Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

Regularity for harmonic maps into certain Pseudo-Riemannian manifolds

In this article, we investigate the regularity for certain elliptic systems without a $L^2$-antisymmetric structure. As applications, we prove some $\epsilon$-regularity theorems for weakly harmonic maps from the unit ball $B= B(m) \subset \mathbb{R}^m$ $(m\geq2)$ into certain pseudo-Riemannian manifolds: standard stationary Lorentzian manifolds, pseudospheres $\mathbb{S}^n_\nu \subset \mathbb{R}^{n+1}_\nu$ $(1\leq\nu \leq n)$ and pseudohyperbolic spaces $\mathbb{H}^n_\nu \subset \mathbb{R}^{n+1}_{\nu+1}$ $(0\leq\nu \leq n-1)$. Consequently, such maps are shown to be H\"{o}lder continuous (and as smooth as the regularity of the targets permits) in dimension $m=2$. In particular, we prove that any weakly harmonic map from a disc into the De-Sitter space $\mathbb{S}^n_1$ or the Anti-de-Sitter space $\mathbb{H}^n_1$ is smooth. Also, we give an alternative proof of the H\"{o}lder continuity of any weakly harmonic map from a disc into the Hyperbolic space $\mathbb{H}^n$ without using the fact that the target is nonpositively curved. Moreover, we extend the notion of generalized (weakly) harmonic maps from a disc into the standard sphere $\mathbb{S}^n$ to the case that the target is $\mathbb{S}^n_\nu$ $(1\leq\nu \leq n)$ or $\mathbb{H}^n_\nu$ $(0\leq\nu \leq n-1)$, and obtain some $\epsilon$-regularity results for such generalized (weakly) harmonic maps.Comment: to appear in J. Math. Pures App

Phylogenomic exploration of the relationships between strains of Mycobacterium avium subspecies paratuberculosis.

BACKGROUND: Mycobacterium avium subspecies paratuberculosis (Map) is an infectious enteric pathogen that causes Johne's disease in livestock. Determining genetic diversity is prerequisite to understanding the epidemiology and biology of Map. We performed the first whole genome sequencing (WGS) of 141 global Map isolates that encompass the main molecular strain types currently reported. We investigated the phylogeny of the Map strains, the diversity of the genome and the limitations of commonly used genotyping methods. RESULTS: Single nucleotide polymorphism (SNP) and phylogenetic analyses confirmed two major lineages concordant with the former Type S and Type C designations. The Type I and Type III strain groups are subtypes of Type S, and Type B strains are a subtype of Type C and not restricted to Bison species. We found that the genome-wide SNPs detected provided greater resolution between isolates than currently employed genotyping methods. Furthermore, the SNP used for IS1311 typing is not informative, as it is likely to have occurred after Type S and C strains diverged and does not assign all strains to the correct lineage. Mycobacterial Interspersed Repetitive Unit-Variable Number Tandem Repeat (MIRU-VNTR) differentiates Type S from Type C but provides limited resolution between isolates within these lineages and the polymorphisms detected do not necessarily accurately reflect the phylogenetic relationships between strains. WGS of passaged strains and coalescent analysis of the collection revealed a very high level of genetic stability, with the substitution rate estimated to be less than 0.5 SNPs per genome per year. CONCLUSIONS: This study clarifies the phylogenetic relationships between the previously described Map strain groups, and highlights the limitations of current genotyping techniques. Map isolates exhibit restricted genetic diversity and a substitution rate consistent with a monomorphic pathogen. WGS provides the ultimate level of resolution for differentiation between strains. However, WGS alone will not be sufficient for tracing and tracking Map infections, yet importantly it can provide a phylogenetic context for affirming epidemiological connections

Wettability decay in an oil-contaminated waste-mineral mixture with dry-wet cycles

