Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform

Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form $T_*f\lesssim M(Tf)$ or $T_*f\lesssim M^2(Tf)$ for certain singular integral operators $T$, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

Fracture risk and zoledronic acid therapy in men with osteoporosis.

BACKGROUND: Fractures in men are a major health issue, and data on the antifracture efficacy of therapies for osteoporosis in men are limited. We studied the effect of zoledronic acid on fracture risk among men with osteoporosis. METHODS: In this multicenter, double-blind, placebo-controlled trial, we randomly assigned 1199 men with primary or hypogonadism-associated osteoporosis who were 50 to 85 years of age to receive an intravenous infusion of zoledronic acid (5 mg) or placebo at baseline and at 12 months. Participants received daily calcium and vitamin D supplementation. The primary end point was the proportion of participants with one or more new morphometric vertebral fractures over a period of 24 months. RESULTS: The rate of any new morphometric vertebral fracture was 1.6% in the zoledronic acid group and 4.9% in the placebo group over the 24-month period, representing a 67% risk reduction with zoledronic acid (relative risk, 0.33; 95% confidence interval, 0.16 to 0.70; P=0.002). As compared with men who received placebo, men who received zoledronic acid had fewer moderate-to-severe vertebral fractures (P=0.03) and less height loss (P=0.002). Fewer participants who received zoledronic acid had clinical vertebral or nonvertebral fractures, although this difference did not reach significance because of the small number of fractures. Bone mineral density was higher and bone-turnover markers were lower in the men who received zoledronic acid (P<0.05 for both comparisons). Results were similar in men with low serum levels of total testosterone. The zoledronic acid and placebo groups did not differ significantly with respect to the incidence of death (2.6% and 2.9%, respectively) or serious adverse events (25.3% and 25.2%). CONCLUSIONS: Zoledronic acid treatment was associated with a significantly reduced risk of vertebral fracture among men with osteoporosis. (Funded by Novartis Pharma; ClinicalTrials.gov number, NCT00439647.).

Crises as a disease of the body politick: a metaphor in the history of nineteenth century economics

This paper examines the use of the medical metaphor in the early theories of crises. It first considers the borrowing of medical terminology and generic references to disease which, notwithstanding their relatively trivial character, illustrate how crises were originally conceived as disturbances (often of a political nature) to a naturally healthy system. Then it shows how a more specific metaphor, the fever of speculation, shifted the emphasis by treating prosperity as the diseased phase, to which crises are a remedy. The metaphor of the epidemic spreading of the disease introduced the theme of the cumulative character of both upswing and downswing, while the similitude with intermittent fevers accounted for the recurring nature of crises. Finally, the paper examines how the medical reflections on the causality of diseases contributed to the epistemology of crises theory, and reflects on the metaphisical shift accompanying the transition from the theories of crises to the theories of cycles.

Whole-Body Vibration Training Elevates Creatine-Kinase Levels in Sedentary Subjects

METHODS: 20 inactive (10 male, 10 female) underwent a single typical WBV session, with a total of 27 minutes of exercise on an oscillating platform at 26 Hz, involving upper and lower body muscles. Each exercise lasted 90 seconds, with 40 seconds pauses inbetween. Muscle enzymes (CK, transaminase, LDH, troponin I) were measured before, at 24, 48 and 96 hours post exercise. Lactate was measured immediately after the session. Muscle aches were assessed during 4 days post-exercise.RESULTS: Subjects' mean age was 23.0 ± 3.5 (male), 22.4 ± 1.4 (female), BMI 22.8 ± 2.3 and 22.1 ± 1.9, and all had been inactive for at least 12 months. Post exercise lactatemia was 10.0 ± 2.4 and 6.9 ± 2.4. CK elevation was significant (at least doubling of baseline values) in 1 male and 4 female subjects, while they remained at baseline values for the remaining 15 subjects. One female subject peaked at 3520 U/l at 96 hours post exercise, and all but one peaked at the same late time. Troponin and CK-MB never increased. No correlation was found between muscle soreness and CK levels.CONCLUSIONS: WBV can elicit important anaerobic processes reflected by the high lactacidemia, and CK elevation was significant in 25 % of subjects, peaking at the fourth day after exercise for 80 % of those. Such exercises should not be regarded as trivial and "easy" as they are advertised, since they can provoke important anaerobia and CK elevation. Many fragile patients or patients treated for cardiovascular disease could benefit from WBV but it is important to recognise these potential effects, especially in those treated with statins, known to cause a myopathy and CK elevation. Before considering a side effect of an important therapeutic agent, doctors should be aware of the possible interaction with not-so-harmless exercising machines.

