The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

The Foundations of Statistics By Prof. Leonard J. Savage. (Wiley Publications in Statistics.) Pp. xv + 294. (New York; John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1954.) 48s. net.

Probability and Statistical Inference

https://www.cell.com/cell-host-microbe/pdf/S1931-3128(16)30153-6.pdf

Genetic Determinants of the Gut Microbiome in UK Twins

We identified rare coding variants associated with Alzheimer's disease in a three-stage case–control study of 85,133 subjects. In stage 1, we genotyped 34,174 samples using a whole-exome microarray. In stage 2, we tested associated variants (P < 1 × 10−4) in 35,962 independent samples using de novo genotyping and imputed genotypes. In stage 3, we used an additional 14,997 samples to test the most significant stage 2 associations (P < 5 × 10−8) using imputed genotypes. We observed three new genome-wide significant nonsynonymous variants associated with Alzheimer's disease: a protective variant in PLCG2 (rs72824905: p.Pro522Arg, P = 5.38 × 10−10, odds ratio (OR) = 0.68, minor allele frequency (MAF)cases = 0.0059, MAFcontrols = 0.0093), a risk variant in ABI3 (rs616338: p.Ser209Phe, P = 4.56 × 10−10, OR = 1.43, MAFcases = 0.011, MAFcontrols = 0.008), and a new genome-wide significant variant in TREM2 (rs143332484: p.Arg62His, P = 1.55 × 10−14, OR = 1.67, MAFcases = 0.0143, MAFcontrols = 0.0089), a known susceptibility gene for Alzheimer's disease. These protein-altering changes are in genes highly expressed in microglia and highlight an immune-related protein–protein interaction network enriched for previously identified risk genes in Alzheimer's disease. These genetic findings provide additional evidence that the microglia-mediated innate immune response contributes directly to the development of Alzheimer's disease.

/pdf/rare-coding-variants-in-plcg2-abi3-and-trem2-implicate-39cc74ny14.pdf

Rare coding variants in PLCG2, ABI3, and TREM2 implicate microglial-mediated innate immunity in Alzheimer's disease

The genetic architecture of common traits, including the number, frequency, and effect sizes of inherited variants that contribute to individual risk, has been long debated. Genome-wide association studies have identified scores of common variants associated with type 2 diabetes, but in aggregate, these explain only a fraction of the heritability of this disease. Here, to test the hypothesis that lower-frequency variants explain much of the remainder, the GoT2D and T2D-GENES consortia performed whole-genome sequencing in 2,657 European individuals with and without diabetes, and exome sequencing in 12,940 individuals from five ancestry groups. To increase statistical power, we expanded the sample size via genotyping and imputation in a further 111,548 subjects. Variants associated with type 2 diabetes after sequencing were overwhelmingly common and most fell within regions previously identified by genome-wide association studies. Comprehensive enumeration of sequence variation is necessary to identify functional alleles that provide important clues to disease pathophysiology, but large-scale sequencing does not support the idea that lower-frequency variants have a major role in predisposition to type 2 diabetes.

The genetic architecture of type 2 diabetes

List of figures List of tables Preface to the Classics Edition Preface Introduction 1. Elementary acquaintance with multigrid Part I. Stages in Developing Fast Solvers: 2. Stable discretization 3. Interior relaxation and smoothing factors 4. Interior two-level cycles 5. Boundary conditions and two-level cycling 6. Many-level cycles 7. Full multi-grid (FMG) algorithms Part II. Advanced Techniques and Insights: 8. Full approximation scheme (FAS) and applications 9. Local refinements and grid adaptation 10. Higher-order techniques 11. Coarsening guided by discretization 12. True role of relaxation 13. Dealgebraization of multigrid 14. Practical role of rigorous analysis and quantitative predictions 15. Chains of problems: frozen tau 16. Time dependent problems Part III. Applications to Fluid Dynamics: 17. Cauchy-Riemann equations 18. Steady-state Stokes equations 19. Steady-state incompressible Navier-Stokes equations 20. Compressible Navier-Stokes and Euler equations 21. Remarks on solvers for transonic potential equations Appendix: test cycle: MATLAB code Bibliography Index.

Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Revised Edition

Laplacian matrices of graphs arise in large-scale computational applications such as semisupervised machine learning; spectral clustering of images, genetic data, and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A lean algebraic multigrid (LAMG) solver of the symmetric linear system $Ax=b$ is presented, where $A$ is a graph Laplacian. LAMG's run time and storage are empirically demonstrated to scale linearly with the number of edges. LAMG consists of a setup phase, during which a sequence of increasingly coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional multigrid applications. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity measure (the affinity), and an energy correction of coarse-level systems. This ...

Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver

A proper coarse variable set for algebraic multigrid (AMG) solvers can be constructed using compatible relaxation (CR). For a given coarse set, CR is a modified relaxation scheme that keeps the values of the coarse variables intact. Its convergence factor is a predictor of the potential AMG efficiency, similarly to the smoothing factor in geometric multigrid. A practical, CR-based coarse set construction algorithm is presented. Numerical results for model problems are demonstrated. Copyright © 2004 John Wiley & Sons, Ltd.

Coarsening by compatible relaxation

Common variants account for only a small amount of the heritable risk for developing asthma. Using a meta-analysis approach, Igartua et al. identify one low-frequency missense mutation and two genes with functional variants that are associated with asthma, but only in specific ethnic groups.

/pdf/ethnic-specific-associations-of-rare-and-low-frequency-dna-4lzk4yakm6.pdf

Ethnic-specific associations of rare and low-frequency DNA sequence variants with asthma.

We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices.

Oren E. Livne

Papers

Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Revised Edition

Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver

Coarsening by compatible relaxation

Ethnic-specific associations of rare and low-frequency DNA sequence variants with asthma.

Scaling by Binormalization