We study the problem of selecting a subset of k random variables to observe that will yield the best linear prediction of another variable of interest, given the pairwise correlations between the observation variables and the predictor variable. Under approximation preserving reductions, this problem is also equivalent to the "sparse approximation" problem of approximating signals concisely.We propose and analyze exact and approximation algorithms for several special cases of practical interest. We give an FPTAS when the covariance matrix has constant bandwidth, and exact algorithms when the associated covariance graph, consisting of edges for pairs of variables with non-zero correlation, forms a tree or has a large (known) independent set. Furthermore, we give an exact algorithm when the variables can be embedded into a line such that the covariance decreases exponentially in the distance, and a constant-factor approximation when the variables have no "conditional suppressor variables".Much of our reasoning is based on perturbation results for the R 2 multiple correlation measure, frequently used as a measure for "goodness-of-fit statistics". It lies at the core of our FPTAS, and also allows us to extend exact algorithms to approximation algorithms when the matrix "nearly" falls into one of the above classes. We also use perturbation analysis to prove approximation guarantees for the widely used "Forward Regression" heuristic when the observation variables are nearly independent.
Rare-earth activated upconversion nanoparticles (UCNPs) are receiving renewed attention for use in bioimaging due to their exceptional photostability and low cytotoxicity. Often, these nanoparticles are attached to plasmonic nanostructures to enhance their photoluminescence (PL) emission. However, current wet-chemistry techniques suffer from large inhomogeneity and thus low enhancement is achieved. In this paper, we report lithographically fabricated metal-insulator-metal (MIM) nanostructures that show over 1000-fold enhancement of their PL. We demonstrate the potential for bioimaging applications by dispersing the MIMs into water and imaging bladder cancer cells with them. To our knowledge, our results represent one and two orders of magnitude improvement, respectively, over the best lithographically fabricated structures and colloidal systems in the literature. The large enhancement will allow for bioimaging and therapeutics using lower particle densities or lower excitation power densities, thus increasing the sensitivity and efficacy of such procedures while decreasing potential side effects.
Our opinions and judgments are increasingly shaped by what we read on social media -whether they be tweets and posts in social networks, blog posts, or review boards. These opinions could be about topics such as consumer products, politics, life style, or celebrities. Understanding how users in a network update opinions based on their neighbor's opinions, as well as what global opinion structure is implied when users iteratively update opinions, is important in the context of viral marketing and information dissemination, as well as targeting messages to users in the network.In this paper, we consider the problem of modeling how users update opinions based on their neighbors' opinions. We perform a set of online user studies based on the celebrated conformity experiments of Asch [1]. Our experiments are carefully crafted to derive quantitative insights into developing a model for opinion updates (as opposed to deriving psychological insights). We show that existing and widely studied theoretical models do not explain the entire gamut of experimental observations we make. This leads us to posit a new, nuanced model that we term the BiasedVoterModel. We present preliminary theoretical and simulation results on the convergence and structure of opinions in the entire network when users iteratively update their respective opinions according to the BiasedVoterModel. We show that consensus and polarization of opinions arise naturally in this model under easy to interpret initial conditions on the network.
Expression of trpB and trpA of the Escherichia coli tryptophan operon is shown to be "translationally coupled", i.e., efficient translation of the t coding region is dependent on prior translation of the trpB coding region and termination of translation at the trpB stop codon.. To examine the dependence of trpA expression on the ribosome binding site sequence in the distal segment of t, deletions were produced that replaced this tpB sequence. Analysis of trpA expression in these deletion mutants establ4ished that the ribosome binding site sequence is required for efficient translation of the trp A segment of trp riRNA. A modest effect of translation over the trpA ri osorme binding site on independent initiation at that site was also served.trpD-trpC and galT-galK gene pairs of E. coli the stop and start codons of © I R L Press Limited, Oxford, England.
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