Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane-Emden equation in dimension two

We study the Lane-Emden problem $$\begin{cases} -\Delta u_p =|u_p|^{p-1}u_p&\text{in}\quad \Omega, u_p=0 &\text{on}\quad\partial\Omega, \end{cases}$$ where $\Omega\subset\mathbb R^2$ is a smooth bounded domain and $p>1$ is sufficiently large. We obtain sharp estimates and non-degeneracy of low energy nodal solutions $u_p$ (i.e. nodal solutions satisfying $\lim_{p\to+\infty}p\int_{\Omega}|u_p|^{p+1}dx=16\pi e$). As applications, we prove that the comparable condition $p(\|u_p^+\|_{\infty}-\|u_p^-\|_{\infty})=O(1)$ holds automatically for least energy nodal solutions, which confirms a conjecture raised by (Grossi-Grumiau-Pacella, Ann.I.H. Poincare-AN, 30 (2013), 121-140) and (Grossi-Grumiau-Pacella, J.Math.Pures Appl. 101 (2014), 735-754)

Deep Learning Features at Scale for Visual Place Recognition

The success of deep learning techniques in the computer vision domain has triggered a range of initial investigations into their utility for visual place recognition, all using generic features from networks that were trained for other types of recognition tasks. In this paper, we train, at large scale, two CNN architectures for the specific place recognition task and employ a multi-scale feature encoding method to generate condition- and viewpoint-invariant features. To enable this training to occur, we have developed a massive Specific PlacEs Dataset (SPED) with hundreds of examples of place appearance change at thousands of different places, as opposed to the semantic place type datasets currently available. This new dataset enables us to set up a training regime that interprets place recognition as a classification problem. We comprehensively evaluate our trained networks on several challenging benchmark place recognition datasets and demonstrate that they achieve an average 10% increase in performance over other place recognition algorithms and pre-trained CNNs. By analyzing the network responses and their differences from pre-trained networks, we provide insights into what a network learns when training for place recognition, and what these results signify for future research in this area.Comment: 8 pages, 10 figures. Accepted by International Conference on Robotics and Automation (ICRA) 2017. This is the submitted version. The final published version may be slightly differen

A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations

Magnetization dynamics in magnetic materials is often modeled by the Landau-Lifshitz equation, which is solved numerically in general. In micromagnetic simulations, the computational cost relies heavily on the time-marching scheme and the evaluation of stray field. Explicit marching schemes are efficient but suffer from severe stability constraints, while nonlinear systems of equations have to be solved in implicit schemes though they are unconditionally stable. A better compromise between stability and efficiency is the semi-implicit scheme, such as the Gauss-Seidel projection method (GSPM) and the second-order backward differentiation formula scheme (BDF2). At each marching step, GSPM solves several linear systems of equations with constant coefficients and updates the stray field several times, while BDF2 updates the stray field only once but solves a larger linear system of equations with variable coefficients and a nonsymmetric structure. In this work, we propose a new method, dubbed as GSPM-BDF2, by combing the advantages of both GSPM and BDF2. Like GSPM, this method is first-order accurate in time and second-order accurate in space, and is unconditionally stable with respect to the damping parameter. However, GSPM-BDF2 updates the stray field only once per time step, leading to an efficiency improvement of about $60\%$ than the state-of-the-art GSPM for micromagnetic simulations. For Standard Problem \#4 and \#5 from National Institute of Standards and Technology, GSPM-BDF2 reduces the computational time over the popular software OOMMF by $82\%$ and $96\%$, respectively. Thus, the proposed method provides a more efficient choice for micromagnetic simulations

Convolutional Neural Network-based Place Recognition

Recently Convolutional Neural Networks (CNNs) have been shown to achieve state-of-the-art performance on various classification tasks. In this paper, we present for the first time a place recognition technique based on CNN models, by combining the powerful features learnt by CNNs with a spatial and sequential filter. Applying the system to a 70 km benchmark place recognition dataset we achieve a 75% increase in recall at 100% precision, significantly outperforming all previous state of the art techniques. We also conduct a comprehensive performance comparison of the utility of features from all 21 layers for place recognition, both for the benchmark dataset and for a second dataset with more significant viewpoint changes.Comment: 8 pages, 11 figures, this paper has been accepted by 2014 Australasian Conference on Robotics and Automation (ACRA 2014) to be held in University of Melbourne, Dec 2~

