The Configuration Interaction Method in the Second Quantization Representation

The mathematical apparatus of the second quantization is applied to the configuration interaction method. The configurations are treated as a system of particles and holes against the vacuum state built by the closed shell of the ground configuration. Expressions for the operators of the basic physical quantities are derived using the hole formalism generalized on an arbitrary orthonormal system of orbitals. Rules for obtaining the result of application of the operator 82 in the second quantization are formulated. An application of Wick\u27s theorems for calculation of the matrix elements over configurations leads to a simple logical scheme of the configuration interaction method which is valid for configurations of an arbitrary complexity and can be easily programed for a computer

Spin Waves in a Periodically Layered Magnetic Nanowire

We report a simple theoretical derivation of the spectrum and damping of spin waves in a cylindrical periodically structured magnetic nanowire (cylindrical magnonic crystal) in the "effective medium" approximation. The dependence of the "effective" magnetic parameters upon the individual layer parameters is shown to be different from the arithmetic average over the volume of the superlattice. The formulae that are obtained can be applied firstly in the description of spin wave dispersion in the first allowed band of the structure; and secondly in the design of a magnonic crystal with band-gaps in an arbitrary part of the spin wave spectrum.Comment: 15 pages, 3 figures; submitted to Journal of Applied Physic

On the rotational dynamics of the Rattleback

The Rattleback is a very popular science toy shown to students all over the world to demonstrate the non-triviality of rotational motion. When spun on a horizontal table, this boat-shaped object behaves in a peculiar way. Although the object appears symmetric, the dynamics of its motion seem very asymmetric. When spun in the preferred direction, it spins smoothly, whereas in the other direction it starts to oscillate wildly. The oscillation soon dies out and the rattleback starts to spin in the preferred way. We will construct and go through an analytical model capable of explaining this behaviour in a simple and intelligible way. Although we aim at a semi-pedagogical treatise, we will study the details only when they are necessary to understand the calculation. After presenting the calculations we will discuss the physical validity of our assumptions and take a look at more sophisticated models requiring numerical analysis. We will then improve our model by assuming a simple friction force.Comment: 17 pages and 2 figures, typos corrected, some minor additions and rewording

Study of the Electronic Structure of Radicals by the CI Method I. Matrix Elements of the Physical Value Operators

The results of a preceding paper which describes the CI method in the second quantization are used to construct basis vectors in the case of singly and doubly excited configurations for molecules and radicals. The matrix elements of the Hamiltonian are also given. A method for calculating the electronic density distribution in the CI method is formulated. An analog of the well known Brillouin theorem for radicals is obtained

Wave modes of collective vortex gyration in dipolar-coupled-dot-array magnonic crystals

Lattice vibration modes are collective excitations in periodic arrays of atoms or molecules. These modes determine novel transport properties in solid crystals. Analogously, in periodical arrangements of magnetic vortex-state disks, collective vortex motions have been predicted. Here, we experimentally observe wave modes of collective vortex gyration in one-dimensional (1D) periodic arrays of magnetic disks using time-resolved scanning transmission x-ray microscopy. The observed modes are interpreted based on micromagnetic simulation and numerical calculation of coupled Thiele equations. Dispersion of the modes is found to be strongly affected by both vortex polarization and chirality ordering, as revealed by the explicit analytical form of 1D infinite arrays. A thorough understanding thereof is fundamental both for lattice vibrations and vortex dynamics, which we demonstrate for 1D magnonic crystals. Such magnetic disk arrays with vortex-state ordering, referred to as magnetic metastructure, offer potential implementation into information processing devices.open8

Spin Caloritronics

This is a brief overview of the state of the art of spin caloritronics, the science and technology of controlling heat currents by the electron spin degree of freedom (and vice versa).Comment: To be published in "Spin Current", edited by S. Maekawa, E. Saitoh, S. Valenzuela and Y. Kimura, Oxford University Pres

Patterns of polymorphism and linkage disequilibrium in cultivated barley

We carried out a genome-wide analysis of polymorphism (4,596 SNP loci across 190 elite cultivated accessions) chosen to represent the available genetic variation in current elite North West European and North American barley germplasm. Population sub-structure, patterns of diversity and linkage disequilibrium varied considerably across the seven barley chromosomes. Gene-rich and rarely recombining haplotype blocks that may represent up to 60% of the physical length of barley chromosomes extended across the ‘genetic centromeres’. By positioning 2,132 bi-parentally mapped SNP markers with minimum allele frequencies higher than 0.10 by association mapping, 87.3% were located to within 5 cM of their original genetic map position. We show that at this current marker density genetically diverse populations of relatively small size are sufficient to fine map simple traits, providing they are not strongly stratified within the sample, fall outside the genetic centromeres and population sub-structure is effectively controlled in the analysis. Our results have important implications for association mapping, positional cloning, physical mapping and practical plant breeding in barley and other major world cereals including wheat and rye that exhibit comparable genome and genetic features

