Codes with Locality for Two Erasures

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated to small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan \textit{et al}, in which recovery from a single erasure is considered. By studying the Generalized Hamming Weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Tur\'an graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from $2$ erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.Comment: 14 pages, 3 figures, Updated for improved readabilit

Effect of herbal combination of triphala and garcinia cambogia extracts on anthropometric measurements and lipid profile in high fat diet induced obesity in rats

Background: Obesity, occurring at epidemic rates globally, is a major risk factor for DM and CVD. Despite advances in understanding its pathogenesis, the pharmacotherapy for obesity remains limited for achievable weight loss, safety and tolerability of the medicines. Almost all approved medications for long term use in obesity treatment result in health issues. Due to the ADRs associated with many antiobesity drugs, the drug trials have focused on screening herbal medicines that are reportedly used in the treatment of obesity and which have minimal side effects.Methods: In this study rats were divided into eight groups of six rats each. In the first approach, the rats were first made obese by feeding HFD for three weeks. In the second, treatment with the herbal extracts was given simultaneously with the HFD to the experimental rats. Rat were fed HFD for six weeks along with treatment of herbal extracts and the effect on their body weight, daily food intake and lipid-profile were evaluated.Results: Results showed that rats fed HFD for a six week period, supplemented with herbal preparations of triphala and G. cambogia presented with significant reduction in body weight, energy intake, and improved the lipid-profile as compared to the rats fed with HFD group.Conclusions: Our findings suggest that triphala and G. cambogia can counter the effects of HFD intake and have the potential for use as antiobesity agents with desirable body weight, food intake, fluid intake, and lipid-profile modulating properties