The dependency of soil particle wettability on soil water content implies that soils subjected to drying-wetting cycles become wettable with wetting and water repellent with drying. While this has been demonstrated widely, the results are contradictory when water repellent soils are subjected to a sequence of cycles. Added to this, past wettability measurements were seldom done in batches of samples collected from the field at natural or dry water contents, with little appreciation that slight particle size variations, different drying-wetting histories and fabric (as required by different wettability measurement methods) may alter the results. This note presents soil particle wettability—soil water content relations by means of an index test following staged drying and wetting paths over a period of 8 months for an untreated, oil-contaminated anthropogenic soil (a mixture of slag, coal particles, fly ash and mineral particles) from Barry Docks (UK), a site formally used for oil storage, which is to be remediated and redeveloped for housing. The results revealed a decrease in the water repellency and increasing mineralization and bacterial activity with the wetting and drying cycles.postprin

Adjusting a cancer mortality-prediction model for disease status-related eligibility criteria

<p>Abstract</p> <p>Background</p> <p>Volunteering participants in disease studies tend to be healthier than the general population partially due to specific enrollment criteria. Using modeling to accurately predict outcomes of cohort studies enrolling volunteers requires adjusting for the bias introduced in this way. Here we propose a new method to account for the effect of a specific form of healthy volunteer bias resulting from imposing disease status-related eligibility criteria, on disease-specific mortality, by explicitly modeling the length of the time interval between the moment when the subject becomes ineligible for the study, and the outcome.</p> <p>Methods</p> <p>Using survival time data from 1190 newly diagnosed lung cancer patients at MD Anderson Cancer Center, we model the time from clinical lung cancer diagnosis to death using an exponential distribution to approximate the length of this interval for a study where lung cancer death serves as the outcome. Incorporating this interval into our previously developed lung cancer risk model, we adjust for the effect of disease status-related eligibility criteria in predicting the number of lung cancer deaths in the control arm of CARET. The effect of the adjustment using the MD Anderson-derived approximation is compared to that based on SEER data.</p> <p>Results</p> <p>Using the adjustment developed in conjunction with our existing lung cancer model, we are able to accurately predict the number of lung cancer deaths observed in the control arm of CARET.</p> <p>Conclusions</p> <p>The resulting adjustment was accurate in predicting the lower rates of disease observed in the early years while still maintaining reasonable prediction ability in the later years of the trial. This method could be used to adjust for, or predict the duration and relative effect of any possible biases related to disease-specific eligibility criteria in modeling studies of volunteer-based cohorts.</p

Optimal central-place foraging by beavers: Tree-size selection in relation to defensive chemicals of quaking aspen

At a newly occupied pond, beavers preferentially felled aspen smaller than 7.5 cm in diameter and selected against larger size classes. After one year of cutting, 10% of the aspen had been cut and 14% of the living aspen exhibited the juvenile growth form. A phenolic compound which may act as a deterrent to beavers was found in low concentrations in aspen bark, and there was no significant regression of relative concentration of this compound on tree diameter. At a pond which had been intermittently occupied by beavers for over 20 years, beavers selected against aspen smaller than 4.5 cm in diameter, and selected in favor of aspen larger than 19.5 cm in diameter. After more than 28 years of cutting at this site, 51% of the aspen had been cut and 49% of the living aspen were juvenileform. The phenolic compound was found in significantly higher concentrations in aspen bark than at the newly occupied site, and there was a significant negative regression of relative concentration on tree diameter. The results of this study show that responses to browsing by trees place constraints on the predictive value of standard energy-based optimal foraging models, and limitations on the use of such models. Future models should attempt to account for inducible responses of plants to damage and increases in concentrations of secondary metabolites through time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47775/1/442_2004_Article_BF00379963.pd

Diverse species-specific phenotypic consequences of loss of function sorting nexin 14 mutations

Mutations in the SNX14 gene cause spinocerebellar ataxia, autosomal recessive 20 (SCAR20) in both humans and dogs. Studies implicating the phenotypic consequences of SNX14 mutations to be consequences of subcellular disruption to autophagy and lipid metabolism have been limited to in vitro investigation of patient-derived dermal fibroblasts, laboratory engineered cell lines and developmental analysis of zebrafish morphants. SNX14 homologues Snz (Drosophila) and Mdm1 (yeast) have also been conducted, demonstrated an important biochemical role during lipid biogenesis. In this study we report the effect of loss of SNX14 in mice, which resulted in embryonic lethality around mid-gestation due to placental pathology that involves severe disruption to syncytiotrophoblast cell differentiation. In contrast to other vertebrates, zebrafish carrying a homozygous, maternal zygotic snx14 genetic loss-of-function mutation were both viable and anatomically normal. Whilst no obvious behavioural effects were observed, elevated levels of neutral lipids and phospholipids resemble previously reported effects on lipid homeostasis in other species. The biochemical role of SNX14 therefore appears largely conserved through evolution while the consequences of loss of function varies between species. Mouse and zebrafish models therefore provide valuable insights into the functional importance of SNX14 with distinct opportunities for investigating its cellular and metabolic function in vivo

