Visual scene understanding is the core task in making any crucial decision in any computer vision system. Although popular computer vision datasets like Cityscapes, MS-COCO, PASCAL provide good benchmarks for several tasks (e.g. image classification, segmentation, object detection), these datasets are hardly suitable for post disaster damage assessments. On the other hand, existing natural disaster datasets include mainly satellite imagery which have low spatial resolution and a high revisit period. Therefore, they do not have a scope to provide quick and efficient damage assessment tasks. Unmanned Aerial Vehicle (UAV) can effortlessly access difficult places during any disaster and collect high resolution imagery that is required for aforementioned tasks of computer vision. To address these issues we present a high resolution UAV imagery, FloodNet, captured after the hurricane Harvey. This dataset demonstrates the post flooded damages of the affected areas. The images are labeled pixel-wise for semantic segmentation task and questions are produced for the task of visual question answering. FloodNet poses several challenges including detection of flooded roads and buildings and distinguishing between natural water and flooded water. With the advancement of deep learning algorithms, we can analyze the impact of any disaster which can make a precise understanding of the affected areas. In this paper, we compare and contrast the performances of baseline methods for image classification, semantic segmentation, and visual question answering on our dataset. FloodNet dataset can be downloaded from here: https://github.com/BinaLab/FloodNet-Challenge-EARTHVISION2021.

Recent deep-learning counting techniques revolve around two distinct features of data—sparse data, which favors detection networks, or dense data where density map networks are used. Both techniques fail to address a third scenario, where dense objects are sparsely located. Raw aerial images represent sparse distributions of data in most situations. To address this issue, we propose a novel and exceedingly portable end-to-end model, DisCountNet, and an example dataset to test it on. DisCountNet is a two-stage network that uses theories from both detection and heat-map networks to provide a simple yet powerful design. The first stage, DiscNet, operates on the theory of coarse detection, but does so by converting a rich and high-resolution image into a sparse representation where only important information is encoded. Following this, CountNet operates on the dense regions of the sparse matrix to generate a density map, which provides fine locations and count predictions on densities of objects. Comparing the proposed network to current state-of-the-art networks, we find that we can maintain competitive performance while using a fraction of the computational complexity, resulting in a real-time solution.

In this paper I will investigate the bifurcation and asymptotic behavior of solutions of the Swift-Hohenberg equation and the generalized Swift-Hohenberg equation with the Dirichlet boundary condition on a onedimensional domain (0, L). I will also study the bifurcation and stability of patterns in the n-dimensional Swift-Hohenberg equation with the odd-periodic and periodic boundary conditions. It is shown that each equation bifurcates from the trivial solution to an attractor A λ when the control parameter λ crosses λc, the principal eigenvalue of (I + ∆) 2 . The local behavior of solutions and their bifurcation to an invariant set near higher eigenvalues are analyzed as well. ∂ 2 u ∂x 2 + u 3 − u = 0, 2000 Mathematics Subject Classification. Primary: 35G25,37G35; Secondary: 35B40.

In this study, our goal is to track internal ice layers on the Snow Radar data collected by NASA Operation IceBridge. We examine the application of deep learning methods on radar data gathered from polar regions. Artificial intelligence techniques have displayed impressive success in many practical fields. Deep neural networks owe their success to the availability of massive labeled data. However, in many real-world problems, even when a large dataset is available, deep learning methods have shown less success, due to causes such as lack of a large labeled dataset, presence of noise in the data or missing data. In our radar data, the presence of noise is one of the main obstacles in utilizing popular deep learning methods such as transfer learning. Our experiments show that if the neural network is trained to detect contours of objects in electro-optical imagery, it can only track a low percentage of contours in radar data. Fine-tuning and further training do not provide any better results. However, we show that selecting the right model and training it on the radar imagery from the start yields far better results.

Visual scene understanding is the core task in making any crucial decision in any computer vision system. Although popular computer vision datasets like Cityscapes, MS-COCO, PASCAL provide good benchmarks for several tasks (e.g. image classification, segmentation, object detection), these datasets are hardly suitable for post disaster damage assessments. On the other hand, existing natural disaster datasets include mainly satellite imagery which have low spatial resolution and a high revisit period. Therefore, they do not have a scope to provide quick and efficient damage assessment tasks. Unmanned Aerial Vehicle (UAV) can effortlessly access difficult places during any disaster and collect high resolution imagery that is required for aforementioned tasks of computer vision. To address these issues we present a high resolution UAV imagery, FloodNet, captured after the hurricane Harvey. This dataset demonstrates the post flooded damages of the affected areas. The images are labeled pixel-wise for semantic segmentation task and questions are produced for the task of visual question answering. FloodNet poses several challenges including detection of flooded roads and buildings and distinguishing between natural water and flooded water. With the advancement of deep learning algorithms, we can analyze the impact of any disaster which can make a precise understanding of the affected areas. In this paper, we compare and contrast the performances of baseline methods for image classification, semantic segmentation, and visual question answering on our dataset.

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Abstract. In this paper we study the dynamic bifurcation of the SwiftHohenberg equation on a periodic cell Ω = [−L, L]. It is shown that the equations bifurcates from the trivial solution to an attractor A λ when the control parameter λ crosses the critical value. In the odd periodic case, A λ is homeomorphic to S 1 and consists of eight singular points and their connecting orbits. In the periodic case, A λ is homeomorphic to S 1 , and contains a torus and two circles which consist of singular points.

This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mourão et all [MSS]. This model investigates the interaction between the microtubule nucleation, essential dynamics parameters and extinction and their impact on the stability of the system. The considered framework encompasses a system of partial differential equations for the elongation and shortening of microtubules, where the rates of elongation as well as the lifetimes of the elongating shortening phases are linear functions of GTP-tubulin concentration. In a novel way, this paper investigates the stability analysis and provides a bifurcation analysis for the dynamic instability of microtubules in the presence of diffusion and all of the fundamental dynamics parameters. Our stability analysis introduces the phase transition method as a new mathematical tool in the study of microtubule dynamics. The mathematical tools introduced to handle the problem should be of general use.