Small Zeros of Quadratic Forms Outside a Union of Varieties

Let be a quadratic form in variables defined on a vector space over a global field , and be a finite union of varieties defined by families of homogeneous polynomials over . We show that if contains a nontrivial zero of , then there exists a linearly independent collection of small-height zeros of in , where the height bound does not depend on the height of , only on the degrees of its defining polynomials. As a corollary of this result, we show that there exists a small-height maximal totally isotropic subspace of the quadratic space such that is not contained in . Our investigation extends previous results on small zeros of quadratic forms, including Cassels\u27 theorem and its various generalizations. The paper also contains an appendix with two variations of Siegel\u27s lemma. All bounds on height are explicit

Psychometric Validation of Four-Item Exercise Identity and Healthy-Eater Identity Scales and Applications in Weight Loss Maintenance

Background: Identifying as someone who engages in health promoting behaviors like healthy eating and exercising may be associated with sustained engagement in those behaviors, but reliable and valid instruments are needed to improve the rigor of this research. Two studies were conducted to (1) examine the psychometric properties of a four-item exerciser identity measure (4-EI) and an adapted healthy-eater identity measure (4-HEI) and (2) examine differences in identity strengths across categories of weight loss success. Methods: Data from 1,709 community dwelling adults in the International Weight Control Registry (IWCR) were used. A random half of the sample was used to assess the proposed unidimensional factor structure of the 4-EI and 4-HEI and examine convergent and discriminant validity using Spearman rank-order correlations. One-way ANOVA was used in the other random half of the sample to compare 4-EI and 4-HEI scores (-3 to + 3) across three self-defined weight loss categories (‘Successful’, ‘Regain’, and ‘Unsuccessful’) and those maintaining ≥ 5% weight loss for &gt; 1 year vs. not. Results: Results support the unidimensional factor structure with all four items (eigenvalue scores &gt; 2.89) as well as convergent and discriminant validity for both measures. Exercise identity was strongly correlated with self-reported physical activity (r (735) = 0.52, p &lt;.001) and measures of autonomous motivation. Healthy eating identity was moderately correlated with cognitive restraint in eating (r (744) = 0.42, p &lt;.001) and other measures predictive of eating behavior. 4-EI and 4-HEI are stronger in Successful (4-EI: M = 0.90, SD = 1.77; 4-HEI: M = 1.56 SD = 1.37) vs. Regain (4-EI: M=-0.18, SD = 1.68; 4-HEI: M =.57, SD = 1.48) and Unsuccessful (4-EI:M=-0.28, SD = 1.62; 4-HEI: M = 0.51, SD = 1.33) and those maintaining ≥ 5% weight loss (4-EI:M = 0.47, SD = 1.78; 4-HEI: M = 1.13, SD = 1.49) vs. not (4-EI:M=-0.27, SD = 1.66; 4-HEI: M = 0.53, SD = 1.47), p’s &lt; 0.001. Conclusions: The 4-EI and 4-HEI have acceptable psychometric properties and can advance understanding of the role of identity in exercise and dietary behaviors and weight loss maintenance. Trial registration: The parent observational study, International Weight Control Registry (IWCR), for these sub-studies is registered in ClinicalTrials.gov (NCT04907396).</p

M-theory Supertubes with Three and Four Charges

Using the covariant M5-brane action, we construct configurations corresponding to supertubes with three and four charges. We derive the BPS equations and study the full structure of the solutions. In particular, we find new solutions involving arbitrariness in field strengths.Comment: 24 pages, references added and typos correcte

Dynamics of 5-carboxylcytosine during hepatic differentiation: potential general role for active demethylation by DNA repair in lineage specification