UV stalled replication forks restart by re-priming in human fibroblasts

Restarting stalled replication forks is vital to avoid fatal replication errors. Previously, it was demonstrated that hydroxyurea-stalled replication forks rescue replication either by an active restart mechanism or by new origin firing. To our surprise, using the DNA fibre assay, we only detect a slightly reduced fork speed on a UV-damaged template during the first hour after UV exposure, and no evidence for persistent replication fork arrest. Interestingly, no evidence for persistent UV-induced fork stalling was observed even in translesion synthesis defective, Polηmut cells. In contrast, using an assay to measure DNA molecule elongation at the fork, we observe that continuous DNA elongation is severely blocked by UV irradiation, particularly in UV-damaged Polηmut cells. In conclusion, our data suggest that UV-blocked replication forks restart effectively through re-priming past the lesion, leaving only a small gap opposite the lesion. This allows continuation of replication on damaged DNA. If left unfilled, the gaps may collapse into DNA double-strand breaks that are repaired by a recombination pathway, similar to the fate of replication forks collapsed after hydroxyurea treatment

Profiling of the BRCA1 transcriptome through microarray and ChIP-chip analysis

A role for BRCA1 in the direct and indirect regulation of transcription is well established. However, a comprehensive view of the degree to which BRCA1 impacts transcriptional regulation on a genome-wide level has not been defined. We performed genome-wide expression profiling and ChIP-chip analysis, comparison of which revealed that although BRCA1 depletion results in transcriptional changes in 1294 genes, only 44 of these are promoter bound by BRCA1. However, 27% of these transcripts were linked to transcriptional regulation possibly explaining the large number of indirect transcriptional changes observed by microarray analysis. We show that no specific consensus sequence exists for BRCA1 DNA binding but rather demonstrate the presence of a number of known and novel transcription factor (TF)- binding sites commonly found on BRCA1 bound promoters. Co-immunoprecipitations confirmed that BRCA1 interacts with a number of these TFs including AP2-α, PAX2 and ZF5. Finally, we show that BRCA1 is bound to a subset of promoters of genes that are not altered by BRCA1 loss, but are transcriptionally regulated in a BRCA1-dependent manner upon DNA damage. These data suggest a model, whereby BRCA1 is present on defined promoters as part of an inactive complex poised to respond to various genotoxic stimuli

Preventing intrusive memories after trauma via a brief intervention involving Tetris computer game play in the emergency department: a proof-of-concept randomized controlled trial.

After psychological trauma, recurrent intrusive visual memories may be distressing and disruptive. Preventive interventions post trauma are lacking. Here we test a behavioural intervention after real-life trauma derived from cognitive neuroscience. We hypothesized that intrusive memories would be significantly reduced in number by an intervention involving a computer game with high visuospatial demands (Tetris), via disrupting consolidation of sensory elements of trauma memory. The Tetris-based intervention (trauma memory reminder cue plus c. 20 min game play) vs attention-placebo control (written activity log for same duration) were both delivered in an emergency department within 6 h of a motor vehicle accident. The randomized controlled trial compared the impact on the number of intrusive trauma memories in the subsequent week (primary outcome). Results vindicated the efficacy of the Tetris-based intervention compared with the control condition: there were fewer intrusive memories overall, and time-series analyses showed that intrusion incidence declined more quickly. There were convergent findings on a measure of clinical post-trauma intrusion symptoms at 1 week, but not on other symptom clusters or at 1 month. Results of this proof-of-concept study suggest that a larger trial, powered to detect differences at 1 month, is warranted. Participants found the intervention easy, helpful and minimally distressing. By translating emerging neuroscientific insights and experimental research into the real world, we offer a promising new low-intensity psychiatric intervention that could prevent debilitating intrusive memories following trauma