Geometry of Polynomials and Root-Finding via Path-Lifting

Using the interplay between topological, combinatorial, and geometric properties of polynomials and analytic results (primarily the covering structure and distortion estimates), we analyze a path-lifting method for finding approximate zeros, similar to those studied by Smale, Shub, Kim, and others. Given any polynomial, this simple algorithm always converges to a root, except on a finite set of initial points lying on a circle of a given radius. Specifically, the algorithm we analyze consists of iterating $$z - \frac{f(z)-t_kf(z_0)}{f'(z)}$$ where the $t_k$ form a decreasing sequence of real numbers and $z_0$ is chosen on a circle containing all the roots. We show that the number of iterates required to locate an approximate zero of a polynomial $f$ depends only on $\log|f(z_0)/\rho_\zeta|$ (where $\rho_\zeta$ is the radius of convergence of the branch of $f^{-1}$ taking $0$ to a root $\zeta$) and the logarithm of the angle between $f(z_0)$ and certain critical values. Previous complexity results for related algorithms depend linearly on the reciprocals of these angles. Note that the complexity of the algorithm does not depend directly on the degree of $f$, but only on the geometry of the critical values. Furthermore, for any polynomial $f$ with distinct roots, the average number of steps required over all starting points taken on a circle containing all the roots is bounded by a constant times the average of $\log(1/\rho_\zeta)$. The average of $\log(1/\rho_\zeta)$ over all polynomials $f$ with $d$ roots in the unit disk is ${\mathcal{O}}({d})$. This algorithm readily generalizes to finding all roots of a polynomial (without deflation); doing so increases the complexity by a factor of at most $d$.Comment: 44 pages, 12 figure

Glucose-induced down regulation of thiamine transporters in the kidney proximal tubular epithelium produces thiamine insufficiency in diabetes

Increased renal clearance of thiamine (vitamin B1) occurs in experimental and clinical diabetes producing thiamine insufficiency mediated by impaired tubular re-uptake and linked to the development of diabetic nephropathy. We studied the mechanism of impaired renal re-uptake of thiamine in diabetes. Expression of thiamine transporter proteins THTR-1 and THTR-2 in normal human kidney sections examined by immunohistochemistry showed intense polarised staining of the apical, luminal membranes in proximal tubules for THTR-1 and THTR-2 of the cortex and uniform, diffuse staining throughout cells of the collecting duct for THTR-1 and THTR-2 of the medulla. Human primary proximal tubule epithelial cells were incubated with low and high glucose concentration, 5 and 26 mmol/l, respectively. In high glucose concentration there was decreased expression of THTR-1 and THTR-2 (transporter mRNA: −76% and −53% respectively, p<0.001; transporter protein −77% and −83% respectively, p<0.05), concomitant with decreased expression of transcription factor specificity protein-1. High glucose concentration also produced a 37% decrease in apical to basolateral transport of thiamine transport across cell monolayers. Intensification of glycemic control corrected increased fractional excretion of thiamine in experimental diabetes. We conclude that glucose-induced decreased expression of thiamine transporters in the tubular epithelium may mediate renal mishandling of thiamine in diabetes. This is a novel mechanism of thiamine insufficiency linked to diabetic nephropathy

Skin advanced glycation end product accumulation and muscle strength among adult men

Aging is associated with decreased skeletal muscle function. Increased levels of advanced glycation end products (AGEs) in skeletal muscle tissue are observed with advancing age and in diabetes. Although serum AGE level is negatively associated with grip strength in elderly people, it is unknown whether this association is present in adult males. To determine the relationship between AGE accumulation in tissue and muscle strength and power among Japanese adult men. Skin autofluorescence (AF) (a noninvasive method for measuring tissue AGEs), grip strength (n = 232), and leg extension power (n = 138) were measured in Japanese adult men [median (interquartile range) age, 46.0 (37.0, 56.0) years]. After adjustment for potential confounders, the adjusted means [95% confidence interval (CI)] for grip strength across the tertiles of skin AF were 44.5 (43.2, 45.9) kg for the lowest tertile, 42.0 (40.6, 43.3) kg for the middle tertile, and 41.7 (40.3, 43.1) kg for the highest tertile (P for trend < 0.01). Moreover, the adjusted geometric means (95% CI) of leg extension power across the tertiles of skin AF were 17.8 (16.6, 19.1) W/kg for the lowest tertile, 17.5 (16.4, 18.7) W/kg for the middle tertile, and 16.0 (14.9, 17.1) W/kg for the highest tertile (P for trend = 0.04). Among Japanese adult men, participants with higher skin AF had lower muscle strength and power, indicating a relationship between AGE accumulation and muscle strength and power. A long-term prospective study is required to clarify the causality

