Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

Weak Liouville-Arnold Theorems & Their Implications

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the Liouville-Arnold theorem. Moreover, we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable Tonelli Hamiltonians.Comment: 24 pages, 1 figure; v2 corrects typo in online abstract; v3 includes new title (was: A Weak Liouville-Arnold Theorem), re-arrangement of introduction, re-numbering of main theorems; v4 updates the authors' email and physical addresses, clarifies notation in section 4. Final versio

On 3d extensions of AGT relation

An extension of the AGT relation from two to three dimensions begins from connecting the theory on domain wall between some two S-dual SYM models with the 3d Chern-Simons theory. The simplest kind of such a relation would presumably connect traces of the modular kernels in 2d conformal theory with knot invariants. Indeed, the both quantities are very similar, especially if represented as integrals of the products of quantum dilogarithm functions. However, there are also various differences, especially in the "conservation laws" for integration variables, which hold for the monodromy traces, but not for the knot invariants. We also discuss another possibility: interpretation of knot invariants as solutions to the Baxter equations for the relativistic Toda system. This implies another AGT like relation: between 3d Chern-Simons theory and the Nekrasov-Shatashvili limit of the 5d SYM.Comment: 23 page

Organic phosphorus in the terrestrial environment: a perspective on the state of the art and future priorities

Background The dynamics of phosphorus (P) in the environment is important for regulating nutrient cycles in natural and managed ecosystems and an integral part in assessing biological resilience against environmental change. Organic P (Po) compounds play key roles in biological and ecosystems function in the terrestrial environment being critical to cell function, growth and reproduction. Scope We asked a group of experts to consider the global issues associated with Po in the terrestrial environment, methodological strengths and weaknesses, benefits to be gained from understanding the Po cycle, and to set priorities for Po research. Conclusions We identified seven key opportunities for Po research including: the need for integrated, quality controlled and functionally based methodologies; assessment of stoichiometry with other elements in organic matter; understanding the dynamics of Po in natural and managed systems; the role of microorganisms in controlling Po cycles; the implications of nanoparticles in the environment and the need for better modelling and communication of the research. Each priority is discussed and a statement of intent for the Po research community is made that highlights there are key contributions to be made toward understanding biogeochemical cycles, dynamics and function of natural ecosystems and the management of agricultural systems

Functional Clustering Drives Encoding Improvement in a Developing Brain Network during Awake Visual Learning

Sensory experience drives dramatic structural and functional plasticity in developing neurons. However, for single-neuron plasticity to optimally improve whole-network encoding of sensory information, changes must be coordinated between neurons to ensure a full range of stimuli is efficiently represented. Using two-photon calcium imaging to monitor evoked activity in over 100 neurons simultaneously, we investigate network-level changes in the developing Xenopus laevis tectum during visual training with motion stimuli. Training causes stimulus-specific changes in neuronal responses and interactions, resulting in improved population encoding. This plasticity is spatially structured, increasing tuning curve similarity and interactions among nearby neurons, and decreasing interactions among distant neurons. Training does not improve encoding by single clusters of similarly responding neurons, but improves encoding across clusters, indicating coordinated plasticity across the network. NMDA receptor blockade prevents coordinated plasticity, reduces clustering, and abolishes whole-network encoding improvement. We conclude that NMDA receptors support experience-dependent network self-organization, allowing efficient population coding of a diverse range of stimuli.Canadian Institutes of Health Researc

Upscaling of methane exchange in a boreal forest using soil chamber measurements and high-resolution LiDAR elevation data

