@article{11704, abstract = {In Fall 2020, several European countries reported rapid increases in COVID-19 cases along with growing estimates of the effective reproduction rates. Such an acceleration in epidemic spread is usually attributed to time-dependent effects, e.g. human travel, seasonal behavioral changes, mutations of the pathogen etc. In this case however the acceleration occurred when counter measures such as testing and contact tracing exceeded their capacity limit. Considering Austria as an example, here we show that this dynamics can be captured by a time-independent, i.e. autonomous, compartmental model that incorporates these capacity limits. In this model, the epidemic acceleration coincides with the exhaustion of mitigation efforts, resulting in an increasing fraction of undetected cases that drive the effective reproduction rate progressively higher. We demonstrate that standard models which does not include this effect necessarily result in a systematic underestimation of the effective reproduction rate.}, author = {Budanur, Nazmi B and Hof, Björn}, issn = {1932-6203}, journal = {PLoS ONE}, number = {7}, publisher = {Public Library of Science}, title = {{An autonomous compartmental model for accelerating epidemics}}, doi = {10.1371/journal.pone.0269975}, volume = {17}, year = {2022}, } @article{11705, abstract = {The broad implementation of thermoelectricity requires high-performance and low-cost materials. One possibility is employing surfactant-free solution synthesis to produce nanopowders. We propose the strategy of functionalizing “naked” particles’ surface by inorganic molecules to control the nanostructure and, consequently, thermoelectric performance. In particular, we use bismuth thiolates to functionalize surfactant-free SnTe particles’ surfaces. Upon thermal processing, bismuth thiolates decomposition renders SnTe-Bi2S3 nanocomposites with synergistic functions: 1) carrier concentration optimization by Bi doping; 2) Seebeck coefficient enhancement and bipolar effect suppression by energy filtering; and 3) lattice thermal conductivity reduction by small grain domains, grain boundaries and nanostructuration. Overall, the SnTe-Bi2S3 nanocomposites exhibit peak z T up to 1.3 at 873 K and an average z T of ≈0.6 at 300–873 K, which is among the highest reported for solution-processed SnTe.}, author = {Chang, Cheng and Liu, Yu and Lee, Seungho and Spadaro, Maria and Koskela, Kristopher M. and Kleinhanns, Tobias and Costanzo, Tommaso and Arbiol, Jordi and Brutchey, Richard L. and Ibáñez, Maria}, issn = {1521-3773}, journal = {Angewandte Chemie - International Edition}, number = {35}, publisher = {Wiley}, title = {{Surface functionalization of surfactant-free particles: A strategy to tailor the properties of nanocomposites for enhanced thermoelectric performance}}, doi = {10.1002/anie.202207002}, volume = {61}, year = {2022}, } @inproceedings{11707, abstract = {In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to “patch a hole.” We explore how mendability is connected to the existence of efficient algorithms, especially in distributed, parallel, and fault-tolerant settings. It is easy to see that O(1)-mendable problems are also solvable in O(log∗n) rounds in the LOCAL model of distributed computing. One of the surprises is that in paths and cycles, a converse also holds in the following sense: if a problem Π can be solved in O(log∗n), there is always a restriction Π′⊆Π that is still efficiently solvable but that is also O(1)-mendable. We also explore the structure of the landscape of mendability. For example, we show that in trees, the mending radius of any locally checkable problem is O(1), Θ(logn), or Θ(n), while in general graphs the structure is much more diverse.}, author = {Balliu, Alkida and Hirvonen, Juho and Melnyk, Darya and Olivetti, Dennis and Rybicki, Joel and Suomela, Jukka}, booktitle = {International Colloquium on Structural Information and Communication Complexity}, editor = {Parter, Merav}, isbn = {9783031099922}, issn = {1611-3349}, location = {Paderborn, Germany}, pages = {1--20}, publisher = {Springer Nature}, title = {{Local mending}}, doi = {10.1007/978-3-031-09993-9_1}, volume = {13298}, year = {2022}, } @misc{11711, abstract = {Codes and data for reproducing the results of N. B. Budanur and B. Hof "An autonomous compartmental model for accelerating epidemics"}, author = {Budanur, Nazmi B}, publisher = {Zenodo}, title = {{burakbudanur/autoacc-public}}, doi = {10.5281/ZENODO.6802720}, year = {2022}, } @article{11713, abstract = {Objective: MazF is a sequence-specific endoribonuclease-toxin of the MazEF toxin–antitoxin system. MazF cleaves single-stranded ribonucleic acid (RNA) regions at adenine–cytosine–adenine (ACA) sequences in the bacterium Escherichia coli. The MazEF system has been used in various