Error Bounds for Compressed Sensing Algorithms With Group Sparsity: A Unified Approach

In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and estimated vectors are given in [1] and reviewed in [2], while bounds for the $\ell_1$-norm are given in [3]. When the unknown vector is not conventionally sparse but is "group sparse" instead, a variety of alternatives to the $\ell_1$-norm have been proposed in the literature, including the group LASSO, sparse group LASSO, and group LASSO with tree structured overlapping groups. However, no error bounds are available for any of these modified objective functions. In the present paper, a unified approach is presented for deriving upper bounds on the error between the true vector and its approximation, based on the notion of decomposable and $\gamma$-decomposable norms. The bounds presented cover all of the norms mentioned above, and also provide a guideline for choosing norms in future to accommodate alternate forms of sparsity.Comment: 28 pages, final version of 1401.6623, accepted for publication. arXiv admin note: substantial text overlap with arXiv:1401.662

A subalgebra of the Hardy algebra relevant in control theory and its algebraic-analytic properties

We denote by A_0+AP_+ the Banach algebra of all complex-valued functions f defined in the closed right half plane, such that f is the sum of a holomorphic function vanishing at infinity and a ``causal'' almost periodic function. We give a complete description of the maximum ideal space M(A_0+AP_+) of A_0+AP_+. Using this description, we also establish the following results: (1) The corona theorem for A_0+AP_+. (2) M(A_0+AP_+) is contractible (which implies that A_0+AP_+ is a projective free ring). (3) A_0+AP_+ is not a GCD domain. (4) A_0+AP_+ is not a pre-Bezout domain. (5) A_0+AP_+ is not a coherent ring. The study of the above algebraic-anlaytic properties is motivated by applications in the frequency domain approach to linear control theory, where they play an important role in the stabilization problem.Comment: 17 page

ETHNOMEDICINAL PLANTS USED BY RAJGOND TRIBES OF HALADKERI VILLAGE IN BIDAR DISTRICT, KARNATAKA, INDIA

Objective: Present work deals with the studies on Ethnomedicinal plants used by Rajgond Tribes of Haladkeri village in Bidar District, Karnataka, IndiaMethods: Field trips were conducted from March to December, 2014 to collect the information on the medicinal plants used in the treatment of different ailments by Rajgond Tribe using the methodology suggested by Jain and Goel.Results: A total of 12 Vaidyas or healers were interviewed and 60 ethno medicinal plants species belonging to 37 families were recorded along with their scientific names, vernacular names, botanical family, parts used and their ethno medicinal significance.Conclusion: Rajgond Tribe of Haladkeri Village in Bidar District is far away from modern medicine even in 21st Century and is known for their unique way of life and disease management. As the majority of people in modern days is much conscious about their health and aware of the side effects of modern drugs, such study of ethnic drugs may turn a useful base in finding out new drug molecules

A NEW ALKALOID FROM DERRIS INDICA (LAM) BENNETT SEED OIL: ISOLATION AND CHARACTERIZATION

Objective: The aim of the study was to isolate alkaloid compound from seed oil of Derris indica (Lam) Bennett where relevant antimicrobial properties in traditional medicines. Methods: The plant was selected based on their usage in traditional medicines and ethnopharmacological importance. Crude extract from D. indica seeds fractioned with different solvents through column chromatography. Isolated pure fraction was identified and characterized using UV, FTIR, 1HNMR and Mass spectroscopy. Results: D. indica seeds hexane extract on fractionation with ethyl acetate and methanol through column chromatography yielded a crystalline fraction. The fraction was identified as alkaloid group and characterized as a 2-(6-methoxyphenanthridin-8-yl) propan-2-ol. The compound is a new report from D. indica seed oil. Conclusion: The usage of D. indica plant is much in traditional health care for treatment of diseases. Isolation of alkaloid compound from D. indica seeds in traditional herbal medicines may be found a good source of drug discovery

