On the Complexity of Solving Zero-Dimensional Polynomial Systems via Projection

Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we propose a certified and complete method to compute all complex solutions of the system as well as a corresponding separating linear form l with coefficients of small bit size. For computing l, we need to project the solutions into one dimension along O(n) distinct directions but no further algebraic manipulations. The solutions are then directly reconstructed from the considered projections. The first step is deterministic, whereas the second step uses randomization, thus being Las-Vegas. The theoretical analysis of our approach shows that the overall cost for the two problems considered above is dominated by the cost of carrying out the projections. We also give bounds on the bit complexity of our algorithms that are exclusively stated in terms of the number of variables, the total degree and the bitsize of the input polynomials

Revisit Sparse Polynomial Interpolation based on Randomized Kronecker Substitution

In this paper, a new reduction based interpolation algorithm for black-box multivariate polynomials over finite fields is given. The method is based on two main ingredients. A new Monte Carlo method is given to reduce black-box multivariate polynomial interpolation to black-box univariate polynomial interpolation over any ring. The reduction algorithm leads to multivariate interpolation algorithms with better or the same complexities most cases when combining with various univariate interpolation algorithms. We also propose a modified univariate Ben-or and Tiwarri algorithm over the finite field, which has better total complexity than the Lagrange interpolation algorithm. Combining our reduction method and the modified univariate Ben-or and Tiwarri algorithm, we give a Monte Carlo multivariate interpolation algorithm, which has better total complexity in most cases for sparse interpolation of black-box polynomial over finite fields

Pink‐ and orange‐pigmented Planctomycetes produce saproxanthin‐type carotenoids including a rare C45 carotenoid

Planctomycetes, are ubiquitous and environmentally important Gram-negative aquatic bacteria with key roles in global carbon and nitrogen cycles. Many planctomycetal species have a pink or orange colour and have been suggested to produce carotenoids. Potential applications as food colorants or anti-oxidants have been proposed. Hitherto, the planctomycetal metabolism is largely unexplored and the strain pigmentation has not been identified. For a holistic view on the complex planctomycetal physiology we analyzed carotenoid profiles of the pink-pigmented strain Rhodopirellula rubra LF2T and of the orange strain Rubinisphaera brasiliensis Gr7. During LC-MS/MS analysis of culture extracts we were able to identify three saproxanthin-type carotenoids including a rare C45 carotenoid. These compounds, saproxanthin, dehydroflexixanthin and 2’-isopentenyldehydrosaproxanthin, derive from the common carotenoid precursor lycopene and are characterized by related end groups, namely a 3-hydroxylated β-carotene-like cyclohexene ring as one end group and simple hydration on the other end of the molecule. Based on the observed molecule structure we present putative pathways for their biosynthesis. Results support Planctomycetes as a promising, yet mostly untapped source of carotenoids

The impact of point mutations in the human androgen receptor : classification of mutations on the basis of transcriptional activity

Peer reviewedPublisher PD

Age at Menarche and Its Association with the Metabolic Syndrome and Its Components: Results from the KORA F4 Study

OBJECTIVE: The metabolic syndrome is a major public health challenge and identifies persons at risk for diabetes and cardiovascular disease. The aim of this study was to examine the association between age at menarche and the metabolic syndrome (IDF and NCEP ATP III classification) and its components. DESIGN: 1536 women aged 32 to 81 years of the German population based KORA F4 study were investigated. Data was collected by standardized interviews, physical examinations, and whole blood and serum measurements. RESULTS: Young age at menarche was significantly associated with elevated body mass index (BMI), greater waist circumference, higher fasting glucose levels, and 2 hour glucose (oral glucose tolerance test), even after adjusting for the difference between current BMI and BMI at age 25. The significant effect on elevated triglycerides and systolic blood pressure was attenuated after adjustment for the BMI change. Age at menarche was inversely associated with the metabolic syndrome adjusting for age (p-values: <0.001 IDF, 0.003 NCEP classification) and additional potential confounders including lifestyle and reproductive history factors (p-values: 0.001, 0.005). Associations remain significant when additionally controlling for recollected BMI at age 25 (p-values: 0.008, 0.033) or the BMI change since age 25 (p-values: 0.005, 0.022). CONCLUSION: Young age at menarche might play a role in the development of the metabolic syndrome. This association is only partially mediated by weight gain and increased BMI. A history of early menarche may help to identify women at risk for the metabolic syndrome

Plasma and Muscle Myostatin in Relation to Type 2 Diabetes

OBJECTIVE: Myostatin is a secreted growth factor expressed in skeletal muscle tissue, which negatively regulates skeletal muscle mass. Recent animal studies suggest a role for myostatin in insulin resistance. We evaluated the possible metabolic role of myostatin in patients with type 2 diabetes and healthy controls. DESIGN: 76 patients with type 2 diabetes and 92 control subjects were included in the study. They were matched for age, gender and BMI. Plasma samples and biopsies from the vastus lateralis muscle were obtained to assess plasma myostatin and expression of myostatin in skeletal muscle. RESULTS: Patients with type 2 diabetes had higher fasting glucose (8.9 versus 5.1 mmol/L, P<0.001), plasma insulin (68.2 versus 47.2 pmol/L, P<0.002) and HOMA2-IR (1.6 versus 0.9, P<0.0001) when compared to controls. Patients with type 2 diabetes had 1.4 (P<0.01) higher levels of muscle myostatin mRNA content than the control subjects. Plasma myostatin concentrations did not differ between patients with type 2 diabetes and controls. In healthy controls, muscle myostatin mRNA correlated with HOMA2-IR (r = 0.30, P<0.01), plasma IL-6 (r = 0.34, P<0.05) and VO2 max (r = -0.26, P<0.05), however, no correlations were observed in patients with type 2 diabetes. CONCLUSIONS: This study supports the idea that myostatin may have a negative effect on metabolism. However, the metabolic effect of myostatin appears to be overruled by other factors in patients with type 2 diabetes