Association analysis of ADPRT1, AKR1B1, RAGE, GFPT2 and PAI-1 gene polymorphisms with chronic renal insufficiency among Asian Indians with type-2 diabetes

<p>Abstract</p> <p>Background</p> <p>To determine association of nine single nucleotide polymorphisms (SNPs) in ADP ribosyltransferase-1 (ADPRT1), aldo-keto reductase family 1 member B1 (AKR1B1), receptor for advanced glycation end-products (RAGE), glutamine:fructose-6-phosphate amidotransferase-2 (GFPT2), and plasminogen activator inhibitor-1 (PAI-1) genes with chronic renal insufficiency (CRI) among Asian Indians with type 2 diabetes; and to identify epistatic interactionss between genes from the present study and those from renin-angiotensin-aldosterone system (RAAS), and chemokine-cytokine, dopaminergic and oxidative stress pathways (previously investigated using the same sample set).</p> <p>Methods</p> <p>Type 2 diabetes subjects with CRI (serum creatinine ≥3.0 mg/dl) constituted the cases (n = 196), and ethnicity and age matched individuals with diabetes for a duration of ≥ 10 years, normal renal functions and normoalbuminuria recruited as controls (n = 225). Allelic and genotypic constitution of 10 polymorphisms (SNPs) from five genes namely- <it>ADPRT1</it>, <it>AKR1B1, RAGE, GFPT2 </it>and <it>PAI-1 </it>with diabetic CRI was investigated. The genetic associations were evaluated by computation of odds ratio and 95% confidence interval. Multiple logistic regression analysis was carried out to correlate various clinical parameters with genotypes, and to study epistatic interactions between SNPs in different genes.</p> <p>Results</p> <p>Single nucleotide polymorphisms -429 T>C in <it>RAGE </it>and rs7725 C>T SNP in 3' UTR in <it>GFPT2 </it>gene showed a trend towards association with diabetic CRI. Investigation using miRBase statistical tool revealed that rs7725 in <it>GFPT2 </it>was a perfect target for predicted miRNA (hsa miR-378) suggesting the presence of the variant 'T' allele may result in an upregulation of GFPT2 contributing to diabetic renal complication. Epistatic interaction between SNPs in transforming growth factor <it>TGF-β1 </it>(investigated using the same sample set and reported elsewhere) and <it>GFPT2 </it>genotype was observed.</p> <p>Conclusions</p> <p>Association of SNPs in <it>RAGE </it>and <it>GFPT2 </it>suggest that the genes involved in modulation of oxidative pathway could be major contributor to diabetic chronic renal insufficiency. In addition, GFPT2 mediated overproduction of TGF-β1 leading to endothelial expansion and thereby CRI seems likely, suggested by our observation of a significant interaction between GFPT2 with TGF-β1 genes. Further, identification of predicted miRNA targets spanning the associated SNP in <it>GFPT2 </it>implicates the rs7725 SNP in transcriptional regulation of the gene, and suggests <it>GFPT2 </it>could be a relevant target for pharmacological intervention. Larger replication studies are needed to confirm these observations.</p

Increased concentration of two different advanced glycation end-products detected by enzyme immunoassays with new monoclonal antibodies in sera of patients with rheumatoid arthritis

<p>Abstract</p> <p>Background</p> <p>Levels of pentosidine (representative of advanced glycation end-products) in sera of patients with rheumatoid arthritis are increased when compared with sera of other diagnoses or healthy controls. These levels have been reported to correlate with clinical indices of rheumatoid arthritis activity and with laboratory markers of inflammation. The purpose of this study was to find out if these findings pertain to other advanced glycation end-products.</p> <p>Methods</p> <p>We have developed two immunoassays based on new monoclonal antibodies to advanced glycation end-products. Antibody 103-E3 reacts with an unidentified antigen, formed in the reaction of proteins with ribose, while antibody 8-C1 responds to N^ε-(carboxyethyl)lysine. We have used these monoclonal antibodies to measure levels of advanced glycation end-products in sera of patients with rheumatoid arthritis, systemic lupus erythematosus, osteoarthritis, and healthy controls. We calculated the correlations between advanced glycation end-product levels in rheumatoid arthritis sera and the Disease Activity Score 28 (DAS28), age, disease duration, CRP, anti-CCP, rheumatoid factor and treatment with corticosteroids, respectively.</p> <p>Results</p> <p>Levels of both glycation products were significantly higher in sera of patients with rheumatoid arthritis when compared with sera of patients with systemic lupus erythematosus, osteoarthritis, or the healthy controls. Neither the level of N^ε-(carboxyethyl)lysine nor the level of the 103-E3 antigen in rheumatoid arthritis sera correlated with the DAS28-scored rheumatoid arthritis activity. The levels of both antigens in rheumatoid arthritis sera did not correlate with age, gender, corticosteroid treatment, or levels of CRP, anti-CCP antibodies, and rheumatoid factor in sera.</p> <p>Conclusions</p> <p>We report highly specific increases in the levels of two advanced glycation end-products in sera of patients with rheumatoid arthritis. This increase could be explained neither by rheumatoid arthritis activity nor by inflammation. We propose a working hypothesis that presumes the existence of a link between advanced glycation end-product formation and induction of autoimmunity.</p

