On the Minimum Ropelength of Knots and Links

The ropelength of a knot is the quotient of its length and its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are $C^{1,1}$ curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.Comment: 29 pages, 14 figures; New version has minor additions and corrections; new section on asymptotic growth of ropelength; several new reference

The Second Hull of a Knotted Curve

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.Comment: 7 pages, 6 figures; final version (only minor changes) to appear in Amer.J.Mat

A Cost-Benefit Interpretation of the Substantially Similar Hurdle in the Congressional Review Act: Can OSHA Ever Utter the E-Word (Ergonomics) Again?

The Congressional Review Act permits Congress to veto proposed regulations via a joint resolution, and prohibits an agency from reissuing a rule “in substantially the same form” as the vetoed rule. Some scholars—and officials within the agencies themselves—have understood the “substantially the same” standard to bar an agency from regulating in the same substantive area covered by a vetoed rule. Courts have not yet provided an authoritative interpretation of the standard. This Article examines a spectrum of possible understandings of the standard, and relates them to the legislative history (of both the Congressional Review Act itself and the congressional veto of the Occupational Safety and Health Administration’s ergonomics rule), the statutory text, case law, and “good government” rationales. It concludes that the outlook is not as bleak as the agency officials and earlier scholarship predict: an agency may reissue a regulation in the same substantive area as a vetoed rule as long as the new rule has significantly greater benefits and/or significantly lower costs than the original rule. The Article then notes the practical implications for future rulemaking in the field of ergonomics, and closes with recommendations to amend the Congressional Review Act so as to better effect its underlying purpose

Sex Differences and Seasonal Trade-Offs in Response to Injured and Non-Injured Conspecifics in Red-Spotted Newts, Notophthalmus viridescens

Injured prey often release alarm chemicals that induce antipredator behaviors in conspecifics. Injured or killed prey most likely release a wide array of chemicals in addition to alarm substances, such as sexual pheromones, which could enhance or compromise antipredator responses. Thus, damage-release cues provide an excellent opportunity to examine the influence of seasonally fluctuating sexual pheromones on antipredator behaviors. We used a series of laboratory and field experiments and meta-analysis to examine seasonal changes and sex differences in the response of red-spot-ted newts, Notophthalmus viridescens, to the odor of non-injured conspecifics and conspecific tissue extracts, the latter of which presumably contain pheromones of non-injured conspecifics combined with alarm chemicals signaling predation. During the peak of the breeding season, males were attracted to females and multiple males, but did not avoid tissue extracts from either sex. As the breeding season waned, male attraction to females and males decreased, while avoidance of alarm extracts from both sexes concurrently increased. In contrast to male behavior, females were indifferent to both sexes during the breeding season, and showed significant avoidance only of female extract. As the breeding season progressed, females displayed no change in response to treatments. Male and female responses to female rinse and extract differed significantly, but their response to male treatments did not. During the non-breeding season, both males and females were indifferent to the odor of conspecifics and avoided conspecific tissue extracts, with the magnitude of male avoidance greater than that of female avoidance, suggesting sex differences in response to alarm cues in both the breed-ing and non-breeding seasons. In general, both male and female response to conspecific odor and tissue extracts covaried positively, suggesting that social pheromones can be detected within conspecific macerates and com-promise alarm-chemical avoidance. Many of the sex differences in both seasons are likely explained by selection pressures imposed on males to intensely mate search during the breeding season, suggesting that the mating system of newts directly influences predation threat during reproductive activity and may have significant indirect consequences on risk during the non-breeding season

Behavioural Responses by Red-Backed Salamanders to Conspecific and Heterospecific Cues

Chemical cues released from injured prey are thought to indicate the proximity of a predator or predation event, and therefore, an area of elevated predation risk. Prey often avoid chemical cues released from injured heterospecifics, but there is little evidence to determine whether this is due to homologous cues among phylogenetically related species, or avoidance of injured syntopic species that experience predation from the same predators. The purpose of this study was to examine the response of terrestrial red-backed salamanders (Plethodon cinereus) to chemical cues from non-injured and injured members of their prey guild that vary in their relatedness to P cinereus. In the laboratory, P. cinereus avoided chemical cues from injured conspecifics, injured and non-injured slimy salamanders (P glutinosus), and injured confamilial dusky salamanders (Desmognathus ochrophaeus). Red-backed salamanders did not avoid rinses from non-injured conspecifics and dusky salamanders, or cues from injured and non-injured earthworms (Lumbricus sp.), a more distantly related prey guild member. These results cannot be fully explained by either phylogenetic relatedness (among plethodontid salamanders) or prey guild membership alone. We suggest that a combination of these factors, and perhaps others, likely influenced the evolution of heterospecific alarm cue avoidance in the red-backed salamander

The Ontogeny of Chemically-Mediated Antipredator Behaviours in Newts (Notophthalmus viridescens): Responses to Injured and Non-Injured Conspecifics

Responses to alarm chemicals from injured prey may influence predation risk and foraging success of receivers and senders, while learning can influence the strength of these responses. Thus, it is important to know when in ontogeny prey produce and detect alarm substances and how learning shapes their response, but surprisingly little is known about either of these topics. We assessed when in the life of red-spotted newts, Notophthalmus viridescens, alarm chemicals are produced and detected by comparing adult versus eft (terrestrial juveniles) and larval responses to rinses and tissue extracts from individuals in each life-history stage. To evaluate the influence of experience in larvae exposed to conspecific alarm substances and rinses from adults known to cannibalize larvae, we compared the response of naive larvae, which had no prior experience with alarm chemicals or predators, to experienced larvae, which were likely to have experienced alarm chemicals and predators in their native pond. Larvae were indifferent to larval rinses and extracts, but reduced their activity in response to adult rinses and extracts. There was no difference between responses of recently hatched naive and experienced larvae, indicating that larvae exhibit innate antipredator behaviors in response to adult odour. Adults were indifferent to all larval treatments and adult rinse, but avoided adult extract. Since neither adults nor larvae responded to larval extract, larvae did not appear to possess alarm chemicals, and consequently, we were unable to assess the influence of experience on alarm substance response in larvae. Adults and efts were indifferent to rinses, but avoided extracts from conspecifics of both life-history stages. Together, these results demonstrate that red-spotted newts do not produce alarm chemicals until late in larval development, but can respond to predation-related chemical cues soon after hatching

