Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such "local" parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.Comment: 13 pages, Shorter version submitted to ISIT 201

Pseudo-scalar Higgs Boson Production at Threshold N3^3LO and N3^3LL QCD

We present the first results on the production of pseudo-scalar through gluon fusion at the LHC to N$^3$LO in QCD taking into account only soft gluon effects. We have used the effective Lagrangian that describes the coupling of pseudo-scalar with the gluons in the large top quark mass limit. We have used recently available quantities namely the three loop pseudo-scalar form factor and the third order universal soft function in QCD to achieve this. Along with the fixed order results, we also present the process dependent resummation coefficient for threshold resummation to N$^3$LL in QCD. Phenomenological impact of these threshold N$^3$LO corrections to pseudo-scalar production at the LHC is presented and their role to reduce the renormalisation scale dependence is demonstrated.Comment: 34 pages, 17 figure

Unparticle physics in diphoton production at the CERN LHC

We have considered the di-photon production with unparticle at LHC. The contributions of spin-0 and spin-2 unparticle to the di-photon production are studied in the invariant mass and other kinematical distributions, along with their dependencies on the model dependent parameters. The signal corresponding to the unparticle is significant for moderate coupling constant values.Comment: 17 pages, 15 eps figure

Outer Bounds on the Storage-Repair Bandwidth Tradeoff of Exact-Repair Regenerating Codes

In this paper, three outer bounds on the normalized storage-repair bandwidth (S-RB) tradeoff of regenerating codes having parameter set $\{(n,k,d),(\alpha,\beta)\}$ under the exact-repair (ER) setting are presented. The first outer bound is applicable for every parameter set $(n,k,d)$ and in conjunction with a code construction known as {\em improved layered codes}, it characterizes the normalized ER tradeoff for the case $(n,k=3,d=n-1)$. It establishes a non-vanishing gap between the ER and functional-repair (FR) tradeoffs for every $(n,k,d)$. The second bound is an improvement upon an existing bound due to Mohajer et al. and is tighter than the first bound, in a regime away from the Minimum Storage Regeneraing (MSR) point. The third bound is for the case of $k=d$, under the linear setting. This outer bound matches with the achievable region of {\em layered codes} thereby characterizing the normalized ER tradeoff of linear ER codes when $k=d=n-1$.Comment: Accepted for publication at International Journal of Information and Coding Theory (Special Issue on Information and Coding Theory for Data Storage

NNLO QCD corrections to production of a spin-2 particle with non-universal couplings in the DY process

We study the phenomenological impact of the interaction of spin-2 fields with those of the Standard Model in a model independent framework up to next-to-next-to-leading order in perturbative Quantum Chromodynamics. We use the invariant mass distribution of the pair of leptons produced at the LHC to demonstrate this. A minimal scenario where the spin-2 fields couple to two gauge invariant operators with different coupling strengths has been considered. These operators being not conserved show very different ultraviolet behaviour increasing the searches options of spin-2 particles at the colliders. We find that our results using the higher order quantum corrections stabilise the predictions with respect to renormalisation and factorisation scales. We also find that corrections are appreciable which need to be taken into account in such searches at the colliders.Comment: 24 pages, 15 figure

Effect of Heavy Metal Ions and Carbohydrates on the Activity of Cauliflower (Brassica oleracea Var. botrytis) Myrosinase

Myrosinase is an enzyme of cruciferous vegetables, hydrolyse glucosinolates. The breakdown products are involved in plant defence against insect and also have anti-fungal property. Myrosinase has been purified to apparent homogeneity from 5 days old germinated cauliflower seedlings having a specific activity of 12.71 units/mg proteins with 54.6 % recovery, using ammonium sulfate fractionation followed by gel filtration chromatography on Sephadex G-100. Effect of some metal ions and carbohydrates on the activity of partially purified cauliflower myrosinase was studied. Sr+2 at 4 mM concentration exhibited marked activating effect on the activity up to 2.7 fold while Fe+2 significantly inhibited. However, Sn+2 and Ba+2 increased the activity to a certain extent and then suppressed. On the other hand, some metal ions [Fe+2, Fe+3, Cu+2 and Zn+2] strongly inhibited the activity even at lower concentrations. Several carbohydrates viz., glucose, fructose, sucrose, maltose and sorbitol even at comparatively higher concentrations had little detectable inhibitory effects. Activation kinetics of myrosinase in presence of Sn+2 and Sr+2 were studied between 0- 20min. The rate of reaction was almost constant till 15 min and then slight deactivation was recorded at various concentrations used

Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously

Asymptomatic Proteinuria and Hematuria in School Going Children

Background: This study was undertaken because many cases of asymptomatic proteinuria and hematuria are present in school children.Aims and Objectives:The study was under taken to evaluate asymptomatic proteinuria and hematuria in 100 school children of both sexes from 6 to 15 years of age. Material and Methods: Samples were collected randomly from students of different classes at the Government Kannada Primary School, K H B Colony,Bijapur, Karnataka (India). The midstream urine sample was collected in a clean wide mouth jar,examined by dipsticks for proteinuria and hematuria by microscopy. Results:We found that asymptomatic proteinuria and hematuria was more prevalent amongst the children between 10 to 13 years of age group with female predominance i.e.16% proteinuria and 5% of microscopic hematuria respectively. Conclusion:By this study we conclude that it would be possible to screen a large population of children for asymptomatic proteinuria and hematuria at a relatively low cost

Simple oxidation of pyrimidinylhydrazones to triazolopyrimidines and their inhibition of Shiga toxin trafficking

The oxidative cyclisation of a range of benzothieno[2,3-d]pyrimidine hydrazones (7a–j) to the 1,2,4-triazolo[4,3-c]pyrimidines (8a–j) catalysed by lithium iodide or to the 1,2,4-triazolo[1,5-c]pyrimidines (10a–j) with sodium carbonate is presented. A complementary synthesis of the 1,2,4-triazolo[1,5-c]pyrimidines starting from the amino imine 11 is also reported. The effect of these compounds on Shiga toxin (STx) trafficking in HeLa cells and comparison to the previously reported Exo2 is also detailed

Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach

Integrated steel manufacturers (ISMs) have no specific product, they just produce finished product from the ore. This enhances the uncertainty prevailing in the ISM regarding the nature of the finished product and significant demand by customers. At present low cost mini-mills are giving firm competition to ISMs in terms of cost, and this has compelled the ISM industry to target customers who want exotic products and faster reliable deliveries. To meet this objective, ISMs are exploring the option of satisfying part of their demand by converting strategically placed products, this helps in increasing the variability of product produced by the ISM in a short lead time. In this paper the authors have proposed a new hybrid evolutionary algorithm named endosymbiotic-psychoclonal (ESPC) to decide what and how much to stock as a semi-product in inventory. In the proposed theory, the ability of previously proposed psychoclonal algorithms to exploit the search space has been increased by making antibodies and antigen more co-operative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results compared with other evolutionary algorithms such as genetic algorithms (GA) and simulated annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained and convergence time required to reach the optimal/near optimal value of the solution