11,770 research outputs found

    A class of index coding problems with rate 1/3

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    An index coding problem with nn messages has symmetric rate RR if all nn messages can be conveyed at rate RR. In a recent work, a class of index coding problems for which symmetric rate 13\frac{1}{3} is achievable was characterised using special properties of the side-information available at the receivers. In this paper, we show a larger class of index coding problems (which includes the previous class of problems) for which symmetric rate 13\frac{1}{3} is achievable. In the process, we also obtain a stricter necessary condition for rate 13\frac{1}{3} feasibility than what is known in literature.Comment: Shorter version submitted to ISIT 201

    On Distance Magic Harary Graphs

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    This paper establishes two techniques to construct larger distance magic and (a, d)-distance antimagic graphs using Harary graphs and provides a solution to the existence of distance magicness of legicographic product and direct product of G with C4, for every non-regular distance magic graph G with maximum degree |V(G)|-1.Comment: 12 pages, 1 figur

    Heat Treat Furnace Operations

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    The subject of heat treatment filrnaces is broad based and the intention of this paper is to cover some aspects of heat treatment operations and control. With my limited exposure to carburising and hardening operations, I would like to share my experiences in the use of furnaces in controlled conditions

    Towards a Finite-NN Hologram

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    We suggest that holographic tensor models related to SYK are viable candidates for exactly (ie., non-perturbatively in NN) solvable holographic theories. The reason is that in these theories, the Hilbert space is a spinor representation, and the Hamiltonian (at least in some classes) can be arranged to commute with the Clifford level. This makes the theory solvable level by level. We demonstrate this for the specific case of the uncolored O(n)3O(n)^3 tensor model with arbitrary even nn, and reduce the question of determining the spectrum and eigenstates to an algebraic equation relating Young tableaux. Solving this reduced problem is conceptually trivial and amounts to matching the representations on either side, as we demonstrate explicitly at low levels. At high levels, representations become bigger, but should still be tractable. None of our arguments require any supersymmetry.Comment: 16 page

    Electron transfer in chemistry and biology - the primary events in photosynthesis

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    One of the most important chemical reactions is electron transfer from one atomic/molecular unit to another. This reaction, accompanied by proton and hydrogen atom transfers, occurs in a cascade in many biological processes, including photosynthesis. The key chemical steps involved in photosynthesis and the many unsolved mysteries are described in this article

    Coded Caching based on Combinatorial Designs

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    We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called \textit{cache}) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. In this work, we propose a binary matrix model to construct the coded caching scheme. The ones in such a \textit{caching matrix} indicate uncached subfiles at the users. Identity submatrices of the caching matrix represent transmissions in the delivery phase. Using this model, we then propose several novel constructions for coded caching based on the various types of combinatorial designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement (uncached fraction being Θ(1K)\Theta(\frac{1}{\sqrt{K}}) or Θ(1K)\Theta(\frac{1}{K}), KK being the number of users), they provide a rate that is either constant or decreasing (O(1K)O(\frac{1}{K})) with increasing KK, and moreover require competitively small levels of subpacketization (being O(Ki),1i3O(K^i), 1\leq i\leq 3), which is an extremely important parameter in practical applications of coded caching. We mark this work as another attempt to exploit the well-developed theory of combinatorial designs for the problem of constructing caching schemes, utilizing the binary caching model we develop.Comment: 10 pages, Appeared in Proceedings of IEEE ISIT 201
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