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In this paper, we model the planar motion of a quadcopter, and develop a linear model of the same. We perform stability analysis of the open loop system and develop a PD controller for its position control. We compare the closed loop response between the linear and non linear systems using the controller developed for the linear system. We also perform stability analysis for the linear and non linear systems, and compare the PD controller with modern deep neural methods based on reinforcement learning actor-critic networks.

In self driving car applications, there is a requirement to predict the location of the lane given an input RGB front facing image. In this paper, we propose an architecture that allows us to increase the speed and robustness of road detection without a large hit in accuracy by introducing an underlying shared feature space that is propagated over time, which serves as a flowing dynamic memory. By utilizing the gist of previous frames, we train the network to predict the current road with a greater accuracy and lesser deviation from previous frames.

Hand gestures are a natural means of interaction in Augmented Reality and Virtual Reality (AR/VR) applications. Recently, there has been an increased focus on removing the dependence of accurate hand gesture recognition on complex sensor setup found in expensive proprietary devices such as the Microsoft HoloLens, Daqri and Meta Glasses. Most such solutions either rely on multi-modal sensor data or deep neural networks that can benefit greatly from abundance of labelled data. Datasets are an integral part of any deep learning based research. They have been the principal reason for the substantial progress in this field, both, in terms of providing enough data for the training of these models, and, for benchmarking competing algorithms. However, it is becoming increasingly difficult to generate enough labelled data for complex tasks such as hand gesture recognition. The goal of this work is to introduce a framework capable of generating photo-realistic videos that have labelled hand bounding box and fingertip that can help in designing, training, and benchmarking models for hand-gesture recognition in AR/VR applications. We demonstrate the efficacy of our framework in generating videos with diverse backgrounds., Comment: Presented at the ICCV 2019 Workshop: The 5th International Workshop on Observing And Understanding Hands In Action

We introduce the concept of design continuums for the data layout of key-value stores. A design continuum unifies major distinct data structure designs under the same model. The critical insight and potential long-term impact is that such unifying models 1) render what we consider up to now as fundamentally different data structures to be seen as views of the very same overall design space, and 2) allow seeing new data structure designs with performance properties that are not feasible by existing designs. The core intuition behind the construction of design continuums is that all data structures arise from the very same set of fundamental design principles, i.e., a small set of data layout design concepts out of which we can synthesize any design that exists in the literature as well as new ones. We show how to construct, evaluate, and expand, design continuums and we also present the first continuum that unifies major data structure designs, i.e., B+tree, B-epsilon-tree, LSM-tree, and LSH-table. The practical benefit of a design continuum is that it creates a fast inference engine for the design of data structures. For example, we can predict near instantly how a specific design change in the underlying storage of a data system would affect performance, or reversely what would be the optimal data structure (from a given set of designs) given workload characteristics and a memory budget. In turn, these properties allow us to envision a new class of self-designing key-value stores with a substantially improved ability to adapt to workload and hardware changes by transitioning between drastically different data structure designs to assume a diverse set of performance properties at will.

We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for 1) conservation of mass, and 2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The resultant algebraic system is extremely sparse even for high degree polynomial basis. Furthermore, the system can be efficiently assembled and solved for each element separately., Comment: submitted to ICOSAHOM 2018

Hand gestures form an intuitive means of interaction in Mixed Reality (MR) applications. However, accurate gesture recognition can be achieved only through state-of-the-art deep learning models or with the use of expensive sensors. Despite the robustness of these deep learning models, they are generally computationally expensive and obtaining real-time performance on-device is still a challenge. To this end, we propose a novel lightweight hand gesture recognition framework that works in First Person View for wearable devices. The models are trained on a GPU machine and ported on an Android smartphone for its use with frugal wearable devices such as the Google Cardboard and VR Box. The proposed hand gesture recognition framework is driven by a cascade of state-of-the-art deep learning models: MobileNetV2 for hand localisation, our custom fingertip regression architecture followed by a Bi-LSTM model for gesture classification. We extensively evaluate the framework on our EgoGestAR dataset. The overall framework works in real-time on mobile devices and achieves a classification accuracy of 80% on EgoGestAR video dataset with an average latency of only 0.12 s., Comment: The AAAI 2019 Workshop on Plan, Activity, and Intent Recognition. arXiv admin note: substantial text overlap with arXiv:1904.06122

Hand gestures are an intuitive, socially acceptable, and a non-intrusive interaction modality in Mixed Reality (MR) and smartphone based applications. Unlike speech interfaces, they tend to perform well even in shared and public spaces. Hand gestures can also be used to interact with smartphones in situations where the user's ability to physically touch the device is impaired. However, accurate gesture recognition can be achieved through state-of-the-art deep learning models or with the use of expensive sensors. Despite the robustness of these deep learning models, they are computationally heavy and memory hungry, and obtaining real-time performance on-device without additional hardware is still a challenge. To address this, we propose AirPen: an analogue to pen on paper, but in air, for in-air writing and gestural commands that works seamlessly in First and Second Person View. The models are trained on a GPU machine and ported on an Android smartphone. AirPen comprises of three deep learning models that work in tandem: MobileNetV2 for hand localisation, our custom fingertip regression architecture followed by a Bi-LSTM model for gesture classification. The overall framework works in real-time on mobile devices and achieves a classification accuracy of 80% with an average latency of only 0.12 s., Comment: Presented at the CHI'19 Workshop: Addressing the Challenges of Situationally-Induced Impairments and Disabilities in Mobile Interaction, 2019 (arXiv:1904.05382)

