A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Revealed preference and indifferent selection

It is shown that preferences can be constructed from observed choice behavior in a way that is robust to indifferent selection (i.e., the agent is indifferent between two alternatives but, nevertheless, is only observed selecting one of them). More precisely, a suggestion by Savage (1954) to reveal indifferent selection by considering small monetary perturbations of alternatives is formalized and generalized to a purely topological framework: references over an arbitrary topological space can be uniquely derived from observed behavior under the assumptions that they are continuous and nonsatiated and that a strictly preferred alternative is always chosen, and indifferent selection is then characterized by discontinuity in choice behavior. Two particular cases are then analyzed: monotonic preferences over a partially ordered set, and preferences representable by a continuous pseudo-utility function.

Notch regulation of lymphocyte development and function.

Notch proteins regulate a broad spectrum of cell fate decisions and differentiation processes during fetal and postnatal development. Mammals have four Notch receptors that bind five different ligands. The function of Notch signaling during lymphopoiesis and T cell neoplasia, based on gain-of-function and conditional loss-of-function approaches for the Notch1 receptor, indicates Notch1 is essential in T cell lineage commitment. Recent studies have addressed the involvement of other Notch receptors and ligands as well as their downstream targets, demonstrating additional functions of Notch signaling in embryonic hematopoiesis, intrathymic T cell development, B cell development and peripheral T cell function.

Acid-sensing channels in human bladder: expression, function and alterations during bladder pain syndrome.

Purpose: To examine the possible role of H+-activated acid-sensing ion channels (ASICs) in pain perception we characterized their expression in bladder dome biopsies of Bladder Pain Syndrome (BPS) patients and controls, in cultured human urothelium and in urothelial TEU-2 cells.Materials and Methods: Cold cut biopsies from the bladder dome were obtained in 8 asymptomatic controls and 28 patients with symptoms of BPS. ASIC expression was analyzed by QPCR and immunofluorescence. The channel function was measured by electrophysiology.Results: ASIC1a, ASIC2a and ASIC3 mRNAs were detected in human bladder. Similar amounts of ASIC1a and -3 were detected in detrusor smooth muscle, whereas in urothelium ASIC3 levels were higher than -1a. ASIC2a mRNA levels were lower than either -1a or -3 in both layers. ASIC currents were measured in TEU-2 cells and in primary cultures of human urothelium, and ASIC expression was confirmed by QPCR. Differentiation of TEU-2 cells caused an up-regulation of ASIC2a and ASIC3, and a down-regulation of ASIC1a mRNAs. BPS patients showed an up-regulation of ASIC2a and -3 mRNA, whereas ASIC1a remained unchanged. In contrast, the mRNA levels of TRPV1 were down-regulated during BPS. All differences were statistically significant (p<0.05)Conclusions: Several different ASIC subunits are expressed in human bladder and TEU-2 cells, where their levels are regulated during urothelial differentiation. An up-regulation of ASIC2a and -3 in BPS suggests their involvement in increased pain and hyperalgesia. A down-regulation of TRPV1 mRNA levels might indicate a different regulatory mechanism, controlling its expression in human bladder.

Cost effectiveness and cost utility of risedronate for osteoporosis treatment and fracture prevention in women: a Swiss perspective.

OBJECTIVES: To assess the incremental cost-effectiveness ratio (ICER) and incremental cost-utility ratio (ICUR) of risedronate compared to no intervention in postmenopausal osteoporotic women in a Swiss perspective. METHODS: A previously validated Markov model was populated with epidemiological and cost data specific to Switzerland and published utility values, and run on a population of 1,000 women of 70 years with established osteoporosis and previous vertebral fracture, treated over 5 years with risedronate 35 mg weekly or no intervention (base case), and five cohorts (according to age at therapy start) with eight risk factor distributions and three lengths of residual effects. RESULTS: In the base case population, the ICER of averting a hip fracture and the ICUR per quality-adjusted life year gained were both dominant. In the presence of a previous vertebral fracture, the ICUR was below euro45,000 (pound30,000) in all the scenarios. For all osteoporotic women>or=70 years of age with at least one risk factor, the ICUR was below euro45,000 or the intervention may even be cost saving. Age at the start of therapy and the fracture risk profile had a significant impact on results. CONCLUSION: Assuming a 2-year residual effect, that ICUR of risedronate in women with postmenopausal osteoporosis is below accepted thresholds from the age of 65 and even cost saving above the age of 70 with at least one risk factor.