biotechnology and synthetic biology applications. In this study, we infer how ectopic mazF overexpression affects production of heterologous proteins. To this end, we quantified the levels of fluorescent proteins expressed in E. coli from reporters translated from the ACA-containing or ACA-less messenger RNAs (mRNAs). Additionally, we addressed the impact of the 5′-untranslated region of these reporter mRNAs under the same conditions by comparing expression from mRNAs that comprise (canonical mRNA) or lack this region (leaderless mRNA). Results: Flow cytometry analysis indicates that during mazF overexpression, fluorescent proteins are translated from the canonical as well as leaderless mRNAs. Our analysis further indicates that longer mazF overexpression generally increases the concentration of fluorescent proteins translated from ACA-less mRNAs, however it also substantially increases bacterial population heterogeneity. Finally, our results suggest that the strength and duration of mazF overexpression should be optimized for each experimental setup, to maximize the heterologous protein production and minimize the amount of phenotypic heterogeneity in bacterial populations, which is unfavorable in biotechnological processes.}, author = {Nikolic, Nela and Sauert, Martina and Albanese, Tanino G. and Moll, Isabella}, issn = {1756-0500}, journal = {BMC Research Notes}, keywords = {General Biochemistry, Genetics and Molecular Biology, General Medicine}, publisher = {Springer Nature}, title = {{Quantifying heterologous gene expression during ectopic MazF production in Escherichia coli}}, doi = {10.1186/s13104-022-06061-9}, volume = {15}, year = {2022}, } @article{11717, abstract = {We study rigidity of rational maps that come from Newton's root finding method for polynomials of arbitrary degrees. We establish dynamical rigidity of these maps: each point in the Julia set of a Newton map is either rigid (i.e. its orbit can be distinguished in combinatorial terms from all other orbits), or the orbit of this point eventually lands in the filled-in Julia set of a polynomial-like restriction of the original map. As a corollary, we show that the Julia sets of Newton maps in many non-trivial cases are locally connected; in particular, every cubic Newton map without Siegel points has locally connected Julia set. In the parameter space of Newton maps of arbitrary degree we obtain the following rigidity result: any two combinatorially equivalent Newton maps are quasiconformally conjugate in a neighborhood of their Julia sets provided that they either non-renormalizable, or they are both renormalizable “in the same way”. Our main tool is a generalized renormalization concept called “complex box mappings” for which we extend a dynamical rigidity result by Kozlovski and van Strien so as to include irrationally indifferent and renormalizable situations.}, author = {Drach, Kostiantyn and Schleicher, Dierk}, issn = {0001-8708}, journal = {Advances in Mathematics}, keywords = {General Mathematics}, number = {Part A}, publisher = {Elsevier}, title = {{Rigidity of Newton dynamics}}, doi = {10.1016/j.aim.2022.108591}, volume = {408}, year = {2022}, } @article{11723, abstract = {Plant cell growth responds rapidly to various stimuli, adapting architecture to environmental changes. Two major endogenous signals regulating growth are the phytohormone auxin and the secreted peptides rapid alkalinization factors (RALFs). Both trigger very rapid cellular responses and also exert long-term effects [Du et al., Annu. Rev. Plant Biol. 71, 379–402 (2020); Blackburn et al., Plant Physiol. 182, 1657–1666 (2020)]. However, the way, in which these distinct signaling pathways converge to regulate growth, remains unknown. Here, using vertical confocal microscopy combined with a microfluidic chip, we addressed the mechanism of RALF action on growth. We observed correlation between RALF1-induced rapid Arabidopsis thaliana root growth inhibition and apoplast alkalinization during the initial phase of the response, and revealed that RALF1 reversibly inhibits primary root growth through apoplast alkalinization faster than within 1 min. This rapid apoplast alkalinization was the result of RALF1-induced net H+ influx and was mediated by the receptor FERONIA (FER). Furthermore, we investigated the cross-talk between RALF1 and the auxin signaling pathways during root growth regulation. The results showed that RALF-FER signaling triggered auxin signaling with a delay of approximately 1 h by up-regulating auxin biosynthesis, thus contributing to sustained RALF1-induced growth inhibition. This biphasic RALF1 action on growth allows plants to respond rapidly to environmental stimuli and also reprogram growth and development in the long term.