Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect

For models of non-interacting fermions moving within sites arranged on a surface in three dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are $K$-theoretic obstructions to approximating almost commuting, complex-valued matrices by commuting matrices, and we demonstrate numerically the presence of this obstruction for a lattice model of the quantum Hall effect in a spherical geometry. The numerical calculation of the obstruction is straightforward, and does not require translational invariance or introducing a flux torus. We further show that there is a $Z_2$ index obstruction to approximating almost commuting self-dual matrices by exactly commuting self-dual matrices, and present additional conjectures regarding the approximation of almost commuting real and self-dual matrices by exactly commuting real and self-dual matrices. The motivation for considering this problem is the case of physical systems with additional antiunitary symmetries such as time reversal or particle-hole conjugation. Finally, in the case of the sphere--mathematically speaking three almost commuting Hermitians whose sum of square is near the identity--we give the first quantitative result showing this index is the only obstruction to finding commuting approximations. We review the known non-quantitative results for the torus.Comment: 35 pages, 2 figure

EDGE: The origin of scatter in ultra-faint dwarf stellar masses and surface brightnesses

We demonstrate how the least luminous galaxies in the Universe, ultra-faint dwarf galaxies, are sensitive to their dynamical mass at the time of cosmic reionization. We select a low-mass ($\sim \text{1.5} \times 10^{9} \, \text{M}_{\odot}$) dark matter halo from a cosmological volume, and perform zoom hydrodynamical simulations with multiple alternative histories using "genetically modified" initial conditions. Earlier forming ultra-faints have higher stellar mass today, due to a longer period of star formation before their quenching by reionization. Our histories all converge to the same final dynamical mass, demonstrating the existence of extended scatter ($\geq$ 1 dex) in stellar masses at fixed halo mass due to the diversity of possible histories. One of our variants builds less than 2 % of its final dynamical mass before reionization, rapidly quenching in-situ star formation. The bulk of its final stellar mass is later grown by dry mergers, depositing stars in the galaxy's outskirts and hence expanding its effective radius. This mechanism constitutes a new formation scenario for highly diffuse ($\text{r}_{1 /2} \sim 820 \, \text{pc}$, $\sim 32 \, \text{mag arcsec}^2$), metal-poor ($\big[ \mathrm{Fe}\, / \mathrm{H} \big]= -2.9$), ultra-faint ($\mathcal{M}_V= -5.7$) dwarf galaxies within the reach of next-generation low surface brightness surveys.Comment: Minor edits to match the published ApJL version. Results unchange

Label-free segmentation of co-cultured cells on a nanotopographical gradient

The function and fate of cells is influenced by many different factors, one of which is surface topography of the support culture substrate. Systematic studies of nanotopography and cell response have typically been limited to single cell types and a small set of topographical variations. Here, we show a radical expansion of experimental throughput using automated detection, measurement, and classification of co-cultured cells on a nanopillar array where feature height changes continuously from planar to 250 nm over 9 mm. Individual cells are identified and characterized by more than 200 descriptors, which are used to construct a set of rules for label-free segmentation into individual cell types. Using this approach we can achieve label-free segmentation with 84% confidence across large image data sets and suggest optimized surface parameters for nanostructuring of implant devices such as vascular stents

Strong signature of natural selection within an FHIT intron implicated in prostate cancer risk

Previously, a candidate gene linkage approach on brother pairs affected with prostate cancer identified a locus of prostate cancer susceptibility at D3S1234 within the fragile histidine triad gene (FHIT), a tumor suppressor that induces apoptosis. Subsequent association tests on 16 SNPs spanning approximately 381 kb surrounding D3S1234 in Americans of European descent revealed significant evidence of association for a single SNP within intron 5 of FHIT. In the current study, resequencing and genotyping within a 28.5 kb region surrounding this SNP further delineated the association with prostate cancer risk to a 15 kb region. Multiple SNPs in sequences under evolutionary constraint within intron 5 of FHIT defined several related haplotypes with an increased risk of prostate cancer in European-Americans. Strong associations were detected for a risk haplotype defined by SNPs 138543, 142413, and 152494 in all cases (Pearson's χ2 = 12.34, df 1, P = 0.00045) and for the homozygous risk haplotype defined by SNPs 144716, 142413, and 148444 in cases that shared 2 alleles identical by descent with their affected brothers (Pearson's χ2 = 11.50, df 1, P = 0.00070). In addition to highly conserved sequences encompassing SNPs 148444 and 152413, population studies revealed strong signatures of natural selection for a 1 kb window covering the SNP 144716 in two human populations, the European American (π = 0.0072, Tajima's D= 3.31, 14 SNPs) and the Japanese (π = 0.0049, Fay & Wu's H = 8.05, 14 SNPs), as well as in chimpanzees (Fay & Wu's H = 8.62, 12 SNPs). These results strongly support the involvement of the FHIT intronic region in an increased risk of prostate cancer. © 2008 Ding et al