Three essays in financial economics: asset pricing, optimal portfolio selection and financial integration

Executive Summary The unifying theme of this thesis is the pursuit of a satisfactory ways to quantify the riskureward trade-off in financial economics. First in the context of a general asset pricing model, then across models and finally across country borders. The guiding principle in that pursuit was to seek innovative solutions by combining ideas from different fields in economics and broad scientific research. For example, in the first part of this thesis we sought a fruitful application of strong existence results in utility theory to topics in asset pricing. In the second part we implement an idea from the field of fuzzy set theory to the optimal portfolio selection problem, while the third part of this thesis is to the best of our knowledge, the first empirical application of some general results in asset pricing in incomplete markets to the important topic of measurement of financial integration. While the first two parts of this thesis effectively combine well-known ways to quantify the risk-reward trade-offs the third one can be viewed as an empirical verification of the usefulness of the so-called "good deal bounds" theory in designing risk-sensitive pricing bounds. Chapter 1 develops a discrete-time asset pricing model, based on a novel ordinally equivalent representation of recursive utility. To the best of our knowledge, we are the first to use a member of a novel class of recursive utility generators to construct a representative agent model to address some long-lasting issues in asset pricing. Applying strong representation results allows us to show that the model features countercyclical risk premia, for both consumption and financial risk, together with low and procyclical risk free rate. As the recursive utility used nests as a special case the well-known time-state separable utility, all results nest the corresponding ones from the standard model and thus shed light on its well-known shortcomings. The empirical investigation to support these theoretical results, however, showed that as long as one resorts to econometric methods based on approximating conditional moments with unconditional ones, it is not possible to distinguish the model we propose from the standard one. Chapter 2 is a join work with Sergei Sontchik. There we provide theoretical and empirical motivation for aggregation of performance measures. The main idea is that as it makes sense to apply several performance measures ex-post, it also makes sense to base optimal portfolio selection on ex-ante maximization of as many possible performance measures as desired. We thus offer a concrete algorithm for optimal portfolio selection via ex-ante optimization over different horizons of several risk-return trade-offs simultaneously. An empirical application of that algorithm, using seven popular performance measures, suggests that realized returns feature better distributional characteristics relative to those of realized returns from portfolio strategies optimal with respect to single performance measures. When comparing the distributions of realized returns we used two partial risk-reward orderings first and second order stochastic dominance. We first used the Kolmogorov Smirnov test to determine if the two distributions are indeed different, which combined with a visual inspection allowed us to demonstrate that the way we propose to aggregate performance measures leads to portfolio realized returns that first order stochastically dominate the ones that result from optimization only with respect to, for example, Treynor ratio and Jensen's alpha. We checked for second order stochastic dominance via point wise comparison of the so-called absolute Lorenz curve, or the sequence of expected shortfalls for a range of quantiles. As soon as the plot of the absolute Lorenz curve for the aggregated performance measures was above the one corresponding to each individual measure, we were tempted to conclude that the algorithm we propose leads to portfolio returns distribution that second order stochastically dominates virtually all performance measures considered. Chapter 3 proposes a measure of financial integration, based on recent advances in asset pricing in incomplete markets. Given a base market (a set of traded assets) and an index of another market, we propose to measure financial integration through time by the size of the spread between the pricing bounds of the market index, relative to the base market. The bigger the spread around country index A, viewed from market B, the less integrated markets A and B are. We investigate the presence of structural breaks in the size of the spread for EMU member country indices before and after the introduction of the Euro. We find evidence that both the level and the volatility of our financial integration measure increased after the introduction of the Euro. That counterintuitive result suggests the presence of an inherent weakness in the attempt to measure financial integration independently of economic fundamentals. Nevertheless, the results about the bounds on the risk free rate appear plausible from the view point of existing economic theory about the impact of integration on interest rates.

Subclinical thyroid dysfunction, cardiac function, and the risk of heart failure. The Cardiovascular Health study.

