On the Symmetries of and Equivalence Test for Design Polynomials

In a Nisan-Wigderson design polynomial (in short, a design polynomial), every pair of monomials share a few common variables. A useful example of such a polynomial, introduced in [Neeraj Kayal et al., 2014], is the following: NW_{d,k}({x}) = sum_{h in F_d[z], deg(h) <= k}{ prod_{i=0}^{d-1}{x_{i, h(i)}}}, where d is a prime, F_d is the finite field with d elements, and k << d. The degree of the gcd of every pair of monomials in NW_{d,k} is at most k. For concreteness, we fix k = ceil[sqrt{d}]. The family of polynomials NW := {NW_{d,k} : d is a prime} and close variants of it have been used as hard explicit polynomial families in several recent arithmetic circuit lower bound proofs. But, unlike the permanent, very little is known about the various structural and algorithmic/complexity aspects of NW beyond the fact that NW in VNP. Is NW_{d,k} characterized by its symmetries? Is it circuit-testable, i.e., given a circuit C can we check efficiently if C computes NW_{d,k}? What is the complexity of equivalence test for NW, i.e., given black-box access to a f in F[{x}], can we check efficiently if there exists an invertible linear transformation A such that f = NW_{d,k}(A * {x})? Characterization of polynomials by their symmetries plays a central role in the geometric complexity theory program. Here, we answer the first two questions and partially answer the third. We show that NW_{d,k} is characterized by its group of symmetries over C, but not over R. We also show that NW_{d,k} is characterized by circuit identities which implies that NW_{d,k} is circuit-testable in randomized polynomial time. As another application of this characterization, we obtain the "flip theorem" for NW. We give an efficient equivalence test for NW in the case where the transformation A is a block-diagonal permutation-scaling matrix. The design of this algorithm is facilitated by an almost complete understanding of the group of symmetries of NW_{d,k}: We show that if A is in the group of symmetries of NW_{d,k} then A = D * P, where D and P are diagonal and permutation matrices respectively. This is proved by completely characterizing the Lie algebra of NW_{d,k}, and using an interplay between the Hessian of NW_{d,k} and the evaluation dimension

Information and communication technology in agribusiness: A study of mobile applications in perspective of India

Federation of Indian Chambers of Commerce and Industry in one of its finding in 2019 stated that about 58%  Indians are dependent on agriculture and agriculture sector make about 15.96 % of India’s GDP. To get the best agriculture inputs and best harvest price is the big question for Indian farmers; thus, we can say that “Agriculture is the foundation of the Indian economy”. With the origin of Mobile Applications (m-apps) for agriculture and a huge dependency on Information and Communication Technology (ICT) in agribusiness, the scenario in rural India has been changing rapidly. Since India’s economy depends mainly on agriculture, there is a lot of potential for Information and Communication Technology and mobile applications for agribusiness and its marketing. With growing smartphones with m-apps penetration in rural India, the agribusiness in rural belts of India is set for extension and further digitalization to revolutionize the agriculture sector. In recent years, nearly all Indian farmers possess a mobile, and 50%are smartphones with internet connections. With Government's new legislative policy changes as the Digital India programme, mobile applications in India's rural belt cannot remain isolated. Digital India will connect rural Indians farmers worldwide through the internet and mobile applications and provide them with all necessary upliftment in agribusiness in India. This study has focused on the ICT and m-applications used in farming today and how they have changed agribusiness by providing a digital platform and with their impact on agribusiness

Single Inventory Cycled Data Population in LEACH-Cluster

Inside a cluster in LEACH based sensor network architecture, data from individual nodes are being populated by individual query or command governed by Cluster-head following TDMA slots. This conventional process can be further minimized with Cluster Energy consumption, Complexity and memory consumption aspects following the proposed architecture where a single inventory command populates all nodal data following the “shortest close-loop energy path” algorithm. The new protocol architecture has been simulated in MATLAB considering 3D domain with some basic consideration of localization and, simulation result with comparison study with some conventional topologies are presented in this paper

Biochemical Evaluation of Forage Sorghum for Stress Tolerance

Abiotic stresses are the major limiting factors in plant growth. With continuous increment in scarcity of water and increased salinization of soil and water, it is estimated that more than 50% of all arable lands will be affected by salinity and drought by 2050. Plants are often exposed to both, soil and atmospheric water deficit during their life cycle. The frequency and intensity of droughts is increasing as a result of global climate change. Understanding how plants respond to water stress is thus crucial for the estimation of impacts of climate change on crop productivity and ecosystem functioning. The knowledge about the mechanism adapted by plant to respond to drought, salt and co-occurring stresses can play an important role in stabilizing crop performance under drought and saline conditions. Sorghum (Sorghum bicolor L.) is an important crop in many parts of the world. It is utilized as food, fodder and several industrial purposes. In general, sorghum is known to be more tolerant to any stresses including heat, drought, salinity and flooding

