Approximate Hypergraph Coloring under Low-discrepancy and Related Promises

A hypergraph is said to be $\chi$-colorable if its vertices can be colored with $\chi$ colors so that no hyperedge is monochromatic. $2$-colorability is a fundamental property (called Property B) of hypergraphs and is extensively studied in combinatorics. Algorithmically, however, given a $2$-colorable $k$-uniform hypergraph, it is NP-hard to find a $2$-coloring miscoloring fewer than a fraction $2^{-k+1}$ of hyperedges (which is achieved by a random $2$-coloring), and the best algorithms to color the hypergraph properly require $\approx n^{1-1/k}$ colors, approaching the trivial bound of $n$ as $k$ increases. In this work, we study the complexity of approximate hypergraph coloring, for both the maximization (finding a $2$-coloring with fewest miscolored edges) and minimization (finding a proper coloring using fewest number of colors) versions, when the input hypergraph is promised to have the following stronger properties than $2$-colorability: (A) Low-discrepancy: If the hypergraph has discrepancy $\ell \ll \sqrt{k}$, we give an algorithm to color the it with $\approx n^{O(\ell^2/k)}$ colors. However, for the maximization version, we prove NP-hardness of finding a $2$-coloring miscoloring a smaller than $2^{-O(k)}$ (resp. $k^{-O(k)}$) fraction of the hyperedges when $\ell = O(\log k)$ (resp. $\ell=2$). Assuming the UGC, we improve the latter hardness factor to $2^{-O(k)}$ for almost discrepancy-$1$ hypergraphs. (B) Rainbow colorability: If the hypergraph has a $(k-\ell)$-coloring such that each hyperedge is polychromatic with all these colors, we give a $2$-coloring algorithm that miscolors at most $k^{-\Omega(k)}$ of the hyperedges when $\ell \ll \sqrt{k}$, and complement this with a matching UG hardness result showing that when $\ell =\sqrt{k}$, it is hard to even beat the $2^{-k+1}$ bound achieved by a random coloring.Comment: Approx 201

Application of a radial basis function neural network for diagnosis of diabetes mellitus

In this article an attempt is made to study the applicability of a general purpose, supervised feed forward neural network with one hidden layer, namely. Radial Basis Function (RBF) neural network. It uses relatively smaller number of locally tuned units and is adaptive in nature. RBFs are suitable for pattern recognition and classification. Performance of the RBF neural network was also compared with the most commonly used multilayer perceptron network model and the classical logistic regression. Diabetes database was used for empirical comparisons and the results show that RBF network performs better than other models

Worshipping Goddess as Mother in Tamil Literature

Human beings are afraid of natural disaster and that is how humans began to worship nature. So, man first started worshiping nature and gradually they started believing that all the things that happens in this world are caused by an invisible divine power. There the worship of man began. Based on the fact that every natural object has a power, the methods of worshiping the respective deities emerged by setting up abodes for it. Deity worship continues till today based on the feelings of devotion, gratitude and faith. Worshipping a deity will guide a man to lead a better life and it helps to mature the ignorant mind. More and more people are worshiping female deities more than worshipping male deities. Female deities are worshiped in abundance because of their respect for sex and forgiving nature like how a mother forgives her children. Through this we can understand how much importance Tamil people give to women and the worship of Mother Goddess

Diversity and distribution of microfungi in foliage leaf, bark and leaf litter of Couroupita guianensis

The diversity and distribution of micro fungal assemblages in the foliage leaf, bark and leaf litter tissues of the Couroupita guianensis sacred plant. For the host, we recorded 1005 fungal species isolates from 900 tissue segments. A total of 62 fungal species were isolated from foliar endophytes, phellophytes and leaf litter. The colonization frequency of the fungi species has been recorded as 111.66% from the endophytes, phellophytes and leaf tissues. The fungi species recovered in various groups included ascomycetes, coelomycetes, hyphomycetes, zygomycetes and sterile fungi. The number of fungal species is increased for the plant tissues, it showed that the species diversity is increasing. A correspondence analysis also showed that the fungal species assemblages were different from each type of tissue

Bioaccumulation of heavy metals in sea turtles from the west coast of India

Sea turtles are widely distributed in the tropical, sub-tropical and temperate waters. Recent reports have indicated that their populations are threatened by the problem of marine pollution . (Stroelli et al., 1998). Heavy metals are one of the major pollutants and have the nature to concentrate in the tissues of animals and their concentrations vary according to biological process such as age, sex, reproduction and migratio

Peack expiratory flow rate in South Indian Children

PEFR is a simple and reliable way of following patients with bronchial asthma and other obstructive airway diseases. Normal data is available for Caucasian and North Indian children but not for ethnic South Indian children. We, therefore, measured Peak Expiratory Flow Rate (PEFR) in 343 healthy South Indian children aged 4-15 years, using the Wright mini peak flow meter. A nomogram was constructed relating PEFR to height. Prediction equations for PEFR using height alone or height, age and weight were determined for both sexes. The prediction equation for boys based on height alone was PEFR = 4.08 height (cm) - 284.55 and for girls was PEFR = 3.92 height (cm) - 277.01

Role of nitric oxide in seed biology and seed production: A review

Nitric oxide (NO) is an important signalling molecule employed by plants to control many physiological aspects. This review summarizes that crosstalk between NO/H2O2/Ca2+ signalling pathways that drive pollen tube for sexual reproduction in flowering plants. NO is produced in seeds by both enzymatic and non-enzymatic sources that control many physiological aspects of seeds. The interplay of NO and Reactive oxygen species are likely important players in hormonal crosstalk controlling seed germination and dormancy. Mechanism of seed germination and dormancy is mainly regulated by plant hormones like Abscisic acid (ABA) and Gibberellic acid (GA). Based on mode of action of NO with reference to triggering the germination of crop seeds under abiotic stress condition it is infer that there is a linkage between NO and plant growth regulator production. NO cross-talk with reactive oxygen species (ROS) during abiotic stress condition, modulate the light and hormone depended developmental process in the early stage of plant development. NO action to enhancing abiotic stress tolerance by improving antioxidant enzymes and protection against oxidative damage in many crops are discussed in detail

Suppression of extreme events and chaos in a velocity-dependent potential system with time-delay feedback

The foremost aim of this study is to investigate the influence of time-delayed feedback on extreme events in a non-polynomial system with velocity dependent potential. To begin, we investigate the effect of this feedback on extreme events for four different values of the external forcing parameter. Among these four values, in the absence of time-delayed feedback, for two values, the system does not exhibit extreme events and for the other two values, the system exhibits extreme events. On the introduction of time-delayed feedback and varying the feedback strength, we found that extreme events get suppressed as well as get induced. When the feedback is positive, suppression occurs for a larger parameter region whereas in the case of negative feedback it is restricted to the limited parameter region. We confirm our results through Lyapunov exponents, probability density function of peaks, $d_{max}$ plot and two parameter probability plot. Finally, we analyze the changes in the overall dynamics of this system under the influence of time-delayed feedback. We notice that complete suppression of chaos occurs in the considered system for higher values of the time-delayed feedback.Comment: 28 pages, 16 figures, 1 table, Accepted for Publication Chaos, Solitons & Fractal