Large deviations for eigenvalues of sample covariance matrices, with applications to mobile communication systems

We study sample covariance matrices of the form $W=\frac 1n C C^T$, where $C$ is a $k\times n$ matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the entries of $C$ are independent and identically distributed standard normal random variables. Such matrices arise in statistics as sample covariance matrices, and the high-dimensional case, when $k$ is large, arises in the analysis of DNA experiments. We investigate the large deviation properties of the largest and smallest eigenvalues of $W$ when either $k$ is fixed and $n\to \infty$, or $k_n\to \infty$ with $k_n=o(n/\log\log{n})$, in the case where the squares of the i.i.d. entries have finite exponential moments. Previous results, proving a.s. limits of the eigenvalues, only require finite fourth moments. Our most explicit results for $k$ large are for the case where the entries of $C$ are $\pm1$ with equal probability. We relate the large deviation rate functions of the smallest and largest eigenvalue to the rate functions for independent and identically distributed standard normal entries of $C$. This case is of particular interest, since it is related to the problem of the decoding of a signal in a code division multiple access system arising in mobile communication systems. In this example, $k$ plays the role of the number of users in the system, and $n$ is the length of the coding sequence of each of the users. Each user transmits at the same time and uses the same frequency, and the codes are used to distinguish the signals of the separate users. The results imply large deviation bounds for the probability of a bit error due to the interference of the various users.Comment: corrected some typing errors, and extended Theorem 3.1 to Wishart matrices; to appear in Advances of Applied Probabilit

Reproducibility of 3D scanning in the periorbital region

The reproducibility of scanning in the periorbital region with 3D technology to enable objective evaluations of surgical treatment in the periorbital region was assessed. Facial 3D-scans of 15 volunteers were captured at different time points with a handheld Artec Space Spider structured light scanner. Two scans were made with a one minute interval and repeated after 1 year; for both a natural head position and with the head in a fixation-device. On assessing the area between the eyelashes and eyebrows, the medians of the average deviations between the various cross-sections of the one minute interval 3D-scans ranged from 0.17 to 0.21 mm at baseline, and from 0.10 to 0.11 mm when the minute-interval scanning was repeated one year later. The systematic differences when scanning in a natural head position and fixated position were comparable. The reproducibility of the 3D processing was excellent (intraclass correlation coefficient > 0.9). The repeated scanning deviations (baseline versus one year data) were well within the accepted clinical threshold of 1 mm. Scanning with a hand-held 3D-scanning device (Artec Space Spider) is a promising tool to assess changes in the periorbital region following surgical treatment since the median deviations are well below the clinically accepted 1 mm measuring error, for both the natural head and fixated positions

A 4-wk high-fructose diet alters lipid metabolism without affecting insulin sensitivity or ectopic lipids in healthy humans

BACKGROUND: High fructose consumption is suspected to be causally linked to the epidemics of obesity and metabolic disorders. In rodents, fructose leads to insulin resistance and ectopic lipid deposition. In humans, the effects of fructose on insulin sensitivity remain debated, whereas its effect on ectopic lipids has never been investigated. OBJECTIVE: We assessed the effect of moderate fructose supplementation on insulin sensitivity (IS) and ectopic lipids in healthy male volunteers (n = 7). DESIGN: IS, intrahepatocellular lipids (IHCL), and intramyocellular lipids (IMCL) were measured before and after 1 and 4 wk of a high-fructose diet containing 1.5 g fructose . kg body wt(-1) . d(-1). Adipose tissue IS was evaluated from nonesterified fatty acid suppression, hepatic IS from suppression of hepatic glucose output (6,6-2H2-glucose), and muscle IS from the whole-body glucose disposal rate during a 2-step hyperinsulinemic euglycemic clamp. IHCL and IMCL were measured by 1H magnetic resonance spectroscopy. RESULTS: Fructose caused significant (P < 0.05) increases in fasting plasma concentrations of triacylglycerol (36%), VLDL-triacylglycerol (72%), lactate (49%), glucose (5.5%), and leptin (48%) without any significant changes in body weight, IHCL, IMCL, or IS. IHCL were negatively correlated with triacylglycerol after 4 wk of the high-fructose diet (r = -0.78, P < 0.05). CONCLUSION: Moderate fructose supplementation over 4 wk increases plasma triacylglycerol and glucose concentrations without causing ectopic lipid deposition or insulin resistance in healthy humans

Transmission of NS5A-Inhibitor Resistance-Associated Substitutions among Men Who Have Sex with Men Recently Infected with Hepatitis C Virus Genotype 1a

The transmission of direct-acting antiviral resistance-associated substitutions (RAS) could hamper hepatitis C virus (HCV) cure rates and elimination efforts. A phylogenetic analysis of 87 men who have sex with men recently infected with HCV genotype 1a placed one-third (28/87) in a large cluster, in which 96% harbored NS5A M28V RAS.</p

Soil networks become more connected and take up more carbon as nature restoration progresses

