Weierstrass integrability of differential equations

The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define {\it Weierstrass integrability} and we determine which Weierstrass integrable systems are Liouvillian integrable. Inside this new class of integrable systems there are non--Liouvillian integrable systems.

Predicción de la resistencia al flujo en ríos de montaña

Se han calibrado, validado y comparado tres modelos de resistencia al flujo de contorno granular: un modelo potencial y otros dos modelos desarrollados para condiciones de alta rugosidad relativa (uno basado en una modificación de la ley logarítmica de Prandtl-von Karman y otro fundamentado en un perfil de velocidad configurado en dos zonas: una uniforme en las proximidades de los elementos de rugosidad y otra superior que sigue una distribución logarítmica). Se ha empleado para ello un numeroso conjunto de 1.533 datos tomados en ríos y en canales de laboratorio, representativo de un amplio intervalo hidráulico y geomorfológico en el ámbito de ríos de grava y de montaña. Han resultado preferibles las ecuaciones ajustadas con los percentiles granulométricos mayores (d90 o d84) que las ajustadas con el diámetro mediano (d50), debido a la mayor capacidad explicativa alcanzada dado un modelo, la menor diferencia en la bondad de ajuste entre los diferentes modelos y la menor influencia del origen de los datos (río o canal de laboratorio). Las ecuaciones ajustadas de acuerdo con los modelos en donde se contemplan condiciones de alta rugosidad relativa presentan predicciones similares, exceptuando el intervalo macrorrugoso (y/d90 < 1), en el que es preferible la correspondiente al modelo fundamentado en el perfil de velocidad configurado en dos zonas. Se recomienda restringir la aplicación de la ecuación ajustada con arreglo a la ley potencial al intervalo de y/d90 comprendido entre uno y veinte, puesto que fuera de dicho intervalo tiende a infraestimar notablemente la resistencia al flujo.

Increased risk of cardiovascular disease (CVD) with age in HIV-positive men : a comparison of the D:A:D CVD risk equation and general population CVD risk equations

OBJECTIVES: The aim of the study was to statistically model the relative increased risk of cardiovascular disease (CVD) per year older in Data collection on Adverse events of anti-HIV Drugs (D:A:D) and to compare this with the relative increased risk of CVD per year older in general population risk equations. METHODS: We analysed three endpoints: myocardial infarction (MI), coronary heart disease (CHD: MI or invasive coronary procedure) and CVD (CHD or stroke). We fitted a number of parametric age effects, adjusting for known risk factors and antiretroviral therapy (ART) use. The best-fitting age effect was determined using the Akaike information criterion. We compared the ageing effect from D:A:D with that from the general population risk equations: the Framingham Heart Study, CUORE and ASSIGN risk scores. RESULTS: A total of 24 323 men were included in analyses. Crude MI, CHD and CVD event rates per 1000 person-years increased from 2.29, 3.11 and 3.65 in those aged 40-45 years to 6.53, 11.91 and 15.89 in those aged 60-65 years, respectively. The best-fitting models included inverse age for MI and age + age(2) for CHD and CVD. In D:A:D there was a slowly accelerating increased risk of CHD and CVD per year older, which appeared to be only modest yet was consistently raised compared with the risk in the general population. The relative risk of MI with age was not different between D:A:D and the general population. CONCLUSIONS: We found only limited evidence of accelerating increased risk of CVD with age in D:A:D compared with the general population. The absolute risk of CVD associated with HIV infection remains uncertain.

Increased risks of early sexual initiators: time makes a difference

BACKGROUND: Years since onset of sexual intercourse (YSSI) is a rarely used variable when studying adolescents- sexual outcomes. The aim of this study is to evaluate the influence of YSSI on the adverse sexual outcomes of early sexual initiators. METHODS: Data were drawn from the 2002 Swiss Multicenter Adolescent Survey on Health database, a nationally representative cross-sectional survey including 7429 adolescents in post mandatory school aged 16-20 years. Only adolescents reporting sexual intercourse (SI) were included (N=4388; 45% females) and divided by age of onset of SI (early initiators, age<16: N=1469, 44% females; and late initiators, age≥16: N=2919, 46% females). Analyses were done separately by gender. Groups were compared for personal characteristics at the bivariate level. We analyzed three sexual outcomes (≥4 sexual partners, pregnancy and non-use of condom at last SI) controlling for all significant personal variables with two logistic regressions first using age, then YSSI as one of the confounding variables. Results are given as adjusted odds ratios (aOR) using lSI as the reference category. RESULTS: After adjusting for YSSI instead of age, negative sexual outcomes among early initiators were no longer significant, except for multiple sexual partners among females, although at a much lower level. Early initiators were less likely to report non-use of condom at last SI when adjusting for YSSI (females: aOR=0.59 [0.44-0.79]; p<0.001; males aOR=0.71 [0.50-1.00]; p=0.053). CONCLUSION: YSSI is an important explanatory variable when studying adolescents- sexuality and needs to be included in future research on adolescents- sexual health.

