A class of index coding problems with rate 1/3

An index coding problem with $n$ messages has symmetric rate $R$ if all $n$ messages can be conveyed at rate $R$. In a recent work, a class of index coding problems for which symmetric rate $\frac{1}{3}$ 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 $\frac{1}{3}$ is achievable. In the process, we also obtain a stricter necessary condition for rate $\frac{1}{3}$ feasibility than what is known in literature.Comment: Shorter version submitted to ISIT 201

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

X-raying the coronae of HD~155555

We present an analysis of the high-resolution Chandra observation of the multiple system, HD 155555 (an RS CVn type binary system, HD 155555 AB, and its spatially resolved low-mass companion HD 155555 C). This is an intriguing system which shows properties of both an active pre-main sequence star and a synchronised (main sequence) binary. We obtain the emission measure distribution, temperature structures, plasma densities, and abundances of this system and compare them with the coronal properties of other young/active stars. HD 155555 AB and HD 155555 C produce copious X-ray emission with log Lx of 30.54 and 29.30, respectively, in the 0.3-6.0 keV energy band. The light curves of individual stars show variability on timescales of few minutes to hours. We analyse the dispersed spectra and reconstruct the emission measure distribution using spectral line analysis. The resulting elemental abundances exhibit inverse first ionisation potential effect in both cases. An analysis of He-like triplets yields a range of coronal electron densities ~10^10-10^13 cm-3. Since HD 155555 AB is classified both as an RS CVn and a PMS star, we compare our results with those of other slightly older active main-sequence stars and T Tauri stars, which indicates that the coronal properties of HD 155555 AB closely resemble that of an older RS CVn binary rather than a younger PMS star. Our results also suggests that the properties of HD 155555 C is very similar to those of other active M dwarfs.Comment: 17 pages, 23 figues, Accepted in Ap

EFFECT OF SILYMARIN ON INTESTINAL ALKALINE PHOSPHATASE LEVEL IN A RAT MODEL OF TYPE 2 DIABETES MELLITUS: STREPTOZOTOCIN AND HIGH-FAT DIET TREATED WISTAR RATS

Objective: This research elucidated the role of silymarin on intestinal alkaline phosphatase (IAP) level in type 2 diabetic rats.Methods: The type 2 diabetes mellitus was induced by a high-fat diet (HFD - 58% calories fat) for 2 weeks, and rats were intraperitoneally injected with streptozotocin (STZ) 35 mg/kg. Wistar rats were divided into four groups. Group I served as a non-diabetic (normal), Group II served as diabetic, Group III diabetic animals treated glibenclamide 600 μg/kg for 14 days, and Group IV diabetic animal treated with glibenclamide and silymarin 50 mg/kg/twice/d for 14 days. At the end of the study, blood glucose, lipid profile, and IAP level were measured.Results: A significant decrease in IAP, elevated levels of blood glucose, and lipid profile was seen in diabetic rats when compared with normal. The silymarin treatment showed a significant increase in IAP level, a significant reduction in glucose and lipid profile than diabetic rats.Conclusion: The present study concludes that silymarin treatment enhances the IAP levels which protect against hyperglycemia, hyperlipidemia, and vascular complications in diabetic rats