Synthetic Polymer Based Coating of Fodder Cowpea Seeds Enhances Germination and Vigour

In Indian arid and semi-arid conditions, comparatively less fertile lands are allotted to forage crops. In addition, erratic weather condition makes the situation more complex where proper seedling emergence and establishment of pastures with economic use of input remains a big question. Our view is that crop seedling production from seed sown into arid or semiarid environments could be significantly enhanced by the use of simple seed coating technologies. Such approaches would make use of newly synthesised seed coat-applied polymers that could be used to hold the desired supplements like powerful germination enhancement chemicals and plant protectants with seed to support both germination and seedling establishment under the crucial stages. This approach would be expected to increase the rate and speed of germination, thereby bringing the uniformity in plant population even under stressful (drought) growing conditions. On the other hand, cowpea seed are highly susceptible to insect pest during storage in addition to seed borne diseases. Hence, coating of seed was envisaged in order to protect the seeds from pest attack and boost initial seedling vigour

Multi-objective optimization of reverse osmosis desalination units using different adaptations of the non-dominated sorting genetic algorithm (NSGA)

Multi-objective optimization using genetic algorithm (GA) is carried out for the desalination of brackish and sea water using spiral wound or tubular modules. A few sample optimization problems involving two and three objective functions are solved, both for the operation of an existing plant (which is almost trivial), as well as, for the design of new plants (associated with a higher degree of freedom). The possible objective functions are: maximize the permeate throughput, minimize the cost of desalination, and minimize the permeate concentration. The operating pressure difference, ΔP, across the membrane is the only important decision variable for an existing unit. In contrast, for a new plant, ΔP, the active area, A, of the membrane, the membrane to be used (characterized by the permeability coefficients for salt and water), and the type of module to be used (spiral wound/tubular, as characterized by the mass transfer coefficient on the feed-side), are the important decision variables. Sets of non-dominated (equally good) Pareto solutions are obtained for the problems studied. The binary coded elitist non-dominated sorting genetic algorithm (NSGA-II) is used to obtain the solutions. It is observed that for maximum throughput, the permeabilities of both the salt and the water should be the highest for those cases studied where there is a constraint on the permeate concentration. If one of the objective functions is to minimize the permeate concentration, the optimum permeability of salt is shifted towards its lower limit. The membrane area is the most important decision variable in designing a spiral wound module for desalination of brackish water as well as seawater, whereas ΔP is the most important decision variable in designing a tubular module for the desalination of brackish water (where the quality of the permeate is of prime importance). The results obtained using NSGA-II are compared with those from recent, more efficient, algorithms, namely, NSGA-II-JG and NSGA-II-aJG. The last of these techniques appears to converge most rapidly

Innovative Technologies for Enhanced Availability of Bajra-Napier Hybrid Rooted Slips

Livestock occupies a crucial position in Indian agriculture and directly contributing 4.1% of total GDP of the country. India, with 2.29% of the world land area, is maintaining about 10.71% of the world’s livestock population. To sustain the present milk growth rate of 4.04% and for further expansion to meet the demands of ever growing human population, livestock needs sustainable supply of feed material. The area under fodder cultivation is estimated to be about 4% of the gross cropped area which remained static for the last four decades.The traditional grazing lands are gradually diminishing because of urbanization, expansion of cultivable area, grazing pressure and industrialization etc. These factors resulted in severe shortage of feed and fodder to the extent of 26% in dry-crop residues, 35.6% in green fodder and 41% of concentrates (Anon, 2013). To reduce the demand and supply gap, the production and productivity of fodder crops needs to be enhanced. The utilization of non-cultivable space viz., field bunds, common grazing lands, backyards apart from regular cultivation of high biomass species like Bajra-Napier hybrid (BN hybrid), guinea grass, Trispecific hybrid helps in enhanced production of green fodder. Bajra-Napier hybrid is one of the high biomass grasses with fodder potential of 300 tons/ha/year. However, this grass can be propagated only through rooted slips as it does not form any viable seed. Several varieties suitable to different agro-climatic zones were released for the successful cultivation of this grass throughout India. Due to increasing demand both from small and marginal farmers as well as well-structured large scale diary industry, there is severe shortage of rooted slips of this grass. The traditional uprooting of tussocks not only destructs the mother tussock but also highly labour intensive and difficult to transport to long distances. Keeping in view of all these constraints, two novel technologies were developed for the large scale multiplication of BN hybrid rooted slips