Soil organisms have an important role in aboveground community dynamics and ecosystem functioning in terrestrial ecosystems. However, most studies have considered soil biota as a black box or focussed on specific groups, whereas little is known about entire soil networks. Here we show that during the course of nature restoration on abandoned arable land a compositional shift in soil biota, preceded by tightening of the belowground networks, corresponds with enhanced efficiency of carbon uptake. In mid- and long-term abandoned field soil, carbon uptake by fungi increases without an increase in fungal biomass or shift in bacterial-to-fungal ratio. The implication of our findings is that during nature restoration the efficiency of nutrient cycling and carbon uptake can increase by a shift in fungal composition and/or fungal activity. Therefore, we propose that relationships between soil food web structure and carbon cycling in soils need to be reconsidered

In vitro functional effects of XPC gene rare variants from bladder cancer patients

The XPC gene is involved in repair of bulky DNA adducts formed by carcinogenic metabolites and oxidative DNA damage, both known bladder cancer risk factors. Single nucleotide polymorphisms (SNPs) in XPC have been associated with increased bladder cancer risk. Recently, rarer genetic variants have been identified but it is difficult to ascertain which are of functional importance. During a mutation screen of XPC in DNA from 33 bladder tumour samples and matched blood samples, we identified five novel variants in the patients’ germ line DNA. In a case–control study of 771 bladder cancer cases and 800 controls, c.905T>C (Phe302Ser), c.1177C>T (Arg393Trp), c.*156G>A [3′ untranslated region (UTR)] and c.2251-37C>A (in an intronic C>G SNP site) were found to be rare variants, with a combined odds ratio of 3.1 (95% confidence interval 1.0–9.8, P = 0.048) for carriage of one variant. The fifth variant was a 2% minor allele frequency SNP not associated with bladder cancer. The two non-synonymous coding variants were predicted to have functional effects using analytical algorithms; a reduced recruitment of GFP-tagged XPC plasmids containing either c.905T>C or c.1177C>T to sites of 408 nm wavelength laser-induced oxidative DNA damage was found in vitro. c.*156G>A appeared to be associated with reduced messenger RNA stability in an in vitro plasmid-based assay. Although the laser microbeam assay is relevant to a range of DNA repair genes, our 3′ UTR assay based on Green fluorescent protein(GFP) has widespread applicability and could be used to assess any gene. These assays may be useful in determining which rare variants are functional, prior to large genotyping efforts

Application of a Mathematical Model to Describe the Effects of Chlorpyrifos on Caenorhabditis elegans Development

The nematode Caenorhabditis elegans is being assessed as an alternative model organism as part of an interagency effort to develop better means to test potentially toxic substances. As part of this effort, assays that use the COPAS Biosort flow sorting technology to record optical measurements (time of flight (TOF) and extinction (EXT)) of individual nematodes under various chemical exposure conditions are being developed. A mathematical model has been created that uses Biosort data to quantitatively and qualitatively describe C. elegans growth, and link changes in growth rates to biological events. Chlorpyrifos, an organophosphate pesticide known to cause developmental delays and malformations in mammals, was used as a model toxicant to test the applicability of the growth model for in vivo toxicological testing.L1 larval nematodes were exposed to a range of sub-lethal chlorpyrifos concentrations (0-75 microM) and measured every 12 h. In the absence of toxicant, C. elegans matured from L1s to gravid adults by 60 h. A mathematical model was used to estimate nematode size distributions at various times. Mathematical modeling of the distributions allowed the number of measured nematodes and log(EXT) and log(TOF) growth rates to be estimated. The model revealed three distinct growth phases. The points at which estimated growth rates changed (change points) were constant across the ten chlorpyrifos concentrations. Concentration response curves with respect to several model-estimated quantities (numbers of measured nematodes, mean log(TOF) and log(EXT), growth rates, and time to reach change points) showed a significant decrease in C. elegans growth with increasing chlorpyrifos concentration.Effects of chlorpyrifos on C. elegans growth and development were mathematically modeled. Statistical tests confirmed a significant concentration effect on several model endpoints. This confirmed that chlorpyrifos affects C. elegans development in a concentration dependent manner. The most noticeable effect on growth occurred during early larval stages: L2 and L3. This study supports the utility of the C. elegans growth assay and mathematical modeling in determining the effects of potentially toxic substances in an alternative model organism using high-throughput technologies

3 versus 6 months of adjuvant oxaliplatin-fluoropyrimidine combination therapy for colorectal cancer (SCOT): an international, randomised, phase 3, non-inferiority trial.