Est-ce qu'en discuter fait la différence ? Opinions de jeunes adultes atteints de maladies chroniques après avoir été transférés vers des soins pour adultes [Does talking about it make a difference? Opinions of chronically ill young adults after being transferred to adult care].

1) Introduction: pour les jeunes souffrant de maladie chronique, l'objectif de la transition vers les soins pour adultes est d'optimiser leur fonctionnement et leur potentiel. Le but de cette étude pilote était d'évaluer si les jeunes adultes souffrant de maladie chronique jugeaient que le passage vers les soins adultes était plus facile lorsque la question de la transition avait été discutée au préalable avec leur pédiatre. 2) Matériel et méthodes: deux groupes de jeunes adultes atteints de maladie chronique ont été identifiés selon l'existence (n = 70) ou non (n = 22) d'une discussion préalable avec leur pédiatre à propos de la transition vers une prise en charge pour adultes. Ces deux groupes ont été comparés pour des variables démographiques et de santé. Les variables significatives en analyse bivariée ont été incluses dans une régression logistique descendante pas à pas. 3) Résultats: les jeunes adultes qui avaient discuté de la transition étaient significativement plus nombreux à se sentir prêts (72,9 % vs 45,5 %) et accompagnés (58,6 % vs 27,3 %) pour le transfert, à avoir consulté leur spécialiste pour adultes (60 % vs 31,8 %) et à voir leur médecin sans la présence de leurs parents (70 % vs 40,9 %). En analyse multivariée, seuls, le fait de se sentir accompagné (odds ratio ajustée [ORa] : 3,56) et celui d'avoir consulté leur spécialiste pour adultes (ORa : 4,14) étaient significatifs. 4) Conclusions: la préparation des jeunes souffrant de maladie chronique au transfert vers les soins pour adultes semble bénéfique. Cependant, le transfert lui-même n'est qu'une petite partie du concept beaucoup plus large de la transition vers la vie adulte. Une transition bien planifiée doit permettre à ces jeunes adultes d'atteindre tout leur potentiel. INTRODUCTION: The goal of transition in healthcare for young people with chronic illnesses is to maximize their functioning and potential. The purpose of this pilot study was to assess whether young adults with chronic illnesses found that the transition to adult care was easier when the transition was discussed in advance with their pediatric specialist. METHODS: Two groups were created according to whether patients had discussed (n=70) or not (n=22) the transition with their pediatric specialist and compared regarding demographic and health-related variables. All the significant variables at the bivariate level were included in a backward stepwise logistic regression. RESULTS: Youth who had discussed the transition were significantly more likely to feel ready for the transfer (72.9% vs 45.5%) and accompanied (58.6% vs 27. %) during transfer, to have consulted their specialist for adults (60.0% vs 31.8%), and seen their doctor without the presence of their parents (70.0% vs 40.9%). At the multivariate level, only feeling accompanied during transfer (adjusted odds ratio (aOR): 3.56) and having consulted their specialist for adults (aOR: 4.14) remained significant. CONCLUSIONS: Preparing chronically ill youths for transfer to adult care appears to be beneficial for them. However, transfer is only a small part of the much broader transition that is preparation for adult life. A well-planned transition should allow these young people to reach their full potential.

Renewal equations for option pricing

In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

Langevin equations with multiplicative noise: Application to domain growth

Langevin Equations of Ginzburg-Landau form, with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hiliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical predictions of the linear analysis. We also present simulation results for spinodal decomposition at large times.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Anticipating linear stochastic differential equations driven by a Lévy process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformations on Wiener space and developped by Buckdahn [7] to the canonical Lévy space, which is introduced in [25].

Mergers and difference-in-difference estimator : why firms do not increase prices?