OBJECTIVES: The goal of this study was to determine whether subclinical thyroid dysfunction was associated with incident heart failure (HF) and echocardiogram abnormalities. BACKGROUND: Subclinical hypothyroidism and hyperthyroidism have been associated with cardiac dysfunction. However, long-term data on the risk of HF are limited. METHODS: We studied 3,044 adults>or=65 years of age who initially were free of HF in the Cardiovascular Health Study. We compared adjudicated HF events over a mean 12-year follow-up and changes in cardiac function over the course of 5 years among euthyroid participants, those with subclinical hypothyroidism (subdivided by thyroid-stimulating hormone [TSH] levels: 4.5 to 9.9, >or=10.0 mU/l), and those with subclinical hyperthyroidism. RESULTS: Over the course of 12 years, 736 participants developed HF events. Participants with TSH>or=10.0 mU/l had a greater incidence of HF compared with euthyroid participants (41.7 vs. 22.9 per 1,000 person years, p=0.01; adjusted hazard ratio: 1.88; 95% confidence interval: 1.05 to 3.34). Baseline peak E velocity, which is an echocardiographic measurement of diastolic function associated with incident HF in the CHS cohort, was greater in those patients with TSH>or=10.0 mU/l compared with euthyroid participants (0.80 m/s vs. 0.72 m/s, p=0.002). Over the course of 5 years, left ventricular mass increased among those with TSH>or=10.0 mU/l, but other echocardiographic measurements were unchanged. Those patients with TSH 4.5 to 9.9 mU/l or with subclinical hyperthyroidism had no increase in risk of HF. CONCLUSIONS: Compared with euthyroid older adults, those adults with TSH>or=10.0 mU/l have a moderately increased risk of HF and alterations in cardiac function but not older adults with TSH<10.0 mU/l. Clinical trials should assess whether the risk of HF might be ameliorated by thyroxine replacement in individuals with TSH>or=10.0 mU/l.

Retinal degeneration depends on Bmi1 function and reactivation of cell cycle proteins.

The epigenetic regulator Bmi1 controls proliferation in many organs. Reexpression of cell cycle proteins such as cyclin-dependent kinases (CDKs) is a hallmark of neuronal apoptosis in neurodegenerative diseases. Here we address the potential role of Bmi1 as a key regulator of cell cycle proteins during neuronal apoptosis. We show that several cell cycle proteins are expressed in different models of retinal degeneration and required in the Rd1 photoreceptor death process. Deleting E2f1, a downstream target of CDKs, provided temporary protection in Rd1 mice. Most importantly, genetic ablation of Bmi1 provided extensive photoreceptor survival and improvement of retinal function in Rd1 mice, mediated by a decrease in cell cycle markers and regulators independent of p16(Ink4a) and p19(Arf). These data reveal that Bmi1 controls the cell cycle-related death process, highlighting this pathway as a promising therapeutic target for neuroprotection in retinal dystrophies.

Investigation of Improved Utility Cut Repair Techniques to Reduce Settlement in Repaired Areas, Phase II, TR-566, 2010

Trench maintenance problems are caused by improper backfill placement and construction procedures. This report is part of a multiphase research project that aims to improve long-term performance of utility cut restoration trenches. The goal of this research is to improve pavement patch life and reduce maintenance of the repaired areas. The objectives were to use field-testing data, laboratory-testing data, and long-term monitoring (elevation survey and falling weight deflectometer testing) to suggest and modify recommendations from Phase I and to identify the principles of trench subsurface settlement and load distribution in utility cut restoration areas by using instrumented trenches. The objectives were accomplished by monitoring local agency utility construction from Phase I, constructing and monitoring the recommended trenches from Phase I, and instrumenting trenches to monitor changes in temperature, pressure, moisture content, and settlement as a function of time to determine the influences of seasonal changes on the utility cut performance.

In conditions of limited chromophore supply rods entrap 11-cis-retinal leading to loss of cone function and cell death.

