Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

Large N Free Energy of 3d N=4 SCFTs and AdS/CFT

We provide a non-trivial check of the AdS_4/CFT_3 correspondence recently proposed in arXiv:1106.4253 by verifying the GKPW relation in the large N limit. The CFT free energy is obtained from the previous works (arXiv:1105.2551, arXiv:1105.4390) on the S^3 partition function for 3-dimensional N=4 SCFT T[SU(N)]. This is matched with the computation of the type IIB action on the corresponding gravity background. We unexpectedly find that the leading behavior of the free energy at large N is 1/2 N^2 ln N. We also extend our results to richer theories and argue that 1/2 N^2 ln N is the maximal free energy at large N in this class of gauge theories.Comment: 20 pages, 3 figure

Energy cost and return for hunting in African wild dogs and Cheetahs

African wild dogs (Lycaon pictus) are reported to hunt with energetically costly long chase distances. We used high-resolution GPS and inertial technology to record 1,119 high-speed chases of all members of a pack of six adult African wild dogs in northern Botswana. Dogs performed multiple short, high-speed, mostly unsuccessful chases to capture prey, while cheetahs (Acinonyx jubatus) undertook even shorter, higher-speed hunts. We used an energy balance model to show that the energy return from group hunting and feeding substantially outweighs the cost of multiple short chases, which indicates that African wild dogs are more energetically robust than previously believed. Comparison with cheetah illustrates the trade-off between sheer athleticism and high individual kill rate characteristic of cheetahs, and the energetic robustness of frequent opportunistic group hunting and feeding by African wild dogs

Interspecific Variation in Life History Relates to Antipredator Decisions by Marine Mesopredators on Temperate Reefs

As upper-level predatory fishes become overfished, mesopredators rise to become the new ‘top’ predators of over-exploited marine communities. To gain insight into ensuing mechanisms that might alter indirect species interactions, we examined how behavioural responses to an upper-level predatory fish might differ between mesopredator species with different life histories. In rocky reefs of the northeast Pacific Ocean, adult lingcod (Ophiodon elongatus) are upper-level predators that use a sit-and-wait hunting mode. Reef mesopredators that are prey to adult lingcod include kelp greenling (Hexagrammos decagrammus), younger lingcod, copper rockfish (Sebastes caurinus) and quillback rockfish (S. maliger). Across these mesopredators species, longevity and age at maturity increases and, consequently, the annual proportion of lifetime reproductive output decreases in the order just listed. Therefore, we hypothesized that the level of risk taken to acquire resources would vary interspecifically in that same order. During field experiments we manipulated predation risk with a model adult lingcod and used fixed video cameras to quantify interactions between mesopredators and tethered prey (Pandalus shrimps). We predicted that the probabilities of inspecting and attacking tethered prey would rank from highest to lowest and the timing of these behaviours would rank from earliest to latest as follows: kelp greenling, lingcod, copper rockfish, and quillback rockfish. We also predicted that responses to the model lingcod, such as avoidance of interactions with tethered prey, would rank from weakest to strongest in the same order. Results were consistent with our predictions suggesting that, despite occupying similar trophic levels, longer-lived mesopredators with late maturity have stronger antipredator responses and therefore experience lower foraging rates in the presence of predators than mesopredators with faster life histories. The corollary is that the fishery removal of top predators, which relaxes predation risk, could potentially lead to stronger increases in foraging rates for mesopredators with slower life histories

Purging Deleterious Mutations under Self Fertilization: Paradoxical Recovery in Fitness with Increasing Mutation Rate in Caenorhabditis elegans

Background: The accumulation of deleterious mutations can drastically reduce population mean fitness. Self-fertilization is thought to be an effective means of purging deleterious mutations. However, widespread linkage disequilibrium generated and maintained by self-fertilization is predicted to reduce the efficacy of purging when mutations are present at multiple loci. Methodology/Principal Findings: We tested the ability of self-fertilizing populations to purge deleterious mutations at multiple loci by exposing obligately self-fertilizing populations of Caenorhabditis elegans to a range of elevated mutation rates and found that mutations accumulated, as evidenced by a reduction in mean fitness, in each population. Therefore, purging in obligate selfing populations is overwhelmed by an increase in mutation rate. Surprisingly, we also found that obligate and predominantly self-fertilizing populations exposed to very high mutation rates exhibited consistently greater fitness than those subject to lesser increases in mutation rate, which contradicts the assumption that increases in mutation rate are negatively correlated with fitness. The high levels of genetic linkage inherent in self-fertilization could drive this fitness increase. Conclusions: Compensatory mutations can be more frequent under high mutation rates and may alleviate a portion of the fitness lost due to the accumulation of deleterious mutations through epistatic interactions with deleterious mutations. Th

Loss and Recovery Potential of Marine Habitats: An Experimental Study of Factors Maintaining Resilience in Subtidal Algal Forests at the Adriatic Sea

