A fundamental problem in network science is the normalization of topological or physical distance between vertices, that requires understanding range variation unnormalized distances. Here we investigate limits linear arrangements vertices trees. In particular, various problems on sum edge lengths trees a fixed size: minimum and maximum value for specific trees, classes (bistar caterpillar tree...

A new study reveals that an apparent mutualism between lycaenid caterpillars and their attendant ants may not be all it seems, as the caterpillars produce secretions that modify the brains and behavior of their attendant ants.

Caterpillar compaction NA compaction, say Ryan Case, YunPei Chang, Nicholas Cozzarelli, Carlos Bustamante, and colleagues (University of California, Berkeley, CA), may work via a cooperative caterpillar-like mechanism. The caterpillar is formed by multiple copies of condensin protein—in this case MukBEF—with each V-shaped condensin contributing two legs. Compaction occurs when the caterpillar’s...

Caterpillar compaction NA compaction, say Ryan Case, YunPei Chang, Nicholas Cozzarelli, Carlos Bustamante, and colleagues (University of California, Berkeley, CA), may work via a cooperative caterpillar-like mechanism. The caterpillar is formed by multiple copies of condensin protein—in this case MukBEF—with each V-shaped condensin contributing two legs. Compaction occurs when the caterpillar’s...

A subtree of a tree is any induced subgraph that again (i.e., connected). The mean order the average number vertices its subtrees. This invariant was first analyzed in 1980s by Jamison. An intriguing open question raised Jamison asks whether maximum order, given tree, always attained some caterpillar. While we do not completely resolve this conjecture, find evidence favor proving different feat...

CASES of ophthalmia nodosa attributable to caterpillar hairs have been recorded in the literature from time to time during the last hundred years. The first description was published by Schon (1861) and further cases have been described by others including Pagenstecher (1883), Wagenmann (1890), Elschnig (1895). The name ophthalmia nodosa was given by Saemisch (1904). Only two British authors ha...

Outbreaks of folivorous Lepidoptera caterpillars are common in temperate forests (Ives and Wong 1988, Butterworth 1990). The high fat content, low chitin content, and large size of these larvae make them an important component of the diet of many temperate birds (Betts 1955, Robinson and Holmes 1982, Holmes and Schultz 1988, Sample et. al. 1993). Outbreaks of most species should increase availa...

Cagle [98]. Calculus [78]. Can [3, 45]. case [11]. Caterpillars [43]. checking [46]. Cheryl [24]. classifications [55]. client [73]. code [49]. collections [13]. Commentary [17]. Companion [24, 96]. Complexity [79]. computer [49]. Conformance [30, 75]. consistently [45]. Consultant [67]. Content [3, 12, 42].