Genome-wide association study identifies 30 loci associated with bipolar disorder.

Bipolar disorder is a highly heritable psychiatric disorder. We performed a genome-wide association study (GWAS) including 20,352 cases and 31,358 controls of European descent, with follow-up analysis of 822 variants with P < 1 × 10-4 in an additional 9,412 cases and 137,760 controls. Eight of the 19 variants that were genome-wide significant (P < 5 × 10-8) in the discovery GWAS were not genome-wide significant in the combined analysis, consistent with small effect sizes and limited power but also with genetic heterogeneity. In the combined analysis, 30 loci were genome-wide significant, including 20 newly identified loci. The significant loci contain genes encoding ion channels, neurotransmitter transporters and synaptic components. Pathway analysis revealed nine significantly enriched gene sets, including regulation of insulin secretion and endocannabinoid signaling. Bipolar I disorder is strongly genetically correlated with schizophrenia, driven by psychosis, whereas bipolar II disorder is more strongly correlated with major depressive disorder. These findings address key clinical questions and provide potential biological mechanisms for bipolar disorder

A high-resolution map of human evolutionary constraint using 29 mammals.

The comparison of related genomes has emerged as a powerful lens for genome interpretation. Here we report the sequencing and comparative analysis of 29 eutherian genomes. We confirm that at least 5.5% of the human genome has undergone purifying selection, and locate constrained elements covering ∼4.2% of the genome. We use evolutionary signatures and comparisons with experimental data sets to suggest candidate functions for ∼60% of constrained bases. These elements reveal a small number of new coding exons, candidate stop codon readthrough events and over 10,000 regions of overlapping synonymous constraint within protein-coding exons. We find 220 candidate RNA structural families, and nearly a million elements overlapping potential promoter, enhancer and insulator regions. We report specific amino acid residues that have undergone positive selection, 280,000 non-coding elements exapted from mobile elements and more than 1,000 primate- and human-accelerated elements. Overlap with disease-associated variants indicates that our findings will be relevant for studies of human biology, health and disease

Genome sequencing of the extinct Eurasian wild aurochs, Bos primigenius, illuminates the phylogeography and evolution of cattle

Background Domestication of the now-extinct wild aurochs, Bos primigenius, gave rise to the two major domestic extant cattle taxa, B. taurus and B. indicus. While previous genetic studies have shed some light on the evolutionary relationships between European aurochs and modern cattle, important questions remain unanswered, including the phylogenetic status of aurochs, whether gene flow from aurochs into early domestic populations occurred, and which genomic regions were subject to selection processes during and after domestication. Here, we address these questions using whole-genome sequencing data generated from an approximately 6,750-year-old British aurochs bone and genome sequence data from 81 additional cattle plus genome-wide single nucleotide polymorphism data from a diverse panel of 1,225 modern animals. Results Phylogenomic analyses place the aurochs as a distinct outgroup to the domestic B. taurus lineage, supporting the predominant Near Eastern origin of European cattle. Conversely, traditional British and Irish breeds share more genetic variants with this aurochs specimen than other European populations, supporting localized gene flow from aurochs into the ancestors of modern British and Irish cattle, perhaps through purposeful restocking by early herders in Britain. Finally, the functions of genes showing evidence for positive selection in B. taurus are enriched for neurobiology, growth, metabolism and immunobiology, suggesting that these biological processes have been important in the domestication of cattle. Conclusions This work provides important new information regarding the origins and functional evolution of modern cattle, revealing that the interface between early European domestic populations and wild aurochs was significantly more complex than previously thought

Dissipative Chaos in Semiconductor Superlattices

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.Comment: 33 pages, 8 figure