Difference-in-Difference (DiD) methods are being increasingly used to analyze the impact of mergers on pricing and other market equilibrium outcomes. Using evidence from an exogenous merger between two retail gasoline companies in a specific market in Spain, this paper shows how concentration did not lead to a price increase. In fact, the conjectural variation model concludes that the existence of a collusive agreement before and after the merger accounts for this result, rather than the existence of efficient gains. This result may explain empirical evidence reported in the literature according to which mergers between firms do not have significant effects on prices.

The difference of disease perception by juvenile idiopathic arthritis patients and their parents : analysis of the JAMAR questionnaire.

BACKGROUND: The JAMAR (Juvenile Arthritis Multidimensional Assessment Report) has been developed to evaluate the perception of the patient and his parents on different items: well-being, pain, functional status, quality of life, disease activity, disease course, side effects of medication, therapeutic compliance and satisfaction with illness outcome. Our aim was to compare disease's perception by JIA patients and their parents. METHODS: We included into the study 100 consecutive patients over 7 years of age. We asked both parent and child to complete the JAMAR questionnaire. For each patient we recorded demographic and disease related data. We examined the level of disagreement between children and parents for the quantitative items of the JAMAR: VAS Pain, VAS Disease Activity, VAS Well Being, Juvenile Arthritis Functional Score, HRQoL. Then we looked for a relation between discordance-rate and demographic and clinical variables. RESULTS: Children and parents' median scores for all five items were similar. Individual dyads agreement was low, with a large amount of pairs (80) discordant for at least one item. We found higher MD VAS and JADAS in more discordant dyads, suggesting that when the disease is more active discordance between child and parent increase. CONCLUSION: The JAMAR questionnaire is an important tool that helps clinicians to detect divergent child and parent's disease perceptions. It is essential that both patients and parents fill the JAMAR questionnaire for a complete clinical and psychosocial evaluation.

Equating accelerometer estimates among youth: The Rosetta Stone 2.

OBJECTIVES: Different accelerometer cutpoints used by different researchers often yields vastly different estimates of moderate-to-vigorous intensity physical activity (MVPA). This is recognized as cutpoint non-equivalence (CNE), which reduces the ability to accurately compare youth MVPA across studies. The objective of this research is to develop a cutpoint conversion system that standardizes minutes of MVPA for six different sets of published cutpoints. DESIGN: Secondary data analysis. METHODS: Data from the International Children's Accelerometer Database (ICAD; Spring 2014) consisting of 43,112 Actigraph accelerometer data files from 21 worldwide studies (children 3-18 years, 61.5% female) were used to develop prediction equations for six sets of published cutpoints. Linear and non-linear modeling, using a leave one out cross-validation technique, was employed to develop equations to convert MVPA from one set of cutpoints into another. Bland Altman plots illustrate the agreement between actual MVPA and predicted MVPA values. RESULTS: Across the total sample, mean MVPA ranged from 29.7MVPAmind(-1) (Puyau) to 126.1MVPAmind(-1) (Freedson 3 METs). Across conversion equations, median absolute percent error was 12.6% (range: 1.3 to 30.1) and the proportion of variance explained ranged from 66.7% to 99.8%. Mean difference for the best performing prediction equation (VC from EV) was -0.110mind(-1) (limits of agreement (LOA), -2.623 to 2.402). The mean difference for the worst performing prediction equation (FR3 from PY) was 34.76mind(-1) (LOA, -60.392 to 129.910). CONCLUSIONS: For six different sets of published cutpoints, the use of this equating system can assist individuals attempting to synthesize the growing body of literature on Actigraph, accelerometry-derived MVPA.

Estimativa da entalpia reticular de adutos (DM Hm o ) utilizando-se formas modificadas da equação de Kapustinskii

In this work are presented two modified forms of Kapustinskii equation that could be used to estimate the values of the lattice enthalphies for adducts: DM Hm o=(-n.z+ .z- .10(2)/D).(1-d*/D) .K and DM Hm o=(-n.z+ .z-.10(2)/d).(1-d*/d).K.d. Two new parameters related with steric effects and donor power of the ligands, J anddare introduced. The proposed equations were tested for 49 adducts (mainly from the zinc group halides). The difference between experimental (calorimetric) and calculated values (using the proposed equations) values are less than 5% for 41 of the tested adducts.