}, author = {Li, Lanxin and Chen, Huihuang and Alotaibi, Saqer S. and Pěnčík, Aleš and Adamowski, Maciek and Novák, Ondřej and Friml, Jiří}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, keywords = {Multidisciplinary}, number = {31}, publisher = {National Academy of Sciences}, title = {{RALF1 peptide triggers biphasic root growth inhibition upstream of auxin biosynthesis}}, doi = {10.1073/pnas.2121058119}, volume = {119}, year = {2022}, } @article{11733, abstract = {Genetically informed, deep-phenotyped biobanks are an important research resource and it is imperative that the most powerful, versatile, and efficient analysis approaches are used. Here, we apply our recently developed Bayesian grouped mixture of regressions model (GMRM) in the UK and Estonian Biobanks and obtain the highest genomic prediction accuracy reported to date across 21 heritable traits. When compared to other approaches, GMRM accuracy was greater than annotation prediction models run in the LDAK or LDPred-funct software by 15% (SE 7%) and 14% (SE 2%), respectively, and was 18% (SE 3%) greater than a baseline BayesR model without single-nucleotide polymorphism (SNP) markers grouped into minor allele frequency–linkage disequilibrium (MAF-LD) annotation categories. For height, the prediction accuracy R2 was 47% in a UK Biobank holdout sample, which was 76% of the estimated h2SNP. We then extend our GMRM prediction model to provide mixed-linear model association (MLMA) SNP marker estimates for genome-wide association (GWAS) discovery, which increased the independent loci detected to 16,162 in unrelated UK Biobank individuals, compared to 10,550 from BoltLMM and 10,095 from Regenie, a 62 and 65% increase, respectively. The average χ2 value of the leading markers increased by 15.24 (SE 0.41) for every 1% increase in prediction accuracy gained over a baseline BayesR model across the traits. Thus, we show that modeling genetic associations accounting for MAF and LD differences among SNP markers, and incorporating prior knowledge of genomic function, is important for both genomic prediction and discovery in large-scale individual-level studies.}, author = {Orliac, Etienne J. and Trejo Banos, Daniel and Ojavee, Sven E. and Läll, Kristi and Mägi, Reedik and Visscher, Peter M. and Robinson, Matthew Richard}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {31}, publisher = {National Academy of Sciences}, title = {{Improving GWAS discovery and genomic prediction accuracy in biobank data}}, doi = {10.1073/pnas.2121279119}, volume = {119}, year = {2022}, } @article{11734, abstract = {Mineral nutrition is one of the key environmental factors determining plant development and growth. Nitrate is the major form of macronutrient nitrogen that plants take up from the soil. Fluctuating availability or deficiency of this element severely limits plant growth and negatively affects crop production in the agricultural system. To cope with the heterogeneity of nitrate distribution in soil, plants evolved a complex regulatory mechanism that allows rapid adjustment of physiological and developmental processes to the status of this nutrient. The root, as a major exploitation organ that controls the uptake of nitrate to the plant body, acts as a regulatory hub that, according to nitrate availability, coordinates the growth and development of other plant organs. Here, we identified a regulatory framework, where cytokinin response factors (CRFs) play a central role as a molecular readout of the nitrate status in roots to guide shoot adaptive developmental response. We show that nitrate-driven activation of NLP7, a master regulator of nitrate response in plants, fine tunes biosynthesis of cytokinin in roots and its translocation to shoots where it enhances expression of CRFs. CRFs, through direct transcriptional regulation of PIN auxin transporters, promote the flow of auxin and thereby stimulate the development of shoot organs.}, author = {Abualia, Rashed and Ötvös, Krisztina and Novák, Ondřej and Bouguyon, Eleonore and Domanegg, Kevin and Krapp, Anne and Nacry, Philip and Gojon, Alain and Lacombe, Benoit and Benková, Eva}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {31}, publisher = {National Academy of Sciences}, title = {{Molecular framework integrating nitrate sensing in root and auxin-guided shoot adaptive responses}}, doi = {10.1073/pnas.2122460119}, volume = {119}, year = {2022}, } @article{11735, abstract = {Interlocking puzzles are intriguing geometric games where the puzzle pieces are held together based on their geometric arrangement, preventing the puzzle from falling apart. High-level-of-difficulty, or simply high-level, interlocking puzzles are a subclass of interlocking puzzles that require multiple moves to take out the first subassembly from the puzzle. Solving a high-level interlocking puzzle is a challenging task since one has to explore