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1.
Vasc Health Risk Manag ; 18: 335-346, 2022.
Article in English | MEDLINE | ID: mdl-35535305

ABSTRACT

Introduction: Endothelin-1 and its prohormone C-terminal pro-endothelin-1 (CT-proET-1) have been linked to metabolic alterations, inflammatory responses and cardiovascular events in selected study populations. We analyzed the association of CT-proET-1 with cardiovascular events and mortality, carotid intima-media-thickness as surrogate for early atherosclerotic lesions, biomarkers of subclinical inflammation and adipokines in a population-based study. Methods: The cross-sectional and prospective analyses used data from the KORA F4 study with a median follow-up time of 9.1 (8.8-9.4) years. Data on CT-proET-1 and mortality were available for 1554 participants, data on the other outcomes in subgroups (n = 596-1554). The associations were estimated using multivariable linear regression and Cox proportional hazard models adjusted for sex, age, body mass index, estimated glomerular filtration rate, arterial hypertension, diabetes, low-density and high-density lipoprotein cholesterol, current and former smoking and physical activity. The Bonferroni method was used to correct for multiple testing. Results: In the fully adjusted model, CT-proET-1 was associated with cardiovascular (hazard ratio (HR) per standard deviation increase: 1.66; 95% confidence interval (CI): 1.10-2.51; p = 0.017) and all-cause mortality (HR: 2.03; 95% CI 1.55-2.67; p < 0.001), but not with cardiovascular events, and was inversely associated with the intima-media thickness (ß: -0.09 ± 0.03; p = 0.001). CT-proET-1 was positively associated with five out of ten biomarkers of subclinical inflammation and with two out of five adipokines after correction for multiple testing. After inclusion of biomarkers of subclinical inflammation in the Cox proportional hazard model, the association of CT-proET-1 with all-cause mortality persisted (p < 0.001). Conclusion: These results emphasize the complexity of endothelin-1 actions and/or indicator functions of CT-proET-1. CT-proET-1 is a risk marker for all-cause mortality, which is likely independent of vascular endothelin-1 actions, cardiovascular disease and inflammation.


Subject(s)
Cardiovascular Diseases , Endothelin-1 , Mortality , Adipokines , Biomarkers , Cardiovascular Diseases/diagnosis , Carotid Intima-Media Thickness , Cross-Sectional Studies , Humans , Inflammation , Peptide Fragments , Prospective Studies
2.
PLoS One ; 17(1): e0262330, 2022.
Article in English | MEDLINE | ID: mdl-34990470

ABSTRACT

BACKGROUND AND AIM: Despite its vasodilatory effect, adrenomedullin and its surrogate mid-regional pro-adrenomedullin (MR-proADM) have been found to be positively associated with all-cause and cardiovascular mortality. However, the underlying mechanisms thereof remain unclear and the associations were mostly shown in geriatric cohorts or in patients with chronic diseases. Therefore, we aimed to investigate the possible involvement of abdominal obesity, selected adipokines, and biomarkers of subclinical inflammation in the association of MR-proADM with mortality in a population based study cohort. METHODS: Prospective analysis of the KORA F4 study; median follow-up 9.1 (8.8-9.4) years. Complete data on MR-proADM and mortality was available for 1551 participants, aged 56.9±12.9 years (mean±SD). Correlation and regression analyses of MR-proADM with overall (BMI) and abdominal obesity (waist circumference), selected adipokines and biomarkers of subclinical inflammation. Cox proportional hazard models on the association of MR-proADM with all-cause and cardiovascular mortality with adjustment for cardiovascular risk factors and selected biomarkers in study subgroups (n = 603-1551). RESULTS: MR-proADM associated with all-cause (HR (95%CI): 2.37 (1.72-3.26) and 2.31 (1.67-3.20)) and cardiovascular mortality (4.28 (2.19-8.39) and 4.44 (2.25-8.76)) after adjustment for traditional cardiovascular risk factors including BMI or waist circumference, respectively. MR-proADM was further associated with four out of seven examined adipokines (leptin, retinol-binding protein-4, chemerin, and adiponectin) and with five out of eleven examined biomarkers of subclinical inflammation (high-sensitivity C-reactive protein, interleukin-6, myeloperoxidase, interleukin-22, and interleukin-1 receptor antagonist) after multivariable adjustment and correction for multiple testing. However, only IL-6 substantially attenuated the association of MR-proADM with all-cause mortality. CONCLUSIONS: We found an association of MR-proADM with (abdominal) obesity, selected adipokines, and biomarkers of subclinical inflammation. However, the association of MR-proADM with mortality was independent of these parameters. Future studies should investigate the role of IL-6 and further characteristics of subclinical inflammation in the association between MR-proADM and all-cause mortality.


