@article{11700, abstract = {This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov equations can be formulated as gradient flow of the free energy in the Wasserstein space of probability measures. The proofs of these results are based on careful regularisation arguments to circumvent some of the difficulties arising in metric graphs, namely, branching of geodesics and the failure of semi-convexity of entropy functionals in the Wasserstein space.}, author = {Erbar, Matthias and Forkert, Dominik L and Maas, Jan and Mugnolo, Delio}, issn = {1556-181X}, journal = {Networks and Heterogeneous Media}, number = {5}, pages = {687--717}, publisher = {American Institute of Mathematical Sciences}, title = {{Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph}}, doi = {10.3934/nhm.2022023}, volume = {17}, year = {2022}, } @article{11701, abstract = {In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi- or semilinear type. This first part is on local existence and well-posedness. A second part in preparation is on blow-up criteria and regularization. Our theory is formulated in an Lp-setting, and because of this we can deal with nonlinearities in a very efficient way. Applications to several concrete problems and their quasilinear variants are given. This includes Burgers' equation, the Allen–Cahn equation, the Cahn–Hilliard equation, reaction–diffusion equations, and the porous media equation. The interplay of the nonlinearities and the critical spaces of initial data leads to new results and insights for these SPDEs. The proofs are based on recent developments in maximal regularity theory for the linearized problem for deterministic and stochastic evolution equations. In particular, our theory can be seen as a stochastic version of the theory of critical spaces due to Prüss–Simonett–Wilke (2018). Sharp weighted time-regularity allow us to deal with rough initial values and obtain instantaneous regularization results. The abstract well-posedness results are obtained by a combination of several sophisticated splitting and truncation arguments.}, author = {Agresti, Antonio and Veraar, Mark}, issn = {1361-6544}, journal = {Nonlinearity}, number = {8}, pages = {4100--4210}, publisher = {IOP Publishing}, title = {{Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence}}, doi = {10.1088/1361-6544/abd613}, volume = {35}, year = {2022}, } @article{11702, abstract = {When Mendel’s work was rediscovered in 1900, and extended to establish classical genetics, it was initially seen in opposition to Darwin’s theory of evolution by natural selection on continuous variation, as represented by the biometric research program that was the foundation of quantitative genetics. As Fisher, Haldane, and Wright established a century ago, Mendelian inheritance is exactly what is needed for natural selection to work efficiently. Yet, the synthesis remains unfinished. We do not understand why sexual reproduction and a fair meiosis predominate in eukaryotes, or how far these are responsible for their diversity and complexity. Moreover, although quantitative geneticists have long known that adaptive variation is highly polygenic, and that this is essential for efficient selection, this is only now becoming appreciated by molecular biologists—and we still do not have a good framework for understanding polygenic variation or diffuse function.}, author = {Barton, Nicholas H}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {30}, publisher = {Proceedings of the National Academy of Sciences}, title = {{The "New Synthesis"}}, doi = {10.1073/pnas.2122147119}, volume = {119}, year = {2022}, } @article{11703, abstract = {Polyploidization may precipitate dramatic changes to the genome, including chromosome rearrangements, gene loss, and changes in gene expression. In dioecious plants, the sex-determining mechanism may also be disrupted by polyploidization, with the potential evolution of hermaphroditism. However, while dioecy appears to have persisted through a ploidy transition in some species, it is unknown whether the newly formed polyploid maintained its sex-determining system uninterrupted, or whether dioecy re-evolved after a period of hermaphroditism. Here, we develop a bioinformatic pipeline using RNA-sequencing data from natural populations to demonstrate that the allopolyploid plant Mercurialis canariensis directly inherited its sex-determining region from one of its diploid progenitor species, M. annua, and likely remained dioecious through the transition. The sex-determining region of M. canariensis is smaller than that of its diploid progenitor, suggesting that the non-recombining region of M. annua expanded subsequent to the polyploid origin of M. canariensis. Homeologous pairs show partial sexual subfunctionalization. We discuss the possibility that gene duplicates created by polyploidization might contribute to resolving sexual antagonism.}, author = {Toups, Melissa A and Vicoso, Beatriz and Pannell, John R.}, issn = {1553-7404}, journal = {PLoS Genetics}, number = {7}, publisher = {Public Library of Science}, title = {{Dioecy and chromosomal sex determination are maintained through allopolyploid speciation in the plant genus Mercurialis}}, doi = {10.1371/journal.pgen.1010226}, volume = {18}, year = {2022}, } @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}, keywords = {Multidisciplinary}, number = {31}, publisher = {Proceedings of the 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{11732, abstract = {We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature.}, author = {Henheik, Sven Joscha and Lauritsen, Asbjørn Bækgaard}, issn = {1572-9613}, journal = {Journal of Statistical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, publisher = {Springer Nature}, title = {{The BCS energy gap at high density}}, doi = {10.1007/s10955-022-02965-9}, volume = {189}, 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 = {Proceedings of the 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 = {Proceedings of the 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{11736, abstract = {This paper introduces a methodology for inverse-modeling of yarn-level mechanics of cloth, based on the mechanical response of fabrics in the real world. We compiled a database from physical tests of several different knitted fabrics used in the textile industry. These data span different types of complex knit patterns, yarn compositions, and fabric finishes, and the results demonstrate diverse physical properties like stiffness, nonlinearity, and anisotropy. We then develop a system for approximating these mechanical responses with yarn-level cloth simulation. To do so, we introduce an efficient pipeline for converting between fabric-level data and yarn-level simulation, including a novel swatch-level approximation for speeding up computation, and some small-but-necessary extensions to yarn-level models used in computer graphics. The dataset used for this paper can be found at http://mslab.es/projects/YarnLevelFabrics.}, author = {Sperl, Georg and Sánchez-Banderas, Rosa M. and Li, Manwen and Wojtan, Christopher J and Otaduy, Miguel A.}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Estimation of yarn-level simulation models for production fabrics}}, doi = {10.1145/3528223.3530167}, 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}, } @inproceedings{11775, abstract = {Quantitative monitoring can be universal and approximate: For every finite sequence of observations, the specification provides a value and the monitor outputs a best-effort approximation of it. The quality of the approximation may depend on the resources that are available to the monitor. By taking to the limit the sequences of specification values and monitor outputs, we obtain precision-resource trade-offs also for limit monitoring. This paper provides a formal framework for studying such trade-offs using an abstract interpretation for monitors: For each natural number n, the aggregate semantics of a monitor at time n is an equivalence relation over all sequences of at most n observations so that two equivalent sequences are indistinguishable to the monitor and thus mapped to the same output. This abstract interpretation of quantitative monitors allows us to measure the number of equivalence classes (or “resource use”) that is necessary for a certain precision up to a certain time, or at any time. Our framework offers several insights. For example, we identify a family of specifications for which any resource-optimal exact limit monitor is independent of any error permitted over finite traces. Moreover, we present a specification for which any resource-optimal approximate limit monitor does not minimize its resource use at any time. }, author = {Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {22nd International Conference on Runtime Verification}, issn = {0302-9743}, location = {Tbilisi, Georgia}, pages = {200--220}, publisher = {Springer Nature}, title = {{Abstract monitors for quantitative specifications}}, doi = {10.1007/978-3-031-17196-3_11}, volume = {13498}, year = {2022}, }