Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory

One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory (DFT) has become the most widely used and successful method for simulating systems of interacting electrons, making their original work one of the most cited in physics. In this letter, we show that the field of computational complexity imposes fundamental limitations on DFT, as an efficient description of the associated universal functional would allow to solve any problem in the class QMA (the quantum version of NP) and thus particularly any problem in NP in polynomial time. This follows from the fact that finding the ground state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, while given the universal functional it can be computed efficiently using DFT. This provides a clear illustration how the field of quantum computing is useful even if quantum computers would never be built.Comment: 8 pages, 3 figures. v2: Version accepted at Nature Physics; differs significantly from v1 (including new title). Includes an extra appendix (not contained in the journal version) on the NP-completeness of Hartree-Fock, which is taken from v

Investigating Microtopographic and Soil Controls on a Mountainous Meadow Plant Community Using High-Resolution Remote Sensing and Surface Geophysical Data

This study aims to investigate the microtopographic controls that dictate the heterogeneity of plant communities in a mountainous floodplain-hillslope system, using remote sensing and surface geophysical techniques. Working within a lower montane floodplain-hillslope study site (750 m × 750 m) in the Upper Colorado River Basin, we developed a new data fusion framework, based on machine learning and feature engineering, that exploits remote sensing optical and light detection and ranging (LiDAR) data to estimate the distribution of key plant meadow communities at submeter resolution. We collected surface electrical resistivity tomography data to explore the variability in soil properties along a floodplain-hillslope transect at 0.50-m resolution and extracted LiDAR-derived metrics to model the rapid change in microtopography. We then investigated the covariability among the estimated plant community distributions, soil information, and topographic metrics. Results show that our framework estimated the distribution of nine plant communities with higher accuracy (87% versus 80% overall; 85% versus 60% for shrubs) compared to conventional classification approaches. Analysis of the covariabilities reveals a strong correlation between plant community distribution, soil electric conductivity, and slope, indicating that soil moisture is a primary control on heterogeneous spatial distribution. At the same time, microtopography plays an important role in creating particular ecosystem niches for some of the communities. Such relationships could be exploited to provide information about the spatial variability of soil properties. This highly transferable framework can be employed within long-term monitoring to capture community-specific physiological responses to perturbations, offering the possibility of bridging local plot-scale observations with large landscape monitoring

The Effect of Transposable Element Insertions on Gene Expression Evolution in Rodents

Background:Many genomes contain a substantial number of transposable elements (TEs), a few of which are known to be involved in regulating gene expression. However, recent observations suggest that TEs may have played a very important role in the evolution of gene expression because many conserved non-genic sequences, some of which are know to be involved in gene regulation, resemble TEs. Results:Here we investigate whether new TE insertions affect gene expression profiles by testing whether gene expression divergence between mouse and rat is correlated to the numbers of new transposable elements inserted near genes. We show that expression divergence is significantly correlated to the number of new LTR and SINE elements, but not to the numbers of LINEs. We also show that expression divergence is not significantly correlated to the numbers of ancestral TEs in most cases, which suggests that the correlations between expression divergence and the numbers of new TEs are causal in nature. We quantify the effect and estimate that TE insertion has accounted for ~20% (95% confidence interval: 12% to 26%) of all expression profile divergence in rodents. Conclusions:We conclude that TE insertions may have had a major impact on the evolution of gene expression levels in rodents

Runge-Kutta residual distribution schemes

We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge–Kutta-type time-stepping (discretisation in time). The introduced non-linear blending procedure allows us to retain the explicit character of the time-stepping procedure. The resulting methods are second order accurate provided that both spatial and temporal approximations are. The proposed approach results in a global linear system that has to be solved at each time-step. An efficient way of solving this system is also proposed. To test and validate this new framework, we perform extensive numerical experiments on a wide variety of classical problems. An extensive numerical comparison of our approach with other multi-stage residual distribution schemes is also given

A database of microRNA expression patterns in Xenopus laevis

MicroRNAs (miRNAs) are short, non-coding RNAs around 22 nucleotides long. They inhibit gene expression either by translational repression or by causing the degradation of the mRNAs they bind to. Many are highly conserved amongst diverse organisms and have restricted spatio-temporal expression patterns during embryonic development where they are thought to be involved in generating accuracy of developmental timing and in supporting cell fate decisions and tissue identity. We determined the expression patterns of 180 miRNAs in Xenopus laevis embryos using LNA oligonucleotides. In addition we carried out small RNA-seq on different stages of early Xenopus development, identified 44 miRNAs belonging to 29 new families and characterized the expression of 5 of these. Our analyses identified miRNA expression in many organs of the developing embryo. In particular a large number were expressed in neural tissue and in the somites. Surprisingly none of the miRNAs we have looked at show expression in the heart. Our results have been made freely available as a resource in both XenMARK and Xenbase

A multimodal approach to cardiovascular risk stratification in patients with type 2 diabetes incorporating retinal, genomic and clinical features