Neural Architecture Search (NAS) has been a source of dramatic improvements in neural network design, with recent results meeting or exceeding the performance of hand-tuned architectures. However, our understanding of how to represent the search space for neural net architectures and how to search that space efficiently are both still in their infancy. We have performed an in-depth analysis to identify limitations in a widely used search space and a recent architecture search method, Differentiable Architecture Search (DARTS). These findings led us to introduce novel network blocks with a more general, balanced, and consistent design; a better-optimized Cosine Power Annealing learning rate schedule; and other improvements. Our resulting sharpDARTS search is 50% faster with a 20-30% relative improvement in final model error on CIFAR-10 when compared to DARTS. Our best single model run has 1.93% (1.98+/-0.07) validation error on CIFAR-10 and 5.5% error (5.8+/-0.3) on the recently released CIFAR-10.1 test set. To our knowledge, both are state of the art for models of similar size. This model also generalizes competitively to ImageNet at 25.1% top-1 (7.8% top-5) error. We found improvements for existing search spaces but does DARTS generalize to new domains? We propose Differentiable Hyperparameter Grid Search and the HyperCuboid search space, which are representations designed to leverage DARTS for more general parameter optimization. Here we find that DARTS fails to generalize when compared against a human's one shot choice of models. We look back to the DARTS and sharpDARTS search spaces to understand why, and an ablation study reveals an unusual generalization gap. We finally propose Max-W regularization to solve this problem, which proves significantly better than the handmade design. Code will be made available., Comment: 9 pages, 6 figures, 4 tables

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric., Comment: 16 pages

A robot can now grasp an object more effectively than ever before, but once it has the object what happens next? We show that a mild relaxation of the task and workspace constraints implicit in existing object grasping datasets can cause neural network based grasping algorithms to fail on even a simple block stacking task when executed under more realistic circumstances. To address this, we introduce the JHU CoSTAR Block Stacking Dataset (BSD), where a robot interacts with 5.1 cm colored blocks to complete an order-fulfillment style block stacking task. It contains dynamic scenes and real time-series data in a less constrained environment than comparable datasets. There are nearly 12,000 stacking attempts and over 2 million frames of real data. We discuss the ways in which this dataset provides a valuable resource for a broad range of other topics of investigation. We find that hand-designed neural networks that work on prior datasets do not generalize to this task. Thus, to establish a baseline for this dataset, we demonstrate an automated search of neural network based models using a novel multiple-input HyperTree MetaModel, and find a final model which makes reasonable 3D pose predictions for grasping and stacking on our dataset. The CoSTAR BSD, code, and instructions are available at https://sites.google.com/site/costardataset., Comment: This is a major revision refocusing the topic towards the JHU CoSTAR Block Stacking Dataset, workspace constraints, and a comparison of HyperTrees with hand-designed algorithms. 12 pages, 10 figures, and 3 tables

In this paper we will consider two curl-curl equation in two dimensions. One curl-curl problem for a scalar quantity $F$ and one problem for a vector field $\bf{E}$. For Dirichlet boundary conditions $\bf{n} \times \bf{E} =$ $ \hat{E}_{\dashv}$ on $\bf{E}$ and Neumann boundary conditions $\bf{n} \times \mbox{curl}$ $F=\hat{E}_{\dashv}$, we expect the solutions to satisfy $\bf{E}=\mbox{curl}$ $F$. When we use algebraic dual polynomial representations, these identities continue to hold at the discrete level. Equivalence will be proved and illustrated with a computational example., Comment: 12 Pages, 4 figures

This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discussed. Differential operators are represented by sparse incidence matrices, while weighted mass matrices play the role of metric-dependent Hodge matrices. The resulting mixed formulations are point-wise divergence-free if the right hand side function f = 0. The method is inf-sup stable and displays optimal convergence on orthogonal and non-affine grids., Comment: 43 pages

Given a sequence of finite element spaces which form a de Rham sequence, we will construct a dual representation of these spaces with associated differential operators which connect these spaces such that they also form a de Rham sequence. The matrix which converts primal representations to dual representations -- the Hodge matrix -- is the mass or Gram matrix. It will be shown that a bilinear form of a primal and a dual representation is equal to the vector inner product of the expansion coefficients (degrees of freedom) of both representations. This leads to very sparse system matrices, even for high order methods. The derivative of dual representations will be defined. Vector operations, grad, curl and div, for primal and dual representations are both topological and do not depend on the metric, i.e. the size and shape of the mesh or the order of the numerical method. Derivatives are evaluated by applying sparse incidence and inclusion matrices to the expansion coefficients of the representations. As illustration of the use of dual representations, the method will be applied to i) a mixed formulation for the Poisson problem in 3D, ii) it will be shown that this approach allows one to preserve the equivalence between Dirichlet and Neumann problems in the finite dimensional setting and, iii) the method will be applied to the approximation of grad-div eigenvalue problem on affine and non-affine meshes., Comment: This is version5 of this article