Vector Linear Error Correcting Index Codes and Discrete Polymatroids

The connection between index coding and matroid theory have been well studied in the recent past. El Rouayheb et al. established a connection between multi linear representation of matroids and wireless index coding. Muralidharan and Rajan showed that a vector linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions. Recently index coding with erroneous transmission was considered by Dau et al.. Error correcting index codes in which all receivers are able to correct a fixed number of errors was studied. In this paper we consider a more general scenario in which each receiver is able to correct a desired number of errors, calling such index codes differential error correcting index codes. We show that vector linear differential error correcting index code exists if and only if there exists a representable discrete polymatroid satisfying certain conditionsComment: arXiv admin note: substantial text overlap with arXiv:1501.0506

Optimal Error Correcting Delivery Scheme for Coded Caching with Symmetric Batch Prefetching

Coded caching is used to reduce network congestion during peak hours. A single server is connected to a set of users through a bottleneck link, which generally is assumed to be error-free. During non-peak hours, all the users have full access to the files and they fill their local cache with portions of the files available. During delivery phase, each user requests a file and the server delivers coded transmissions to meet the demands taking into consideration their cache contents. In this paper we assume that the shared link is error prone. A new delivery scheme is required to meet the demands of each user even after receiving finite number of transmissions in error. We characterize the minimum average rate and minimum peak rate for this problem. We find closed form expressions of these rates for a particular caching scheme namely \textit{symmetric batch prefetching}. We also propose an optimal error correcting delivery scheme for coded caching problem with symmetric batch prefetching.Comment: 9 pages and 4 figure

Technology Supported University Evaluation System for an Affiliated University Administration

Any affiliating university in India has a number of teaching and research departments as well as a number of affiliating institutions offering undergraduate and/or postgraduate programs with some of them having research centers approved by the university. Universities may have a number of non-teaching departments offering different types of services to the university community. An affiliated University in Kerala state has teaching departments both in the regular and self-financing streams and affiliated colleges including professional colleges in the aided and unaided sectors

Performance Analysis of a Web Application Using Standard Tools - A Case Study of Paper less E-Governance System for Examinations of University of Kerala

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Consciencialização e Conhecimento Sobre Diabetes Mellitus Gestacional em Mulheres Grávidas

Aim: The study examined the awareness and knowledge about gestational-diabetes-mellitus (GDM) among antenatal-women and found its influential factors through three phases. Method: The sample for phase I was 523 antenatal women. In phases II and III, 33 participants who were identified to be aware of GDM from Phase I were included. Measures used were Gestational-Diabetes-Knowledge-Questionnaire (GDKQ) and an open-ended questionnaire. Results: Age and “number of Pregnancies to date” significantly predicted awareness. Kruskal-Wallis H test indicated that antenatal-women differed in their ‘knowledge' across the trimesters. Mann-Whitney U showed a difference in ‘knowledge' among participants, ‘with' and ‘without' a history of diabetes. Electronic and print-media were identified to be the significant sources of knowledge. Conclusion: The study highlights the importance of implementing methods that enhance the awareness and knowledge of GDM among the antenatal women.Objetivo: Este estudo investigou a perceção e conhecimento sobre Diabetes Mellitus Gestacional (DMG) em mulheres grávidas, bem como os fatores que a influenciam ao longo de três fases. Método: A amostra utilizada na fase I incluiu 523 mulheres grávidas. Nas fases II e III foram consideradas 33 participantes identificadas na fase I como estando consciencializadas para a DMG. As medidas utilizadas foram o Gestational-Diabetes-Knowledge-Questionnaire (GDKQ) e um questionário de respostas abertas. Resultados: A Idade e o Número de Gestações foram preditores significativos da perceção. O teste H de Kruskal-Wallis indicou diferenças no “conhecimento” das mulheres grávidas ao longo dos trimestres. O teste U de Mann-Whitney mostrou diferenças ao nível do “conhecimento” entre as participantes com e sem historial clínico de diabetes. Os meios de comunicação social impressos e eletrónicos foram identificados como fontes significativas de conhecimento. Conclusões: Este estudo salienta a importância de implementar ações com vista a desenvolver a perceção e o conhecimento sobre a DMG, em mulheres grávidas

Multi-access Coded Caching with Decentralized Prefetching

An extension of coded caching referred to as multi-access coded caching where each user can access multiple caches and each cache can serve multiple users is considered in this paper. Most of the literature in multi-access coded caching focuses on cyclic wrap-around cache access where each user is allowed to access an exclusive set of consecutive caches only. In this paper, a more general framework of multi-access caching problem is considered in which each user is allowed to randomly connect to a specific number of caches and multiple users can access the same set of caches. For the proposed system model considering decentralized prefetching, a new delivery scheme is proposed and an expression for per user delivery rate is obtained. A lower bound on the delivery rate is derived using techniques from index coding. The proposed scheme is shown to be optimal among all the linear schemes under certain conditions. An improved delivery rate and a lower bound for the decentralized multi-access coded caching scheme with cyclic wrap-around cache access can be obtained as a special case. By giving specific values to certain parameters, the results of decentralized shared caching scheme and of conventional decentralized caching scheme can be recovered.Comment: 26 pages, 6 figures, 6 tables, Submitted to IEEE Transactions on Communication

Enumerating Stable Nanopores in Graphene and their Geometrical Properties Using the Combinatorics of Hexagonal Lattices

Nanopores in two-dimensional (2D) materials, including graphene, can be used for a variety of applications, such as gas separations, water desalination, and DNA sequencing. So far, however, all plausible isomeric shapes of graphene nanopores have not been enumerated. Instead, a probabilistic approach has been followed to predict nanopore shapes in 2D materials, due to the exponential increase in the number of nanopores as the size of the vacancy increases. For example, there are 12 possible isomers when N=6 atoms are removed, a number that theoretically increases to 11.7 million when N=20 atoms are removed from the graphene lattice. The development of a smaller, exhaustive dataset of stable nanopore shapes can help future experimental and theoretical studies focused on using nanoporous 2D materials in various applications. In this work, we use the theory of 2D triangular "lattice animals" to create a library of all stable graphene nanopore shapes based on a modification of a well-known algorithm in the mathematical combinatorics of polyforms known as Redelmeier's algorithm. We show that there exists a correspondence between graphene nanopores and triangular polyforms (called polyiamonds) as well as hexagonal polyforms (called polyhexes). We develop the concept of a polyiamond ID to identify unique nanopore isomers. We also use concepts from polyiamond and polyhex geometry to eliminate unstable nanopores containing dangling atoms, bonds, and moieties. The exclusion of such unstable nanopores leads to a remarkable reduction in the possible nanopores from 11.7 million for N=20 to only 0.184 million nanopores, thereby indicating that the number of stable nanopores is almost two orders of magnitude lower and is much more tractable. Not only that, by extracting the polyhex outline, our algorithm allows searching for nanopores with dimensions and shape factors in a specified range.Comment: 27 pages and 12 figures in the main text, 6 pages and 5 figures in the supporting informatio