Unsupervised Deep Single-Image Intrinsic Decomposition using Illumination-Varying Image Sequences

Machine learning based Single Image Intrinsic Decomposition (SIID) methods decompose a captured scene into its albedo and shading images by using the knowledge of a large set of known and realistic ground truth decompositions. Collecting and annotating such a dataset is an approach that cannot scale to sufficient variety and realism. We free ourselves from this limitation by training on unannotated images. Our method leverages the observation that two images of the same scene but with different lighting provide useful information on their intrinsic properties: by definition, albedo is invariant to lighting conditions, and cross-combining the estimated albedo of a first image with the estimated shading of a second one should lead back to the second one's input image. We transcribe this relationship into a siamese training scheme for a deep convolutional neural network that decomposes a single image into albedo and shading. The siamese setting allows us to introduce a new loss function including such cross-combinations, and to train solely on (time-lapse) images, discarding the need for any ground truth annotations. As a result, our method has the good properties of i) taking advantage of the time-varying information of image sequences in the (pre-computed) training step, ii) not requiring ground truth data to train on, and iii) being able to decompose single images of unseen scenes at runtime. To demonstrate and evaluate our work, we additionally propose a new rendered dataset containing illumination-varying scenes and a set of quantitative metrics to evaluate SIID algorithms. Despite its unsupervised nature, our results compete with state of the art methods, including supervised and non data-driven methods.Comment: To appear in Pacific Graphics 201

The Geography of Non-formal Manifolds

We show that there exist non-formal compact oriented manifolds of dimension $n$ and with first Betti number $b_1=b\geq 0$ if and only if $n\geq 3$ and $b\geq 2$, or $n\geq (7-2b)$ and $0\leq b\leq 2$. Moreover, we present explicit examples for each one of these cases.Comment: 8 pages, one reference update

Seidel elements and mirror transformations

The goal of this article is to give a precise relation between the mirror symmetry transformation of Givental and the Seidel elements for a smooth projective toric variety $X$ with $-K_X$ nef. We show that the Seidel elements entirely determine the mirror transformation and mirror coordinates.Comment: 36 pages. We corrected several issues as pointed out by the refere

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

Bott periodicity and stable quantum classes

We use Bott periodicity to relate previously defined quantum classes to certain "exotic Chern classes" on $BU$. This provides an interesting computational and theoretical framework for some Gromov-Witten invariants connected with cohomological field theories. This framework has applications to study of higher dimensional, Hamiltonian rigidity aspects of Hofer geometry of $\mathbb{CP} ^{n}$, one of which we discuss here.Comment: prepublication versio

Endoparasites in the feces of arctic foxes in a terrestrial ecosystem in Canada

AbstractThe parasites of arctic foxes in the central Canadian Arctic have not been well described. Canada’s central Arctic is undergoing dramatic environmental change, which is predicted to cause shifts in parasite and wildlife species distributions, and trophic interactions, requiring that baselines be established to monitor future alterations. This study used conventional, immunological, and molecular fecal analysis techniques to survey the current gastrointestinal endoparasite fauna currently present in arctic foxes in central Nunavut, Canada. Ninety-five arctic fox fecal samples were collected from the terrestrial Karrak Lake ecosystem within the Queen Maud Gulf Migratory Bird Sanctuary. Samples were examined by fecal flotation to detect helminths and protozoa, immunofluorescent assay (IFA) to detect Cryptosporidium and Giardia, and quantitative PCR with melt-curve analysis (qPCR-MCA) to detect coccidia. Positive qPCR-MCA products were sequenced and analyzed phylogenetically. Arctic foxes from Karrak Lake were routinely shedding eggs from Toxascaris leonina (63%). Taeniid (15%), Capillarid (1%), and hookworm eggs (2%), Sarcocystis sp. sporocysts 3%), and Eimeria sp. (6%), and Cystoisospora sp. (5%) oocysts were present at a lower prevalence on fecal flotation. Cryptosporidium sp. (9%) and Giardia sp. (16%) were detected by IFA. PCR analysis detected Sarcocystis (15%), Cystoisospora (5%), Eimeria sp., and either Neospora sp. or Hammondia sp. (1%). Through molecular techniques and phylogenetic analysis, we identified two distinct lineages of Sarcocystis sp. present in arctic foxes, which probably derived from cervid and avian intermediate hosts. Additionally, we detected previously undescribed genotypes of Cystoisospora. Our survey of gastrointestinal endoparasites in arctic foxes from the central Canadian Arctic provides a unique record against which future comparisons can be made

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

Birational cobordism invariance of uniruled symplectic manifolds

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and blow-down. This theorem follows from a general Relative/Absolute correspondence for a symplectic manifold together with a symplectic submanifold. A direct consequence is that symplectic uniruledness is a symplectic birational invariant. Here we use Guillemin and Sternberg's notion of cobordism as the symplectic analogue of the birational equivalence.Comment: To appear in Invent. Mat