Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Collaborative International Research in Clinical and Longitudinal Experience Study in NMOSD

OBJECTIVE: To develop a resource of systematically collected, longitudinal clinical data and biospecimens for assisting in the investigation into neuromyelitis optica spectrum disorder (NMOSD) epidemiology, pathogenesis, and treatment. METHODS: To illustrate its research-enabling purpose, epidemiologic patterns and disease phenotypes were assessed among enrolled subjects, including age at disease onset, annualized relapse rate (ARR), and time between the first and second attacks. RESULTS: As of December 2017, the Collaborative International Research in Clinical and Longitudinal Experience Study (CIRCLES) had enrolled more than 1,000 participants, of whom 77.5% of the NMOSD cases and 71.7% of the controls continue in active follow-up. Consanguineous relatives of patients with NMOSD represented 43.6% of the control cohort. Of the 599 active cases with complete data, 84% were female, and 76% were anti-AQP4 seropositive. The majority were white/Caucasian (52.6%), whereas blacks/African Americans accounted for 23.5%, Hispanics/Latinos 12.4%, and Asians accounted for 9.0%. The median age at disease onset was 38.4 years, with a median ARR of 0.5. Seropositive cases were older at disease onset, more likely to be black/African American or Hispanic/Latino, and more likely to be female. CONCLUSION: Collectively, the CIRCLES experience to date demonstrates this study to be a useful and readily accessible resource to facilitate accelerating solutions for patients with NMOSD

Increased Vascular α1-adrenergic Sensitivity In Patients With Renal Failure: Receiving Recombinant Erythropoeitin

