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The spread of a group $G$, written $s(G)$, is the largest $k$ such that for any nontrivial elements $x_1, \dots, x_k \in G$ there exists $y \in G$ such that $G = \langle x_i, y \rangle$ for all $i$. Burness, Guralnick and Harper recently classified the finite groups $G$ such that $s(G) > 0$, which involved a reduction to almost simple groups. In this paper, we prove an asymptotic result that determines exactly when $s(G_n) \to \infty$ for a sequence of almost simple groups $(G_n)$. We apply probabilistic and geometric ideas, but the key tool is Shintani descent, a technique from the theory of algebraic groups that provides a bijection, the Shintani map, between conjugacy classes of almost simple groups. We provide a self-contained presentation of a general version of Shintani descent, and we prove that the Shintani map preserves information about maximal overgroups. This is suited to further applications. Indeed, we also use it to study $\mu(G)$, the minimal number of maximal overgroups of an element of $G$. We show that if $G$ is almost simple, then $\mu(G) \leqslant 3$ when $G$ has an alternating or sporadic socle, but in general, unlike when $G$ is simple, $\mu(G)$ can be arbitrarily large., Comment: 30 pages; to appear in Journal of Algebra

Every finite simple group can be generated by two elements, and Guralnick and Kantor proved that, moreover, every nontrivial element is contained in a generating pair. Groups with this property are said to be 3 2-generated. Thompson’s group V was the first finitely presented infinite simple group to be discovered. The Higman–Thompson groups Vn and the Brin–Thompson groups mV are two families of finitely presented groups that generalise V. In this paper, we prove that all of the groups Vn, V0 n and mV are 3 2-generated. As far as the authors are aware, the only previously known examples of infinite noncyclic 3 2-generated groups are the pathological Tarski monsters. We conclude with several open questions motivated by our results.

Variability exists amongst reported levelized costs of energy (LCOEs) for wind. Wind is unique from traditional energy sources in that the fuel is free, with the majority of costs determined by capital expenses. Power purchase agreements (PPAs) are critical to the success of a project, offering a guarantee of long-term revenue. Integral to negotiating a PPA is having an accurate estimate of the LCOE for the project. This research will evaluate LCOEs for wind to uncover reasons for substantial differences. PPA ownership structures and elements will also be evaluated with consideration of how objectives, resources, and farm management will impact decisions. The importance of understanding LCOE components as they relate to PPA negotiations will be highlighted with a focus on emerging markets and case analyses using NREL's System Advisor Model (SAM). Keywords: Levelized cost of energy, Wind power, Power purchase agreement, Renewable energy, Energy economics

The distinguishing number of $G \leqslant \sym(\Omega)$ is the smallest size of a partition of $\Omega$ such that only the identity of $G$ fixes all the parts of the partition. Extending earlier results of Cameron, Neumann, Saxl and Seress on the distinguishing number of finite primitive groups, we show that all imprimitive quasiprimitive groups have distinguishing number two, and all non-quasiprimitive semiprimitive groups have distinguishing number two, except for $\mathrm{GL}(2, 3)$ acting on the eight non-zero vectors of $\mathbb F_2^3$, which has distinguishing number three., Comment: 10 pages

We present an approach to enhance wheeled planetary rover dead-reckoning localization performance by leveraging the use of zero-type constraint equations in the navigation filter. Without external aiding, inertial navigation solutions inherently exhibit cubic error growth. Furthermore, for planetary rovers that are traversing diverse types of terrain, wheel odometry is often unreliable for use in localization, due to wheel slippage. For current Mars rovers, computer vision-based approaches are generally used whenever there is a high possibility of positioning error; however, these strategies require additional computational power, energy resources, and significantly slow down the rover traverse speed. To this end, we propose a navigation approach that compensates for the high likelihood of odometry errors by providing a reliable navigation solution that leverages non-holonomic vehicle constraints as well as state-aware pseudo-measurements (e.g., zero velocity and zero angular rate) updates during periodic stops. By using this, computationally expensive visual-based corrections could be performed less often. Experimental tests that compare against GPS-based localization are used to demonstrate the accuracy of the proposed approach. The source code, post-processing scripts, and example datasets associated with the paper are published in a public repository., 8 pages, 9 figures, Accepted to IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2019

A group is $\frac{3}{2}$-generated if every non-identity element is contained in a generating pair. A conjecture of Breuer, Guralnick and Kantor from 2008 asserts that a finite group is $\frac{3}{2}$-generated if and only if every proper quotient of the group is cyclic, and recent work of Guralnick reduces this conjecture to almost simple groups. In this paper, we prove a stronger form of the conjecture for almost simple symplectic and odd-dimensional orthogonal groups. More generally, we study the uniform spread of these groups, obtaining lower bounds and related asymptotics. This builds on earlier work of Burness and Guest, who established the conjecture for almost simple linear groups., 32 pages; to appear in J. Algebra

Let $G$ be a finite simple group. By a theorem of Guralnick and Kantor, $G$ contains a conjugacy class $C$ such that for each non-identity element $x \in G$, there exists $y \in C$ with $G = \langle x,y\rangle$. Building on this deep result, we introduce a new invariant $\gamma_u(G)$, which we call the uniform domination number of $G$. This is the minimal size of a subset $S$ of conjugate elements such that for each $1 \ne x \in G$, there exists $s \in S$ with $G = \langle x, s \rangle$. (This invariant is closely related to the total domination number of the generating graph of $G$, which explains our choice of terminology.) By the result of Guralnick and Kantor, we have $\gamma_u(G) \leqslant |C|$ for some conjugacy class $C$ of $G$, and the aim of this paper is to determine close to best possible bounds on $\gamma_u(G)$ for each family of simple groups. For example, we will prove that there are infinitely many non-abelian simple groups $G$ with $\gamma_u(G) = 2$. To do this, we develop a probabilistic approach, based on fixed point ratio estimates. We also establish a connection to the theory of bases for permutation groups, which allows us to apply recent results on base sizes for primitive actions of simple groups., Comment: 35 pages; to appear in Trans. Amer. Math. Soc

The purpose of this paper is twofold: (1) we study different notions of the average distance between two points of a self-similar subset of $${\mathbb {R}}$$ , and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of $${\mathbb {R}}$$ .

Objective The objective of this study was to compare the antimicrobial activity of commercially available antiseptic mouthrinses against saliva-derived plaque biofilms in static and flow-through biofilm systems in vitro. Methods Nine mouthrinses were tested in a recirculating flow-through biofilm model (RFTB) with viability assessment by ATP bioluminescence. In addition, five mouthrinses were evaluated in a batch chamber slide biofilm (BCSB) model, using live/dead staining and confocal laser scanning microscopy. Results In the RFTB model, essential oil (EO) and chlorhexidine (CHX)-containing rinses showed equivalent antimicrobial activity and were more effective than a range of cetyl pyridinium chloride (CPC1) formulations. In the BCSB model, twice-daily mouthrinse exposure demonstrated that the EO rinse was significantly more effective than rinses containing amine and stannous fluorides (AFSF), a combination of CPC/CHX, and another CPC formulation (CPC2). EO showed biofilm kill comparable to the CHX rinse. Conclusions The present studies have shown that mouthrinses vary significantly in their capability to kill plaque biofilm bacteria in BCSB and RFTB models. The EO mouthrinse demonstrated superior antiplaque biofilm activity to AFSF, CPC/CHX, and CPC rinses and comparable activity to CHX. The methods tested may be of value for the in-vitro screening of antiseptic rinses with different modes of antimicrobial action.