KnotProt: a database of proteins with knots and slipknots.

The protein topology database KnotProt, http://knotprot.cent.uw.edu.pl/, collects information about protein structures with open polypeptide chains forming knots or slipknots. The knotting complexity of the cataloged proteins is presented in the form of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of its subchains. The pattern visible in the matrix gives the knotting fingerprint of a given protein and permits users to determine, for example, the minimal length of the knotted regions (knot's core size) or the depth of a knot, i.e. how many amino acids can be removed from either end of the cataloged protein structure before converting it from a knot to a different type of knot. In addition, the database presents extensive information about the biological functions, families and fold types of proteins with non-trivial knotting. As an additional feature, the KnotProt database enables users to submit protein or polymer chains and generate their knotting fingerprints.

Electoral Platforms, Implemented Policies, and Abstention

Recent studies of American politics evidence that political polarization of both the electorate and the political elite have moved 'almost in tandem for the past half century' (McCarty et al., 2003, p.2), and that party polarization has steadily increased since the 1970s. On the other hand, the empirical literature on party platforms and implemented policies has consistently found an imperfect but nonnegligible correlation between electoral platforms and governmental policies: while platforms tend to be polarized, policies are moderate or centrist. However, existing theoretical models of political competition are not manifestly compatible with these observations. In this paper, we distinguish between electoral platforms and implemented policies by incorporating a non-trivial policy-setting process. It follows that voters may care not only about the implemented policy but also about the platform they support with their vote. We find that while parties tend to polarize their positions, the risk of alienating their constituency prevents them from radicalizing. The analysis evidences that the distribution of the electorate, and not only the (expected) location of a pivotal voter, matters in determining policies. Our results are consistent with the observation of polarized platforms and moderate policies, and the alienation and indifference components of abstention.

Postoperative delirium. Part 1: pathophysiology and risk factors.

Delirium presents clinically with differing subtypes ranging from hyperactive to hypoactive. The clinical presentation is not clearly linked to specific pathophysiological mechanisms. Nevertheless, there seem to be different mechanisms that lead to delirium; for example the mechanisms leading to alcohol-withdrawal delirium are different from those responsible for postoperative delirium. In many forms of delirium, the brain's reaction to a peripheral inflammatory process is considered to be a pathophysiological key element and the aged brain seems to react more markedly to a peripheral inflammatory stimulus than a younger brain. The effects of inflammatory mediators on the brain include changes in neurotransmission and apoptosis. On a neurotransmitter level, impaired cholinergic transmission and disturbances of the intricate interactions between dopamine, serotonin and acetylcholine seem to play an important role in the development of delirium. The risk factors for delirium are categorised as predisposing or precipitating factors. In the presence of many predisposing factors, even trivial precipitating factors may trigger delirium, whereas in patients without or with only a few predisposing factors, a major precipitating insult is necessary to trigger delirium. Well documented predisposing factors are age, medical comorbidities, cognitive, functional, visual and hearing impairment and institutional residence. Important precipitating factors apart from surgery are admission to an ICU, anticholinergic drugs, alcohol or drug withdrawal, infections, iatrogenic complications, metabolic derangements and pain. Scores to predict the risk of delirium based on four or five risk factors have been validated in surgical patients.

Real wage rigidities and the new Keynesian model

Most central banks perceive a trade-off between stabilizing inflation and stabilizing the gap between output and desired output. However, the standard new Keynesian framework implies no such trade-off. In that framework, stabilizing inflation is equivalent to stabilizing the welfare-relevant output gap. In this paper, we argue that this property of the new Keynesian framework, which we call the divine coincidence, is due to a special feature of the model: the absence of non trivial real imperfections.We focus on one such real imperfection, namely, real wage rigidities. When the baseline new Keynesian model is extended to allow for real wage rigidities, the divine coincidence disappears, and central banks indeed face a trade-off between stabilizing inflation and stabilizing the welfare-relevant output gap. We show that not only does the extended model have more realistic normative implications, but it also has appealing positive properties. In particular, it provides a natural interpretation for the dynamic inflation-unemployment relation found in the data.