End stage renal disease (ESRD) is associated with altered hemodynamic regulation as a result of the pathophysiology or treatment of renal failure. Hypertension, common among dialysis patients, is a recognized complication of recombinant human erythropoietin (rHuEPO) therapy. We determined vascular adrenergic and nitric-oxide-mediated responsiveness in 7 patients with established ESRD on rHuEPO treatment and in 13 healthy volunteers using the dorsal hand vein technique. Sensitivity to the α1-adrenergic selective agonist phenylephrine was significantly increased in patients with ESRD on rHuEPO. The mean dose of phenylephrine producing 50% venoconstriction (ED50) was 38 ± 1.6 ng/min in patients with ESRD and 135 ± 1.3 ng/min in healthy volunteers-almost a 4-fold increase in dose, P = 0.01. In contrast, maximal venodilation mediated by bradykinin, an endothelium-dependent vasodilator, was not different in the 2 groups. To determine whether rHuEPO has a direct vasoconstrictor effect, we studied venous responsiveness to local infusions of rHuEPO in healthy volunteers. Increasing concentrations of rHuEPO produced no vasoconstriction in hand veins of healthy volunteers. These results suggest that vascular responsiveness to α-adrenergic stimulation in patients with ESRD on rHuEPO is increased whereas bradykinin-mediated venodilation remains intact. This increase in vascular α-adrenergic responsiveness may contribute to the increased peripheral vascular resistance and hypertension seen in patients with ESRD on rHuEPO. © 2007 Lippincott Williams & Wilkins, Inc.145427434Eschbach, J., Egrie, J., Downing, M., Correction of the anemia of ESRD with recombinant human erythropoietin. Results of a combined phase I & II clinical trials (1987) N Eng J Med, 316, pp. 73-78Yamakado, M., Umezu, M., Nagano, M., Mechanism of hypertension induced by erythropoietin in patients on hemodialysis (1991) Clin Invest Med, 14, pp. 623-629Smith, K.J., Bleyer, A.J., Little, W.C., The cardiovascular effects of erythropoietin (2003) Cardiovas Res, 59, pp. 538-548Raine, A.E., Roger, S.D., Effects of erythropoietin on blood pressure (1991) Am J Kidney Dis, 18, pp. 76-83Vaziri, N.D., Zhou, X.J., Smith, J., In vivo and in vitro pressor effects of erythropoietin in rats (1995) Am J Physiol, 269, pp. F838-F845Mayer, G., Horl, W.H., Cardiovascular effects of increasing hemoglobin in chronic renal failure (1996) Am J Nephrol, 16, pp. 263-269Heindenreich, S., Rahn, K.-H., Zidek, W., Direct vasopressor effect of recombinant human erythropoietin on renal resistance vessels (1991) Kidney Int, 39, pp. 259-265Tsukada, M., Ishimitsu, T., Ogawa, Y., Direct vasopressor effects of erythropoietin in genetically hypertensive rats (1993) Life Sci, 52, pp. 1425-1434Neusser, M., Tepel, M., Zidek, W., Erythropoietin increases cytosolic free calcium concentration in vascular smooth muscle cells (1993) Cardiovasc Res, 27, pp. 1233-1236Bund, S., Heagerty, A., Edmunds, M., Erythropoietin does not induce vasoconstriction directly in human subcutaneous resistance arterioles (1989) Nephron, 53, p. 173Pagel, H., Jelkmann, W., Weiss, C., Erythropoietin and blood pressure (1989) Horm Metab Res, 21, p. 224Lai, K.N., Lui, S.F., Leung, J.C., Effect of subcutaneous and intraperitoneal administration of recombinant human erythropoietin on blood pressure and vasoactive hormones in patients on continuous ambulatory peritoneal dialysis (1991) Nephron, 57, pp. 394-400Yaqoob, M., Morris, K., Bell, G., Suppression of the renin-angiotensin-aldosterone axis with erythropoietin therapy by a negative feedback loop (1992) Nephrol Dial Transplant, 7, pp. 125-128Lebel, M., Kingma, I., Grose, J.H., Hemodynamic and hormonal changes during erythropoietin treatment in hemodialysis patients (1998) J Am Soc Nephrol, 9, pp. 97-104Hand, M., Haynes, W., Johnstone, H., Erythropoietin enhances vascular responsiveness to norepinephrine in renal failure (1995) Kidney Int, 48, pp. 806-813Bode-Boger, S., Boger, R., Kuhn, M., Recombinant human erythropoietin enhance vasoconstriction tone via endothelin-1 and constrictor prostanoids (1996) Kidney Int, 50, pp. 1255-1261Zhou, X.J., Pandian, D., Wang, X.Q., Erythropoietin-induced hypertension in rats is not mediated by alterations of plasma endothelin, vasopressin, or atrial natriuretic peptide levels (1997) J Am Soc Nephrol, 8, pp. 901-905Vallance, P., Leone, A., Calver, A., Accumulation of an endogenous inhibitor of nitric oxide synthesis in chronic renal failure (1992) Lancet, 339, pp. 572-575Dachman, W., Ford, G., Blaschke, T., Mechanism of bradykinin-induced venodilation in humans (1993) J Cardiovasc Pharmacol, 21, pp. 241-248Calver, A., Collier, J., Leone, A., Effect of local intraarterial asymmetric dimethylarginine (ADMA) on the forearm arteriolar bed of healthy volunteers (1993) J Hum Hypertens, 7, pp. 193-194Pan, H., Hoffman, B., Pershe, R., Decline in beta adrenergic receptor-mediated relaxation with aging in man (1986) J Pharmacol Exp Ther, 239, pp. 802-807Fleming, W., Westfall, D., De La Lande, I., Log-normal distribution of effective doses of norepinephrine and acetylcholine in several tissues (1972) J Pharmacol Exp Ther, 181, pp. 339-345Warren, D., Mathias, C., Naik, R., Hemodynamic effects of noradrenaline and isoprenaline in chronic renal failure (1984) Contr Nephrol, 41, pp. 420-424Pan, H., Hoffman, B., Persche, R., Differences in recovery from vasoconstriction due to alpha agonists studiedwith the dorsal hand vein technique (1985) Clin Pharmacol Ther, 37, p. 219Alradi, A., Carruthers, S., Evaluation and application of the linear variable differential transformer technique for the assessment of human dorsal vein alpha receptor activity (1985) Clin Pharmacol Ther, 38, pp. 495-502Bauersachs, J., Popp, R., Hecker, M., Nitric oxide attenuates the release of endothelium-derived hyperpolarizing factor (1996) Circulation, 94, pp. 3341-3347McCulloch, A.I., Bottrill, F.E., Randall, M.D., Characterization and modulation of EDHF-mediated relaxations in the rat isolated superior mesenteric arterial bed (1997) Br J Pharmacol, 120, pp. 1431-1438Taddei, S., Ghiadoni, L., Virdis, A., Vasodilation to Bradykinin is mediated by an Oubain-sensitive pathway as a compensatory mechanism for impaired Nitric oxide availability in essential hypertensive patients (1999) Circulation, 100, pp. 1400-1405Quilley, J., Fulton, D., McGiff, J.C., Hyperpolarizing factors (1997) Biochem Pharmacol, 54, pp. 1059-1070Ford, G., Katzir, D., Blaschke, T., Responsiveness of peripheral veins to vasodilators and the effect of nifedipine on alpha adrenergic responsiveness in hypertension (1991) Clin Pharmacol Ther, 50, p. 198Eichler, H., Ford, G., Blaschke, T., Responsiveness of superficial hand veins to phenylephrine in essential hypertension (1989) J Clin Invest, 83, pp. 108-112Feldman, R., Freedman, D., Bierbrier, G., Beta adrenergic responsiveness is regulated selectively in hypertension (1993) Clin Pharmacol Ther, 54, pp. 654-66

