Scale insects (Hemiptera: Coccoidea) are small herbivorous insects found on all continents except Antarctica. They are extremely invasive, and many species are serious agricultural pests. They are also emerging models for studies of the evolution of genetic systems, endosymbiosis and plant-insect interactions. ScaleNet was launched in 1995 to provide insect identifiers, pest managers, insect systematists, evolutionary biologists and ecologists efficient access to information about scale insect biological diversity. It provides comprehensive information on scale insects taken directly from the primary literature. Currently, it draws from 23 477 articles and describes the systematics and biology of 8194 valid species. For 20 years, ScaleNet ran on the same software platform. That platform is no longer viable. Here, we present a new, open-source implementation of ScaleNet. We have normalized the data model, begun the process of correcting invalid data, upgraded the user interface, and added online administrative tools. These improvements make ScaleNet easier to use and maintain and make the ScaleNet data more accurate and extendable.Database URL: http://scalenet.info

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A collection of n balls in d dimensions forms a k-ply system if no point in the space is covered by more than k balls. We show that for every k-ply system ⌫, there is a sphere S that intersects at most O(k 1/d n 1Ϫ1/d) balls of ⌫ and divides the remainder of ⌫ into two parts: those in the interior and those in the exterior of the sphere S, respectively, so that the larger part contains at most (1 Ϫ 1/(d ϩ 2))n balls. This bound of O(k 1/d n 1Ϫ1/d) is the best possible in both n and k. We also present a simple randomized algorithm to find such a sphere in O(n) time. Our result implies that every k-nearest neighbor graphs of n points in d dimensions has a separator of size O(k 1/d n 1Ϫ1/d). In conjunction with a result of Koebe that every triangulated planar graph is isomorphic to the intersection graph of a disk-packing, our result not only gives a new geometric proof of the planar separator theorem of Lipton and Tarjan, but also generalizes it to higher dimensions. The separator algorithm can be used for point location and geometric divide and conquer in a fixed dimensional space.

W.T. Tutte showed that if G is an arc transitive connected cubic graph then the automorphism group of G is in fact regular on s-arcs for some s < 5. We analyze these arc transitive cubic graphs using the unifying concepts of the infinite cubic tree, f3' and coverings. We are able to answer a large number of questions, open and otherwise. As an example, suppose G is a 4-arc transi tive cubic graph and the automorphism group of G contains a 1-regular subgroup, then G is a covering of Heawood's graph. Abstract W.T. Tutte showed that if G is an arc transitive connected cubic graph then the automorphism group of G is in fact regular on s-arcs for some s < 5. We analyze these arc transitive cubic graphs -> using the unifying concepts of the infinite cubic tree, r 3 , and coverings. We are able to answer a large number of questions, open and otherwise. As an example, suppose G is a 4-arc transitive cubic graph and the automorphism group of G contains a l-regular subgroup, then G is a covering of Heawood1s graph. Regular Groups of Automorphisms of Cubic Graphs v Dragomir Z. Djokovit and Gary L. Miller O. Introduction. This paper is concerned with s-regular groups of automorphisms of connected cubic graphs. (See next section for definitions.) The subject was started by W.T. Tutte [13] by proving the basic fact that s s 5 in the case of finite cubic graphs. (See also [15]). He also proved in that case that if the graph is l-transitive then it must be s-regular for some s, 1 s s s 5. With slight modifications these results remain valid for infinite cubic graphs. Let G be a connected cubic graph and let {u.y} be an edge of G. Let A be an s-regular subgroup of Aut{G), Then we associate to A the amalgam (A(u),A[u,v]) where A{u) is the fixer of u in A and A[u,v] is the stabilizer of . {u,v} in A. This amalgam is independent (up to isomorphism) of the chosen edge {u,v}. Moreover, if s = 1,3, or 5 this amalgam is even independent of the choice of G and A and if s = 2 or 4 there are two possible amalgams in each case. Hence we obtain seven possible types of. s-regular groups (ls-ss5): 1',2 1 ,2",3',4',4", and 51. The group of type Sl is s-regular and has an involution which flips an edge. The groups of type s" are s-regular and they do not possess any involution flipping an edge. Let r3 be the cubic tree. We show that Aut(r 3 ) contains regular subgroups of all seven types, moreover two regular subgroups of the same type are conjugate. -1 ... 3 Moreover, in this way we obtain all such pairs (G,B) (up to isomorphism).This correspondence N~ (GN,A N ) is either one -one or two -one, i.e., the same pair can be obtained from at most two normal subgroups •. Hence the problem of classifying pairs (G,B) of the given type reduces to the problem of classifying normal subgroups of A.This latter problem is still far from its solution. For instance, if we consider the type l' then A is the modular group and in spite of an enormous number of papers on normal subgroups of it (see the references, in [9]) the final answer is still lacking. It is e...