many different configurations of the puzzle pieces until reaching a configuration where the first subassembly can be taken out. Designing a high-level interlocking puzzle with a user-specified level of difficulty is even harder since the puzzle pieces have to be interlocking in all the configurations before the first subassembly is taken out. In this paper, we present a computational approach to design high-level interlocking puzzles. The core idea is to represent all possible configurations of an interlocking puzzle as well as transitions among these configurations using a rooted, undirected graph called a disassembly graph and leverage this graph to find a disassembly plan that requires a minimal number of moves to take out the first subassembly from the puzzle. At the design stage, our algorithm iteratively constructs the geometry of each puzzle piece to expand the disassembly graph incrementally, aiming to achieve a user-specified level of difficulty. We show that our approach allows efficient generation of high-level interlocking puzzles of various shape complexities, including new solutions not attainable by state-of-the-art approaches.}, author = {Chen, Rulin and Wang, Ziqi and Song, Peng and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Computational design of high-level interlocking puzzles}}, doi = {10.1145/3528223.3530071}, volume = {41}, year = {2022}, } @article{11737, abstract = {Spin-orbit coupling in thin HgTe quantum wells results in a relativistic-like electron band structure, making it a versatile solid state platform to observe and control nontrivial electrodynamic phenomena. Here we report an observation of universal terahertz (THz) transparency determined by fine-structure constant α≈1/137 in 6.5-nm-thick HgTe layer, close to the critical thickness separating phases with topologically different electronic band structure. Using THz spectroscopy in a magnetic field we obtain direct evidence of asymmetric spin splitting of the Dirac cone. This particle-hole asymmetry facilitates optical control of edge spin currents in the quantum wells.}, author = {Dziom, Uladzislau and Shuvaev, A. and Gospodarič, J. and Novik, E. G. and Dobretsova, A. A. and Mikhailov, N. N. and Kvon, Z. D. and Alpichshev, Zhanybek and Pimenov, A.}, issn = {2469-9969}, journal = {Physical Review B}, number = {4}, publisher = {American Physical Society}, title = {{Universal transparency and asymmetric spin splitting near the Dirac point in HgTe quantum wells}}, doi = {10.1103/PhysRevB.106.045302}, volume = {106}, year = {2022}, } @article{11739, abstract = {We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.}, author = {Forkert, Dominik L and Maas, Jan and Portinale, Lorenzo}, issn = {1095-7154}, journal = {SIAM Journal on Mathematical Analysis}, keywords = {Fokker--Planck equation, gradient flow, evolutionary $\Gamma$-convergence}, number = {4}, pages = {4297--4333}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions}}, doi = {10.1137/21M1410968}, volume = {54}, year = {2022}, } @article{11740, abstract = {We consider a generalised model of a random simplicial complex, which arises from a random hypergraph. Our model is generated by taking the downward-closure of a non-uniform binomial random hypergraph, in which for each k, each set of k+1 vertices forms an edge with some probability pk independently. As a special case, this contains an extensively studied model of a (uniform) random simplicial complex, introduced by Meshulam and Wallach [Random Structures & Algorithms 34 (2009), no. 3, pp. 408–417]. We consider a higher-dimensional notion of connectedness on this new model according to the vanishing of cohomology groups over an arbitrary abelian group R. We prove that this notion of connectedness displays a phase transition and determine the threshold. We also prove a hitting time result for a natural process interpretation, in which simplices and their downward-closure are added one by one. In addition, we determine the asymptotic behaviour of cohomology groups inside the critical window around the time of the phase transition.}, author = {Cooley, Oliver and Del Giudice, Nicola and Kang, Mihyun and Sprüssel, Philipp}, issn = {1077-8926}, journal = {Electronic Journal of Combinatorics}, number = {3}, publisher = {Electronic Journal of Combinatorics}, title = {{Phase transition in cohomology groups of non-uniform random simplicial complexes}}, doi = {10.37236/10607}, volume = {29}, year = {2022}, } @article{11783, abstract = {We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix.}, author = {Bossmann, Lea}, issn = {1089-7658}, journal = {Journal of Mathematical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, number = {6}, publisher = {AIP Publishing}, title = {{Low-energy spectrum and dynamics of the weakly interacting Bose gas}}, doi = {10.1063/5.0089983}, volume = {63}, year = {2022}, } @inproceedings{11808, abstract = {In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.