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 - 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 -