Patterns of DNA methylation (5-methylcytosine, 5mC) are rearranged during differentiation contributing to the regulation of cell type-specific gene expression. TET proteins oxidise 5mC to 5-hydroxymethylcytosine (5hmC), 5-formylcytosine (5fC) and 5-carboxylcytosine (5caC). Both 5fC and 5caC can be recognised and excised from DNA by thymine-DNA glycosylase (TDG) followed by the subsequent incorporation of unmodified cytosine into the abasic site via the base excision repair (BER) pathway. We previously demonstrated that 5caC accumulates during lineage specification of neural stem cells (NSCs) suggesting that such active demethylation pathway is operative in this system, however it is still unknown if TDG/BER-dependent demethylation is utilised during other types of cellular differentiation. Here we analyse dynamics of the global levels of 5hmC and 5caC during differentiation of human pluripotent stem cells (hPSCs) towards hepatic endoderm. We show that, similar to differentiating NSCs, 5caC transiently accumulates during hepatic differentiation. The levels of 5caC increase during specification of foregut, peak at the stage of hepatic endoderm commitment and drop in differentiating cells concurrently with the onset of expression of Alpha Fetoprotein, a marker of committed hepatic progenitors. Moreover, we show that 5caC accumulates at promoter regions of several genes expressed during hepatic specification at differentiation stages corresponding to the commencement of their expression. Our data indicate that transient 5caC accumulation is a common feature of two different types (neural/glial and endoderm/hepatic) of cellular differentiation. This suggests that oxidation of 5mC may represent a general mechanism of rearrangement of 5mC profiles during lineage specification of somatic cells in mammals

Glutamate dehydrogenase (GLUD1) expression in breast cancer

Dysregulated cellular metabolism is regarded as one of the hallmarks of cancer with some tumours utilising the glutamine metabolism pathway for their sustained proliferation and survival. Glutamate dehydrogenase (GLUD1) is a key enzyme in glutaminolysis converting glutamate to α-Ketoglutarate for entry into the TCA cycle. Breast cancer (BC) comprises a heterogeneous group of tumours in terms of molecular biology and clinical behaviour, and we have previously shown that altered glutamine metabolism varies substantially among the different molecular subtypes. We hypothesise that the prognostic value of GLUD1 expression will differ between the BC molecular subtypes and may act as a potential therapeutic target for BC tumours.Methods: GLUD1 was assessed at the DNA, mRNA (n=1,980) and protein (n=1,300) levels in large and well-characterised cohorts and correlated with clinicopathological parameters, molecular subtypes, patient outcome and treatments. Results: There was a correlation between GLUD1 mRNA and GLUD1 protein expression which were highly expressed in low grade Luminal/ER+ BC (

Identification of the protein kinases Pyk3 and Phg2 as regulators of the STATc-mediated response to hyperosmolarity

Cellular adaptation to changes in environmental osmolarity is crucial for cell survival. In Dictyostelium, STATc is a key regulator of the transcriptional response to hyperosmotic stress. Its phosphorylation and consequent activation is controlled by two signaling branches, one cGMP- and the other Ca(2+)-dependent, of which many signaling components have yet to be identified. The STATc stress signalling pathway feeds back on itself by upregulating the expression of STATc and STATc-regulated genes. Based on microarray studies we chose two tyrosine-kinase like proteins, Pyk3 and Phg2, as possible modulators of STATc phosphorylation and generated single and double knock-out mutants to them. Transcriptional regulation of STATc and STATc dependent genes was disturbed in pyk3(-), phg2(-), and pyk3(-)/phg2(-) cells. The absence of Pyk3 and/or Phg2 resulted in diminished or completely abolished increased transcription of STATc dependent genes in response to sorbitol, 8-Br-cGMP and the Ca(2+) liberator BHQ. Also, phospho-STATc levels were significantly reduced in pyk3(-) and phg2(-) cells and even further decreased in pyk3(-)/phg2(-) cells. The reduced phosphorylation was mirrored by a significant delay in nuclear translocation of GFP-STATc. The protein tyrosine phosphatase 3 (PTP3), which dephosphorylates and inhibits STATc, is inhibited by stress-induced phosphorylation on S448 and S747. Use of phosphoserine specific antibodies showed that Phg2 but not Pyk3 is involved in the phosphorylation of PTP3 on S747. In pull-down assays Phg2 and PTP3 interact directly, suggesting that Phg2 phosphorylates PTP3 on S747 in vivo. Phosphorylation of S448 was unchanged in phg2(-) cells. We show that Phg2 and an, as yet unknown, S448 protein kinase are responsible for PTP3 phosphorylation and hence its inhibition, and that Pyk3 is involved in the regulation of STATc by either directly or indirectly activating it. Our results add further complexities to the regulation of STATc, which presumably ensure its optimal activation in response to different environmental cues