A Holistic Visual Place Recognition Approach Using Lightweight CNNs for Significant ViewPoint and Appearance Changes

This article presents a lightweight visual place recognition approach, capable of achieving high performance with low computational cost, and feasible for mobile robotics under significant viewpoint and appearance changes. Results on several benchmark datasets confirm an average boost of 13% in accuracy, and 12x average speedup relative to state-of-the-art methods

A practical guide to promote informatics-driven efficient biotopographic material development

Micro/nano topographic structures have shown great utility in many biomedical areas including cell therapies, tissue engineering, and implantable devices. Computer-assisted informatics methods hold great promise for the design of topographic structures with targeted properties for a specific medical application. To benefit from these methods, researchers and engineers require a highly reusable “one structural parameter – one set of cell responses” database. However, existing confounding factors in topographic cell culture devices seriously impede the acquisition of this kind of data. Through carefully dissecting the confounding factors and their possible reasons for emergence, we developed corresponding guideline requirements for topographic cell culture device development to remove or control the influence of such factors. Based on these requirements, we then suggested potential strategies to meet them. In this work, we also experimentally demonstrated a topographic cell culture device with controlled confounding factors based on these guideline requirements and corresponding strategies. A “guideline for the development of topographic cell culture devices” was summarized to instruct researchers to develop topographic cell culture devices with the confounding factors removed or well controlled. This guideline aims to promote the establishment of a highly reusable “one structural parameter – one set of cell responses” database that could facilitate the application of informatics methods, such as artificial intelligence, in the rational design of future biotopographic structures with high efficacy

WeedMap: A large-scale semantic weed mapping framework using aerial multispectral imaging and deep neural network for precision farming

We present a novel weed segmentation and mapping framework that processes multispectral images obtained from an unmanned aerial vehicle (UAV) using a deep neural network (DNN). Most studies on crop/weed semantic segmentation only consider single images for processing and classification. Images taken by UAVs often cover only a few hundred square meters with either color only or color and near-infrared (NIR) channels. Computing a single large and accurate vegetation map (e.g., crop/weed) using a DNN is non-trivial due to difficulties arising from: (1) limited ground sample distances (GSDs) in high-altitude datasets, (2) sacrificed resolution resulting from downsampling high-fidelity images, and (3) multispectral image alignment. To address these issues, we adopt a stand sliding window approach that operates on only small portions of multispectral orthomosaic maps (tiles), which are channel-wise aligned and calibrated radiometrically across the entire map. We define the tile size to be the same as that of the DNN input to avoid resolution loss. Compared to our baseline model (i.e., SegNet with 3 channel RGB inputs) yielding an area under the curve (AUC) of [background=0.607, crop=0.681, weed=0.576], our proposed model with 9 input channels achieves [0.839, 0.863, 0.782]. Additionally, we provide an extensive analysis of 20 trained models, both qualitatively and quantitatively, in order to evaluate the effects of varying input channels and tunable network hyperparameters. Furthermore, we release a large sugar beet/weed aerial dataset with expertly guided annotations for further research in the fields of remote sensing, precision agriculture, and agricultural robotics.Comment: 25 pages, 14 figures, MDPI Remote Sensin

Whole-genome sequencing of <em>Oryza brachyantha</em> reveals mechanisms underlying <em>Oryza</em> genome evolution

The wild species of the genus Oryza contain a largely untapped reservoir of agronomically important genes for rice improvement. Here we report the 261-Mb de novo assembled genome sequence of Oryza brachyantha. Low activity of long-terminal repeat retrotransposons and massive internal deletions of ancient long-terminal repeat elements lead to the compact genome of Oryza brachyantha. We model 32,038 protein-coding genes in the Oryza brachyantha genome, of which only 70% are located in collinear positions in comparison with the rice genome. Analysing breakpoints of non-collinear genes suggests that double-strand break repair through non-homologous end joining has an important role in gene movement and erosion of collinearity in the Oryza genomes. Transition of euchromatin to heterochromatin in the rice genome is accompanied by segmental and tandem duplications, further expanded by transposable element insertions. The high-quality reference genome sequence of Oryza brachyantha provides an important resource for functional and evolutionary studies in the genus Oryza