We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, introduced in [1], 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. Starting from [1], 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 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( 1 √ K ) or Θ( 1 K ), K being the number of users), they provide a rate that is either constant or decreasing (O( 1 K )) with increasing K, and moreover require competitively small levels of subpacketization (being O(K i ), 1 ≤ i ≤ 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.

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We consider the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. For this framework, we propose the use of binary matrices (with 0, 1 entries) called computing matrices to describe the map phase and the shuffle phase. Similar binary matrices were recently proposed for the coded caching framework. The structure of ones and zeroes in the binary computing matrix captures the map phase of the MapReduce framework. We present a new simple coded data shuffling scheme for this binary matrix model, based on a identity submatrix cover of the computing matrix. This new coded shuffling scheme has in general a larger communication load than existing schemes, but has the advantage of less complexity overhead than the well-known earlier schemes in literature in terms of the file-splitting and associated indexing and coordination required. We also show that there exists a binary matrix based distributed computing scheme with our new data-shuffling scheme which has strictly less than twice than the communication load of the known optimal scheme in literature. The structure of this new scheme enables it to be applied to the framework of MapReduce with stragglers also, in a straightforward manner, borrowing its advantages and disadvantages from the no-straggler situation. Finally, using binary matrices derived from combinatorial designs, we show specific classes of computing schemes with very low file complexity (number of subfiles in the file), with marginally higher communication load compared to the optimal scheme for equivalent parameters.

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Introduction: Candida is the most important fungal opportunistic pathogen, though it is a normal commensal ora then also it can cause infections in the immunocompromised hosts. As non-albicans Candida have replaced Candida albicans as the predominant pathogen which is more life- threatening, more resistant to antifungal drugs so speciation of Candida is important. To identify & speciate Candida isolates fromObjective: various clinical samples and to nd out their antifungal susceptibility pattern. Samples were screened for budding yeastMaterial and method: cells with the help of Gram stain & KOH mount and then inoculated on SDA with gentamycin and chloramphenicol. For speciation, Germ tube testing was done followed by CHROM agar and chlamydospores on Cornmeal agar. Out of 100 Candida isolates, 19 were CandidaResults: albicans and 81 were non-albicans Candida. Among four antifungals tested, Amphotericin B showed the best efcacy with 83% strains sensitive to it and uconazole showed the least efcacy with 47% strains resistant to it. Though Candida albicans and non-albicans Candida areConclusion: closely related but differ from each other with respect to epidemiology, virulence factors, and antifungal susceptibility. As non-albicans Candida is more life-threatening and more resistant to antifungal agents; speciation of Candida becomes mandatory so that mortality and morbidity of the patients can be overcome.