates of SDICs compared to model parameters and forcings. We find that Pléiades SDICs improve the simulation of snow-covered area, glacier mass balance, and monthly streamflow compared to alternative SDICs based upon extrapolation of meteorological variables or statistical methods to estimate SDICs based upon topography. Model simulations are found to be sensitive to SDICs in the early spring (up to 48% variability in modeled streamflow compared to the best estimate model), and to temperature gradients in all months that control albedo and melt rates over a large elevation range (>2,400 m). As such, appropriately characterizing the distribution of total snow volume with elevation is important for reproducing total streamflow and the proportions of snowmelt. Therefore, optical stereo-photogrammetry offers an advantage for obtaining SDICs that aid both the timing and magnitude of streamflow simulations, process representation (e.g., snow cover evolution) and has the potential for large spatial domains.}, author = {Shaw, Thomas E. and Caro, Alexis and Mendoza, Pablo and Ayala, Álvaro and Pellicciotti, Francesca and Gascoin, Simon and McPhee, James}, issn = {1944-7973}, journal = {Water Resources Research}, keywords = {Water Science and Technology}, number = {8}, publisher = {American Geophysical Union}, title = {{The utility of optical satellite winter snow depths for initializing a glacio‐hydrological model of a High‐Elevation, Andean catchment}}, doi = {10.1029/2020wr027188}, volume = {56}, year = {2020}, }