A model to study intestinal and hepatic metabolism of propranolol in the dog

A model to investigate hepatic drug uptake and metabolism in the dog was developed for this study. Catheters were placed in the portal and hepatic veins during exploratory laparotomy to collect pre- and posthepatic blood samples at defined intervals. Drug concentrations in the portal vein were taken to reflect intestinal uptake and metabolism of an p.o. administered drug (propranolol), while differences in drug and metabolite concentrations between portal and hepatic veins reflected hepatic uptake and metabolism. A significant difference in propranolol concentration between hepatic and portal veins confirmed a high hepatic extraction of this therapeutic agent in the dog. This technically uncomplicated model may be used experimentally or clinically to determine hepatic function and metabolism of drugs that may be administered during anaesthesia and surgery

Risk assessment and communication tools for genotype associations with multifactorial phenotypes: The concept of "edge effect" and cultivating an ethical bridge between omics innovations and society

Applications of omics technologies in the postgenomics era swiftly expanded from rare monogenic disorders to multifactorial common complex diseases, pharmacogenomics, and personalized medicine. Already, there are signposts indicative of further omics technology investment in nutritional sciences (nutrigenomics), environmental health/ecology (ecogenomics), and agriculture (agrigenomics). Genotype–phenotype association studies are a centerpiece of translational research in omics science. Yet scientific and ethical standards and ways to assess and communicate risk information obtained from association studies have been neglected to date. This is a significant gap because association studies decisively influence which genetic loci become genetic tests in the clinic or products in the genetic test marketplace. A growing challenge concerns the interpretation of large overlap typically observed in distribution of quantitative traits in a genetic association study with a polygenic/multifactorial phenotype. To remedy the shortage of risk assessment and communication tools for association studies, this paper presents the concept of edge effect. That is, the shift in population edges of a multifactorial quantitative phenotype is a more sensitive measure (than population averages) to gauge the population level impact and by extension, policy significance of an omics marker. Empirical application of the edge effect concept is illustrated using an original analysis of warfarin pharmacogenomics and the VKORC1 genetic variation in a Brazilian population sample. These edge effect analyses are examined in relation to regulatory guidance development for association studies. We explain that omics science transcends the conventional laboratory bench space and includes a highly heterogeneous cast of stakeholders in society who have a plurality of interests that are often in conflict. Hence, communication of risk information in diagnostic medicine also demands attention to processes involved in production of knowledge and human values embedded in scientific practice, for example, why, how, by whom, and to what ends association studies are conducted, and standards are developed (or not). To ensure sustainability of omics innovations and forecast their trajectory, we need interventions to bridge the gap between omics laboratory and society. Appreciation of scholarship in history of omics science is one remedy to responsibly learn from the past to ensure a sustainable future in omics fields, both emerging (nutrigenomics, ecogenomics), and those that are more established (pharmacogenomics). Another measure to build public trust and sustainability of omics fields could be legislative initiatives to create a multidisciplinary oversight body, at arm's length from conflict of interests, to carry out independent, impartial, and transparent innovation analyses and prospective technology assessment.Vural Ozdemir, Guilherme Suarez-Kurtz, Raphaëlle Stenne, Andrew A. Somogyi, Toshiyuki Someya, S. Oğuz Kayaalp, and Eugene Kolke