Divergence in right-angled Coxeter groups

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex.Comment: This version incorporates the referee's comments. It contains the complete appendix (which will be abbreviated in the journal version). To appear in Transactions of the AM

Divergence in right-angled Coxeter groups

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex

Farm vehicles approaching weights of sauropods exceed safe mechanical limits for soil functioning

Mechanization has greatly contributed to the success of modern agriculture, with vastly expanded food production capabilities achieved by the higher capacity of farm machinery. However, the increase in capacity has been accompanied by higher vehicle weights that increase risks of subsoil compaction. We show here that while surface contact stresses remained nearly constant over the course of modern mechanization, subsoil stresses have propagated into deeper soil layers and now exceed safe mechanical limits for soil ecological functioning. We developed a global map for delineating subsoil compaction susceptibility based on estimates of mechanization level, mean tractor size, soil texture, and climatic conditions. The alarming trend of chronic subsoil compaction risk over 20% of arable land, with potential loss of productivity, calls for a more stringent design of farm machinery that considers intrinsic subsoil mechanical limits. As the total weight of modern harvesters is now approaching that of the largest animals that walked Earth, the sauropods, a paradox emerges of potential prehistoric subsoil compaction. We hypothesize that unconstrained roaming of sauropods would have had similar adverse effects on land productivity as modern farm vehicles, suggesting that ecological strategies for reducing subsoil compaction, including fixed foraging trails, must have guided these prehistoric giants

Bowditch\u27s JSJ tree and the quasi-isometry classification of certain Coxeter groups

Bowditch\u27s JSJ tree for splittings over 2-ended subgroups is a quasi-isometry invariant for 1-ended hyperbolic groups which are not cocompact Fuchsian [Bowditch, Acta Math. 180 (1998) 145-186]. Our main result gives an explicit, computable \u27visual\u27 construction of this tree for certain hyperbolic right-angled Coxeter groups. As an application of our construction we identify a large class of such groups for which the JSJ tree, and hence the visual boundary, is a complete quasi-isometry invariant, and thus the quasi-isometry problem is decidable. We also give a direct proof of the fact that among the Coxeter groups we consider, the cocompact Fuchsian groups form a rigid quasi-isometry class. In Appendix B, written jointly with Christopher Cashen, we show that the JSJ tree is not a complete quasi-isometry invariant for the entire class of Coxeter groups we consider

How to Wake up Your Neighbors: Safe and Nearly Optimal Generic Energy Conservation in Radio Networks

Recent work [Chang et al., 2018; Chang et al., 2020; Varsha Dani et al., 2021] has shown that it is sometimes feasible to significantly reduce the energy usage of some radio-network algorithms by adaptively powering down the radio receiver when it is not needed. Although past work has focused on modifying specific network algorithms in this way, we now ask the question of whether this problem can be solved in a generic way, treating the algorithm as a kind of black box. We are able to answer this question in the affirmative, presenting a new general way to modify arbitrary radio-network algorithms in an attempt to save energy. At the expense of a small increase in the time complexity, we can provably reduce the energy usage to an extent that is provably nearly optimal within a certain class of general-purpose algorithms. As an application, we show that our algorithm reduces the energy cost of breadth-first search in radio networks from the previous best bound of 2^O(?{log n}) to polylog(n), where n is the number of nodes in the network A key ingredient in our algorithm is hierarchical clustering based on additive Voronoi decomposition done at multiple scales. Similar clustering algorithms have been used in other recent work on energy-aware computation in radio networks, but we believe the specific approach presented here may be of independent interest

Spawning behaviour and embryonic development in the sebae anemonefish Amphiprion sebae (Bleeker, 1853)

The present paper describes the spawning behaviour and embryonic development of Amphiprion sebae (Bleeker, 1853) under captive conditions. Ten functional breeding pairs of A. sebae ranging in total length from 90 to 100 mm (female) and 60 to 80 mm (male) collected from the inshore waters of Gulf of Mannar, along with sea anemones, Stichodactyla haddoni were acclimatised to captive conditions in 500 l glass tanks fitted with biofilter. Fishes spawned within 45 to 60 days of rearing. Sexual dichromatism was visible in spawning pairs during the breeding season. The number of eggs in each clutch varied between 300 to 1500 and the interval between successive spawning ranged between 15 - 26 days. The eggs were adhesive, capsule shaped and bright orange in colour measuring 2.10±0.031 mm in length and 1.02±0.037 mm in width. The eggs were bright orange for initial two days, turned black on 3rd to 5th day and silvery on 6th to 7th day of incubation. The embryonic development was divided into two phases based on the morphological characteristics. The overall understanding of spawning behaviour and embryonic development of A. sebae could help to improve the commercial production and culture of other coral reef fishes as well