Subject(s)
Adrenomedullin/blood , Cardiovascular Diseases/blood , Cardiovascular Diseases/mortality , Cardiovascular System/metabolism , Peptide Fragments/blood , Protein Precursors/blood , Adrenomedullin/metabolism , Biomarkers/blood , Female , Humans , Inflammation/blood , Inflammation/metabolism , Male , Middle Aged , Obesity/blood , Obesity/metabolism , Prospective Studies , Risk Factors
3.
Article in English | MEDLINE | ID: mdl-35086943

ABSTRACT

INTRODUCTION: Primary aldosteronism is associated with impaired glucose tolerance. Whether plasma aldosterone and/or renin concentrations are associated with type 2 diabetes and continuous measures of glucose metabolism in the general population is still under debate. RESEARCH DESIGN AND METHODS: The analyses included 2931 participants of the KORA F4 study at baseline and 2010 participants of the KORA FF4 study after a median follow-up of 6.5 years. The associations of active plasma renin and aldosterone concentrations with type 2 diabetes and continuous measures of glucose metabolism were assessed using logistic and linear regression models. Results were adjusted for sex, age, body mass index (BMI), estimated glomerular filtration rate, potassium, use of ACE inhibitors, angiotensin receptor blockers, beta blockers, diuretics and calcium channel blockers. RESULTS: Cross-sectionally, renin was associated with type 2 diabetes (OR per SD: 1.25, 95% CI 1.10 to 1.43, p<0.001), fasting glucose, 2-hour glucose, insulin, proinsulin, HOMA-B (homeostasis model assessment of beta cell function) and HOMA-IR (homeostasis model assessment of insulin resistance) (all p values <0.001). Aldosterone was not associated with type 2 diabetes (OR: 1.04, 95% CI 0.91 to 1.19; p=0.547) but with insulin, proinsulin and HOMA-IR (all p values <0.001). The aldosterone-renin ratio was inversely associated with type 2 diabetes and several measures of glucose metabolism. Longitudinally, neither renin (OR: 1.12, 95% CI 0.92 to 1.36) nor aldosterone (OR: 0.91, 95% CI 0.74 to 1.11) were associated with incident type 2 diabetes. Renin was inversely associated with changes of insulin concentrations. CONCLUSIONS: In the KORA F4/FF4 study, renin and aldosterone were not associated with incident type 2 diabetes and largely unrelated to changes of measures of glucose metabolism. Cross-sectionally, aldosterone was associated with surrogate parameters of insulin resistance. However, these associations were not independent of renin.


Subject(s)
Diabetes Mellitus, Type 2 , Insulin Resistance , Aldosterone , Diabetes Mellitus, Type 2/epidemiology , Glucose , Humans , Renin
4.
Cytokine ; 150: 155786, 2022 02.
Article in English | MEDLINE | ID: mdl-34920231

ABSTRACT

BACKGROUND: The renal tubular glycoprotein uromodulin is associated with obesity and type 2 diabetes, but the underlying mechanisms are elusive. We investigated the association of serum uromodulin with adipokines and tested the effect modification by diabetes status. METHODS: The associations of serum uromodulin with eight adipokines were assessed in 795-1080 participants of the KORA F4 study aged 62-81 years using linear regression models adjusted for sex, age, BMI, estimated glomerular filtration rate and diabetes. Significant associations were assessed for effect modification by diabetes status. We further tested using logistic regression whether adjustment for the significant adipokines affected the association of uromodulin with type 2 diabetes. RESULTS: Serum uromodulin was inversely associated with chemerin and retinol-binding protein-4 after multivariable adjustment (p < 0.001) and Bonferroni correction for multiple testing. No significant association was observed between uromodulin and the other adipokines (leptin, adiponectin, secreted frizzled-related protein 5, progranulin, omentin-1 and vaspin) after correcting for multiple testing. The association of uromodulin with chemerin and retinol-binding protein-4 was stronger in participants with type 2 diabetes than in participants without diabetes (p for interaction < 0.05). However, inclusion of chemerin and retinol-binding protein-4 in logistic regression models did not attenuate the association of serum uromodulin with diabetes. CONCLUSIONS: Serum uromodulin was inversely associated with the predominantly pro-inflammatory adipokines chemerin and retinol-binding protein-4. The associations were stronger in participants with type 2 diabetes compared to participants without diabetes. However, the association of serum uromodulin with type 2 diabetes was independent of chemerin and retinol-binding protein-4.


