Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions

In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of different mesoscopic distributions. Second, a new variant of the sigma model for interacting electrons in disordered normal and superconducting systems is presented, with demonstrating how to reduce it, under certain controlled approximations, to known ``phase-only'' actions, including that of the ``dirty bosons'' model.Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly Correlated Fermions and Bosons in Low - Dimensional Disordered Systems", Windsor, August, 2001; to be published by Kluwe

Genetic Modulation of Lipid Profiles following Lifestyle Modification or Metformin Treatment: the Diabetes Prevention Program

Weight-loss interventions generally improve lipid profiles and reduce cardiovascular disease risk, but effects are variable and may depend on genetic factors. We performed a genetic association analysis of data from 2,993 participants in the Diabetes Prevention Program to test the hypotheses that a genetic risk score (GRS) based on deleterious alleles at 32 lipid-associated single-nucleotide polymorphisms modifies the effects of lifestyle and/or metformin interventions on lipid levels and nuclear magnetic resonance (NMR) lipoprotein subfraction size and number. Twenty-three loci previously associated with fasting LDL-C, HDL-C, or triglycerides replicated (P=0.04–1×10$^{−17}$). Except for total HDL particles (r=−0.03, P=0.26), all components of the lipid profile correlated with the GRS (partial |r|=0.07–0.17, P=5×10$^{−5}$–1×10$^{−19}$). The GRS was associated with higher baseline-adjusted 1-year LDL cholesterol levels (β=+0.87, SEE±0.22 mg/dl/allele, P=8×10−5, P$_{interaction}$=0.02) in the lifestyle intervention group, but not in the placebo (β=+0.20, SEE±0.22 mg/dl/allele, P=0.35) or metformin (β=−0.03, SEE±0.22 mg/dl/allele, P=0.90; P$_{interaction}$=0.64) groups. Similarly, a higher GRS predicted a greater number of baseline-adjusted small LDL particles at 1 year in the lifestyle intervention arm (β=+0.30, SEE±0.012 ln nmol/L/allele, P=0.01, P$_{interaction}$=0.01) but not in the placebo (β=−0.002, SEE±0.008 ln nmol/L/allele, P=0.74) or metformin (β=+0.013, SEE±0.008 nmol/L/allele, P=0.12; P$_{interaction}$ = 0.24) groups. Our findings suggest that a high genetic burden confers an adverse lipid profile and predicts attenuated response in LDL-C levels and small LDL particle number to dietary and physical activity interventions aimed at weight loss

Long Wavelength Anomalous Diffusion Mode in the 2D XY Dipole Magnet

In 2D XY ferromagnet the dipole force induces a strong interaction between spin-waves in the long-wavelength limit. The major effect of this interaction is the transformation of a propagating spin-wave into a diffusion mode. We study the anomalous dynamics of such diffusion modes. We find that the Janssen-De Dominics functional, which governs this dynamics, approaches the non-Gaussian fixed-point. A spin-wave propagates by an anomalous anisotropic diffusion with the dispersion relation: $i\omega{\sim}k_{y}^{\Delta_y}$ and $i\omega{\sim}k_{x}^{\Delta_x}$, where ${\Delta_y}=47/27$ and ${\Delta_x}=47/36$. The low-frequency response to the external magnetic field is found.Comment: 34 pages, RevTeX, 2 .ps figures, the third figure is available upon reques

Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach

We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature $T_X$ which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a non-linear sigma model (NL$\sigma$M) that we derive from the Hubbard model. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentially small; there are well-defined Bogoliubov quasi-particles (QP's) (carrying most of the spectral weight) coexisting with a high-energy incoherent excitation background. As $U$ increases, the Slater antiferromagnet progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands evolve into Mott-Hubbard bands separated by a large AF gap. A significant fraction of spectral weight is transferred from the Bogoliubov QP's to incoherent excitations. At finite temperature, there is a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling. Finally, we point out that our results straightforwardly translate to the half-filled attractive Hubbard model, where the ${\bf q}=(\pi,\pi)$ charge and ${\bf q}=0$ pairing fluctuations combine to form an order parameter with SO(3) symmetry.Comment: Revtex4, 19 pages, 14 figures; (v2) final version as publishe

