Phase Transition in Limiting Distributions of Coherence of High-Dimensional Random Matrices

The coherence of a random matrix, which is defined to be the largest magnitude of the Pearson correlation coefficients between the columns of the random matrix, is an important quantity for a wide range of applications including high-dimensional statistics and signal processing. Inspired by these applications, this paper studies the limiting laws of the coherence of n×p random matrices for a full range of the dimension p with a special focus on the ultra high-dimensional setting. Assuming the columns of the random matrix are independent random vectors with a common spherical distribution, we give a complete characterization of the behavior of the limiting distributions of the coherence. More specifically, the limiting distributions of the coherence are derived separately for three regimes: 1⁄n log p → 0, 1⁄n log p → β ∈ (0, ∞), and 1⁄n log p → ∞. The results show that the limiting behavior of the coherence differs significantly in different regimes and exhibits interesting phase transition phenomena as the dimension p grows as a function of n. Applications to statistics and compressed sensing in the ultra high-dimensional setting are also discussed

Limiting Laws of Coherence of Random Matrices With Applications to Testing Covariance Structure and Construction of Compressed Sensing Matrices

Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this paper the limiting laws of the coherence of an n × p random matrix in the high-dimensional setting where p can be much larger than n. Both the law of large numbers and the limiting distribution are derived. We then consider testing the bandedness of the covariance matrix of a high-dimensional Gaussian distribution which includes testing for independence as a special case. The limiting laws of the coherence of the data matrix play a critical role in the construction of the test. We also apply the asymptotic results to the construction of compressed sensing matrices

Distributions of Angles in Random Packing on Spheres

This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in Rp as the number of points n → ∞, while the dimension p is either fixed or growing with n. For both settings, we derive the limiting empirical distribution of the random angles and the limiting distributions of the extreme angles. The results reveal interesting differences in the two settings and provide a precise characterization of the folklore that “all high-dimensional random vectors are almost always nearly orthogonal to each other”. Applications to statistics and machine learning and connections with some open problems in physics and mathematics are also discussed

Distributions of Angles in Random Packing on Spheres

This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in Rp as the number of points n → ∞, while the dimension p is either fixed or growing with n. For both settings, we derive the limiting empirical distribution of the random angles and the limiting distributions of the extreme angles. The results reveal interesting differences in the two settings and provide a precise characterization of the folklore that “all high-dimensional random vectors are almost always nearly orthogonal to each other”. Applications to statistics and machine learning and connections with some open problems in physics and mathematics are also discussed

Cross-Generational Reproductive Fitness Enforced by Microchimeric Maternal Cells

SummaryExposure to maternal tissue during in utero development imprints tolerance to immunologically foreign non-inherited maternal antigens (NIMA) that persists into adulthood. The biological advantage of this tolerance, conserved across mammalian species, remains unclear. Here, we show maternal cells that establish microchimerism in female offspring during development promote systemic accumulation of immune suppressive regulatory T cells (Tregs) with NIMA specificity. NIMA-specific Tregs expand during pregnancies sired by males expressing alloantigens with overlapping NIMA specificity, thereby averting fetal wastage triggered by prenatal infection and non-infectious disruptions of fetal tolerance. Therefore, exposure to NIMA selectively enhances reproductive success in second-generation females carrying embryos with overlapping paternally inherited antigens. These findings demonstrate that genetic fitness, canonically thought to be restricted to Mendelian inheritance, is enhanced in female placental mammals through vertically transferred maternal cells that promote conservation of NIMA and enforce cross-generational reproductive benefits

Scaling of laser produced plasma UTA emission down to 3 nm for next generation lithography and short wavelength imaging

Presented at a poster session at Advances in X-Ray/EUV Optics and Components VI, Monday 22 August 2011, San Diego, California, USAAn engineering prototype high average power 13.5-nm source has been shipped to semiconductor facilities to permit the commencement of high volume production at a 100 W power level in 2011. In this source, UTA (unresolved transition array) emission of highly ionized Sn is optimized for high conversion efficiency and full recovery of the injected fuel is realized through ion deflection in a magnetic field. By use of a low-density target, satellite emission is suppressed and full ionization attained with short pulse CO2 laser irradiation. The UTA is scalable to shorter wavelengths, and Gd is shown to have similar conversion efficiency to Sn (13.5 nm) at a higher plasma temperature, with a narrow spectrum centered at 6.7 nm, where a 70% reflectivity mirror is anticipated. Optimization of short pulse CO2 laser irradiation is studied, and further extension of the same method is discussed, to realize 100 W average power down to a wavelength of 3 nmScience Foundation Irelandau, ke, co, li - TS 28.03.1

Electron pumping in graphene mechanical resonators

The combination of high frequency vibrations and metallic transport in graphene makes it a unique material for nano-electromechanical devices. In this letter, we show that graphene-based nano-electromechanical devices are extremely well suited for charge pumping, due to the sensitivity of its transport coefficients to perturbations in electrostatic potential and mechanical deformations, with the potential for novel small scale devices with useful applications

Protein kinase activity of phosphoinositide 3-kinase regulates cytokine-dependent cell survival

Extent: 14 p.The dual specificity protein/lipid kinase, phosphoinositide 3-kinase (PI3K), promotes growth factor-mediated cell survival and is frequently deregulated in cancer. However, in contrast to canonical lipid-kinase functions, the role of PI3K protein kinase activity in regulating cell survival is unknown. We have employed a novel approach to purify and pharmacologically profile protein kinases from primary human acute myeloid leukemia (AML) cells that phosphorylate serine residues in the cytoplasmic portion of cytokine receptors to promote hemopoietic cell survival. We have isolated a kinase activity that is able to directly phosphorylate Ser585 in the cytoplasmic domain of the interleukin 3 (IL-3) and granulocyte macrophage colony stimulating factor (GM-CSF) receptors and shown it to be PI3K. Physiological concentrations of cytokine in the picomolar range were sufficient for activating the protein kinase activity of PI3K leading to Ser585 phosphorylation and hemopoietic cell survival but did not activate PI3K lipid kinase signaling or promote proliferation. Blockade of PI3K lipid signaling by expression of the pleckstrin homology of Akt1 had no significant impact on the ability of picomolar concentrations of cytokine to promote hemopoietic cell survival. Furthermore, inducible expression of a mutant form of PI3K that is defective in lipid kinase activity but retains protein kinase activity was able to promote Ser585 phosphorylation and hemopoietic cell survival in the absence of cytokine. Blockade of p110α by RNA interference or multiple independent PI3K inhibitors not only blocked Ser585 phosphorylation in cytokine-dependent cells and primary human AML blasts, but also resulted in a block in survival signaling and cell death. Our findings demonstrate a new role for the protein kinase activity of PI3K in phosphorylating the cytoplasmic tail of the GM-CSF and IL-3 receptors to selectively regulate cell survival highlighting the importance of targeting such pathways in cancer.Daniel Thomas, Jason A. Powell, Benjamin D. Green, Emma F. Barry, Yuefang Ma, Joanna Woodcock, Stephen Fitter, Andrew C.W. Zannettino, Stuart M. Pitson, Timothy P. Hughes, Angel F. Lopez, Peter R. Shepherd, Andrew H. Wei, Paul G. Ekert and Mark A. Guthridg