Actin: its cumbersome pilgrimage through cellular compartments

In this article, we follow the history of one of the most abundant, most intensely studied proteins of the eukaryotic cells: actin. We report on hallmarks of its discovery, its structural and functional characterization and localization over time, and point to present days’ knowledge on its position as a member of a large family. We focus on the rather puzzling number of diverse functions as proposed for actin as a dual compartment protein. Finally, we venture on some speculations as to its origin

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Topiramate-Induced Modulation of Hepatic Molecular Mechanisms: An Aspect for Its Anti-Insulin Resistant Effect

Topiramate is an antiepileptic drug known to ameliorate insulin resistance besides reducing body weight. Albeit liver plays a fundamental role in regulation of overall insulin resistance, yet the effect of topiramate on this organ is controversial and is not fully investigated. The current work aimed to study the potential hepatic molecular mechanistic cassette of the anti-insulin resistance effect of topiramate. To this end, male Wistar rats were fed high fat/high fructose diet (HFFD) for 10 weeks to induce obese, insulin resistant, hyperglycemic animals, but with no overt diabetes. Two HFFD-groups received oral topiramate, 40 or 100 mg/kg, for two weeks. Topiramate, on the hepatic molecular level, has opposed the high fat/high fructose diet effect, where it significantly increased adiponectin receptors, GLUT2, and tyrosine kinase activity, while decreased insulin receptor isoforms. Besides, it improved the altered glucose homeostasis and lipid profile, lowered the ALT level, caused subtle, yet significant decrease in TNF-α, and boosted adiponectin in a dose dependent manner. Moreover, topiramate decreased liver weight/, visceral fat weight/, and epididymal fat weight/body weight ratios. The study proved that insulin-resistance has an effect on hepatic molecular level and that the topiramate-mediated insulin sensitivity is ensued partly by modulation of hepatic insulin receptor isoforms, activation of tyrosine kinase, induction of GLUT2 and elevation of adiponectin receptors, as well as their ligand, adiponectin, besides its known improving effect on glucose tolerance and lipid homeostasis

Anti-inflammatory agents and monoHER protect against DOX-induced cardiotoxicity and accumulation of CML in mice

Cardiac damage is the major limiting factor for the clinical use of doxorubicin (DOX). Preclinical studies indicate that inflammatory effects may be involved in DOX-induced cardiotoxicity. Nɛ-(carboxymethyl) lysine (CML) is suggested to be generated subsequent to oxidative stress, including inflammation. Therefore, the aim of this study was to investigate whether CML increased in the heart after DOX and whether anti-inflammatory agents reduced this effect in addition to their possible protection on DOX-induced cardiotoxicity. These effects were compared with those of the potential cardioprotector 7-monohydroxyethylrutoside (monoHER)

Advanced glycation end-products, a pathophysiological pathway in the cardiorenal syndrome

The prevalence of heart failure (HF) is increasing. A distinction is made between diastolic HF (preserved left ventricular ejection fraction (LVEF)) and systolic HF (reduced LVEF). Advanced glycation end-products (AGEs) are crystallized proteins that accumulate during ageing, but are particularly increased in patients with diabetes mellitus and in patients with renal failure. Through the formation of collagen crosslinks, and by interaction with the AGE-receptor, which impairs calcium handling and increases fibrosis, AGE-accumulation has pathophysiologically been associated with the development of diastolic and renal dysfunction. Interestingly, diastolic dysfunction is a frequent finding in elderly patients, diabetic patients and in patients with renal failure. Taken together, this suggests that AGEs are related to the development and progression of diastolic HF and renal failure. In this review, the role of AGEs as a possible pathophysiological factor that link the development and progression of heart and renal failure, is discussed. Finally, the role of AGE intervention as a possible treatment in HF patients will be discussed