Subject(s)
Adipokines , Diabetes Mellitus, Type 2 , Adiponectin , Aged , Aged, 80 and over , Humans , Middle Aged , Obesity , Uromodulin
5.
Clin Kidney J ; 14(6): 1618-1625, 2021 Jun.
Article in English | MEDLINE | ID: mdl-34221377

ABSTRACT

BACKGROUND: Uromodulin is a kidney-specific glycoprotein synthesized in tubular cells of Henle's loop exerting nephroprotective and immunomodulatory functions in the urinary tract. A small amount of uromodulin is also released into the systemic circulation, where its physiological role is unknown. Serum uromodulin (sUmod) has been associated with metabolic risk factors and with cardiovascular events and mortality, where these associations were partly stronger in men than in women. In this study, we investigated the associations of sUmod with biomarkers of subclinical inflammation in a population-based sample of women and men. METHODS: Associations of sUmod with 10 biomarkers of subclinical inflammation were assessed in 1065 participants of the Cooperative Health Research in the Region of Augsburg (KORA) F4 study aged 62-81 years using linear regression models adjusted for sex, age, body mass index, estimated glomerular filtration rate and diabetes. Analyses were performed in the total study sample and stratified by sex. RESULTS: sUmod was inversely associated with white blood cell count, high-sensitive C-reactive protein, interleukin (IL)-6, tumour necrosis factor-α, myeloperoxidase, superoxide dismutase-3, IL-1 receptor antagonist and IL-22 after multivariable adjustment and correction for multiple testing (P < 0.001 for each observation). There was a trend towards a stronger association of sUmod with pro-inflammatory markers in men than in women, with a significant P for sex interaction (<0.001) regarding the relation of sUmod with IL-6. CONCLUSIONS: sUmod was inversely associated with biomarkers of subclinical inflammation in older participants of the KORA F4 study. The association of sUmod with IL-6 differed between women and men. Future research should focus on whether the immunomodulatory properties of sUmod are one explanation for the association of sUmod with cardiovascular outcomes and mortality.

6.
Clin Kidney J ; 14(1): 205-211, 2021 Jan.
Article in English | MEDLINE | ID: mdl-33564420

ABSTRACT

BACKGROUND: Uromodulin, a tissue-specific tubular glycoprotein, has recently emerged as a promising biomarker for kidney function and tubular integrity. However, the association of serum uromodulin (sUmod) with renal function decline is still unknown in an older general population. METHODS: We analysed the association of sUmod with the estimated glomerular filtration rate (eGFR) and albuminuria in 1075 participants of the population-based Cooperative Health Research in the Region of Augsburg (KORA) F4 study, ages 62-81 years, at baseline and prospectively after a mean follow-up time of 6.5 years (n = 605) using logistic and linear regression models as well as receiver operating characteristics (ROC) analyses. RESULTS: Cross-sectionally, sUmod was positively associated with eGFR (ß = 0.31 ± 0.02 per higher standard deviation sUmod; P < 0.001) and inversely associated with the urinary albumin:creatinine ratio (ß = -0.19 ± 0.04; P < 0.001) after adjustment for sex, age, body mass index, arterial hypertension, prediabetes and diabetes. After multivariable adjustment including baseline eGFR, sUmod was not associated with incident chronic kidney disease (CKD), defined as a decrease in eGFR <60 mL/min/1.73 m2 after 6.5 years of follow-up {odds ratio [OR] 1.02 [95% confidence interval (CI) 0.77-1.36] per higher SD sUmod} but was inversely associated with advanced CKD, defined as incident eGFR <45 mL/min/1.73 m2 [OR 0.64 (95% CI 0.42-0.98)]. The ROC showed no added predictive value of sUmod for kidney function decline in the fully adjusted model. CONCLUSIONS: Higher sUmod was inversely associated with progression to advanced kidney disease but does not provide additional predictive value for the development of CKD in elderly participants of the population-based KORA study.

