Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

AbstractA new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example

Comorbidity and Sex-Related Differences in Mortality in Oxygen-Dependent Chronic Obstructive Pulmonary Disease

Background: It is not known why survival differs between men and women in oxygen-dependent chronic obstructive pulmonary disease (COPD). The present study evaluates differences in comorbidity between men and women, and tests the hypothesis that comorbidity contributes to sex-related differences in mortality in oxygen-dependent COPD. Methods: National prospective study of patients aged 50 years or older, starting long-term oxygen therapy (LTOT) for COPD in Sweden between 1992 and 2008. Comorbidities were obtained from the Swedish Hospital Discharge Register. Sex-related differences in comorbidity were estimated using logistic regression, adjusting for age, smoking status and year of inclusion. The effect of comorbidity on overall mortality and the interaction between comorbidity and sex were evaluated using Cox regression, adjusting for age, sex, Pa O2 breathing air, FEV 1, smoking history and year of inclusion. Results: In total, 8,712 patients (55 % women) were included and 6,729 patients died during the study period. No patient was lost to follow-up. Compared with women, men had significantly more arrhythmia, cancer, ischemic heart disease and renal failure, and less hypertension, mental disorders, osteoporosis and rheumatoid arthritis (P,0.05 for all odds ratios). Comorbidity was an independent predictor of mortality, and the effect was similar for the sexes. Women had lower mortality, which remained unchanged even after adjusting for comorbidity; hazard ratio 0.73 (95 % confidence interval, 0.68–0.77; P,0.001)

Prevalence of unknown and untreated arrhythmias in an older outpatient population screened by wireless long-term recording ECG

Purpose: With longer life expectancies, the prevalence of arrhythmias is increasing; thus, there is a need for new methods to screen the older outpatient population. This population-based study describes the prevalence of arrhythmias in 200 outpatients aged ≥66 years. We also investigated the feasibility of wireless long-term recording (LTR) using the ECG-BodyKom®. Methods: Two hundred elderly persons aged 66–93 years were recruited from the Swedish National Study on Aging and Care in 2010–2013, and data were collected via wireless LTR ECG-BodyKom. Results: Screening with the LTR ECG revealed that persistent atrial fibrillation (AF) occurred in 10% of the outpatient population aged ≥66 years. Paroxysmal AF occurred in 5.5% of the population, with no difference between younger (60–80 years) and older (≥80 years) elderly participants. Furthermore, all patients with paroxysmal AF had a CHA2DS2VASc score of ≥2 and were therefore potential candidates for follow-up and medical examination. LTR ECG-BodyKom can be considered a feasible method to screen for arrhythmias in older outpatient populations. This simple method requires little of the user, and there was high satisfaction with the equipment and a good overall experience wearing it. Conclusion: The increasing occurrence of arrhythmias in the older population, as well as the high number of untreated cases of arrhythmias such as persistent AF and paroxysmal AF, poses a challenge for health care. Therefore, it is essential to develop effective strategies for their prevention and treatment

Prevalence and sex-related odds of comorbidity in patients starting long-term oxygen therapy for chronic obstructive pulmonary disease, 1992–2008.

<p>Percentages may not add up to 100 due to rounding.</p>*<p>Odds ratio adjusted for age, smoking history and year of starting long-term oxygen therapy.</p>†<p>Entities with significant sex-related difference in odds.</p

Prevalence and sex-related odds of Charlson score in patients starting long-term oxygen therapy for chronic obstructive pulmonary disease, 1992–2008.

<p>Percentages may not add up to 100 due to rounding.</p>*<p>Generalized ordered odds ratio adjusted for age, smoking history and year of inclusion. It is interpreted as the odds ratio of having a higher score than the present category.</p

Baseline characteristics of patients starting long-term oxygen therapy for chronic obstrucitve pulmonary disease, 1992–2008.

<p>Data presented as mean ± SD unless otherwise specified.</p><p><i>Definition of abbreviations:</i> FEV₁ = forced expiratory volume in one second; FVC = forced vital capacity; Pa_CO2 air = arterial blood gas tension of carbon dioxide while breathing ambient air; Pa_CO2 oxygen = arterial blood gas tension of carbon dioxide while breathing oxygen; Pa_O2 air = arterial blood gas tension of oxygen while breathing ambient air; Pa_O2 oxygen = arterial blood gas tension of oxygen while breathing oxygen.</p>*<p>Hospitalizations and in-hospital days within 5 years prior to starting LTOT, presented as median (first quartile – third quartile).</p

Cox regression of overall mortality in patients starting long-term oxygen therapy, 1992–2008.

<p><i>Definition of abbreviations:</i> FEV₁ = forced expiratory volume in one second; Pa_O2 air = arterial blood gas tension of oxygen while breathing ambient air.</p>*<p>Never smoking is used as reference category.</p>†<p>Charlson score 0 is used as reference category.</p

Cox regression of the effects of individual comorbidities on overall mortality.

*<p>Never smoking is used as reference category.</p

Relationships Between Frequency of Moderate Physical Activity and Longevity : An 11-Year Follow-up Study

Objectives: Moderate physical activity gains survival. There are, however, several variables that may affect this relationship. In this study, the relationship between moderate physical activity and longevity was investigated, taking into account age, gender, smoking habits, cohabitation status, body mass index, leg strength and balance, education level and cognitive function. Method: A sample of 8,456 individuals aged 60 to 96 years, representative of the Swedish population, was included. Participants were followed from 2004 to 2015. Cox regression analyses were used to investigate the predictive value of physical activity on longevity. Results: Participants still alive in the follow-up measure were more physically active on a moderate level. Being active 2 to 3 times a week or more was related to a 28% lower risk of not being alive at the follow-up measure. Discussion: The low frequency of physical activity, necessary for survival benefits should be considered in public health programs