Fourier PCA and Robust Tensor Decomposition

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main application is the first provably polynomial-time algorithm for underdetermined ICA, i.e., learning an $n \times m$ matrix $A$ from observations $y=Ax$ where $x$ is drawn from an unknown product distribution with arbitrary non-Gaussian components. The number of component distributions $m$ can be arbitrarily higher than the dimension $n$ and the columns of $A$ only need to satisfy a natural and efficiently verifiable nondegeneracy condition. As a second application, we give an alternative algorithm for learning mixtures of spherical Gaussians with linearly independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected; exposition improve

Oxidative Stress Detection With Escherichia Coli Harboring A katG\u27::lux Fusion

A plasmid containing a transcriptional fusion of the Escherichia coli katG promoter to a truncated Vibrio fischeri lux operon (luxCDABE) was constructed. An E. coli strain bearing this plasmid (strain DPD2511) exhibited low basal levels of luminescence, which increased up to 1,000-fold in the presence of hydrogen peroxide, organic peroxides, redox-cycling agents (methyl viologen and menadione), a hydrogen peroxide-producing enzyme system (xanthine and xanthine oxidase), and cigarette smoke. An oxyR deletion abolished hydrogen peroxide-dependent induction, confirming that oxyR controlled katG\u27::lux luminescence. Light emission was also induced by ethanol by an unexplained mechanism. A marked synergistic response was observed when cells were exposed to both ethanol and hydrogen peroxide; the level of luminescence measured in the presence of both inducers was much higher than the sum of the level of luminescence observed with ethanol and the level of luminescence observed with hydrogen peroxide. It is suggested that this construction or similar constructions may be used as a tool for assaying oxidant and antioxidant properties of chemicals, as a biosensor for environmental monitoring and as a tool for studying cellular responses to oxidative hazards

Detection Of DNA Damage By Use Of Escherichia Coli Carrying recA\u27::lux, uvrA\u27::lux, And alkA\u27::lux Reporter Plasmids

Plasmids were constructed in which DNA damage-inducible promoters recA, uvrA, and alkA from Escherichia coli were fused to the Vibrio fischeri luxCDABE operon. Introduction of these plasmids into E. coli allowed the detection of a dose-dependent response to DNA-damaging agents, such as mitomycin and UV irradiation. Bioluminescence was measured in real time over extended periods. The fusion of the recA promoter to luxCDABE showed the most dramatic and sensitive responses. lexA dependence of the bioluminescent SOS response was demonstrated, confirming that this biosensor\u27s reports were transmitted by the expected regulatory circuitry. Comparisons were made between luxCDABE and lacZ fusions to each promoter. It is suggested that the lux biosensors may have use in monitoring chemical, physical, and genotoxic agents as well as in further characterizing the mechanisms of DNA repair

Chevkinite-Group Minerals from Granulite-Facies Metamorphic Rocks and Associated Pegmatites of East Antarctica and South India

Electron microprobe data are presented for chevkinite-group minerals from granulite-facies rocks and associated pegmatities of the Napier Complex and Mawson Station charnockite in East Antarctica and from the Eastern Ghats, South India. Their compositions conform to the general formula for this group, viz. A(4)BC(2)D(2)Si(4)O(22) where, in the analysed specimens A = (rare-earth elements (REE), Ca, Y, Th), B = Fe(2+) Mg, C = (Al, Mg, Ti, Fe(2+), Fe(3+), Zr) and D = Ti and plot within the perrierite field oftlic total Fe (as FeO) (wt.%) vs. CaO (wt.%) discriminator diagram of Macdonald and Belkin (2002). In contrast to most chevkinite-group minerals, the A site shows unusual enrichment in the MREE and HREE relative to the LREE and Ca. In one sample from the Napier Complex, Y is the dominant cation among the total REE + Y in the A site, the first reported case of Y-dominance in the chevkinite group. The minerals include the most Al-rich yet reported in the chevkinite group (\u3c= 9.15 wt.% Al(2)O(3)), sufficient to fill the C site in two samples. Conversely, the amount of Ti in these samples does not fill the D site. and, thus, some of the Al could be making up the deficiency at D, a situation not previously reported in the chevkinite group. Fe abudances are low, requiring Mg to occupy up to 45% of the B site. The chevkinite-group minerals analysed originated from three distinct parageneses: (1) pegmatites containing hornblende and orthopyroxene or garnet; (2) orthopyroxene-bearing gneiss and granulite; (3) highly aluminous paragneisses in which the associated minerals are relatively magnesian or aluminous. Chevkinite-group minerals from the first two parageneses have relatively high FeO content and low MgO and Al(2)O(3) contents; their compositions plot in the field for mafic and intermediate igneous rocks. In contrast, chevkinite-group minerals from the third paragenesis are notably more aluminous and have greater Mg/Fe ratios

Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

Adaptive query-based sampling of distributed collections

As part of a Distributed Information Retrieval system a de-scription of each remote information resource, archive or repository is usually stored centrally in order to facilitate resource selection. The ac-quisition ofprecise resourcedescriptionsistherefore animportantphase in Distributed Information Retrieval, as the quality of such represen-tations will impact on selection accuracy, and ultimately retrieval per-formance. While Query-Based Sampling is currently used for content discovery of uncooperative resources, the application of this technique is dependent upon heuristic guidelines to determine when a sufficiently accurate representation of each remote resource has been obtained. In this paper we address this shortcoming by using the Predictive Likelihood to provide both an indication of thequality of an acquired resource description estimate, and when a sufficiently good representation of a resource hasbeen obtained during Query-Based Sampling

Mathematical Modeling of a Bioluminescent E. Coli Based Biosensor

In this work we present a mathematical model for the bioreporter activity of an E. coli based bioluminescent bioreporter. This bioreporter is based on a genetically modified E. coli which harbors the recA promoter, a member of the bacterial SOS response, fused to the bacterial luminescence (lux) genes. This bioreporter responds to the presence of DNA damaging agents such as heavy metals, H2O2 and Nalidixic Acid (NA) that activate the SOS response. In our mathematical model we implemented basic physiological mechanisms such as: the penetration of the NA into the biosensor; gyrase enzyme inhibition by the NA; gyrase level regulation; creation of chromosomal DNA damage; DNA repair and release of ssDNA into the cytoplasm; SOS induction and chromosomal DNA repair; activation of lux genes by the fused recA promoter carried on a plasmidal DNA; transcription and translation of the luminescence responsible enzymes; luminescence cycle; energy molecules level regulation and the regulation of the O2 consumption. The mathematical model was defined using a set of ordinary differential equations (ODE) and solved numerically. We simulated the system for different concentrations of NA in water for specific biosensors concentration, and under limited O2 conditions. The simulated results were compared to experimental data and satisfactory matching was obtained. This manuscript presents a proof of concept showing that real biosensors can be modeled and simulated. This sets the ground to the next stage of implementing a comprehensive physiological model using experimentally extracted parameters. Following the completion of the next stage, it will be possible to construct a “Computer Aided Design” tool for the simulation of the genetically engineered biosensors. We define a term “bioCAD” for a Biological System Computer Aided Design. The specific bioCAD that is described here is aimed towards whole cell biosensors which are under investigation today for functional sensing. Usage of the bioCAD will improve the biosensors design process and boost their performance. It will also reduce Non Recurring Engineering (NRE) cost and time. Finally, using a parameterized solution will allow fair and quick evaluation of whole cell biosensors for various applications

Responses To Toxicants Of An Escherichia Coli Strain Carrying A uspA\u27::lux Genetic Fusion And An E. Coli Strain Carrying A grpE\u27::lux Fusion Are Similar

A transcriptional fusion of the Escherichia coli uspA promoter to luxCDABE was characterized and compared with a heat shock-responsive grpE\u27::lux fusion. Similarities in range and rank order of inducing conditions were observed; however, the magnitude of induction was typically greater for the grpE\u27::lux fusion strain

Personalisation and recommender systems in digital libraries

Widespread use of the Internet has resulted in digital libraries that are increasingly used by diverse communities of users for diverse purposes and in which sharing and collaboration have become important social elements. As such libraries become commonplace, as their contents and services become more varied, and as their patrons become more experienced with computer technology, users will expect more sophisticated services from these libraries. A simple search function, normally an integral part of any digital library, increasingly leads to user frustration as user needs become more complex and as the volume of managed information increases. Proactive digital libraries, where the library evolves from being passive and untailored, are seen as offering great potential for addressing and overcoming these issues and include techniques such as personalisation and recommender systems. In this paper, following on from the DELOS/NSF Working Group on Personalisation and Recommender Systems for Digital Libraries, which met and reported during 2003, we present some background material on the scope of personalisation and recommender systems in digital libraries. We then outline the working group’s vision for the evolution of digital libraries and the role that personalisation and recommender systems will play, and we present a series of research challenges and specific recommendations and research priorities for the field