Marchenko-Pastur law with relaxed independence conditions

We prove the Marchenko-Pastur law for the eigenvalues of $p \times p$ sample covariance matrices in two new situations where the data does not have independent coordinates. In the first scenario - the block-independent model - the $p$ coordinates of the data are partitioned into blocks in such a way that the entries in different blocks are independent, but the entries from the same block may be dependent. In the second scenario - the random tensor model - the data is the homogeneous random tensor of order $d$, i.e. the coordinates of the data are all $\binom{n}{d}$ different products of $d$ variables chosen from a set of $n$ independent random variables. We show that Marchenko-Pastur law holds for the block-independent model as long as the size of the largest block is $o(p)$ and for the random tensor model as long as $d = o(n^{1/3})$. Our main technical tools are new concentration inequalities for quadratic forms in random variables with block-independent coordinates, and for random tensors

An LpL^p theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions

We introduce and develop a theory of limits for sequences of sparse graphs based on $L^p$ graphons, which generalizes both the existing $L^\infty$ theory of dense graph limits and its extension by Bollob\'as and Riordan to sparse graphs without dense spots. In doing so, we replace the no dense spots hypothesis with weaker assumptions, which allow us to analyze graphs with power law degree distributions. This gives the first broadly applicable limit theory for sparse graphs with unbounded average degrees. In this paper, we lay the foundations of the $L^p$ theory of graphons, characterize convergence, and develop corresponding random graph models, while we prove the equivalence of several alternative metrics in a companion paper.Comment: 44 page

The Effects of the Web as a Form of Stakeholder Communication: An empirical case study of a co-operative

This research aims to add some understanding to the existing stakeholder management literature with a focus on the management of stakeholder communication. It explores how the Web can assist the management of the communication between a dairy co-operative and its farmer supplier-shareholders. An exploratory case study and semi-structured in-depth interview research design is used to collect, analyse, and present the perceptions of interview participants. This research highlights a paradox, which results from the inconsistent needs of the farmers as both suppliers and shareholders of the co-operative. A number of factors that have influenced farmer interviewees' decisions to either reject or embrace the Web are also identified. These factors are divided into two categories, those closely associated with individual characteristics, namely, perceived values, perceived self-efficacy, and awareness; and these outside the individual's control, namely, infrastructure and media conflict. These findings suggest that the Web adds flexibility to organisations' stakeholder communication strategies by offering an additional communication form. In particular, this research shows that the Web contributes to overall management of stakeholder communication through 1) increased accessibility to personalised and up-to-date information, 2) added flexibility to self-service programs, and 3) a recreated sense of 'conventional' community. Furthermore, the Web should be used as a complement to, rather than a replacement for, conventional communication forms in stakeholder communication strategies. Although the Web may not be the answer for all stakeholder communication challenges; what seems undeniable is the tremendous potential of the Web in facilitating and leveraging the management of stakeholder communication. Three considerations are proposed for organisations planning to include the Web as part of their stakeholder communication strategy: organisational needs, stakeholder characteristics, and communication media factors. Research limitations are discussed, and recommendations for further study are outlined in the conclusion

Stability of extemporaneously prepared ophthalmic solutions for mydriasis

Purpose Results of an evaluation of the physical and chemical stability of extemporaneously prepared adult and pediatric ophthalmic solutions containing combinations of phenylephrine, tropicamide, and cyclopentolate are reported. Methods A stability study was conducted to help determine the feasibility of innovative formulations to meet an unmet clinical need for combination mydriatic ophthalmic eyedrops. An adult mydriatic ophthalmic solution containing phenylephrine hydrochloride 2.5% and tropicamide 1.0% and a pediatric formulation containing phenylephrine hydrochloride 2.5%, tropicamide 0.5%, and cyclopentolate hydrochloride 0.5% were prepared using proper aseptic techniques. Triplicate samples of each formulation were stored for 60 days at refrigeration temperatures (2–8 °C) and analyzed on day 0 and days 7, 14, 28, and 60. At each time point, the stability samples were assessed by visual inspection, pH measurement, and stability-indicating high-performance liquid chromatography (HPLC) analysis. Results Over the 60-day storage period, there was no significant change in the visual appearance or pH level of any of the adult or pediatric solution samples. The results of HPLC analysis indicated that all samples retained 97–102% of the initial drug concentrations for up to 60 days. Conclusion Both adult and pediatric ophthalmic formulations containing combinations of phenylephrine, tropicamide, and cyclopentolate were stable physically and chemically for up to 60 days when stored at refrigeration temperatures (2–8 °C)

Implementing Polar Projections with OGC Services for the Enhancement of AIRS NRT Visualization in LANCE

The Atmospheric Infrared Sounder (AIRS) NRT product is one important element in the Land, Atmosphere Near real-time Capability for EOS (LANCE). The LANCE processing of AIRS NRT products and the image generation are performed at the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC). The Open Geospatial Consortium (OGC) services are being utilized to access AIRS NRT images. The ongoing AIRS NRT imagery enhancement work includes adding a new set of the images in polar projections. Polar projections are commonly used for mapping Antarctica and Arctic regions. We have implemented more precise south polar (EPSG:3031) projection and north polar (EPSG:3413) projection making our OGC service instances more useful and interoperable. Thus, AIRS NRT data can be easily accessed and integrated with other applications. It greatly increases the impact of our data on researches in polar regions.In this presentation, we will introduce the optimized processing workflow for OGC services from data access with spatial-temporal index to data visualization with different SLD, and demonstrate how to use open source software to provide more precise map images in polar projections