Cardiovascular diseases are a public health concern; they remain the leading cause of morbidity and mortality in patients with type 2 diabetes. Phenotypic information available from retinal fundus images and clinical measurements, in addition to genomic data, can identify relevant biomarkers of cardiovascular health. In this study, we assessed whether such biomarkers stratified risks of major adverse cardiac events (MACE). A retrospective analysis was carried out on an extract from the Tayside GoDARTS bioresource of participants with type 2 diabetes (n = 3,891). A total of 519 features were incorporated, summarising morphometric properties of the retinal vasculature, various single nucleotide polymorphisms (SNPs), as well as routine clinical measurements. After imputing missing features, a predictive model was developed on a randomly sampled set (n = 2,918) using L1-regularised logistic regression (lasso). The model was evaluated on an independent set (n = 973) and its performance associated with overall hazard rate after censoring (log-rank p < 0.0001), suggesting that multimodal features were able to capture important knowledge for MACE risk assessment. We further showed through a bootstrap analysis that all three sources of information (retinal, genetic, routine clinical) offer robust signal. Particularly robust features included: tortuousity, width gradient, and branching point retinal groupings; SNPs known to be associated with blood pressure and cardiovascular phenotypic traits; age at imaging; clinical measurements such as blood pressure and high density lipoprotein. This novel approach could be used for fast and sensitive determination of future risks associated with MACE

ExpressionPlot: a web-based framework for analysis of RNA-Seq and microarray gene expression data

RNA-Seq and microarray platforms have emerged as important tools for detecting changes in gene expression and RNA processing in biological samples. We present ExpressionPlot, a software package consisting of a default back end, which prepares raw sequencing or Affymetrix microarray data, and a web-based front end, which offers a biologically centered interface to browse, visualize, and compare different data sets. Download and installation instructions, a user's manual, discussion group, and a prototype are available at http://expressionplot.com/ webcite.ALS Therapy Allianc

Microsomal epoxide hydrolase gene polymorphism and susceptibility to colon cancer

We examined polymorphisms in exons 3 and 4 of microsomal epoxide hydrolase in 101 patients with colon cancer and compared the results with 203 control samples. The frequency of the exon 3 T to C mutation was higher in cancer patients than in controls (odds ratio 3.8; 95% confidence intervals 1.8–8.0). This sequence alteration changes tyrosine residue 113 to histidine and is associated with lower enzyme activity when expressed in vitro. This suggests that putative slow epoxide hydrolase activity may be a risk factor for colon cancer. This appears to be true for both right- and left-sided tumours, but was more apparent for tumours arising distally (odds ratio 4.1; 95% confidence limits 1.9–9.2). By contrast, there was no difference in prevalence of exon 4 A to G transition mutation in cancer vs controls. This mutation changes histidine residue 139 to arginine and produces increased enzyme activity. There was no association between epoxide hydrolase genotype and abnormalities of p53 or Ki- Ras. © 1999 Cancer Research Campaig

Decoding the Folding of Burkholderia glumae Lipase: Folding Intermediates En Route to Kinetic Stability

The lipase produced by Burkholderia glumae folds spontaneously into an inactive near-native state and requires a periplasmic chaperone to reach its final active and secretion-competent fold. The B. glumae lipase-specific foldase (Lif) is classified as a member of the steric-chaperone family of which the propeptides of α-lytic protease and subtilisin are the best known representatives. Steric chaperones play a key role in conferring kinetic stability to proteins. However, until present there was no solid experimental evidence that Lif-dependent lipases are kinetically trapped enzymes. By combining thermal denaturation studies with proteolytic resistance experiments and the description of distinct folding intermediates, we demonstrate that the native lipase has a kinetically stable conformation. We show that a newly discovered molten globule-like conformation has distinct properties that clearly differ from those of the near-native intermediate state. The folding fingerprint of Lif-dependent lipases is put in the context of the protease-prodomain system and the comparison reveals clear differences that render the lipase-Lif systems unique. Limited proteolysis unveils structural differences between the near-native intermediate and the native conformation and sets the stage to shed light onto the nature of the kinetic barrier

Background Light in Potential Sites for the ANTARES Undersea Neutrino Telescope

The ANTARES collaboration has performed a series of {\em in situ} measurements to study the background light for a planned undersea neutrino telescope. Such background can be caused by $^{40}$K decays or by biological activity. We report on measurements at two sites in the Mediterranean Sea at depths of 2400~m and 2700~m, respectively. Three photomultiplier tubes were used to measure single counting rates and coincidence rates for pairs of tubes at various distances. The background rate is seen to consist of three components: a constant rate due to $^{40}$K decays, a continuum rate that varies on a time scale of several hours simultaneously over distances up to at least 40~m, and random bursts a few seconds long that are only correlated in time over distances of the order of a meter. A trigger requiring coincidences between nearby photomultiplier tubes should reduce the trigger rate for a neutrino telescope to a manageable level with only a small loss in efficiency.Comment: 18 pages, 8 figures, accepted for publication in Astroparticle Physic