Quasi-morphisms and L^p-metrics on groups of volume-preserving diffeomorphisms

Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. We show that every homogeneous quasi-morphism on the identity component $Diff_0(M,vol)$ of the group of volume preserving diffeomorphisms of M, which is induced by a quasi-morphism on the fundamental group, is Lipschitz with respect to the L^p-metric on the group $Diff_0(M,vol)$. As a consequence, assuming certain conditions on the fundamental group, we construct bi-Lipschitz embeddings of finite dimensional vector spaces into $Diff_0(M,vol)$.Comment: This is a published versio

In situ analysis for intelligent control

We report a pilot study on in situ analysis of backscatter data for intelligent control of a scientific instrument on an Autonomous Underwater Vehicle (AUV) carried out at the Monterey Bay Aquarium Research Institute (MBARI). The objective of the study is to investigate techniques which use machine intelligence to enable event-response scenarios. Specifically we analyse a set of techniques for automated sample acquisition in the water-column using an electro-mechanical "Gulper", designed at MBARI. This is a syringe-like sampling device, carried onboard an AUV. The techniques we use in this study are clustering algorithms, intended to identify the important distinguishing characteristics of bodies of points within a data sample. We demonstrate that the complementary features of two clustering approaches can offer robust identification of interesting features in the water-column, which, in turn, can support automatic event-response control in the use of the Gulper

Do logarithmic proximity measures outperform plain ones in graph clustering?

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.Comment: 11 pages, 5 tables, 9 figures. Accepted for publication in the Proceedings of 6th International Conference on Network Analysis, May 26-28, 2016, Nizhny Novgorod, Russi

Capillary origami: spontaneous wrapping of a droplet with an elastic sheet

The interaction between elasticity and capillarity is used to produce three dimensional structures, through the wrapping of a liquid droplet by a planar sheet. The final encapsulated 3D shape is controlled by tayloring the initial geometry of the flat membrane. A 2D model shows the evolution of open sheets to closed structures and predicts a critical length scale below which encapsulation cannot occur, which is verified experimentally. This {\it elastocapillary length} is found to depend on the thickness as $h^{3/2}$, a scaling favorable to miniaturization which suggests a new way of mass production of 3D micro- or nano-scale objects.Comment: 5 pages, 5 figure

Microsatellites retain phylogenetic signals across genera in eucalypts (Myrtaceae)

The utility of microsatellites (SSRs) in reconstructing phylogenies is largely confined to studies below the genus level, due to the potential of homoplasy resulting from allele size range constraints and poor SSR transferability among divergent taxa. The eucalypt genus Corymbia has been shown to be monophyletic using morphological characters, however, analyses of intergenic spacer sequences have resulted in contradictory hypotheses- showing the genus as either equivocal or paraphyletic. To assess SSR utility in higher order phylogeny in the family Myrtaceae, phylogenetic relationships of the bloodwood eucalypts Corymbia and related genera were investigated using eight polymorphic SSRs. Repeat size variation using the average square and Nei’s distance were congruent and showed Corymbia to be a monophyletic group, supporting morphological characters and a recent combination of the internal and external transcribed spacers dataset. SSRs are selectively neutral and provide data at multiple genomic regions, thus may explain why SSRs retained informative phylogenetic signals despite deep divergences. We show that where the problems of size-range constraints, high mutation rates and size homoplasy are addressed, SSRs might resolve problematic phylogenies of taxa that have diverged for as long as three million generations or 30 million years. Key word

Imaging characteristics and treatment of a penetrating brain injury caused by an oropharyngeal foreign body in a dog

A 4-year-old Border collie was presented with one episode of collapse, altered mentation, and a suspected pharyngeal stick injury. Magnetic resonance imaging (MRI) and computed tomography showed a linear foreign body penetrating the right oropharynx, through the foramen ovale and the brain parenchyma. The foreign body was surgically removed and medical treatment initiated. Complete resolution of clinical signs was noted at recheck 8 weeks later. Repeat MRI showed chronic secondary changes in the brain parenchyma. To the authors' knowledge, this is the first report of the advanced imaging findings and successful treatment of a penetrating oropharyngeal intracranial foreign body in a dog

Inner Space Preserving Generative Pose Machine

Image-based generative methods, such as generative adversarial networks (GANs) have already been able to generate realistic images with much context control, specially when they are conditioned. However, most successful frameworks share a common procedure which performs an image-to-image translation with pose of figures in the image untouched. When the objective is reposing a figure in an image while preserving the rest of the image, the state-of-the-art mainly assumes a single rigid body with simple background and limited pose shift, which can hardly be extended to the images under normal settings. In this paper, we introduce an image "inner space" preserving model that assigns an interpretable low-dimensional pose descriptor (LDPD) to an articulated figure in the image. Figure reposing is then generated by passing the LDPD and the original image through multi-stage augmented hourglass networks in a conditional GAN structure, called inner space preserving generative pose machine (ISP-GPM). We evaluated ISP-GPM on reposing human figures, which are highly articulated with versatile variations. Test of a state-of-the-art pose estimator on our reposed dataset gave an accuracy over 80% on PCK0.5 metric. The results also elucidated that our ISP-GPM is able to preserve the background with high accuracy while reasonably recovering the area blocked by the figure to be reposed.Comment: http://www.northeastern.edu/ostadabbas/2018/07/23/inner-space-preserving-generative-pose-machine