0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary). AU - Bonolis, Dante ID - 9364 JF - Mathematical Proceedings of the Cambridge Philosophical Society SN - 03050041 TI - On the size of the maximum of incomplete Kloosterman sums ER - TY - JOUR AB - Shigella are pathogens originating within the Escherichia lineage but frequently classified as a separate genus. Shigella genomes contain numerous insertion sequences (ISs) that lead to pseudogenisation of affected genes and an increase of non-homologous recombination. Here, we study 414 genomes of E. coli and Shigella strains to assess the contribution of genomic rearrangements to Shigella evolution. We found that Shigella experienced exceptionally high rates of intragenomic rearrangements and had a decreased rate of homologous recombination compared to pathogenic and non-pathogenic E. coli. The high rearrangement rate resulted in independent disruption of syntenic regions and parallel rearrangements in different Shigella lineages. Specifically, we identified two types of chromosomally encoded E3 ubiquitin-protein ligases acquired independently by all Shigella strains that also showed a high level of sequence conservation in the promoter and further in the 5′-intergenic region. In the only available enteroinvasive E. coli (EIEC) strain, which is a pathogenic E. coli with a phenotype intermediate between Shigella and non-pathogenic E. coli, we found a rate of genome rearrangements comparable to those in other E. coli and no functional copies of the two Shigella-specific E3 ubiquitin ligases. These data indicate that the accumulation of ISs influenced many aspects of genome evolution and played an important role in the evolution of intracellular pathogens. Our research demonstrates the power of comparative genomics-based on synteny block composition and an important role of non-coding regions in the evolution of genomic islands. AU - Seferbekova, Zaira AU - Zabelkin, Alexey AU - Yakovleva, Yulia AU - Afasizhev, Robert AU - Dranenko, Natalia O. AU - Alexeev, Nikita AU - Gelfand, Mikhail S. AU - Bochkareva, Olga ID - 9380 JF - Frontiers in Microbiology TI - High rates of genome rearrangements and pathogenicity of Shigella spp. VL - 12 ER - TY - JOUR AB - A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium. AU - Kleshnina, Maria AU - Streipert, Sabrina S. AU - Filar, Jerzy A. AU - Chatterjee, Krishnendu ID - 9381 IS - 4 JF - PLoS Computational Biology SN - 1553734X TI - Mistakes can stabilise the dynamics of rock-paper-scissors games VL - 17 ER - TY - CONF AB - Modern neural networks can easily fit their training set perfectly. Surprisingly, despite being “overfit” in this way, they tend to generalize well to future data, thereby defying the classic bias–variance trade-off of machine learning theory. Of the many possible explanations, a prevalent one is that training by stochastic gradient descent (SGD) imposes an implicit bias that leads it to learn simple functions, and these simple functions generalize well. However, the specifics of this implicit bias are not well understood. In this work, we explore the smoothness conjecture which states that SGD is implicitly biased towards learning functions that are smooth. We propose several measures to formalize the intuitive notion of smoothness, and we conduct experiments to determine whether SGD indeed implicitly optimizes for these measures. Our findings rule out the possibility that smoothness measures based on first-order derivatives are being implicitly enforced. They are supportive, though, of the smoothness conjecture for measures based on second-order derivatives. AU - Volhejn, Vaclav AU - Lampert, Christoph ID - 9210 SN - 03029743 T2 - 42nd German Conference on Pattern Recognition TI - Does SGD implicitly optimize for smoothness? VL - 12544 LNCS ER - TY - JOUR AB - A primary roadblock to our understanding of speciation is that it usually occurs over a timeframe that is too long to study from start to finish. The idea of a speciation continuum provides something of a solution to this problem; rather than observing the entire process, we can simply reconstruct it from the multitude of speciation events that surround us. But what do we really mean when we talk about the speciation continuum, and can it really help us understand speciation? We explored these questions using a literature review and online survey of speciation researchers. Although most researchers were familiar with the concept and thought it was useful, our survey revealed extensive disagreement about what the speciation continuum actually tells us. This is due partly to the lack of a clear definition. Here, we provide an explicit definition that is compatible with the Biological Species Concept. That is, the speciation continuum is a continuum of reproductive isolation. After outlining the logic of the definition in light of alternatives, we explain why