On Temporal Variation and Conflicting Selection Pressures: A Test of Theory Using Newts

Most studies that examine conflicting selection pressures hold resources and risks constant, despite their ubiquitous fluctuation. Since little is known about the consequences of neglecting this variation, we examined the temporal response of male red-spotted newts, Notophthalmus viridescens, to conflicting female pheromones and damage-release alarm chemicals signaling predation. After a single exposure in both the laboratory and field, males were attracted to female odor and avoided conspecific alarm chemicals. Response to these combined cues depended on time after exposure, with males initially avoiding, and then being attracted to, the cue combination. This response shift was due to the resource and risk declining at different rates, and female odor accelerating male recovery from antipredator behavior. In the laboratory, males suppressed activity when exposed to alarm chemicals alone but increased their activity when female odor was added. Iterative exposures through the breeding season revealed that, as male mate search activity declined, male avoidance of alarm chemicals increased, but alarm chemical production appeared unchanged. Thawing dates differed between ponds of the same and different populations, which offset levels of mate search activity and consequently alarm chemical avoidance. As a result, simultaneous pond surveys made it appear as though there was geographic variation in reproductive and predator-avoidance behaviors. However, when thawing dates were aligned, the time courses of reproductive and predator-avoidance behaviors for the ponds coincided, demonstrating that observed site differences were predominantly due to different behavioral onsets, which would have gone overlooked had the larger temporal scale not been considered. These results indicate that temporal variation can be easily mistaken for geographic variation in behavior, increasing the potential for data interpretation errors. These studies underscore the importance of considering temporal variation when examining conflicting selection pressures

Criticality for the Gehring link problem

In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy class: we prove ropelength minimizers exist and introduce a theory of ropelength criticality. Our balance criterion is a set of necessary and sufficient conditions for criticality, based on a strengthened, infinite-dimensional version of the Kuhn--Tucker theorem. We use this to prove that every critical link is C^1 with finite total curvature. The balance criterion also allows us to explicitly describe critical configurations (and presumed minimizers) for many links including the Borromean rings. We also exhibit a surprising critical configuration for two clasped ropes: near their tips the curvature is unbounded and a small gap appears between the two components. These examples reveal the depth and richness hidden in Gehring's problem and our natural extension.Comment: This is the version published by Geometry & Topology on 14 November 200

Enduring Neurobehavioral Effects of Early Life Trauma Mediated Through Learning and Corticosterone Suppression

Early life trauma alters later life emotions, including fear. To better understand mediating mechanisms, we subjected pups to either predictable or unpredictable trauma, in the form of paired or unpaired odor-0.5 mA shock conditioning which, during a sensitive period, produces an odor preference and no learning respectively. Fear conditioning and its neural correlates were then assessed after the sensitive period at postnatal day (PN)13 or in adulthood, ages when amygdala-dependent fear occurs. Our results revealed that paired odor-shock conditioning starting during the sensitive period (PN8–12) blocked fear conditioning in older infants (PN13) and pups continued to express olfactory bulb-dependent odor preference learning. This PN13 fear learning inhibition was also associated with suppression of shock-induced corticosterone, although the age appropriate amygdala-dependent fear learning was reinstated with systemic corticosterone (3 mg/kg) during conditioning. On the other hand, sensitive period odor-shock conditioning did not prevent adult fear conditioning, although freezing, amygdala and hippocampal 2-DG uptake and corticosterone levels were attenuated compared to adult conditioning without infant conditioning. Normal levels of freezing, amygdala and hippocampal 2-DG uptake were induced with systemic corticosterone (5 mg/kg) during adult conditioning. These results suggest that the contingency of early life trauma mediates at least some effects of early life stress through learning and suppression of corticosterone levels. However, developmental differences between infants and adults are expressed with PN13 infants' learning consistent with the original learned preference, while adult conditioning overrides the original learned preference with attenuated amygdala-dependent fear learning

msmsEval: tandem mass spectral quality assignment for high-throughput proteomics

BACKGROUND: In proteomics experiments, database-search programs are the method of choice for protein identification from tandem mass spectra. As amino acid sequence databases grow however, computing resources required for these programs have become prohibitive, particularly in searches for modified proteins. Recently, methods to limit the number of spectra to be searched based on spectral quality have been proposed by different research groups, but rankings of spectral quality have thus far been based on arbitrary cut-off values. In this work, we develop a more readily interpretable spectral quality statistic by providing probability values for the likelihood that spectra will be identifiable. RESULTS: We describe an application, msmsEval, that builds on previous work by statistically modeling the spectral quality discriminant function using a Gaussian mixture model. This allows a researcher to filter spectra based on the probability that a spectrum will ultimately be identified by database searching. We show that spectra that are predicted by msmsEval to be of high quality, yet remain unidentified in standard database searches, are candidates for more intensive search strategies. Using a well studied public dataset we also show that a high proportion (83.9%) of the spectra predicted by msmsEval to be of high quality but that elude standard search strategies, are in fact interpretable. CONCLUSION: msmsEval will be useful for high-throughput proteomics projects and is freely available for download from . Supports Windows, Mac OS X and Linux/Unix operating systems