The genome sequence of <i>Trypanosoma brucei gambiense</i>, causative agent of chronic Human African Trypanosomiasis

&lt;p&gt;&lt;b&gt;Background:&lt;/b&gt; &lt;i&gt;Trypanosoma brucei gambiense&lt;/i&gt; is the causative agent of chronic Human African Trypanosomiasis or sleeping sickness, a disease endemic across often poor and rural areas of Western and Central Africa. We have previously published the genome sequence of a &lt;i&gt;T. b. brucei&lt;/i&gt; isolate, and have now employed a comparative genomics approach to understand the scale of genomic variation between &lt;i&gt;T. b. gambiense&lt;/i&gt; and the reference genome. We sought to identify features that were uniquely associated with &lt;i&gt;T. b. gambiense&lt;/i&gt; and its ability to infect humans.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods and findings:&lt;/b&gt; An improved high-quality draft genome sequence for the group 1 &lt;i&gt;T. b. gambiense&lt;/i&gt; DAL 972 isolate was produced using a whole-genome shotgun strategy. Comparison with &lt;i&gt;T. b. brucei&lt;/i&gt; showed that sequence identity averages 99.2% in coding regions, and gene order is largely collinear. However, variation associated with segmental duplications and tandem gene arrays suggests some reduction of functional repertoire in &lt;i&gt;T. b. gambiense&lt;/i&gt; DAL 972. A comparison of the variant surface glycoproteins (VSG) in &lt;i&gt;T. b. brucei&lt;/i&gt; with all &lt;i&gt;T. b. gambiense&lt;/i&gt; sequence reads showed that the essential structural repertoire of VSG domains is conserved across &lt;i&gt;T. brucei&lt;/i&gt;.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusions:&lt;/b&gt; This study provides the first estimate of intraspecific genomic variation within &lt;i&gt;T. brucei&lt;/i&gt;, and so has important consequences for future population genomics studies. We have shown that the &lt;i&gt;T. b. gambiense&lt;/i&gt; genome corresponds closely with the reference, which should therefore be an effective scaffold for any &lt;i&gt;T. brucei&lt;/i&gt; genome sequence data. As VSG repertoire is also well conserved, it may be feasible to describe the total diversity of variant antigens. While we describe several as yet uncharacterized gene families with predicted cell surface roles that were expanded in number in &lt;i&gt;T. b. brucei&lt;/i&gt;, no &lt;i&gt;T. b. gambiense&lt;/i&gt;-specific gene was identified outside of the subtelomeres that could explain the ability to infect humans.&lt;/p&gt

Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes

We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve transitions with a topological order parameter associated with dislocations in collinear spin density wave ("stripe") correlations: the gapping of the order parameter fluctuations leads to a fractionalization of spin and charge collective modes, and this transition has been proposed as a candidate for the cuprates near optimal doping. The coupling between the order parameter and long-wavelength volume and shape deformations of the Fermi surface is analyzed by the renormalization group, and a runaway flow to a non-perturbative regime is found in most cases. A phenomenological scaling analysis of simple observable properties of possible second order quantum critical points is presented, with results quite similar to those near quantum spin glass transitions and to phenomenological forms proposed by Schroeder et al. (cond-mat/0011002).Comment: 16 pages, 4 figures; (v2) additional clarifying remark

Prospective functional classification of all possible missense variants in PPARG.

Clinical exome sequencing routinely identifies missense variants in disease-related genes, but functional characterization is rarely undertaken, leading to diagnostic uncertainty. For example, mutations in PPARG cause Mendelian lipodystrophy and increase risk of type 2 diabetes (T2D). Although approximately 1 in 500 people harbor missense variants in PPARG, most are of unknown consequence. To prospectively characterize PPARγ variants, we used highly parallel oligonucleotide synthesis to construct a library encoding all 9,595 possible single-amino acid substitutions. We developed a pooled functional assay in human macrophages, experimentally evaluated all protein variants, and used the experimental data to train a variant classifier by supervised machine learning. When applied to 55 new missense variants identified in population-based and clinical sequencing, the classifier annotated 6 variants as pathogenic; these were subsequently validated by single-variant assays. Saturation mutagenesis and prospective experimental characterization can support immediate diagnostic interpretation of newly discovered missense variants in disease-related genes.This work was supported by grants from the National Institute of Diabetes and Digestive and Kidney Diseases (1K08DK102877-01, to A.R.M.; 1R01DK097768-01, to D.A.), NIH/Harvard Catalyst (1KL2TR001100-01, to A.R.M.), the Broad Institute (SPARC award, to A.R.M. and T.M.), and the Wellcome Trust (095564, to K.C.; 107064, to D.B.S.).This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/ng.370