attempts to reconstruct the speciation process from present‐day populations will ultimately fail. We then outline how we think the speciation continuum concept can continue to act as a foundation for understanding the continuum of reproductive isolation that surrounds us. AU - Stankowski, Sean AU - Ravinet, Mark ID - 9383 JF - Evolution SN - 00143820 TI - Defining the speciation continuum ER - TY - JOUR AU - Bolger-Munro, Madison AU - Choi, Kate AU - Cheung, Faith AU - Liu, Yi Tian AU - Dang-Lawson, May AU - Deretic, Nikola AU - Keane, Connor AU - Gold, Michael R. ID - 9379 JF - Frontiers in Cell and Developmental Biology KW - B cell KW - actin KW - immune synapse KW - cell spreading KW - cofilin KW - WDR1 (AIP1) KW - LIM domain kinase KW - B cell receptor (BCR) TI - The Wdr1-LIMK-Cofilin axis controls B cell antigen receptor-induced actin remodeling and signaling at the immune synapse VL - 9 ER - TY - JOUR AB - We report the complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This result suggests that fixation of a deleterious allele that follows a click of the Muller’s ratchet is governed by natural selection, instead of random drift. AU - Khudiakova, Kseniia AU - Neretina, Tatiana Yu. AU - Kondrashov, Alexey S. ID - 9387 JF - Journal of Theoretical Biology KW - General Biochemistry KW - Genetics and Molecular Biology KW - Modelling and Simulation KW - Statistics and Probability KW - General Immunology and Microbiology KW - Applied Mathematics KW - General Agricultural and Biological Sciences KW - General Medicine SN - 0022-5193 TI - Two linked loci under mutation-selection balance and Muller’s ratchet VL - 524 ER - TY - JOUR AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff, the ratio, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with bounded treewidth—a class that contains the control flow graphs of most programs. Let n denote the number of nodes of a graph, m the number of edges (for bounded treewidth 𝑚=𝑂(𝑛)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for the minimum initial credit problem we show that (1) for general graphs the problem can be solved in 𝑂(𝑛2⋅𝑚) time and the associated decision problem in 𝑂(𝑛⋅𝑚) time, improving the previous known 𝑂(𝑛3⋅𝑚⋅log(𝑛⋅𝑊)) and 𝑂(𝑛2⋅𝑚) bounds, respectively; and (2) for bounded treewidth graphs we present an algorithm that requires 𝑂(𝑛⋅log𝑛) time. Second, for bounded treewidth graphs we present an algorithm that approximates the mean-payoff value within a factor of 1+𝜖 in time 𝑂(𝑛⋅log(𝑛/𝜖)) as compared to the classical exact algorithms on general graphs that require quadratic time. Third, for the ratio property we present an algorithm that for bounded treewidth graphs works in time 𝑂(𝑛⋅log(|𝑎⋅𝑏|))=𝑂(𝑛⋅log(𝑛⋅𝑊)), when the output is 𝑎𝑏, as compared to the previously best known algorithm on general graphs with running time 𝑂(𝑛2⋅log(𝑛⋅𝑊)). We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks. AU - Chatterjee, Krishnendu AU - Ibsen-Jensen, Rasmus AU - Pavlogiannis, Andreas ID - 9393 JF - Formal Methods in System Design SN - 09259856 TI - Faster algorithms for quantitative verification in bounded treewidth graphs ER - TY - JOUR AB - Chromosomal inversions have long been recognized for their role in local adaptation. By suppressing recombination in heterozygous individuals, they can maintain coadapted gene complexes and protect them from homogenizing effects of gene flow. However, to fully understand their importance for local adaptation we need to know their influence on phenotypes under divergent selection. For this, the marine snail Littorina saxatilis provides an ideal study system. Divergent ecotypes adapted to wave action and crab predation occur in close proximity on intertidal shores with gene flow between them. Here, we used F2 individuals obtained from crosses between the ecotypes to test for associations between genomic regions and traits distinguishing the Crab‐/Wave‐adapted ecotypes including size, shape, shell thickness, and behavior. We show that most of these traits are influenced by two previously detected inversion regions that are divergent between ecotypes. We thus gain a better understanding of one important underlying mechanism responsible for the rapid and repeated formation of ecotypes: divergent selection acting on inversions. We also found that some inversions contributed to more than one trait suggesting that they may contain several loci involved in adaptation, consistent with the hypothesis that suppression of recombination within inversions facilitates differentiation in the presence of gene flow. AU - Koch, Eva L. AU - Morales, Hernán E. AU - Larsson, Jenny AU - Westram, Anja M AU - Faria, Rui AU - Lemmon, Alan R. AU - Lemmon, E. Moriarty AU - Johannesson, Kerstin AU - Butlin, Roger K. ID - 9394 JF - Evolution Letters TI - Genetic variation for adaptive traits is associated with polymorphic inversions in Littorina saxatilis ER -