On network coding for sum-networks

A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably) equivalent sum-network for any multiple-unicast network, and thus for any directed acyclic communication network. It is also shown that there exists a linear solvably equivalent multiple-unicast network for every sum-network. It is shown that for any set of polynomials having integer coefficients, there exists a sum-network which is scalar linear solvable over a finite field F if and only if the polynomials have a common root in F. For any finite or cofinite set of prime numbers, a network is constructed which has a vector linear solution of any length if and only if the characteristic of the alphabet field is in the given set. The insufficiency of linear network coding and unachievability of the network coding capacity are proved for sum-networks by using similar known results for communication networks. Under fractional vector linear network coding, a sum-network and its reverse network are shown to be equivalent. However, under non-linear coding, it is shown that there exists a solvable sum-network whose reverse network is not solvable.Comment: Accepted to IEEE Transactions on Information Theor

FRUIT CHARACTERISTICS OF LITCHI GENOTYPES UNDER CHOTANAGPUR CONDITIONS

The litchi (Litchi chinensis Sonn.) is an important evergreen sub-tropical fruit tree specific to climatic requirement for 'its production. Litchi possesses a narrow genetic base for various agrom ophol ogical traits. Continuous vegetative propagation of commercial cultivars has further narrowed down the genetic base resulting in the .restricted period of availability of fruits in the market. Cultivars have been classified on the basis of economic traits in China and on the basis of growth and flowering pattern in India (Arora et al. 1996; Singh, 1998). Rai and Vishal Nath (2001) reported a total of 51 genotypes being augmented from different litchi growing regions and maintained at HARP, Ranchi. Xuequin (1995) reported 20-25 main litchi types possessing characters of larger fruit size, small stone, thick and free aril of good quality with good flavor having canning quality from south China. However, cultivar synonymy does exit due to the insufficient information on i:;haracterization for different fruit morphological traits and delineation of the characters in its original name. Only few cultivars and be distinguished based on their fruits characters and maturity period. which creates confusion in identifying the suitable cultivar for any specific region. Keeping this in view, a study was carried out to characterize the different litchi genotypes on the basis of physico-chemical characteristics of fruit under the Chotanagpur plateau region of eastern IndiaUtchi has narrow genetic base owing to greater use of asexual propagation. Cultivar synonymy on the basis of local nomenclature causes confusion in identifying a genotype for any specific purpose. There fore, 17 genotypes under study have been characterized on the basis of fruit shape index (FSI), specific gravity, seed shape index (SS/), flatness of seed, number of protuberances/cm' and other physico-chemica/ characters of fruit. The cultivars China, Purbi and Bombaiya-11 found to have elongated fruit shape whereas Bedana, Swarna Roopa, Trikolia and Shahi posses roundish fruit shape. Regarding pulp %, the cultivars Bedana, D. Rose, Late Bedana, Green and Rose Scented has the high values. The cultivars Purbi, China, Swarna Roopa and Dehradun has thick peel. Widely spread protuberances was noticed in cultivars Swarna Roopa, Dehradun and Bedana. Bedana, Late Bed;ma and Swarna Roopa had smaller seeds. The cul/ivars Bombaiya-1, Bombaiya-11, Late Bedana, CHES-II, China and Purbi had slender seeds while Deshi, Bombaiya-1 and Late Bedana has flat seeds.Not Availabl

Perspectives of traditional health care system of Sikkim, North-East India – Anethno-pharmacological survey and analysis

The Indo-Himalayan mountain state of Sikkim has abundant reserves of bio-diversity of ancient ancestry. Many folklore healers renowned in Sikkim for their valuable traditional knowledge, especially for the use of combination drug therapy to treat bone fracture. In the cross-cultural ethnopharmacological survey, a predesigned questionnaire was used for interviews at the residence of respective folklore healers. Their patient handling and preparations of formulations have documented in written and audio-visual format. The standard statistical indices selected relevant for the present study. The record of traditional knowledge on 193 different formulations used for 49 various human ailments has enumerated during this survey. A total of 121 plants belonging to 65 families were found to be used as a component for 193 formulations. Graphical representation of the frequency of citation, especially survey and reference data shown significant correlation indicating common and specific use of plants in the treatment of different diseases. The scientific research on medicinal plants used by traditional practitioners and the application of ethnobotanical products in the folklore healthcare system significantly help in the sustainable development of traditional healthcare practices of the region. For the research fraternity, the quantitative analysis of survey data is gaining wider acceptability due to relative importance

Perspectives of traditional health care system of Sikkim, North-East India – An ethno-pharmacological survey and analysis

965-981The Indo-Himalayan Mountain state of Sikkim has abundant reserves of bio-diversity of ancient ancestry. Many folklore healers are renowned in Sikkim for their valuable traditional knowledge, especially for the use of combination drug therapy to treat bone fracture. In the cross-cultural ethnopharmacological survey, a predesigned questionnaire was used for interviews at the residence of respective folklore healers. Their patient handling and preparations of formulations have been documented in written and audio-visual format. The standard statistical indices selected relevant for the present study. The record of traditional knowledge on 193 different formulations used for 49 various human ailments have been enumerated during this survey. A total of 121 plants belonging to 65 families were found to be used as a component for 193 formulations. Graphical representation of the frequency of citation, especially survey and reference data shown significant correlation indicating common and specific use of plants in the treatment of different diseases. The scientific research on medicinal plants used by traditional practitioners and the application of ethnobotanical products in the folklore healthcare system significantly help in the sustainable development of traditional healthcare practices of the region. For the research fraternity, the quantitative analysis of survey data is gaining wider acceptability due to relative importance