Combinatorial limitations of average-radius list-decoding

We study certain combinatorial aspects of list-decoding, motivated by the exponential gap between the known upper bound (of $O(1/\gamma)$) and lower bound (of $\Omega_p(\log (1/\gamma))$) for the list-size needed to decode up to radius $p$ with rate $\gamma$ away from capacity, i.e., 1-\h(p)-\gamma (here $p\in (0,1/2)$ and $\gamma > 0$). Our main result is the following: We prove that in any binary code $C \subseteq \{0,1\}^n$ of rate 1-\h(p)-\gamma, there must exist a set $\mathcal{L} \subset C$ of $\Omega_p(1/\sqrt{\gamma})$ codewords such that the average distance of the points in $\mathcal{L}$ from their centroid is at most $pn$. In other words, there must exist $\Omega_p(1/\sqrt{\gamma})$ codewords with low "average radius." The standard notion of list-decoding corresponds to working with the maximum distance of a collection of codewords from a center instead of average distance. The average-radius form is in itself quite natural and is implied by the classical Johnson bound. The remaining results concern the standard notion of list-decoding, and help clarify the combinatorial landscape of list-decoding: 1. We give a short simple proof, over all fixed alphabets, of the above-mentioned $\Omega_p(\log (\gamma))$ lower bound. Earlier, this bound followed from a complicated, more general result of Blinovsky. 2. We show that one {\em cannot} improve the $\Omega_p(\log (1/\gamma))$ lower bound via techniques based on identifying the zero-rate regime for list decoding of constant-weight codes. 3. We show a "reverse connection" showing that constant-weight codes for list decoding imply general codes for list decoding with higher rate. 4. We give simple second moment based proofs of tight (up to constant factors) lower bounds on the list-size needed for list decoding random codes and random linear codes from errors as well as erasures.Comment: 28 pages. Extended abstract in RANDOM 201

Balancing sums of random vectors

We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to keep the sums of the vectors in the different bins close together; how close can we keep these sums almost surely? This question, our primary focus in this paper, is closely related to the classical problem of partitioning a sequence of vectors into balanced subsequences, in addition to having applications to some problems in computer science.Comment: 17 pages, Discrete Analysi

Development and evaluation of controlled porosity osmotic pump for Nifedipine and Metoprolol combination

BACKGROUND: A system that can deliver multi-drug at a prolonged rate is very important for the treatment of various chronic diseases such as diabetes, asthma and heart disease. Controlled porosity osmotic pump tablet (CPOP) system was designed to deliver Nifedipine (NP) and Metoprolol (MP) in a controlled manner up to 12 h. It was prepared by incorporating drugs in the core and coated with various types (PVP, PEG-400 and HPMC) and levels (30, 40 and 50% w/w of polymer) of pore former at a weight gain of 8, 12 & 15%. RESULTS: Formulation variables like type and level of pore former and percent weight gain of membrane was found to affect the drug release from the developed formulations. Drug release was inversely proportional to the membrane weight but directly related to the level of pore former. Burst strength of the exhausted shell was inversely proportional to the level of pore former, but directly affected by the membrane weight. Results of scanning electron microscopy (SEM) studies showed the formation of pores in the membrane from where the drug release occurred. Dissolution models were applied to drug release data in order to establish the mechanism of drug release kinetics. In vitro release kinetics was subjected to superposition method to predict in vivo performance of the developed formulation. CONCLUSION: The developed osmotic system is effective in the multi-drug therapy of hypertension by delivering both drugs in a controlled manner

CHEMOPREVENTIVE ROLE OF COMBINATION OF ETORICOXIB AND ATORVASTATIN ON COLON CANCER INDUCED BY 1, 2-DIMETHYL HYDRAZINE ON RATS

Objective: To investigate and compare the efficacy of atorvastatin, etoricoxib and combination of both drugs against colon carcinogenesis in male wistar rats.Methods: Male wistar rats were divided into five groups. Group-1 served as normal control. Group-2 subcutaneously received 1,2-dimethylhydrazine (DMH) (20 mg/kg body weight(b. w.)) and served as DMH control. Groups-3, 4 and 5 were treated with DMH once in a week for 17 weeks. One week before the administration of DMH, group-3 and group-4 received etoricoxib (0.64 mg/kg per oral (p. o)), atorvastatin (2.5 mg/kg subcutaneously (s. c)) respectively and group-5 received both drugs and lasted until the end of the experiment. The effect of drugs on body weight gain, food and water intake, haematological parameter and histopathological view of the colon was observed in the entire group of animals.Results: The experimental evidences showed that significant effect of the combined dose of etoricoxib and atorvastatin against DMH induced colon cancer by increasing the level of antioxidant enzymes. The combination was found to decrease the occurrence of multiple plaque lesions which may become the basis for its better chemo preventive action against the progression of colon carcinogenesis as compared to individual drugs. The histopathological study demonstrated that the combination treatment showed more positive effect then individual drug in prevention of colon carcinogenesis by reducing the inflammation, hyperplastic and dysplastic changes in colon crypt cells.Conclusion: This study was concluded that the combination of atorvastatin and etori coxib may be potential chemo preventive agents against DMH-induced colon cancer and showed prominent positive effects as compared to individual drugs.Â

Evaluation of PCR Using TRC4 and IS6110 Primers in Detection of Tuberculous Meningitis

We have evaluated a new set of primers (TRC4) in comparison with the IS6110 primers commonly used in PCR to detect tuberculous meningitis among children. The levels of concordance between the results of IS6110 PCR and TRC4 PCR with cerebrospinal fluid specimens from patients with clinically confirmed tuberculous meningitis were 80 and 86%, respectively. Results with the two primer sets were concordant for 55 positive and 22 negative specimens (n 5 98). We conclude that the sensitivity of PCR can be increased by using both IS6110 and TRC4 primers

A rare case of cutaneous granular cell tumour

Granular cell tumors are uncommon tumors of uncertain etiology. It accounts for approximately 0.5% of all soft tissue tumors. However, the involvement of skin is rare. Only few cases of cutaneous granular cell tumor is reported till date. Here, we present a case of cutaneous granular cell tumor in a 48 years female patient

Simple spectrofluorimetric and microbiological assay methods for the estimation of ofloxacin in biological fluids

Objective: To evolve simple methods for the assay of ofloxacin in biological fluids. Methods: Simple methods for the estimation of ofloxacin in plasma, saliva and urine employing microbiological assay using plate diffusion technique and by fluorimetric method based on the measurement of native fluorescence emitted by ofloxacin, have been described. Results: The recovery of ofloxacin from all the three biologial fluids was 93-98% and the sensitivity was 0.5 μg/ml on all 5 different occasions by both the methods. Anti-TB drugs viz., rifampicin, ethambutol, isoniazid and pyrazinamide and also anti-leprosy drugs viz., dapsone and clofazimine at concentrations of 10 and 20 μg/ml did not interfere with the estimation of ofloxacin by either method. Ofloxacin is stable in biological fluids for a period of at least 8 days at -20°C. Conclusion: Both the methods described are simple, involve very few steps and do not need either costly chemicals or sophisticated equipments