An Alternate Construction of an Access-Optimal Regenerating Code with Optimal Sub-Packetization Level

Given the scale of today's distributed storage systems, the failure of an individual node is a common phenomenon. Various metrics have been proposed to measure the efficacy of the repair of a failed node, such as the amount of data download needed to repair (also known as the repair bandwidth), the amount of data accessed at the helper nodes, and the number of helper nodes contacted. Clearly, the amount of data accessed can never be smaller than the repair bandwidth. In the case of a help-by-transfer code, the amount of data accessed is equal to the repair bandwidth. It follows that a help-by-transfer code possessing optimal repair bandwidth is access optimal. The focus of the present paper is on help-by-transfer codes that employ minimum possible bandwidth to repair the systematic nodes and are thus access optimal for the repair of a systematic node. The zigzag construction by Tamo et al. in which both systematic and parity nodes are repaired is access optimal. But the sub-packetization level required is $r^k$ where $r$ is the number of parities and $k$ is the number of systematic nodes. To date, the best known achievable sub-packetization level for access-optimal codes is $r^{k/r}$ in a MISER-code-based construction by Cadambe et al. in which only the systematic nodes are repaired and where the location of symbols transmitted by a helper node depends only on the failed node and is the same for all helper nodes. Under this set-up, it turns out that this sub-packetization level cannot be improved upon. In the present paper, we present an alternate construction under the same setup, of an access-optimal code repairing systematic nodes, that is inspired by the zigzag code construction and that also achieves a sub-packetization level of $r^{k/r}$.Comment: To appear in National Conference on Communications 201

Why my photos look sideways or upside down? Detecting Canonical Orientation of Images using Convolutional Neural Networks

Image orientation detection requires high-level scene understanding. Humans use object recognition and contextual scene information to correctly orient images. In literature, the problem of image orientation detection is mostly confronted by using low-level vision features, while some approaches incorporate few easily detectable semantic cues to gain minor improvements. The vast amount of semantic content in images makes orientation detection challenging, and therefore there is a large semantic gap between existing methods and human behavior. Also, existing methods in literature report highly discrepant detection rates, which is mainly due to large differences in datasets and limited variety of test images used for evaluation. In this work, for the first time, we leverage the power of deep learning and adapt pre-trained convolutional neural networks using largest training dataset to-date for the image orientation detection task. An extensive evaluation of our model on different public datasets shows that it remarkably generalizes to correctly orient a large set of unconstrained images; it also significantly outperforms the state-of-the-art and achieves accuracy very close to that of humans

Mass-Transport Models with Fragmentation and Aggregation

We present a review of nonequilibrium phase transitions in mass-transport models with kinetic processes like fragmentation, diffusion, aggregation, etc. These models have been used extensively to study a wide range of physical problems. We provide a detailed discussion of the analytical and numerical techniques used to study mass-transport phenomena.Comment: 29 pages, 4 figure

Compact Environment-Invariant Codes for Robust Visual Place Recognition

Robust visual place recognition (VPR) requires scene representations that are invariant to various environmental challenges such as seasonal changes and variations due to ambient lighting conditions during day and night. Moreover, a practical VPR system necessitates compact representations of environmental features. To satisfy these requirements, in this paper we suggest a modification to the existing pipeline of VPR systems to incorporate supervised hashing. The modified system learns (in a supervised setting) compact binary codes from image feature descriptors. These binary codes imbibe robustness to the visual variations exposed to it during the training phase, thereby, making the system adaptive to severe environmental changes. Also, incorporating supervised hashing makes VPR computationally more efficient and easy to implement on simple hardware. This is because binary embeddings can be learned over simple-to-compute features and the distance computation is also in the low-dimensional hamming space of binary codes. We have performed experiments on several challenging data sets covering seasonal, illumination and viewpoint variations. We also compare two widely used supervised hashing methods of CCAITQ and MLH and show that this new pipeline out-performs or closely matches the state-of-the-art deep learning VPR methods that are based on high-dimensional features extracted from pre-trained deep convolutional neural networks.Comment: Conference on Computer and Robot Vision (CRV) 201

Codes With Hierarchical Locality

In this paper, we study the notion of {\em codes with hierarchical locality} that is identified as another approach to local recovery from multiple erasures. The well-known class of {\em codes with locality} is said to possess hierarchical locality with a single level. In a {\em code with two-level hierarchical locality}, every symbol is protected by an inner-most local code, and another middle-level code of larger dimension containing the local code. We first consider codes with two levels of hierarchical locality, derive an upper bound on the minimum distance, and provide optimal code constructions of low field-size under certain parameter sets. Subsequently, we generalize both the bound and the constructions to hierarchical locality of arbitrary levels.Comment: 12 pages, submitted to ISIT 201

Tuning density profiles and mobility of inhomogeneous fluids

Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or enhance the particle layering of a model confined fluid impacts its self-diffusivity, viscosity, and entropy. Interestingly, interactions that eliminate particle layering significantly reduce confined fluid mobility, whereas those that enhance layering can have the opposite effect. Excess entropy helps to understand and predict these trends.Comment: 5 pages, 3 figure

Perturbations of the Kerr spacetime in horizon penetrating coordinates

We derive the Teukolsky equation for perturbations of a Kerr spacetime when the spacetime metric is written in either ingoing or outgoing Kerr-Schild form. We also write explicit formulae for setting up the initial data for the Teukolsky equation in the time domain in terms of a three metric and an extrinsic curvature. The motivation of this work is to have in place a formalism to study the evolution in the ``close limit'' of two recently proposed solutions to the initial value problem in general relativity that are based on Kerr-Schild slicings. A perturbative formalism in horizon penetrating coordinates is also very desirable in connection with numerical relativity simulations using black hole ``excision''.Comment: 8 pages, RevTex, 2 figures, final version to appear in CQ