RPE65 is a retinoid isomerase required for the production of 11-cis-retinal, the chromophore of both cone and rod visual pigments. We recently established an R91W knock-in mouse strain as homologous animal model for patients afflicted by this mutation in RPE65. These mice have impaired vision and can only synthesize minute amounts of 11-cis-retinal. Here, we investigated the consequences of this chromophore insufficiency on cone function and pathophysiology. We found that the R91W mutation caused cone opsin mislocalization and progressive geographic cone atrophy. Remnant visual function was mostly mediated by rods. Ablation of rod opsin corrected the localization of cone opsin and improved cone retinal function. Thus, our analyses indicate that under conditions of limited chromophore supply rods and cones compete for 11-cis-retinal that derives from regeneration pathway(s) which are reliant on RPE65. Due to their higher number and the instability of cone opsin, rods are privileged under this condition while cones suffer chromophore deficiency and degenerate. These findings reinforce the notion that in patients any effective gene therapy with RPE65 needs to target the cone-rich macula directly to locally restore the cones' chromophore supply outside the reach of rods.

Discrepancy between Visual Acuity and Microperimetry in AMD Patients: Visual Acuity Appears as an Inadequate Parameter to Test Macular Function.

BACKGROUND: Best corrected visual acuity (BCVA) of 0.8 or above in AMD patients can sometimes correspond to poor macular function inducing a serious visual handicap. Microperimetry can be used to objectivize this difference. PATIENTS AND METHODS: A retrospective study was undertaken on 233 files of AMD patients of whom 82 had had a microperimetry. BCVA was compared with microperimetry performance. All examinations were performed in an identical setting by the same team of 3 persons. RESULTS: Among the 82 patients included, 32 (39.0%) had a BCVA equal to or above 0.8 even though their microperimetry performance was lower than 200/560 db. 10 of them (12.2% of total) had an even poorer microperimetry below 120/560 db indicating poor macular function. CONCLUSIONS: More than a third of the AMD patients had a bad or very bad microperimetry performance in parallel with a good visual acuity. Microperimetry is a valuable tool to assess and follow real macular function in AMD patients when visual acuity alone can be misleading.

Skeletal Muscle Mitochondrial Function and Fatigability in Older Adults.

BACKGROUND: Fatigability increases while the capacity for mitochondrial energy production tends to decrease significantly with age. Thus, diminished mitochondrial function may contribute to higher levels of fatigability in older adults. METHODS: The relationship between fatigability and skeletal muscle mitochondrial function was examined in 30 participants aged 78.5 ± 5.0 years (47% female, 93% white), with a body mass index of 25.9 ± 2.7 kg/m(2) and usual gait-speed of 1.2 ± 0.2 m/s. Fatigability was defined using rating of perceived exertion (6-20 point Borg scale) after a 5-minute treadmill walk at 0.72 m/s. Phosphocreatine recovery in the quadriceps was measured using (31)P magnetic resonance spectroscopy and images of the quadriceps were captured to calculate quadriceps volume. ATPmax (mM ATP/s) and oxidative capacity of the quadriceps (ATPmax·Quadriceps volume) were calculated. Peak aerobic capacity (VO2peak) was measured using a modified Balke protocol. RESULTS: ATPmax·Quadriceps volume was associated with VO2peak and was 162.61mM ATP·mL/s lower (p = .03) in those with high (rating of perceived exertion ≥10) versus low (rating of perceived exertion ≤9) fatigability. Participants with high fatigability required a significantly higher proportion of VO2peak to walk at 0.72 m/s compared with those with low fatigability (58.7 ± 19.4% vs 44.9 ± 13.2%, p < .05). After adjustment for age and sex, higher ATPmax was associated with lower odds of having high fatigability (odds ratio: 0.34, 95% CI: 0.11-1.01, p = .05). CONCLUSIONS: Lower capacity for oxidative phosphorylation in the quadriceps, perhaps by contributing to lower VO2peak, is associated with higher fatigability in older adults.