Electoral platforms, implemented policies and abstention

Recent studies of American politics evidence that political polarization of both the electorate and the political elite have moved 'almost in tandem for the past half century' (McCarty et al., 2003, p.2), and that party polarization has steadily increased since the 1970s. On the other hand, the empirical literature on party platforms and implemented policies has consistently found an imperfect but nonnegligible correlation between electoral platforms and governmental policies: while platforms tend to be polarized, policies are moderate or centrist. However, existing theoretical models of political competition are not manifestly compatible with these observations.In this paper, we distinguish between electoral platforms and implemented policies by incorporating a non-trivial policy-setting process. It follows that voters may care not only about the implemented policy but also about the platform they support with their vote. We find that while parties tend to polarize their positions, the risk of alienating their constituency prevents them from radicalizing. The analysis evidences that the distribution of the electorate, and not only the (expected) location of a pivotal voter, matters in determining policies. Our results are consistent with the observation of polarized platforms and moderate policies, and the alienation and indifference components of abstention.

Convergence in panel data: Evidence from the skipping estimation

This paper demonstrates that, unlike what the conventional wisdom says, measurement error biases in panel data estimation of convergence using OLS with fixed effects are huge, not trivial. It does so by way of the "skipping estimation"': taking data from every m years of the sample (where m is an integer greater than or equal to 2), as opposed to every single year. It is shown that the estimated speed of convergence from the OLS with fixed effects is biased upwards by as much as 7 to 15%.

Data-based approach for developing a physical activity frequency questionnaire.

Measurement of total energy expenditure may be crucial to an understanding of the relation between physical activity and disease and in order to frame public health intervention. To devise a self-administered physical activity frequency questionnaire (PAFQ), the following data-based approach was used. A 24-hour recall was administered to a random sample of 919 adult residents of Geneva, Switzerland. The data obtained were used to establish the list of activities (and their median duration) that contributed to 95% of the energy expended, separately for men and women. Activities that were trivial for the whole sample but that contributed to > or = 10% of an individual's energy expenditure were also selected. The final PAFQ lists 70 activities or group of activities with their typical duration. About 20 minutes are required for respondents to indicate the number of days and the number of hours per day that they performed each activity. The PAFQ method was validated against a heart rate monitor, a more objective method. The total energy estimated by the PAFQ in 41 volunteers correlated well (r = 0.76) with estimates using a heart rate monitor. The authors conclude that the design of their self-administered physical activity frequency questionnaire based on data from 24-hour recall appeared to accurately estimate energy expenditure.

Conglomeration with bankruptcy costs: Separate or joint financing?

The paper analyzes the determinants of the optimal scope of incorporation in the presenceof bankruptcy costs. Bankruptcy costs alone generate a non-trivial tradeoff between thebenefit of coinsurance and the cost of risk contamination associated to joint financing corporate projects through debt. This tradeoff is characterized for projects with binary returns,depending on the distributional characteristics of returns (mean, variability, skewness, heterogeneity, correlation, and number of projects), the bankruptcy recovery rate, and the taxrate advantage of debt relative to equity. Our testable predictions are broadly consistentwith existing empirical evidence on conglomerate mergers, spin-offs, project finance, andsecuritization.

Modeling complex wells with the multi-scale finite-volume method

In this paper, an extension of the multi-scale finite-volume (MSFV) method is devised, which allows to Simulate flow and transport in reservoirs with complex well configurations. The new framework fits nicely into the data Structure of the original MSFV method,and has the important property that large patches covering the whole well are not required. For each well. an additional degree of freedom is introduced. While the treatment of pressure-constraint wells is trivial (the well-bore reference pressure is explicitly specified), additional equations have to be solved to obtain the unknown well-bore pressure of rate-constraint wells. Numerical Simulations of test cases with multiple complex wells demonstrate the ability of the new algorithm to capture the interference between the various wells and the reservoir accurately. (c) 2008 Elsevier Inc. All rights reserved.