Semidefinite Characterization and Computation of Real Radical Ideals

For an ideal $I\subseteq\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety $V_\mathbb{R}(I)$ as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gr\"obner basis. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.Comment: 41 page

Employment of gene expression profiling to identify transcriptional regulators of hepatic stellate cells

Activated hepatic stellate cells (HSC) play a central role in scar formation that leads to liver fibrosis. The molecular mechanisms underlying this process are not fully understood. Microarray and bioinformatics analyses have proven to be useful in identifying transcription factors that regulate cellular processes such as cell differentiation. Using oligonucleotide microarrays, we performed transcriptional analyses of activated human HSC cultured on Matrigel-coated tissue culture dishes. Examination of microarray data following Matrigel-induced deactivation of HSC revealed a significant down-regulation of myocardin, an important transcriptional regulator in smooth and cardiac muscle development. Thus, gene expression profiling as well as functional assays of activated HSC have provided the first evidence of the involvement of myocardin in HSC activation

Age at Menarche, the Leg Length to Sitting Height Ratio, and Risk of Diabetes in Middle-Aged and Elderly Chinese Men and Women

To evaluate the associations of age at menarche and the leg length-to-sitting-height ratio, markers of adolescent growth, with risk of diabetes in later life.Information from 69,385 women and 55,311 men, aged 40-74 years from the Shanghai Women's Health Study and Shanghai Men's Health Study, were included in the current analyses. Diabetes status was ascertained through biennial in person follow-up. Cox models, with age as the time scale, were used.There were 2369 cases of diabetes (1831 women; 538 men) during an average of 7.3 and 3.6 years of follow-up of the women and men, respectively. In females, menarche age was inversely associated with diabetes risk after adjustment for birth cohort, education, and income (HR = 0.95, 0.92-0.98). In both genders, leg length-to-sitting-height ratio was inversely related to diabetes (HR = 0.88, 0.80-0.97 for men; HR = 0.91, 0.86-0.96 for women) after adjustment for birth cohort, education, and income. Further adjustment for adult BMI at study enrollment completely eliminated the associations of age at menarche (HR = 0.99, 0.96-1.02) and the leg length-to-sitting-height ratio (HR = 1.00, 0.91-1.10 for men; HR = 1.01, 0.96-1.07 for women) with diabetes risk.Our study suggests that markers of an early age at peak height velocity, i.e. early menarche age and low leg-length-to-sitting height ratio, may be associated with diabetes risk later in life and this association is likely to be mediated through obesity

Cost-Effectiveness of “Golden Mustard” for Treating Vitamin A Deficiency in India

BACKGROUND: Vitamin A deficiency (VAD) is an important nutritional problem in India, resulting in an increased risk of severe morbidity and mortality. Periodic, high-dose vitamin A supplementation is the WHO-recommended method to prevent VAD, since a single dose can compensate for reduced dietary intake or increased need over a period of several months. However, in India only 34 percent of targeted children currently receive the two doses per year, and new strategies are urgently needed. METHODOLOGY: Recent advancements in biotechnology permit alternative strategies for increasing the vitamin A content of common foods. Mustard (Brassica juncea), which is consumed widely in the form of oil by VAD populations, can be genetically modified to express high levels of beta-carotene, a precursor to vitamin A. Using estimates for consumption, we compare predicted costs and benefits of genetically modified (GM) fortification of mustard seed with high-dose vitamin A supplementation and industrial fortification of mustard oil during processing to alleviate VAD by calculating the avertable health burden in terms of disability-adjusted life years (DALY). PRINCIPAL FINDINGS: We found that all three interventions potentially avert significant numbers of DALYs and deaths. Expanding vitamin A supplementation to all areas was the least costly intervention, at $23-$50 per DALY averted and $1,000-$6,100 per death averted, though cost-effectiveness varied with prevailing health subcenter coverage. GM fortification could avert 5 million-6 million more DALYs and 8,000-46,000 more deaths, mainly because it would benefit the entire population and not just children. However, the costs associated with GM fortification were nearly five times those of supplementation. Industrial fortification was dominated by both GM fortification and supplementation. The cost-effectiveness ratio of each intervention decreased with the prevalence of VAD and was sensitive to the efficacy rate of averted mortality. CONCLUSIONS: Although supplementation is the least costly intervention, our findings also indicate that GM fortification could reduce the VAD disease burden to a substantially greater degree because of its wider reach. Given the difficulties in expanding supplementation to areas without health subcenters, GM fortification of mustard seed is an attractive alternative, and further exploration of this technology is warranted