}, author = {Hanauer, Kathrin and Henzinger, Monika H and Schulz, Christian}, booktitle = {1st Symposium on Algorithmic Foundations of Dynamic Networks}, isbn = {9783959772242}, issn = {1868-8969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Recent advances in fully dynamic graph algorithms}}, doi = {10.4230/LIPIcs.SAND.2022.1}, volume = {221}, year = {2022}, } @inproceedings{11812, abstract = {This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic amortized O(m^{1/2}) update time, and any other connected four-vertex subgraph which is not a clique in deterministic amortized update time O(m^{2/3}). Queries can be answered in constant time. We also study the query times for subgraphs containing an arbitrary edge that is supplied only with the query as well as the case where only subgraphs containing a vertex s that is fixed beforehand are considered. For length-3 paths, paws, 4-cycles, and diamonds our bounds match or are not far from (conditional) lower bounds: Based on the OMv conjecture we show that any dynamic algorithm that detects the existence of paws, diamonds, or 4-cycles or that counts length-3 paths takes update time Ω(m^{1/2-δ}). Additionally, for 4-cliques and all connected induced subgraphs, we show a lower bound of Ω(m^{1-δ}) for any small constant δ > 0 for the amortized update time, assuming the static combinatorial 4-clique conjecture holds. This shows that the O(m) algorithm by Eppstein et al. [David Eppstein et al., 2012] for these subgraphs cannot be improved by a polynomial factor.}, author = {Hanauer, Kathrin and Henzinger, Monika H and Hua, Qi Cheng}, booktitle = {1st Symposium on Algorithmic Foundations of Dynamic Networks}, isbn = {9783959772242}, issn = {1868-8969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Fully dynamic four-vertex subgraph counting}}, doi = {10.4230/LIPIcs.SAND.2022.18}, volume = {221}, year = {2022}, } @article{11841, abstract = {Primary nucleation is the fundamental event that initiates the conversion of proteins from their normal physiological forms into pathological amyloid aggregates associated with the onset and development of disorders including systemic amyloidosis, as well as the neurodegenerative conditions Alzheimer’s and Parkinson’s diseases. It has become apparent that the presence of surfaces can dramatically modulate nucleation. However, the underlying physicochemical parameters governing this process have been challenging to elucidate, with interfaces in some cases having been found to accelerate aggregation, while in others they can inhibit the kinetics of this process. Here we show through kinetic analysis that for three different fibril-forming proteins, interfaces affect the aggregation reaction mainly through modulating the primary nucleation step. Moreover, we show through direct measurements of the Gibbs free energy of adsorption, combined with theory and coarse-grained computer simulations, that overall nucleation rates are suppressed at high and at low surface interaction strengths but significantly enhanced at intermediate strengths, and we verify these regimes experimentally. Taken together, these results provide a quantitative description of the fundamental process which triggers amyloid formation and shed light on the key factors that control this process.}, author = {Toprakcioglu, Zenon and Kamada, Ayaka and Michaels, Thomas C.T. and Xie, Mengqi and Krausser, Johannes and Wei, Jiapeng and Šarić, Anđela and Vendruscolo, Michele and Knowles, Tuomas P.J.}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {31}, publisher = {National Academy of Sciences}, title = {{Adsorption free energy predicts amyloid protein nucleation rates}}, doi = {10.1073/pnas.2109718119}, volume = {119}, year = {2022}, } @article{11843, abstract = {A key attribute of persistent or recurring bacterial infections is the ability of the pathogen to evade the host’s immune response. Many Enterobacteriaceae express type 1 pili, a pre-adapted virulence trait, to invade host epithelial cells and establish persistent infections. However, the molecular mechanisms and strategies by which bacteria actively circumvent the immune response of the host remain poorly understood. Here, we identified CD14, the major co-receptor for lipopolysaccharide detection, on mouse dendritic cells (DCs) as a binding partner of FimH, the protein located at the tip of the type 1 pilus of Escherichia coli. The FimH amino acids involved in CD14 binding are highly conserved across pathogenic and non-pathogenic strains. Binding of the pathogenic strain CFT073 to CD14 reduced DC migration by overactivation of integrins and blunted expression of co-stimulatory molecules by overactivating the NFAT (nuclear factor of activated T-cells) pathway, both rate-limiting factors of T cell activation. This response was binary at the single-cell level, but averaged in larger populations exposed to both piliated and non-piliated pathogens, presumably via the exchange of immunomodulatory cytokines. While defining an active molecular mechanism of immune evasion by pathogens, the interaction between FimH and CD14 represents a potential target to interfere with persistent and recurrent infections, such as urinary tract infections or Crohn’s disease.