Peak reduction technique in commutative algebra

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.Comment: survey; 10 page

The Łojasiewicz exponent over a field of arbitrary characteristic

Let K be an algebraically closed field and let K((XQ)) denote the field of generalized series with coefficients in K. We propose definitions of the local Łojasiewicz exponent of F = ( f1, . . . , fm) ∈ K[[X, Y ]]m as well as of the Łojasiewicz exponent at infinity of F = ( f1, . . . , fm) ∈ K[X, Y ]m, which generalize the familiar case of K = C and F ∈ C{X, Y }m (resp. F ∈ C[X, Y ]m), see Cha˛dzy´nski and Krasi´nski (In: Singularities, 1988; In: Singularities, 1988; Ann Polon Math 67(3):297–301, 1997; Ann Polon Math 67(2):191–197, 1997), and prove some basic properties of such numbers. Namely, we show that in both cases the exponent is attained on a parametrization of a component of F (Theorems 6 and 7), thus being a rational number. To this end, we define the notion of the Łojasiewicz pseudoexponent of F ∈ (K((XQ))[Y ])m for which we give a description of all the generalized series that extract the pseudoexponent, in terms of their jets. In particular, we show that there exist only finitely many jets of generalized series giving the pseudoexponent of F (Theorem 5). The main tool in the proofs is the algebraic version of Newton’s Polygon Method. The results are illustrated with some explicit examples

An embedding of ℂ in ℂ 2 with hyperbolic complement

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46249/1/208_2005_Article_BF01445264.pd

Global analysis of gene expression in response to L-Cysteine deprivation in the anaerobic protozoan parasite Entamoeba histolytica

<p>Abstract</p> <p>Background</p> <p><it>Entamoeba histolytica</it>, an enteric protozoan parasite, causes amebic colitis and extra intestinal abscesses in millions of inhabitants of endemic areas. <it>E. histolytica </it>completely lacks glutathione metabolism but possesses L-cysteine as the principle low molecular weight thiol. L-Cysteine is essential for the structure, stability, and various protein functions, including catalysis, electron transfer, redox regulation, nitrogen fixation, and sensing for regulatory processes. Recently, we demonstrated that in <it>E. histolytica</it>, L-cysteine regulates various metabolic pathways including energy, amino acid, and phospholipid metabolism.</p> <p>Results</p> <p>In this study, employing custom-made Affymetrix microarrays, we performed time course (3, 6, 12, 24, and 48 h) gene expression analysis upon L-cysteine deprivation. We identified that out of 9,327 genes represented on the array, 290 genes encoding proteins with functions in metabolism, signalling, DNA/RNA regulation, electron transport, stress response, membrane transport, vesicular trafficking/secretion, and cytoskeleton were differentially expressed (≥3 fold) at one or more time points upon L-cysteine deprivation. Approximately 60% of these modulated genes encoded proteins of no known function and annotated as hypothetical proteins. We also attempted further functional analysis of some of the most highly modulated genes by L-cysteine depletion.</p> <p>Conclusions</p> <p>To our surprise, L-cysteine depletion caused only limited changes in the expression of genes involved in sulfur-containing amino acid metabolism and oxidative stress defense. In contrast, we observed significant changes in the expression of several genes encoding iron sulfur flavoproteins, a major facilitator super-family transporter, regulator of nonsense transcripts, NADPH-dependent oxido-reductase, short chain dehydrogenase, acetyltransferases, and various other genes involved in diverse cellular functions. This study represents the first genome-wide analysis of transcriptional changes induced by L-cysteine deprivation in protozoan parasites, and in eukaryotic organisms where L-cysteine represents the major intracellular thiol.</p

Values clarification in a decision aid about fertility preservation: does it add to information provision?

Background We aimed to evaluate the effect of a decision aid (DA) with information only compared to a DA with values clarification exercise (VCE), and to study the role of personality and information seeking style in DA-use, decisional conflict (DC) and knowledge. Methods Two scenario-based experiments were conducted with two different groups of healthy female participants. Dependent measures were: DC, knowledge, and DA-use (time spent, pages viewed, VCE used). Respondents were randomized between a DA with information only (VCE-) and a DA with information plus a VCE(VCE+) (experiment 1), or between information only (VCE-), information plus VCE without referral to VCE(VCE+), and information plus a VCE with specific referral to the VCE, requesting participants to use the VCE(VCE++) (experiment 2). In experiment 2 we additionally measured personality (neuroticism/conscientiousness) and information seeking style (monitoring/blunting). Results Experiment 1. There were no differences in DC, knowledge or DA-use between VCE- (n=70) and VCE+ (n=70). Both DAs lead to a mean gain in knowledge from 39% at baseline to 73% after viewing the DA. Within VCE+, VCE-users (n=32, 46%) reported less DC compared to non-users. Since there was no difference in DC between VCE- and VCE+, this is likely an effect of VCE-use in a self-selected group, and not of the VCE per se. Experiment 2. There were no differences in DC or knowledge between VCE- (n=65), VCE+ (n=66), VCE++ (n=66). In all groups, knowledge increased on average from 42% at baseline to 72% after viewing the DA. Blunters viewed fewer DA-pages (R=0.38, p<.001). More neurotic women were less certain (R=0.18, p<.01) and felt less supported in decision making (R=0.15, p<.05); conscientious women felt more certain (R=-0.15, p<.05) and had more knowledge after viewing the DA (R=0.15, p<.05). Conclusions Both DAs lead to increased knowledge in healthy populations making hypothetical decisions, and use of the VCE did not improve knowledge or DC. Personality characteristics were associated to some extent with DA-use, information seeking styles with aspects of DC. More research is needed to make clear recommendations regarding the need for tailoring of information provision to personality characteristics, and to assess the effect of VCE use in actual patients

Systems microscopy approaches to understand cancer cell migration and metastasis

Cell migration is essential in a number of processes, including wound healing, angiogenesis and cancer metastasis. Especially, invasion of cancer cells in the surrounding tissue is a crucial step that requires increased cell motility. Cell migration is a well-orchestrated process that involves the continuous formation and disassembly of matrix adhesions. Those structural anchor points interact with the extra-cellular matrix and also participate in adhesion-dependent signalling. Although these processes are essential for cancer metastasis, little is known about the molecular mechanisms that regulate adhesion dynamics during tumour cell migration. In this review, we provide an overview of recent advanced imaging strategies together with quantitative image analysis that can be implemented to understand the dynamics of matrix adhesions and its molecular components in relation to tumour cell migration. This dynamic cell imaging together with multiparametric image analysis will help in understanding the molecular mechanisms that define cancer cell migration

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.