BACKGROUND: Predicting and abating the loss of natural habitats present a huge challenge in science, conservation and management. Algal forests are globally threatened by loss and severe recruitment failure, but our understanding of resilience in these systems and its potential disruption by anthropogenic factors lags well behind other habitats. We tested hypotheses regarding triggers for decline and recovery potential in subtidal forests of canopy-forming algae of the genus Cystoseira. METHODOLOGY/PRINCIPAL FINDINGS: By using a combination of historical data, and quantitative in situ observations of natural recruitment patterns we suggest that recent declines of forests along the coasts of the north Adriatic Sea were triggered by increasing cumulative impacts of natural- and human-induced habitat instability along with several extreme storm events. Clearing and transplantation experiments subsequently demonstrated that at such advanced stages of ecosystem degradation, increased substratum stability would be essential but not sufficient to reverse the loss, and that for recovery to occur removal of the new dominant space occupiers (i.e., opportunistic species including turf algae and mussels) would be required. Lack of surrounding adult canopies did not seem to impair the potential for assisted recovery, suggesting that in these systems recovery could be actively enhanced even following severe depletions. CONCLUSIONS/SIGNIFICANCE: We demonstrate that sudden habitat loss can be facilitated by long term changes in the biotic and abiotic conditions in the system, that erode the ability of natural ecosystems to absorb and recover from multiple stressors of natural and human origin. Moreover, we demonstrate that the mere restoration of environmental conditions preceding a loss, if possible, may be insufficient for ecosystem restoration, and is scarcely cost-effective. We conclude that the loss of complex marine habitats in human-dominated landscapes could be mitigated with appropriate consideration and management of incremental habitat changes and of attributes facilitating system recovery

Green Crab (Carcinus maenas) Foraging Efficiency Reduced by Fast Flows

Predators can strongly influence prey populations and the structure and function of ecosystems, but these effects can be modified by environmental stress. For example, fluid velocity and turbulence can alter the impact of predators by limiting their environmental range and altering their foraging ability. We investigated how hydrodynamics affected the foraging behavior of the green crab (Carcinus maenas), which is invading marine habitats throughout the world. High flow velocities are known to reduce green crab predation rates and our study sought to identify the mechanisms by which flow affects green crabs. We performed a series of experiments with green crabs to determine: 1) if their ability to find prey was altered by flow in the field, 2) how flow velocity influenced their foraging efficiency, and 3) how flow velocity affected their handling time of prey. In a field study, we caught significantly fewer crabs in baited traps at sites with fast versus slow flows even though crabs were more abundant in high flow areas. This finding suggests that higher velocity flows impair the ability of green crabs to locate prey. In laboratory flume assays, green crabs foraged less efficiently when flow velocity was increased. Moreover, green crabs required significantly more time to consume prey in high velocity flows. Our data indicate that flow can impose significant chemosensory and physical constraints on green crabs. Hence, hydrodynamics may strongly influence the role that green crabs and other predators play in rocky intertidal communities

Bias and Evolution of the Mutationally Accessible Phenotypic Space in a Developmental System

Genetic and developmental architecture may bias the mutationally available phenotypic spectrum. Although such asymmetries in the introduction of variation may influence possible evolutionary trajectories, we lack quantitative characterization of biases in mutationally inducible phenotypic variation, their genotype-dependence, and their underlying molecular and developmental causes. Here we quantify the mutationally accessible phenotypic spectrum of the vulval developmental system using mutation accumulation (MA) lines derived from four wild isolates of the nematodes Caenorhabditis elegans and C. briggsae. The results confirm that on average, spontaneous mutations degrade developmental precision, with MA lines showing a low, yet consistently increased, proportion of developmental defects and variants. This result indicates strong purifying selection acting to maintain an invariant vulval phenotype. Both developmental system and genotype significantly bias the spectrum of mutationally inducible phenotypic variants. First, irrespective of genotype, there is a developmental bias, such that certain phenotypic variants are commonly induced by MA, while others are very rarely or never induced. Second, we found that both the degree and spectrum of mutationally accessible phenotypic variation are genotype-dependent. Overall, C. briggsae MA lines exhibited a two-fold higher decline in precision than the C. elegans MA lines. Moreover, the propensity to generate specific developmental variants depended on the genetic background. We show that such genotype-specific developmental biases are likely due to cryptic quantitative variation in activities of underlying molecular cascades. This analysis allowed us to identify the mutationally most sensitive elements of the vulval developmental system, which may indicate axes of potential evolutionary variation. Consistent with this scenario, we found that evolutionary trends in the vulval system concern the phenotypic characters that are most easily affected by mutation. This study provides an empirical assessment of developmental bias and the evolution of mutationally accessible phenotypes and supports the notion that such bias may influence the directions of evolutionary change