High-dimensional Ising model selection using ℓ1{\ell_1}-regularized logistic regression

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an $\ell_1$-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes $p$ and maximum neighborhood size $d$ are allowed to grow as a function of the number of observations $n$. Our main results provide sufficient conditions on the triple $(n,p,d)$ and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes $n=\Omega(d^3\log p)$ with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of $n=\Omega(d^2\log p)$ suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.Comment: Published in at http://dx.doi.org/10.1214/09-AOS691 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization

Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is important. In this paper, we study the complexity of stochastic convex optimization in an oracle model of computation. We improve upon known results and obtain tight minimax complexity estimates for various function classes

Biodiesel Production from Oleaginous Fungi

Biodiesel involves the mixture of fatty acyl methyl/ethyl esters, produced from transesterification neutral lipids and if the origin of the source is from oleaginous micro organisms, then it is termed as micro diesel. In the present work, aiming to exploit fungi for biodiesel production, 12 fungal isolates were screened for lipid content by Sudan Black B staining method. Among 12 isolates, lipid rich five species viz, Mortierella alpina , M.ramanianna, M.vinancea, M.hyalina and M.verticella have been taken for fatty acids analysis by spectrophotometry, which revealed that the amount of free fatty acids were ranged from highest in M.alpina 35 ?moles of Oleic acid , 25 ?moles of Palmitic acid and 14 ?moles of Myristic acids to lower as much as 21 ?moles of Oleic acid , 18 ?moles of Palmitic acid and 16 ?moles of Myristic acids respectively in M.ramanianna

Microalgae Cultivation in Different pH, Temperature and Media for Lipid Production

Lipids produced by microalgal biomass can be grouped into nonpolar lipids and polar lipids, which can be easily converted into biofuels. Microalgal samples were collected from three different ponds of Bangalore and cultured in the laboratory to find the effect of different pH, temperature and media on the production of biomass and lipids. Among these, pH-9, temperature -25 ° C and Beneck’s media was most suitable for production of biomass (35.80 g/L) and lipids from the isolated microalgae Chlorella sp. compare to Chladospora sp. (13.33 g/L). Chlorella sp. Showed 0.32 (OD) at pH-9, 0.43 (OD) at temperature-25 ° C and 2.94 (OD) in Beneck’s media. Our result revealed that nutrient supply along with measured variables affects the production of biomass and lipids in different microalgae. DOI: http://dx.doi.org/10.3126/ijls.v8i2.10227 International Journal of Life Sciences Vol.8(2): 2014; 13-1

Stable and Metastable vortex states and the first order transition across the peak effect region in weakly pinned 2H-NbSe_2

The peak effect in weakly pinned superconductors is accompanied by metastable vortex states. Each metastable vortex configuration is characterized by a different critical current density J_c, which mainly depends on the past thermomagnetic history of the superconductor. A recent model [G. Ravikumar, et al, Phys. Rev. B 61, R6479 (2000)] proposed to explain the history dependent J_c postulates a stable state of vortex lattice with a critical current density J_c^{st}, determined uniquely by the field and temperature. In this paper, we present evidence for the existence of the stable state of the vortex lattice in the peak effect region of 2H-NbSe_2. It is shown that this stable state can be reached from any metastable vortex state by cycling the applied field by a small amplitude. The minor magnetization loops obtained by repeated field cycling allow us to determine the pinning and "equilibrium" properties of the stable state of the vortex lattice at a given field and temperature unambiguously. The data imply the occurence of a first order phase transition from an ordered phase to a disordered vortex phase across the peak effect.Comment: 20 pages, 10 figures. Corresponding author: S. Ramakrishna

Superconductivity-driven magnetization modulation in YBa2Cu3O7-{\delta} /SrTiO3/La0.67Sr0.33MnO3 heterostructures

Using spin polarized neutron reflectivity experiments, we demonstrate an unusual proximity behaviour when the superconductor (SC) and the ferromagnet (FM) are coupled through an insulator (I) in YBa2Cu3O7-{\delta} (SC)/SrTiO3 (I)/La0.67Sr0.33MnO3 (FM) heterostructures. We have observed an unexpected magnetic modulation at the interface region of the FM below the superconducting transition temperature. The magnetization of the FM layer at the I/FM interface was drastically reduced as compared to the magnetization in the rest of the FM layer. This result indicates that the Cooper pairs tunnel across the insulator and interact with the local magnetization at the interface region (extending ~ 30 {\AA}) of the FM causing modification of the magnetization at the interface. This unexpected magnetic behavior cannot be explained on the basis of the existing theoretical models. However, the length scale associated here clearly suggests the long range proximity effect as a result of tunneling of Cooper pairs.Comment: 6 figure