Genome-wide association filtering using a highly locus-specific transmission/disequilibrium test

Multimarker transmission/disequilibrium tests (TDTs) are powerful association and linkage tests used to perform genome-wide filtering in the search for disease susceptibility loci. In contrast to case/control studies, they have a low rate of false positives for population stratification and admixture. However, the length of a region found in association with a disease is usually very large because of linkage disequilibrium (LD). Here, we define a multimarker proportional TDT (mTDTP) designed to improve locus specificity in complex diseases that has good power compared to the most powerful multimarker TDTs. The test is a simple generalization of a multimarker TDT in which haplotype frequencies are used to weight the effect that each haplotype has on the whole measure. Two concepts underlie the features of the metric: the ‘common disease, common variant’ hypothesis and the decrease in LD with chromosomal distance. Because of this decrease, the frequency of haplotypes in strong LD with common disease variants decreases with increasing distance from the disease susceptibility locus. Thus, our haplotype proportional test has higher locus specificity than common multimarker TDTs that assume a uniform distribution of haplotype probabilities. Because of the common variant hypothesis, risk haplotypes at a given locus are relatively frequent and a metric that weights partial results for each haplotype by its frequency will be as powerful as the most powerful multimarker TDTs. Simulations and real data sets demonstrate that the test has good power compared with the best tests but has remarkably higher locus specificity, so that the association rate decreases at a higher rate with distance from a disease susceptibility or disease protective locus

An investigation of the effects of lipid-lowering medications: genome-wide linkage analysis of lipids in the HyperGEN study

BACKGROUND: Use of anti-hyperlipidemic medications compromises genetic analysis because of altered lipid profiles. We propose an empirical method to adjust lipid levels for medication effects so that the adjusted lipid values substitute the unmedicated lipid values in the genetic analysis. RESULTS: Published clinical trials were reviewed for HMG-CoA reductase inhibitors and fibric acid derivatives as mono-drug therapy. HMG-CoA reductase inhibitors showed similar effects in African Americans (AA) and non-African Americans (non-AA) for lowering total cholesterol (TC, -50.7 mg/dl), LDL cholesterol (LDL-C, -48.1 mg/dl), and triglycerides (TG, -19.7 mg/dl). Their effect on increasing HDL cholesterol (HDL-C) in AA (+0.4 mg/dl) was lower than in Non-AA (+2.3 mg/dl). The effects of fibric acid derivatives were estimated as -46.1 mg/dl for TC, -40.1 mg/dl for LDL-C, and +5.9 mg/dl for HDL-C in non-AA. The corresponding effects in AA were less extreme (-20.1 mg/dl, -11.4 mg/dl, and +3.1 mg/dl). Similar effect for TG (59.0 mg/dl) was shown in AA and non-AA. The above estimated effects were applied to a multipoint variance components linkage analysis on the lipid levels in 2,403 Whites and 2,214 AA in the HyperGEN study. The familial effects did vary depending on whether the lipids were adjusted for medication use. For example, the heritabilities increased after medication adjustment for TC and LDL-C, but did not change significantly for HDL-C and TG. CONCLUSION: Ethnicity-specific medication adjustments using our empirical method can be employed in epidemiological and genetic analysis of lipids.National Heart, Lung, and Blood Institute (HL554471, HL54472, HL54473, HL54495, HL54496, HL54497, HL54509, HL54515

Recombinational Landscape and Population Genomics of Caenorhabditis elegans

Recombination rate and linkage disequilibrium, the latter a function of population genomic processes, are the critical parameters for mapping by linkage and association, and their patterns in Caenorhabditis elegans are poorly understood. We performed high-density SNP genotyping on a large panel of recombinant inbred advanced intercross lines (RIAILs) of C. elegans to characterize the landscape of recombination and, on a panel of wild strains, to characterize population genomic patterns. We confirmed that C. elegans autosomes exhibit discrete domains of nearly constant recombination rate, and we show, for the first time, that the pattern holds for the X chromosome as well. The terminal domains of each chromosome, spanning about 7% of the genome, exhibit effectively no recombination. The RIAILs exhibit a 5.3-fold expansion of the genetic map. With median marker spacing of 61 kb, they are a powerful resource for mapping quantitative trait loci in C. elegans. Among 125 wild isolates, we identified only 41 distinct haplotypes. The patterns of genotypic similarity suggest that some presumed wild strains are laboratory contaminants. The Hawaiian strain, CB4856, exhibits genetic isolation from the remainder of the global population, whose members exhibit ample evidence of intercrossing and recombining. The population effective recombination rate, estimated from the pattern of linkage disequilibrium, is correlated with the estimated meiotic recombination rate, but its magnitude implies that the effective rate of outcrossing is extremely low, corroborating reports of selection against recombinant genotypes. Despite the low population, effective recombination rate and extensive linkage disequilibrium among chromosomes, which are techniques that account for background levels of genomic similarity, permit association mapping in wild C. elegans strains