7.
PLoS One ; 15(8): e0237364, 2020.
Article in English | MEDLINE | ID: mdl-32764816

ABSTRACT

OBJECTIVES: Uromodulin has been associated with arterial hypertension in genome-wide association studies, but data from clinical and preclinical studies are inconsistent. We here analyzed the association of serum uromodulin (sUmod) with arterial hypertension and vasoactive hormones in a population-based study. METHODS: In 1108 participants of the KORA F4 study aged 62-81 years, sUmod was measured and the association of sUmod with arterial hypertension was assessed using logistic regression models. The associations of sUmod with renin and aldosterone and with the vasoconstrictive prohormone C-terminal pro-endothelin-1 (CT-proET-1) were analyzed in 1079 participants and in 618 participants, respectively, using linear regression models. RESULTS: After multivariable adjustment including sex, age, eGFR, BMI, fasting glucose, current smoking, previous stroke and myocardial infarction, sUmod was inversely associated with arterial hypertension (OR 0.78; 95% CI 0.68-0.91; p = 0.001). SUmod was not significantly associated with renin and aldosterone after adjustment for sex, age and eGFR. However, sUmod was inversely associated with CT-proET-1 (ß -0.19 ± 0.04; p < 0.001) after adjustment for sex, age, eGFR, BMI, arterial hypertension, fasting glucose, current smoking, previous stroke and myocardial infarction. The association with CT-proET-1 was stronger in participants with hypertension (ß -0.22 ± 0.04) than in normotensive participants (ß -0.13 ± 0.06; p for interaction hypertension = 0.003 in the model adjusted for hypertension). CONCLUSIONS: SUmod was inversely associated with arterial hypertension and the vasoconstrictive prohormone CT-proET-1, suggesting direct or indirect effects of sUmod on blood pressure regulation.


Subject(s)
Endothelin-1/blood , Hypertension/blood , Peptide Fragments/blood , Uromodulin/blood , Aged , Aldosterone/blood , Female , Humans , Hypertension/epidemiology , Male , Renin/blood
8.
Article in English | MEDLINE | ID: mdl-32423965

ABSTRACT

INTRODUCTION: We investigated the association of the proinsulin to insulin ratio (PIR) with prevalent and incident type 2 diabetes (T2D), components of the metabolic syndrome, and renal and cardiovascular outcomes in the population-based Cooperative Health Research in the Region of Augsburg (KORA) F4 study (2006-2008)/FF4 study (2013-2014). RESEARCH DESIGN AND METHODS: The analyses included 1514 participants of the KORA F4 study at baseline and 1132 participants of the KORA FF4 study after a median follow-up time of 6.6 years. All-cause and cardiovascular mortality as well as cardiovascular events were analyzed after a median time of 9.1 and 8.6 years, respectively. The association of PIR with T2D, renal and cardiovascular characteristics and mortality were assessed using logistic regression models. Linear regression analyses were used to assess the association of PIR with components of the metabolic syndrome. RESULTS: After adjustment for sex, age, body mass index (BMI), and physical activity, PIR was associated with prevalent (OR: 2.24; 95% CI 1.81 to 2.77; p<0.001) and incident T2D (OR: 1.66; 95% CI 1.26 to 2.17; p<0.001). PIR was associated with fasting glucose (ß per SD: 0.11±0.02; p<0.001) and HbA1c (ß: 0.21±0.02; p<0.001). However, PIR was not positively associated with other components of the metabolic syndrome and was even inversely associated with waist circumference (ß: -0.22±0.03; p<0.001), BMI (ß: -0.11±0.03; p<0.001) and homeostatic model assessment of insulin resistance (ß: -0.22±0.02; p<0.001). PIR was not significantly associated with the intima-media thickness (IMT), decline of kidney function, incident albuminuria, myocardial infarction, stroke, cardiovascular or all-cause mortality. CONCLUSIONS: In the KORA F4/FF4 cohort, PIR was positively associated with prevalent and incident T2D, but inversely associated with waist circumference, BMI and insulin resistance, suggesting that PIR might serve as a biomarker for T2D risk independently of the metabolic syndrome, but not for microvascular or macrovascular complications.


