Morphological filtering on hypergraphs

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H, by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of H. Afterward, we propose several new openings, closings, granulometries and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of H and (ii) on the subhypergraphs of a hypergraph

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on Communication, Control and Computing, September 200

Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact-repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d) the construction, also explicit, of MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the non-existence proof for d < 2k-3. To the best of our knowledge, the constructions presented in this paper are the first, explicit constructions of regenerating codes that achieve the cut-set bound.Comment: 38 pages, 12 figures, submitted to the IEEE Transactions on Information Theory;v3 - The title has been modified to better reflect the contributions of the submission. The paper is extensively revised with several carefully constructed figures and example

Antimicrobial Activity of Sphaeranthus indicus L.

Aerial parts and flowers of Sphaeranthus indicus were extracted with n-hexane, benzene, chloroform, ehtylacetate and acetone. The extracts were screened for their antimicrobial activity using in vitro disc diffusion method at concentrations of 5, 2.5 and 1.25 mg/disc. The Minimum Inhibitory Concentration (MIC) was tested using broth micro dilution method at concentrations ranging from 5 to 0.039 mg/ml. Significant antibacterial and antifungal activity was observed in hexane extract of flower and aerial parts. The flower extract showed MIC as 0.15 mg/ml against Staphylococcus aureus and the highest MIC (5 mg/ml) was noted for S. epidermidis. The n-hexane extracts of flower and aerial parts showed MIC as 0.15 and 1.25 mg/ml respectively against Candida albicans. In conclusion, the S. indicus flower n-hexane extract seems to be a promising antimicrobial agent

Factors influencing development of trans urethral resection of prostate (TURP) syndrome in benign prostatic hyperplasia patients with various co morbid medical illness: a prospective study

Background: The aim of this prospective study is to analyse the factors influencing development of trans urethral resection of prostate (TURP) syndrome in benign Prostatic hyperplasia patients with various co morbid medical illness in Thanjavur Medical College Hospital, from February 2015 to January 2017.Methods: This prospective study was done among 38 benign hyperplasia prostate patients with various co morbid medical illness underwent TURP. Pre-operative and post-operative serum sodium levels correlated with signs and symptoms developed in various prostate gland sizes, resection times and volume of irrigation fluids.Results: Sodium level has gone down to 14 meq/L, gone up to 2 meq/L post-operatively. Major fluctuations in serum sodium was seen in prostate size more than 50 grams, resection time more than 40 mints, irrigant volume more than 24 litres. Mean sodium decrease was increased when gland size was increased, resection time was increased, irrigant volume was increased.Conclusions: In renal insufficiency patients, it is safe to complete the procedure within 40 minutes and restrict irrigant volume 15 litres, in coronary artery disease patients it is safe to restrict irrigant fluid volume less than 20 litres. In Diabetes Mellitus patients, it is safe to restrict irrigant fluid volume less than 24 litres. In hypertensive patients, it is safe to restrict the resection time less than 45 minutes. In patients with Diabetes and hypertension, it is safe to restrict the resection time less than 40 minutes and irrigant fluid less than 20 litres

Star formation in mergers with cosmologically motivated initial conditions

We use semi-analytic models and cosmological merger trees to provide the initial conditions for multi-merger numerical hydrodynamic simulations, and exploit these simulations to explore the effect of galaxy interaction and merging on star formation (SF). We compute numerical realisations of twelve merger trees from z=1.5 to z=0. We include the effects of the large hot gaseous halo around all galaxies, following recent obervations and predictions of galaxy formation models. We find that including the hot gaseous halo has a number of important effects. Firstly, as expected, the star formation rate on long timescales is increased due to cooling of the hot halo and refuelling of the cold gas reservoir. Secondly, we find that interactions do not always increase the SF in the long term. This is partially due to the orbiting galaxies transferring gravitational energy to the hot gaseous haloes and raising their temperature. Finally we find that the relative size of the starburst, when including the hot halo, is much smaller than previous studies showed. Our simulations also show that the order and timing of interactions are important for the evolution of a galaxy. When multiple galaxies interact at the same time, the SF enhancement is less than when galaxies interact in series. All these effects show the importance of including hot gas and cosmologically motivated merger trees in galaxy evolution models.Comment: 19 pages, 15 figures, 6 tables. Accepted for publication in MNRA

From Discs to Bulges: effect of mergers on the morphology of galaxies

We study the effect of mergers on the morphology of galaxies by means of the simulated merger tree approach first proposed by Moster et al. This method combines N-body cosmological simulations and semi-analytic techniques to extract realistic initial conditions for galaxy mergers. These are then evolved using high resolution hydrodynamical simulations, which include dark matter, stars, cold gas in the disc and hot gas in the halo. We show that the satellite mass accretion is not as effective as previously thought, as there is substantial stellar stripping before the final merger. The fraction of stellar disc mass transferred to the bulge is quite low, even in the case of a major merger, mainly due to the dispersion of part of the stellar disc mass into the halo. We confirm the findings of Hopkins et al., that a gas rich disc is able to survive major mergers more efficiently. The enhanced star formation associated with the merger is not localised to the bulge of galaxy, but a substantial fraction takes place in the disc too. The inclusion of the hot gas reservoir in the galaxy model contributes to reducing the efficiency of bulge formation. Overall, our findings suggest that mergers are not as efficient as previously thought in transforming discs into bulges. This possibly alleviates some of the tensions between observations of bulgeless galaxies and the hierarchical scenario for structure formation.Comment: MNRAS Accepted, 17 pages, 11 figures, 3 Table

Capparis sepiaria Linn - Pharmacognostical standardization and toxicity profile with chemical compounds identification (GC-MS)

The present study was intended to evaluate the various pharmacognostical procedures in the leaves of Capparis sepiaria Linn., (Capparidaceae). The various pharmacognostical parameters were carried out as per WHO guidelines procedure i.e., bitterness, fineness, microscopical sections, loss on drying, water and alcoholic extractive values, water insoluble ash, acid soluble ash, total ash, swelling index, foaming index, heavy metal analysis, phytochemical analysis and toxicity studies (acute, subacute and chronic toxicity). The study was extended with analyzing the chemical compounds identification in the EECS (ethanolic extract of Capparis sepiaria by using GC-MS. The presence of various phytoconstituents such as glycosides, reducing sugars, flavonoids, saponins, starch and terpenoids is evidenced in EECS &amp; AECS. The results showed that acid insoluble ash (1.70%), total ash (8.68%), water soluble ash (3.42%), water extractive (31.55%), alcohol extractive (5.06%), foaming index (105.26 Unit), loss on drying (9.84%), swelling index (4.16%), acute toxicity (nil), sub-acute toxicity (nil), chronic toxicity (nil). The study was concluded with the plant has standardized as per the World Health Organization procedures. The result of the pharmacognostical standardization of this plant serves as a reference piece and helps in future identification and authentication of this plant specimen. Might be the plant C. sepiaria has potential property by the standardization and it can be included in the normal flora of the plant kingdom.Keywords: C. sepiaria; Microscopical; Macroscopical standardization