Quantum phase transitions

In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behavior of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions are boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed on bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview over a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.Comment: 50 pages, 7 figs; (v2) final version as publishe

Imputation of variants from the 1000 Genomes Project modestly improves known associations and can identify low-frequency variant-phenotype associations undetected by HapMap based imputation

notes: PMCID: PMC3655956This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Genome-wide association (GWA) studies have been limited by the reliance on common variants present on microarrays or imputable from the HapMap Project data. More recently, the completion of the 1000 Genomes Project has provided variant and haplotype information for several million variants derived from sequencing over 1,000 individuals. To help understand the extent to which more variants (including low frequency (1% ≤ MAF <5%) and rare variants (<1%)) can enhance previously identified associations and identify novel loci, we selected 93 quantitative circulating factors where data was available from the InCHIANTI population study. These phenotypes included cytokines, binding proteins, hormones, vitamins and ions. We selected these phenotypes because many have known strong genetic associations and are potentially important to help understand disease processes. We performed a genome-wide scan for these 93 phenotypes in InCHIANTI. We identified 21 signals and 33 signals that reached P<5×10(-8) based on HapMap and 1000 Genomes imputation, respectively, and 9 and 11 that reached a stricter, likely conservative, threshold of P<5×10(-11) respectively. Imputation of 1000 Genomes genotype data modestly improved the strength of known associations. Of 20 associations detected at P<5×10(-8) in both analyses (17 of which represent well replicated signals in the NHGRI catalogue), six were captured by the same index SNP, five were nominally more strongly associated in 1000 Genomes imputed data and one was nominally more strongly associated in HapMap imputed data. We also detected an association between a low frequency variant and phenotype that was previously missed by HapMap based imputation approaches. An association between rs112635299 and alpha-1 globulin near the SERPINA gene represented the known association between rs28929474 (MAF = 0.007) and alpha1-antitrypsin that predisposes to emphysema (P = 2.5×10(-12)). Our data provide important proof of principle that 1000 Genomes imputation will detect novel, low frequency-large effect associations

Novel Interactions between Actin and the Proteasome Revealed by Complex Haploinsufficiency

Saccharomyces cerevisiae has been a powerful model for uncovering the landscape of binary gene interactions through whole-genome screening. Complex heterozygous interactions are potentially important to human genetic disease as loss-of-function alleles are common in human genomes. We have been using complex haploinsufficiency (CHI) screening with the actin gene to identify genes related to actin function and as a model to determine the prevalence of CHI interactions in eukaryotic genomes. Previous CHI screening between actin and null alleles for non-essential genes uncovered ∼240 deleterious CHI interactions. In this report, we have extended CHI screening to null alleles for essential genes by mating a query strain to sporulations of heterozygous knock-out strains. Using an act1Δ query, knock-outs of 60 essential genes were found to be CHI with actin. Enriched in this collection were functional categories found in the previous screen against non-essential genes, including genes involved in cytoskeleton function and chaperone complexes that fold actin and tubulin. Novel to this screen was the identification of genes for components of the TFIID transcription complex and for the proteasome. We investigated a potential role for the proteasome in regulating the actin cytoskeleton and found that the proteasome physically associates with actin filaments in vitro and that some conditional mutations in proteasome genes have gross defects in actin organization. Whole-genome screening with actin as a query has confirmed that CHI interactions are important phenotypic drivers. Furthermore, CHI screening is another genetic tool to uncover novel functional connections. Here we report a previously unappreciated role for the proteasome in affecting actin organization and function