PLANT PROFILE, PHYTOCHEMISTRY AND PHARMACOLOGY OF ARGEMONE MEXICANA LINN.A REVIEW

Argemonemexicanais extensively used as traditional medicine for the treatment of numerous diseases. Various parts of the plant were extensively used in Ayurveda, Siddha, Unani and Homeopathic medicines.It is reported to have antimicrobial activity, wound healing property, larvicidal and chemosterilant activity, ne­maticidal and allelopathic potential, antimalarial, antibacterial and antifungal, molluscicidal, anticancer, hepatoprotective, anti-HIV and neuropharmacological activity. Chemical investigations of this plant have revealed the presence of alkaloids, amino acids, phenolics and fatty acids. A. mexicana has shown promise as an effective bio-control agent. The present review includes the detailed exploration of traditional uses, phytochemical and pharmacological properties and actions of whole plant extract reported so far

Convergence of Batch Asynchronous Stochastic Approximation With Applications to Reinforcement Learning

The stochastic approximation algorithm is a widely used probabilistic method for finding a zero of a vector-valued funtion, when only noisy measurements of the function are available. In the literature to date, one can make a distinction between "synchronous" updating, whereby every component of the current guess is updated at each time, and `"synchronous" updating, whereby only one component is updated. In principle, it is also possible to update, at each time instant, some but not all components of $\theta_t$, which might be termed as "batch asynchronous stochastic approximation" (BASA). Also, one can also make a distinction between using a "local" clock versus a "global" clock. In this paper, we propose a unified formulation of batch asynchronous stochastic approximation (BASA) algorithms, and develop a general methodology for proving that such algorithms converge, irrespective of whether global or local clocks are used. These convergence proofs make use of weaker hypotheses than existing results. For example: existing convergence proofs when a local clock is used require that the measurement noise is an i.i.d sequence. Here, it is assumed that the measurement errors form a martingale difference sequence. Also, all results to date assume that the stochastic step sizes satisfy a probabilistic analog of the Robbins-Monro conditions. We replace this by a purely deterministic condition on the irreducibility of the underlying Markov processes. As specific applications to Reinforcement Learning, we introduce ``batch'' versions of the temporal difference algorithm $TD(0)$ for value iteration, and the $Q$-learning algorithm for finding the optimal action-value function, and also permit the use of local clocks instead of a global clock. In all cases, we establish the convergence of these algorithms, under milder conditions than in the existing literature.Comment: 27 page

Occurrence and extracellular enzyme potential of Actinomycetes of a thermoltalerant, northern region of Karanataka, Inida

Occurrence and extracellular enzyme activities of a thermotalerent actinomycetes isolated from thermal spring of compost pit area, hair, feathers dumping places and municipal wastes of Gulbarga and Bellary (Northern part of Karnataka) and tested their degradability against hair and feather. A total of 67 actinomycetes were isolated, out of these 57 actinomycetes screened exhibited amylase, protease, chitinase, cellulase and keratinase activity determined in the petriplate using on starch casein agar (SCA) and nutrient agar media (NA). Out of 57 actinomycetes, 50 isolates showed amylase, 54 protease, 50 chitenase, 52 cellulase and 41 isolates showed keratinase activities respectively. The Maximum keratinase activity shows VSAC-12, this study shows that the isolates were found to be capable using keratin substrates as sole source of carbon and energy for further investigation

Applications for RFID in pharmaceutical industry

Security and safety are two important features desired in pharmaceutical supply chain and achieving the same is a challenging task. The need to secure and authenticate pharmaceutical products has increased tremendously with the emerging counterfeit product market. The motivation to introduce counterfeit pharmaceutical products in the supply chain could be to gain rapid economic benefits or affecting the reputation of strong brand in the pharmaceutical industry. RFID technology can be used to deter counterfeiting attempts. It can also be used in various other domains in the pharmaceutical industry. The main aim of this paper is to outline all the applications of RFID in the pharmaceutical industry. After explaining the main applications, we discuss how information hiding techniques could be used with RFID to offer efficient expiry date management, pharmaceutical tamper detection, and fraud detection and prevention