Forest soils are generally considered to be net sinks of methane (CH4), but CH4 fluxes vary spatially depending on soil conditions. Measuring CH4 exchange with chambers, which are commonly used for this purpose, might not result in representative fluxes at site scale. Appropriate methods for upscaling CH4 fluxes from point measurements to site scale are therefore needed. At the boreal forest research site, Norunda, chamber measurements of soils and vegetation indicate that the site is a net sink of CH4, while tower gradient measurements indicate that the site is a net source of CH4. We investigated the discrepancy between chamber and tower gradient measurements by upscaling soil CH4 exchange to a 100 ha area based on an empirical model derived from chamber measurements of CH4 exchange and measurements of soil moisture, soil temperature and water table depth. A digital elevation model (DEM) derived from high-resolution airborne Light Detection and Ranging (LiDAR) data was used to generate gridded water table depth and soil moisture data of the study area as input data for the upscaling. Despite the simplistic approach, modeled fluxes were significantly correlated to four out of five chambers with R>0.68. The upscaling resulted in a net soil sink of CH4 of -10 mu mol m(-2) h(-1), averaged over the entire study area and time period June-September, 2010). Our findings suggest that additional contributions from CH4 soil sources outside the upscaling study area and possibly CH4 emissions from vegetation could explain the net emissions measured by tower gradient measurements. (C) 2015 Elsevier B.V. All rights reserved

Developmental differences in children’s interpersonal emotion regulation

Previous research on interpersonal emotion regulation (ER) in childhood has been rather unsystematic, focusing mainly on children’s prosocial behaviour, and has been conducted in the absence of an integrative emotion theoretical framework. The present research relied on the interpersonal affect classification proposed by Niven, Totterdell, and Holman (2009) to investigate children’s use of different interpersonal ER strategies. The study drew on two samples: 180 parents of children aged between 3 and 8 years reported about a situation where their child was able to change what another person was feeling in order to make them feel better. In addition, 126 children between 3- and 8-years old answered two questions about how they could improve others’ mood. Results from both samples showed age differences in children’s use of interpersonal ER strategies. As expected, ‘affective engagement’ (i.e., focusing on the person or the problem) and ‘cognitive engagement’ (i.e., appraising the situation from a different perspective) were mainly used by 7-8 years-old, whereas ‘attention’ (i.e., distracting and valuing) was most used by 3-4 and 5-6 years-old. ‘Humor’ (i.e., laughing with the target) remained stable across the different age groups. The present research provides more information about the developmental patterns for each specific interpersonal emotion regulation strategy

Methane exchange in a boreal forest estimated by gradient method

Forests are generally considered to be net sinks of atmospheric methane (CH4) because of oxidation by methanotrophic bacteria in well-aerated forests soils. However, emissions from wet forest soils, and sometimes canopy fluxes, are often neglected when quantifying the CH4 budget of a forest. We used a modified Bowen ratio method and combined eddy covariance and gradient methods to estimate net CH4 exchange at a boreal forest site in central Sweden. Results indicate that the site is a net source of CH4. This is in contrast to soil, branch and leaf chamber measurements of uptake of CH4. Wetter soils within the footprint of the canopy are thought to be responsible for the discrepancy. We found no evidence for canopy emissions per se. However, the diel pattern of the CH4 exchange with minimum emissions at daytime correlated well with gross primary production, which supports an uptake in the canopy. More distant source areas could also contribute to the diel pattern; their contribution might be greater at night during stable boundary layer conditions

Novel facultative Methylocella strains are active methane consumers at terrestrial natural gas seeps

Natural gas seeps contribute to global climate change by releasing substantial amounts of the potent greenhouse gas methane and other climate-active gases including ethane and propane to the atmosphere. However, methanotrophs, bacteria capable of utilising methane as the sole source of carbon and energy, play a significant role in reducing the emissions of methane from many environments. Methylocella-like facultative methanotrophs are a unique group of bacteria that grow on other components of natural gas (i.e. ethane and propane) in addition to methane but a little is known about the distribution and activity of Methylocella in the environment. The purposes of this study were to identify bacteria involved in cycling methane emitted from natural gas seeps and, most importantly, to investigate if Methylocella-like facultative methanotrophs were active utilisers of natural gas at seep sites