Tribological investigation of graphene as lubricant additive in vegetable oil

In this study, the tribological behaviours of graphene nanoparticles as lubricant additive in vegetable oil were investigated as a function of nanoparticle concentration. Graphene nanoparticles were added at 25 ppm, 50 ppm and 100 ppm as additive into vegetable oil as lubricant through hydrodynamic and acoustic cavitation as homogenising mechanism. The tribological properties of each homogenised solution were tested using a four-ball machine according to ASTM D4172. Wear scar diameter and friction coefficient were the determining parameters in this study. The results showed that 50 ppm is the optimum concentration that recorded the lowest wear scar diameter and friction coefficient as compared to control sample

The Spread of Scientific Information: Insights from the Web Usage Statistics in PLoS Article-Level Metrics

The presence of web-based communities is a distinctive signature of Web 2.0. The web-based feature means that information propagation within each community is highly facilitated, promoting complex collective dynamics in view of information exchange. In this work, we focus on a community of scientists and study, in particular, how the awareness of a scientific paper is spread. Our work is based on the web usage statistics obtained from the PLoS Article Level Metrics dataset compiled by PLoS. The cumulative number of HTML views was found to follow a long tail distribution which is reasonably well-fitted by a lognormal one. We modeled the diffusion of information by a random multiplicative process, and thus extracted the rates of information spread at different stages after the publication of a paper. We found that the spread of information displays two distinct decay regimes: a rapid downfall in the first month after publication, and a gradual power law decay afterwards. We identified these two regimes with two distinct driving processes: a short-term behavior driven by the fame of a paper, and a long-term behavior consistent with citation statistics. The patterns of information spread were found to be remarkably similar in data from different journals, but there are intrinsic differences for different types of web usage (HTML views and PDF downloads versus XML). These similarities and differences shed light on the theoretical understanding of different complex systems, as well as a better design of the corresponding web applications that is of high potential marketing impact

On finite-horizon control of genetic regulatory networks with multiple hard-constraints

<p>Abstract</p> <p>Background</p> <p>Probabilistic Boolean Networks (PBNs) provide a convenient tool for studying genetic regulatory networks. There are three major approaches to develop intervention strategies: (1) resetting the state of the PBN to a desirable initial state and letting the network evolve from there, (2) changing the steady-state behavior of the genetic network by minimally altering the rule-based structure and (3) manipulating external control variables which alter the transition probabilities of the network and therefore desirably affects the dynamic evolution. Many literatures study various types of external control problems, with a common drawback of ignoring the number of times that external control(s) can be applied.</p> <p>Results</p> <p>This paper studies the intervention problem by manipulating multiple external controls in a finite time interval in a PBN. The maximum numbers of times that each control method can be applied are given. We treat the problem as an optimization problem with multi-constraints. Here we introduce an algorithm, the "Reserving Place Algorithm'', to find all optimal intervention strategies. Given a fixed number of times that a certain control method is applied, the algorithm can provide all the sub-optimal control policies. Theoretical analysis for the upper bound of the computational cost is also given. We also develop a heuristic algorithm based on Genetic Algorithm, to find the possible optimal intervention strategy for networks of large size. </p> <p>Conclusions</p> <p>Studying the finite-horizon control problem with multiple hard-constraints is meaningful. The problem proposed is NP-hard. The Reserving Place Algorithm can provide more than one optimal intervention strategies if there are. Moreover, the algorithm can find all the sub-optimal control strategies corresponding to the number of times that certain control method is conducted. To speed up the computational time, a heuristic algorithm based on Genetic Algorithm is proposed for genetic networks of large size.</p