Role and Function of c-Jun Protein Complex in Cancer Cell Behavior

Transcription factors play a crucial role in the regulation of cell behavior by modulating gene expression profiles. Previous studies have described a dual role for the AP-1 family transcription factor c-Jun in the regulation of cellular fate. In various cell types weak and transient activations of c-Jun N-terminal kinase (JNK) and c-Jun appear to contribute to proliferation and survival, whereas strong and prolonged activation of JNK and c-Jun result in apoptosis. These opposite roles played by c-Jun are cell type specific and the molecular mechanisms defining these antonymous c-Jun-mediated responses remain incompletely understood. c-Jun activity in transformed cells is regulated by signalling cascades downstream of oncoproteins such as Ras and Raf. In addition, the pro-proliferative role and the survival promoting function for c-Jun has been described in various cancer models. Furthermore, c-Jun was described to be overexpressed in different cancer types. However, the molecular mechanisms by which c-Jun exerts these oncogenic functions are not all clearly established. Therefore it is of primary interest to further identify molecular mechanisms and functions for c-Jun in cancer. Regulation of gene expression is tightly dependent on accurate protein-protein interactions. Therefore, co-factors for c-Jun may define the functions for c-Jun in cancer. Identification of protein-protein interactions promoting cancer may provide novel possibilities for cancer treatment. In this study, we show that DNA topoisomerase I (TopoI) is a transcriptional co-factor for c-Jun. Moreover, c-Jun and TopoI together promote expression of epidermal growth factor receptor (EGFR) in cancer cells. We also show that the clinically used TopoI inhibitor topotecan reduces EGFR expression. Importantly, the effect of TopoI on EGFR transcription was shown to depend on c-Jun as Jun-/- cells or cells treated with JNK inhibitor SP600125 are resistant to topotecan treatment both in regulation of EGFR expression and cell proliferation. Moreover, c-Jun regulates the nucleolar localization and the function of the ribonucleic acid (RNA) helicase DDX21, a previously identified member of c-Jun protein complex. In addition, c-Jun stimulates rRNA processing by supporting DDX21 rRNA binding. Finally, this study characterizes a DDX21 dependent expression of cyclin dependent kinase (Cdk) 6, a correlation of DDX21 expression with prostate cancer progression and a substrate binding dependency of DDX21 nucleolar localization in prostate cancer cells. Taken together, the results of this study validate the c-Jun-TopoI interaction and precise the c-Jun-DDX21 interaction. Moreover, these results show the importance for protein-protein interaction in the regulation of their cellular functions in cancer cell behavior. Finally, the results presented here disclose new exciting therapeutic opportunities for cancer treatment.

Blockade of the action of nitric oxide in human septic shock increases systemic vascular resistance and has detrimental effects on pulmonary function after a short infusion of methylene blue

To investigate the role of nitric oxide in human sepsis, ten patients with severe septic shock requiring vasoactive drug therapy and mechanical ventilation were enrolled in a prospective, open, non-randomized clinical trial to study the acute effects of methylene blue, an inhibitor of guanylate cyclase. Hemodynamic and metabolic variables were measured before and 20, 40, 60, and 120 min after the start of a 1-h intravenous infusion of 4 mg/kg of methylene blue. Methylene blue administration caused a progressive increase in mean arterial pressure (60 [55-70] to 70 [65-100] mmHg, median [25-75th percentiles]; P<0.05), systemic vascular resistance index (649 [479-1084] to 1066 [585-1356] dyne s-1 cm-5 m-2; P<0.05) and the left ventricular stroke work index (35 [27-47] to 38 [32-56] g m-1 m-2; P<0.05) from baseline to 60 min. The pulmonary vascular resistance index increased from 150 [83-207] to 186 [121-367] dyne s-1 cm-5 m-2 after 20 min (P<0.05). Mixed venous saturation decreased from 65 [56-76] to 63 [55-69]% (P<0.05) after 60 min. The PaO2/FiO2 ratio decreased from 168 [131-215] to 132 [109-156] mmHg (P<0.05) after 40 min. Arterial lactate concentration decreased from 5.1 ± 2.9 to 4.5 ± 2.1 mmol/l, mean ± SD (P<0.05) after 60 min. Heart rate, cardiac filling pressures, cardiac output, oxygen delivery and consumption did not change. Methylene blue administration was safe and no adverse effect was observed. In severe human septic shock, a short infusion of methylene blue increases systemic vascular resistance and may improve myocardial function. Although there was a reduction in blood lactate concentration, this was not explained by an improvement in tissue oxygenation, since overall oxygen availability did not change. However, there was a significant increase in pulmonary vascular tone and a deterioration in gas exchange. Further studies are needed to demonstrate if nitric oxide blockade with methylene blue can be safe for patients with septic shock and, particularly, if it has an effect on pulmonary function.