Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

Biological Soil Crusts as Modern Analogues for the Archean Continental Biosphere: Insights from Carbon and Nitrogen Isotopes

Stable isotope signatures of elements related to life such as carbon and nitrogen can be powerful biomarkers that provide key information on the biological origin of organic remains and their paleoenvironments. Marked advances have been achieved in the last decade in our understanding of the coupled evolution of biological carbon and nitrogen cycling and the chemical evolution of the early Earth thanks, in part, to isotopic signatures preserved in fossilized microbial mats and organic matter of marine origin. However, the geologic record of the early continental biosphere, as well as its evolution and biosignatures, is still poorly constrained. Following a recent report of direct fossil evidence of life on land at 3.22 Ga, we compare here the carbon and nitrogen isotopic signals of this continental Archean biosphere with biosignatures of cyanobacteria biological soil crusts (cyanoBSCs) colonizing modern arid environments. We report the first extended δ13C and δ15N data set from modern cyanoBSCs and show that these modern communities harbor specific isotopic biosignatures that compare well with continental Archean organic remains. We therefore suggest that cyanoBSCs are likely relevant analogues for the earliest continental ecosystems. As such, they can provide key information on the timing, extent, and possibly mechanism of colonization of the early Earth's emergent landmasses

Authigenic iron oxide proxies for marine zinc over geological time and implications for eukaryotic metallome evolution

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Geobiology 11 (2013): 295-306, doi:10.1111/gbi.12036.Here we explore enrichments in paleomarine Zn as recorded by authigenic iron oxides including Precambrian iron formations, ironstones and Phanerozoic hydrothermal exhalites. This compilation of new and literature-based iron formation analyses track dissolved Zn abundances and constrain the magnitude of the marine reservoir over geological time. Overall, the iron formation record is characterized by a fairly static range in Zn/Fe ratios throughout the Precambrian, consistent with the shale record (Scott et al., 2013, Nature Geoscience, 6, 125-128). When hypothetical partitioning scenarios are applied to this record, paleomarine Zn concentrations within about an order of magnitude of modern are indicated. We couple this examination with new chemical speciation models used to interpret the iron formation record. We present two scenarios: first, under all but the most sulfidic conditions and with Zn binding organic ligand concentrations similar to modern oceans, the amount of bioavailable Zn remained relatively unchanged through time. Late proliferation of Zn in eukaryotic metallomes has previously been linked to marine Zn biolimitation, but under this scenario, the expansion in eukaryotic Zn metallomes may be better linked to biologically intrinsic evolutionary factors. In this case zinc’s geochemical and biological evolution may be decoupled, and viewed as a function of increasing need for genome regulation and diversification of Zn-binding transcription factors. In the second scenario, we consider Archean organic ligand complexation in such excess that it may render Zn bioavailability low. However, this is dependent on Zn organic ligand complexes not being bioavailable, which remains unclear. In this case, although bioavailability may be low, sphalerite precipitation is prevented, thereby maintaining a constant Zn inventory throughout both ferruginous and euxinic conditions. These results provide new perspectives and constraints 50 on potential couplings between the trajectory of biological and marine geochemical coevolution.This work was supported by a NSERC Discovery Grant to KOK, a NSERC PDF to SVL, a NSERC CGSM to LJR, and an NSF-EAR-PDF to NJP. MAS acknowledges support from the Gordon and Betty Moore Foundation Grant #2724. This work was also supported by grants from the Deutsche Forschungsgemeinschaft (DFG) to A.K. (KA 1736/4-1 and 12-1)

Regulation of Motor Function and Behavior by Atypical Chemokine Receptor 1

The final publication is available at Springer via http://dx.doi.org/10.1007/s10519-014-9665-7Atypical Chemokine Receptor 1 (ACKR1), previously known as the Duffy Antigen Receptor for Chemokines, stands out among chemokine receptors for its high selective expression on Purkinje cells of the cerebellum, consistent with the ability of ACKR1 ligands to activate Purkinje cells in vitro. Nevertheless, evidence for ACKR1 regulation of brain function in vivo has been lacking. Here we demonstrate that Ackr1−/− mice have markedly impaired balance and ataxia when placed on a rotating rod and increased tremor when injected with harmaline, a drug that induces whole-body tremor by activating Purkinje cells. Ackr1−/− mice also exhibited impaired exploratory behavior, increased anxiety-like behavior and frequent episodes of marked hypoactivity under low-stress conditions. The behavioral phenotype of Ackr1−/− mice was the opposite of the phenotype occurring in mice with cerebellar degeneration and the defects persisted when Ackr1 was deficient only on non-hematopoietic cells. We conclude that normal motor function and behavior depend in part on negative regulation of Purkinje cell activity by Ackr1

Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio

Deep Markov Random Field for Image Modeling

Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic factors to capture local patterns. In this paper, we move beyond such limitations, and propose a novel MRF model that uses fully-connected neurons to express the complex interactions among pixels. Through theoretical analysis, we reveal an inherent connection between this model and recurrent neural networks, and thereon derive an approximated feed-forward network that couples multiple RNNs along opposite directions. This formulation combines the expressive power of deep neural networks and the cyclic dependency structure of MRF in a unified model, bringing the modeling capability to a new level. The feed-forward approximation also allows it to be efficiently learned from data. Experimental results on a variety of low-level vision tasks show notable improvement over state-of-the-arts.Comment: Accepted at ECCV 201

Predicting language learners' grades in the L1, L2, L3 and L4: the effect of some psychological and sociocognitive variables

This study of 89 Flemish high-school students' grades for L1 (Dutch), L2 (French), L3 (English) and L4 (German) investigates the effects of three higher-level personality dimensions (psychoticism, extraversion, neuroticism), one lower-level personality dimension (foreign language anxiety) and sociobiographical variables (gender, social class) on the participants' language grades. Analyses of variance revealed no significant effects of the higher-level personality dimensions on grades. Participants with high levels of foreign language anxiety obtained significantly lower grades in the L2 and L3. Gender and social class had no effect. Strong positive correlations between grades in the different languages could point to an underlying sociocognitive dimension. The implications of these findings are discussed

Proterozoic ocean redox and biogeochemical stasis

The partial pressure of oxygen in Earth’s atmosphere has increased dramatically through time, and this increase is thought to have occurred in two rapid steps at both ends of the Proterozoic Eon (∼2.5–0.543 Ga). However, the trajectory and mechanisms of Earth’s oxygenation are still poorly constrained, and little is known regarding attendant changes in ocean ventilation and seafloor redox. We have a particularly poor understanding of ocean chemistry during the mid-Proterozoic (∼1.8–0.8 Ga). Given the coupling between redox-sensitive trace element cycles and planktonic productivity, various models for mid-Proterozoic ocean chemistry imply different effects on the biogeochemical cycling of major and trace nutrients, with potential ecological constraints on emerging eukaryotic life. Here, we exploit the differing redox behavior of molybdenum and chromium to provide constraints on seafloor redox evolution by coupling a large database of sedimentary metal enrichments to a mass balance model that includes spatially variant metal burial rates. We find that the metal enrichment record implies a Proterozoic deep ocean characterized by pervasive anoxia relative to the Phanerozoic (at least ∼30–40% of modern seafloor area) but a relatively small extent of euxinic (anoxic and sulfidic) seafloor (less than ∼1–10% of modern seafloor area). Our model suggests that the oceanic Mo reservoir is extremely sensitive to perturbations in the extent of sulfidic seafloor and that the record of Mo and chromium enrichments through time is consistent with the possibility of a Mo–N colimited marine biosphere during many periods of Earth’s history

Self-supervised Outdoor Scene Relighting

Outdoor scene relighting is a challenging problem that requires good understanding of the scene geometry, illumination and albedo. Current techniques are completely supervised, requiring high quality synthetic renderings to train a solution. Such renderings are synthesized using priors learned from limited data. In contrast, we propose a self-supervised approach for relighting. Our approach is trained only on corpora of images collected from the internet without any user-supervision. This virtually endless source of training data allows training a general relighting solution. Our approach first decomposes an image into its albedo, geometry and illumination. A novel relighting is then produced by modifying the illumination parameters. Our solution capture shadow using a dedicated shadow prediction map, and does not rely on accurate geometry estimation. We evaluate our technique subjectively and objectively using a new dataset with ground-truth relighting. Results show the ability of our technique to produce photo-realistic and physically plausible results, that generalizes to unseen scenes.Comment: Published in ECCV '20, http://gvv.mpi-inf.mpg.de/projects/SelfRelight