Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice *

Abstract. We study homoclinic snaking of one-dimensional, localized states on two-dimensional, bistable lattices via the method of exponential asymptotics. Within a narrow region of parameter space, fronts connecting the two stable states are pinned to the underlying lattice. Localized solutions are formed by matching two such stationary fronts back-to-back; depending on the orientation relative to the lattice, the solution branch may "snake" back and forth within the pinning region via successive saddle-node bifurcations. Standard continuum approximations in the weakly nonlinear limit (equivalently, the limit of small mesh size) do not exhibit this behavior, due to the resultant leading-order reaction-diffusion equation lacking a periodic spatial structure. By including exponentially small effects hidden beyond all algebraic orders in the asymptotic expansion, we find that exponentially small but exponentially growing terms are switched on via error function smoothing near Stokes lines. Eliminating these otherwise unbounded beyond-all-orders terms selects the origin (modulo the mesh size) of the front, and matching two fronts together yields a set of equations describing the snaking bifurcation diagram. This is possible only within an exponentially small region of parameter space-the pinning region. Moreover, by considering fronts orientated at an arbitrary angle ψ to the x-axis, we show that the width of the pinning region is nonzero only if tan ψ is rational or infinite. The asymptotic results are compared with numerical calculations, with good agreement. Key words. homoclinic snaking, direction-dependent pinning, exponential asymptotics, square lattice AMS subject classifications. 34A33, 34E05, 34K18 DOI. 10.1137/140966897 1. Introduction. The phenomenon known as homoclinic snaking, referring to the existence of a multiplicity of localized solutions within a narrow region of parameter space, has been observed in a wide variety of experimental and theoretical context

A Robust Numerical Method to Study Oscillatory Instability of Gap Solitary Waves *

Abstract. The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. These problems may exhibit oscillatory instabilities where eigenvalues detach from the edges of the continuous spectrum-socalled edge bifurcations. A numerical framework, based on a fast robust shooting algorithm using exterior algebra, is described. The complete algorithm is robust in the sense that it does not produce spurious unstable eigenvalues. The algorithm allows us to locate exactly where the unstable discrete eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows for stable shooting along multidimensional stable and unstable manifolds. The method is illustrated by computing the stability and instability of gap solitary waves of a coupled mode model

Entamoeba chiangraiensis n. sp. (Amoebozoa: Entamoebidae) isolated from the gut of Asian swamp eel (Monopterus albus) in northern Thailand.

The genus Entamoeba comprises mostly gut parasites and commensals of invertebrate and vertebrate animals including humans. Herein, we report a new species of Entamoeba isolated from the gut of Asian swamp eels (Monopterus albus) in northern Thailand. Morphologically, the trophozoite is elongated and has a single prominent pseudopodium with no clear uroid. The trophozoite is actively motile, 30-50 µm in length and 9-13 µm in width. Observed cysts were uninucleate, ranging in size from 10 to 17.5 µm in diameter. Chromatin forms a fine, even lining along the inner nuclear membrane. Fine radial spokes join the karyosome to peripheral chromatin. Size, host and nucleus morphology set our organism apart from other members of the genus reported from fish. The SSU rRNA gene sequences of the new isolates are the first molecular data of an Entamoeba species from fish. Phylogenetic analysis places the new organism as sister to Entamoeba invadens. Based on the distinct morphology and SSU rRNA gene sequence we describe it as a new species, Entamoeba chiangraiensis

On The Nature of Ring Patterns In Ice Crystals of Hailstones: A Signature of Global Warming

In the present work we report for the first time the ring patterns in the ice crystals procured from hailstones at Doom Dooma (27.40N, 95.30E) on March 17, 2016 and April 9, 2017. We have measured the intensity patterns of the rings with the help of a software (ImageJ). Since the ring patterns have been observed in the ice crystals of hailstones only in recent years, it is reasonable to believe that they will give valuable information on the process of ice nucleation and possibly on global warming

Water resources: future Nile river flows

Climate change is projected to increase annual Nile river flow; importantly, year-to-year variability is also expected to increase markedly. More variable flows could present a challenge for consistent water resource provision in this region

Use of Surrogate end points in HTA

The different actors involved in health system decision-making and regulation have to deal with the question which are valid parameters to assess the health value of health technologies

Core Microbial Functional Activities in Ocean Environments Revealed by Global Metagenomic Profiling Analyses

Metagenomics-based functional profiling analysis is an effective means of gaining deeper insight into the composition of marine microbial populations and developing a better understanding of the interplay between the functional genome content of microbial communities and abiotic factors. Here we present a comprehensive analysis of 24 datasets covering surface and depth-related environments at 11 sites around the world's oceans. The complete datasets comprises approximately 12 million sequences, totaling 5,358 Mb. Based on profiling patterns of Clusters of Orthologous Groups (COGs) of proteins, a core set of reference photic and aphotic depth-related COGs, and a collection of COGs that are associated with extreme oxygen limitation were defined. Their inferred functions were utilized as indicators to characterize the distribution of light- and oxygen-related biological activities in marine environments. The results reveal that, while light level in the water column is a major determinant of phenotypic adaptation in marine microorganisms, oxygen concentration in the aphotic zone has a significant impact only in extremely hypoxic waters. Phylogenetic profiling of the reference photic/aphotic gene sets revealed a greater variety of source organisms in the aphotic zone, although the majority of individual photic and aphotic depth-related COGs are assigned to the same taxa across the different sites. This increase in phylogenetic and functional diversity of the core aphotic related COGs most probably reflects selection for the utilization of a broad range of alternate energy sources in the absence of light.This work was supported by King Abdullah University for Science and Technology Global Collaborative Partners (GCR) program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

ShadowTutor: Distributed Partial Distillation for Mobile Video DNN Inference

Following the recent success of deep neural networks (DNN) on video computer vision tasks, performing DNN inferences on videos that originate from mobile devices has gained practical significance. As such, previous approaches developed methods to offload DNN inference computations for images to cloud servers to manage the resource constraints of mobile devices. However, when it comes to video data, communicating information of every frame consumes excessive network bandwidth and renders the entire system susceptible to adverse network conditions such as congestion. Thus, in this work, we seek to exploit the temporal coherence between nearby frames of a video stream to mitigate network pressure. That is, we propose ShadowTutor, a distributed video DNN inference framework that reduces the number of network transmissions through intermittent knowledge distillation to a student model. Moreover, we update only a subset of the student's parameters, which we call partial distillation, to reduce the data size of each network transmission. Specifically, the server runs a large and general teacher model, and the mobile device only runs an extremely small but specialized student model. On sparsely selected key frames, the server partially trains the student model by targeting the teacher's response and sends the updated part to the mobile device. We investigate the effectiveness of ShadowTutor with HD video semantic segmentation. Evaluations show that network data transfer is reduced by 95% on average. Moreover, the throughput of the system is improved by over three times and shows robustness to changes in network bandwidth.Comment: Accepted at ICPP 202