Subject(s)
Cardiovascular Diseases , Diabetes Mellitus, Type 2 , Cardiovascular Diseases/epidemiology , Carotid Intima-Media Thickness , Diabetes Mellitus, Type 2/epidemiology , Humans , Insulin , Proinsulin
9.
Atherosclerosis ; 297: 1-7, 2020 03.
Article in English | MEDLINE | ID: mdl-32058862

ABSTRACT

BACKGROUND AND AIMS: Serum uromodulin, a novel biomarker of kidney function and tubular integrity, has been linked to cardiovascular events and total mortality in patients at high cardiovascular risk. Here, we analyze the association of serum uromodulin with cardiovascular morbidity and cardiovascular as well as total mortality in the population-based KORA F4 study stratified by sex. METHODS: Baseline serum uromodulin was measured in 1079 participants of the KORA F4 study (age 62-81 years). Using multivariable adjusted Cox proportional hazards models, the associations of serum uromodulin with total mortality and cardiovascular mortality were analyzed after a median follow-up period of 8.6 years, and with non-fatal and fatal stroke and myocardial infarction/coronary death after a median follow-up time of 8.4 years. RESULTS: Serum uromodulin was significantly inversely associated with total mortality (HR 0.65; 95% CI 0.53-0.79 per standard deviation of logarithmized serum uromodulin; p < 0.001) and cardiovascular mortality (HR 0.70; 95% CI 0.52-0.93) in men, but not in women (HR for all-cause mortality in women 0.98; 95% CI 0.77-1.25, HR for cardiovascular mortality 0.78; 95% CI 0.56-1.11) after adjustment for age, BMI, diabetes and eGFR. In addition, serum uromodulin was significantly inversely associated with incident stroke in men (HR 0.68; 95% CI 0.50-0.92), but not in women (HR 0.96; 95% CI 0.68-1.38) after multivariable adjustment. The association of serum uromodulin with incident myocardial infarction was attenuated and lost significance after multivariable adjustment in both sexes. CONCLUSIONS: Serum uromodulin is an independent biomarker for total and cardiovascular mortality in men from the general community aged 62 years or older.


Subject(s)
Cardiovascular Diseases/blood , Cardiovascular Diseases/mortality , Uromodulin/blood , Aged , Aged, 80 and over , Biomarkers/blood , Cardiovascular Diseases/diagnosis , Female , Germany/epidemiology , Heart Disease Risk Factors , Humans , Incidence , Male , Middle Aged , Myocardial Infarction/blood , Myocardial Infarction/diagnosis , Myocardial Infarction/mortality , Prognosis , Risk Assessment , Sex Factors , Stroke/blood , Stroke/diagnosis , Stroke/mortality
10.
Endocr Connect ; 8(10): 1363-1371, 2019 Oct.
Article in English | MEDLINE | ID: mdl-31505464

ABSTRACT

OBJECTIVE: Metabolic syndrome and obesity are risk factors for chronic kidney disease. However, early kidney alterations may escape diagnosis in these conditions due to glomerular hyperfiltration. Uromodulin, a glycoprotein exclusively synthesized in tubular cells of the thick ascending limb of Henle's loop, is a novel tissue-specific biomarker for kidney function. In contrast to the commonly used markers creatinine and cystatin C, serum uromodulin does not primarily depend on glomerular filtration. We hypothesized that serum uromodulin is a marker for metabolic syndrome and related components. DESIGN: The analyses included 1088 participants of the population-based KORA F4 study aged 62-81 years. Metabolic syndrome was present in 554 participants. After a mean follow-up time of 6.5 years, 621 participants were reevaluated, of which 92 had developed incident metabolic syndrome. METHODS: The association of serum uromodulin with metabolic syndrome and its components were assessed using multivariable logistic regression models. RESULTS: Serum uromodulin was inversely associated with metabolic syndrome after adjustment for sex, age, estimated glomerular filtration rate, physical activity, smoking, alcohol consumption and high-sensitivity C-reactive protein (OR 0.65; 95% CI 0.56-0.76 per standard deviation uromodulin; P < 0.001). Serum uromodulin was inversely associated with all single components of metabolic syndrome. However, serum uromodulin was not associated with new-onset metabolic syndrome after the follow-up period of 6.5 ± 0.3 years (OR 1.18; 95% CI 0.86-1.60). CONCLUSIONS: Serum uromodulin is independently associated with prevalent, but not with incident metabolic syndrome. Low serum uromodulin may indicate a decreased renal reserve in the metabolic syndrome.

