We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We propose an independence criterion based on the eigen-spectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

Measuring statistical dependence with Hilbert-Schmidt norms

Occurrence, Biogenesis, and Synthesis of Biologically Active Carbazole Alkaloids

http://www.optimization-online.org/DB_FILE/2012/07/3537.pdf

Recent advances in robust optimization: An overview☆

https://cyberleninka.org/article/n/365946.pdf

The use of plants in the traditional management of diabetes in Nigeria: pharmacological and toxicological considerations.

Acetylcholinesterase enzyme inhibitory potential of standardized extract of Trigonella foenum graecum L and its constituents.

Immunomodulation is the alteration of immune response which may increase or decrease the immune responsiveness. Medicinal plants, since times immemorial, have been used virtually in all cultures as a source of medicine for altering the immune systems. Several medicinal plants have been investigated for immunomodulatory potentials and they are proved to have beneficial effect on alteration of immune system by diverse mechanisms in animals. The present review will provide an up to date knowledge about the medicinal plants used as immunomodulators and their phytoconstituents. This article highlights on the phytochemistry, pharmacology, therapeutic usage and related aspects of 55 medicinal plants, such as Allium sativum, Aloe vera, Andrographis paniculata, Azadirachta indica, Boerhaavia diffusa, Boswellia serrata, Curcuma longa, Centella asiatica, Carica papaya, Datura quercifolia, Emblica officinalis, Hydrastis Canadensis, Hypericum perforatum, Ocimum sanctum, Panax ginseng, Plantago major, Plantago asiatica, Piper longum, Tinospora cordifolia, Mangifera indica, Momordica charantia, Withania somnifera, etc. which have been investigated for their immunomodulatory potentials, and they are proved to acquire beneficial effect on alteration of immune system by diverse mechanisms. Thus an approach for integration of the available information on several species of medicinal plants used as immunomodulators along with the metabolites responsible for the same has been made in this article.

http://nopr.niscair.res.in/bitstream/123456789/27905/1/IJTK%2013%282%29%20235-256.pdf

Immunomodulatory leads from medicinal plants

Anticholinesterase activity of standardized extract of Illicium verum Hook. f. fruits

This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain data points are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as a convex second order cone program whose solution is guaranteed to satisfy the probabilistic constraint. Prior to this work, only the Chebyshev based relaxations were exploited in learning algorithms. Bernstein bounds employ richer partial information and hence can be far less conservative than Chebyshev bounds. Due to this efficient modeling of uncertainty, the resulting classifiers achieve higher classification margins and hence better generalization. Methodologies for classifying uncertain test data points and error measures for evaluating classifiers robust to uncertain data are discussed. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle data uncertainty and outperform state-of-the-art in many cases.

/pdf/chance-constrained-uncertain-classification-via-robust-11v27d4j4w.pdf

Chance constrained uncertain classification via robust optimization

In this paper, we introduce the first method that (1) can complete kernel matrices with completely missing rows and columns as opposed to individual missing kernel values, with help of information from other incomplete kernel matrices. Moreover, (2) the method does not require any of the kernels to be complete a priori, and (3) can tackle non-linear kernels. The kernel completion is done by finding, from the set of available incomplete kernels, an appropriate set of related kernels for each missing entry. These aspects are necessary in practical applications such as integrating legacy data sets, learning under sensor failures and learning when measurements are costly for some of the views. The proposed approach predicts missing rows by modelling both within-view and between-view relationships among kernel values. For within-view learning, we propose a new kernel approximation that generalizes and improves Nystrom approximation. We show, both on simulated data and real case studies, that the proposed method outperforms existing techniques in the settings where they are available, and extends applicability to new settings.

/pdf/multi-view-kernel-completion-1pr0axf8tq.pdf

Sahely Bhadra

Papers

Acetylcholinesterase enzyme inhibitory potential of standardized extract of Trigonella foenum graecum L and its constituents.

Immunomodulatory leads from medicinal plants

Anticholinesterase activity of standardized extract of Illicium verum Hook. f. fruits

Chance constrained uncertain classification via robust optimization

Multi-view kernel completion