}, author = {Tomasek, Kathrin and Leithner, Alexander F and Glatzová, Ivana and Lukesch, Michael S. and Guet, Calin C and Sixt, Michael K}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Type 1 piliated uropathogenic Escherichia coli hijack the host immune response by binding to CD14}}, doi = {10.7554/eLife.78995}, volume = {11}, year = {2022}, } @inproceedings{11844, abstract = {In the stochastic population protocol model, we are given a connected graph with n nodes, and in every time step, a scheduler samples an edge of the graph uniformly at random and the nodes connected by this edge interact. A fundamental task in this model is stable leader election, in which all nodes start in an identical state and the aim is to reach a configuration in which (1) exactly one node is elected as leader and (2) this node remains as the unique leader no matter what sequence of interactions follows. On cliques, the complexity of this problem has recently been settled: time-optimal protocols stabilize in Θ(n log n) expected steps using Θ(log log n) states, whereas protocols that use O(1) states require Θ(n2) expected steps. In this work, we investigate the complexity of stable leader election on general graphs. We provide the first non-trivial time lower bounds for leader election on general graphs, showing that, when moving beyond cliques, the complexity landscape of leader election becomes very diverse: the time required to elect a leader can range from O(1) to Θ(n3) expected steps. On the upper bound side, we first observe that there exists a protocol that is time-optimal on many graph families, but uses polynomially-many states. In contrast, we give a near-time-optimal protocol that uses only O(log2n) states that is at most a factor log n slower. Finally, we show that the constant-state protocol of Beauquier et al. [OPODIS 2013] is at most a factor n log n slower than the fast polynomial-state protocol. Moreover, among constant-state protocols, this protocol has near-optimal average case complexity on dense random graphs.}, author = {Alistarh, Dan-Adrian and Rybicki, Joel and Voitovych, Sasha}, booktitle = {Proceedings of the Annual ACM Symposium on Principles of Distributed Computing}, isbn = {9781450392624}, location = {Salerno, Italy}, pages = {246--256}, publisher = {Association for Computing Machinery}, title = {{Near-optimal leader election in population protocols on graphs}}, doi = {10.1145/3519270.3538435}, year = {2022}, } @article{11858, abstract = {This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth and rough initial values from critical spaces. In the first main result we obtain several new blow-up criteria for quasi- and semilinear stochastic evolution equations. In particular, for semilinear equations we obtain a Serrin type blow-up criterium, which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074, 2018) to the stochastic setting. Blow-up criteria can be used to prove global well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights in time play a central role in the proofs. Our second contribution is a new method to bootstrap Sobolev and Hölder regularity in time and space, which does not require smoothness of the initial data. The blow-up criteria are at the basis of these new methods. Moreover, in applications the bootstrap results can be combined with our blow-up criteria, to obtain efficient ways to prove global existence. This gives new results even in classical 𝐿2-settings, which we illustrate for a concrete SPDE. In future works in preparation we apply the results of the current paper to obtain global well-posedness results and regularity for several concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into a more flexible framework, where less restrictions on the nonlinearities are needed, and we are able to treat rough initial values from critical spaces. Moreover, we will obtain higher-order regularity results.}, author = {Agresti, Antonio and Veraar, Mark}, issn = {1424-3202}, journal = {Journal of Evolution Equations}, keywords = {Mathematics (miscellaneous)}, number = {2}, publisher = {Springer Nature}, title = {{Nonlinear parabolic stochastic evolution equations in critical spaces part II}}, doi = {10.1007/s00028-022-00786-7}, volume = {22}, year = {2022}, }