11.
J Clin Endocrinol Metab ; 104(9): 3795-3802, 2019 Sep 01.
Article in English | MEDLINE | ID: mdl-30892596

ABSTRACT

AIMS: Serum uromodulin has recently emerged as promising biomarker for kidney function and was suggested to be associated with type 2 diabetes (T2D) in patients with coronary heart disease. Here, we analyzed the association of serum uromodulin with T2D in the population-based KORA F4/FF4 study. METHODS: In 1119 participants of the KORA F4 study aged 62 to 81 years, serum uromodulin was measured, and the association of serum uromodulin with T2D was assessed using logistic and linear regression models stratified for sex. After a mean follow-up time of 6.5 years, 635 participants where re-evaluated. Glucose tolerance status was determined by oral glucose tolerance test at baseline and at the follow-up examination except in cases of known T2D. RESULTS: Serum uromodulin was inversely associated with T2D in the crude analysis and after adjustment for age and body mass index in men (P < 0.001) and in women (P < 0.05). After further adjustment for estimated glomerular filtration rate, serum uromodulin was significantly inversely associated with T2D in men (P < 0.001) but not in women. Serum uromodulin was not associated with prediabetes after multivariate adjustment and did not predict T2D in men or in women after the follow-up time of 6.5 ± 0.3 years. CONCLUSIONS: In participants of the KORA F4 study, serum uromodulin is independently associated with T2D in men but is not a predictor of future development of T2D.

12.
Phys Rev E Stat Nonlin Soft Matter Phys ; 81(4 Pt 1): 041117, 2010 Apr.
Article in English | MEDLINE | ID: mdl-20481687

ABSTRACT

The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free-energy based on work measurements of nonequilibrium, finite-time processes, and their reversed counterparts by applying Bennett's acceptance ratio method. A nice property of this method is that each free-energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free-energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett's acceptance ratio method.

13.
Phys Rev E Stat Nonlin Soft Matter Phys ; 80(3 Pt 1): 031111, 2009 Sep.
Article in English | MEDLINE | ID: mdl-19905066

ABSTRACT

A powerful and well-established tool for free-energy estimation is Bennett's acceptance ratio method. Central properties of this estimator, which employs samples of work values of a forward and its time-reversed process, are known: for given sets of measured work values, it results in the best estimate of the free-energy difference in the large sample limit. Here we state and prove a further characteristic of the acceptance ratio method: the convexity of its mean-square error. As a two-sided estimator, it depends on the ratio of the numbers of forward and reverse work values used. Convexity of its mean-square error immediately implies that there exists a unique optimal ratio for which the error becomes minimal. Further, it yields insight into the relation of the acceptance ratio method and estimators based on the Jarzynski equation. As an application, we study the performance of a dynamic strategy of sampling forward and reverse work values.

14.
Phys Rev E Stat Nonlin Soft Matter Phys ; 77(4 Pt 1): 041105, 2008 Apr.
Article in English | MEDLINE | ID: mdl-18517576

ABSTRACT

Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time, Schmiedl and Seifert [T. Schmiedl and U. Seifert, Phys. Rev. Lett. 98, 108301 (2007)] found the Euler-Lagrange equation to be a nonlocal integrodifferential equation of correlation functions. For two linear examples, we show how this integrodifferential equation can be solved analytically. For nonlinear physical systems we show how the optimal protocol can be found numerically and demonstrate that there may exist several distinct optimal protocols simultaneously, and we present optimal protocols that have one, two, and three jumps, respectively.

15.
Phys Rev Lett ; 94(2): 021301, 2005 Jan 21.
Article in English | MEDLINE | ID: mdl-15698160

ABSTRACT

It is shown that the recent observations of NASA's Explorer mission, "Wilkinson Microwave Anisotropy Probe," hint that our Universe may possess a nontrivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.

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