BACKGROUND: 6 months of oxaliplatin-containing chemotherapy is usually given as adjuvant treatment for stage 3 colorectal cancer. We investigated whether 3 months of oxaliplatin-containing chemotherapy would be non-inferior to the usual 6 months of treatment. METHODS: The SCOT study was an international, randomised, phase 3, non-inferiority trial done at 244 centres. Patients aged 18 years or older with high-risk stage II and stage III colorectal cancer underwent central randomisation with minimisation for centre, choice of regimen, sex, disease site, N stage, T stage, and the starting dose of capecitabine. Patients were assigned (1:1) to receive 3 months or 6 months of adjuvant oxaliplatin-containing chemotherapy. The chemotherapy regimens could consist of CAPOX (capecitabine and oxaliplatin) or FOLFOX (bolus and infused fluorouracil with oxaliplatin). The regimen was selected before randomisation in accordance with choices of the patient and treating physician. The primary study endpoint was disease-free survival and the non-inferiority margin was a hazard ratio of 1·13. The primary analysis was done in the intention-to-treat population and safety was assessed in patients who started study treatment. This trial is registered with ISRCTN, number ISRCTN59757862, and follow-up is continuing. FINDINGS: 6088 patients underwent randomisation between March 27, 2008, and Nov 29, 2013. The intended treatment was FOLFOX in 1981 patients and CAPOX in 4107 patients. 3044 patients were assigned to 3 month group and 3044 were assigned to 6 month group. Nine patients in the 3 month group and 14 patients in the 6 month group did not consent for their data to be used, leaving 3035 patients in the 3 month group and 3030 patients in the 6 month group for the intention-to-treat analyses. At the cutoff date for analysis, there had been 1482 disease-free survival events, with 740 in the 3 month group and 742 in the 6 month group. 3 year disease-free survival was 76·7% (95% CI 75·1-78·2) for the 3 month group and 77·1% (75·6-78·6) for the 6 month group, giving a hazard ratio of 1·006 (0·909-1·114, test for non-inferiority p=0·012), significantly below the non-inferiority margin. Peripheral neuropathy of grade 2 or worse was more common in the 6 month group (237 [58%] of 409 patients for the subset with safety data) than in the 3 month group (103 [25%] of 420) and was long-lasting and associated with worse quality of life. 1098 serious adverse events were reported (492 reports in the 3 month group and 606 reports in the 6 month group) and 32 treatment-related deaths occurred (16 in each group). INTERPRETATION: In the whole study population, 3 months of oxaliplatin-containing adjuvant chemotherapy was non-inferior to 6 months of the same therapy for patients with high-risk stage II and stage III colorectal cancer and was associated with reduced toxicity and improved quality of life. Despite the fact the study was underpowered, these data suggest that a shorter duration leads to similar survival outcomes with better quality of life and thus might represent a new standard of care. FUNDING: Medical Research Council, Swedish Cancer Society, NETSCC, and Cancer Research UK

Mining protein loops using a structural alphabet and statistical exceptionality

<p>Abstract</p> <p>Background</p> <p>Protein loops encompass 50% of protein residues in available three-dimensional structures. These regions are often involved in protein functions, e.g. binding site, catalytic pocket... However, the description of protein loops with conventional tools is an uneasy task. Regular secondary structures, helices and strands, have been widely studied whereas loops, because they are highly variable in terms of sequence and structure, are difficult to analyze. Due to data sparsity, long loops have rarely been systematically studied.</p> <p>Results</p> <p>We developed a simple and accurate method that allows the description and analysis of the structures of short and long loops using structural motifs without restriction on loop length. This method is based on the structural alphabet HMM-SA. HMM-SA allows the simplification of a three-dimensional protein structure into a one-dimensional string of states, where each state is a four-residue prototype fragment, called structural letter. The difficult task of the structural grouping of huge data sets is thus easily accomplished by handling structural letter strings as in conventional protein sequence analysis. We systematically extracted all seven-residue fragments in a bank of 93000 protein loops and grouped them according to the structural-letter sequence, named structural word. This approach permits a systematic analysis of loops of all sizes since we consider the structural motifs of seven residues rather than complete loops. We focused the analysis on highly recurrent words of loops (observed more than 30 times). Our study reveals that 73% of loop-lengths are covered by only 3310 highly recurrent structural words out of 28274 observed words). These structural words have low structural variability (mean RMSd of 0.85 Å). As expected, half of these motifs display a flanking-region preference but interestingly, two thirds are shared by short (less than 12 residues) and long loops. Moreover, half of recurrent motifs exhibit a significant level of amino-acid conservation with at least four significant positions and 87% of long loops contain at least one such word. We complement our analysis with the detection of statistically over-represented patterns of structural letters as in conventional DNA sequence analysis. About 30% (930) of structural words are over-represented, and cover about 40% of loop lengths. Interestingly, these words exhibit lower structural variability and higher sequential specificity, suggesting structural or functional constraints.</p> <p>Conclusions</p> <p>We developed a method to systematically decompose and study protein loops using recurrent structural motifs. This method is based on the structural alphabet HMM-SA and not on structural alignment and geometrical parameters. We extracted meaningful structural motifs that are found in both short and long loops. To our knowledge, it is the first time that pattern mining helps to increase the signal-to-noise ratio in protein loops. This finding helps to better describe protein loops and might permit to decrease the complexity of long-loop analysis. Detailed results are available at <url>http://www.mti.univ-paris-diderot.fr/publication/supplementary/2009/ACCLoop/</url>.</p