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The paper expands the finite difference method to the complex plane, and thus obtains an improvement in the resolution of differential equations with an increase in numerical precision and a generalization in the mathematical modeling of problems. The article begins with a selection of the best techniques for obtaining finite difference coefficients for approximating derivatives in the real domain. Then, the calculation is expanded to the complex domain. The research expands forward, backward, and central difference approximations of the real case by a quadrant approximation in the complex plane, which facilitates the use in boundary conditions of differential equations. The article shows many real and complex finite difference equations with their respective order of error, intended to serve as a basis and reference, which have been tested in practical examples of solving differential equations used in engineering. Finally, a comparison is made between the real and complex techniques of finite difference methods applied in the Theory of Elasticity. As a surprising result, the article shows that the finite difference method has great advantages in numerical precision, diversity of formulas, and modeling generalities in the complex domain when compared to the real domain. [ABSTRACT FROM AUTHOR]

Introduction: There remains a dearth of knowledge concerning the phenomenology of suicidal thoughts, with research focusing on reasons for feeling suicidal rather than their mental expression. While clinical interviews remain the standard phenomenological approach, such exploration of lived experiences may prove challenging for this sensitive topic. As a complementary alternative, the use of naturally-occurring online data is opportune for capturing elaborations on tabooed phenomena. Methods: In this phenomenological study, we present a thematic analysis on lived experiences of suicidal thoughts as spontaneously reported by nonidentified users of a Reddit online board (r/Depression), collecting 668 posts using the search terms "suicidal ideation," "suicidal thoughts," and "suicide." Codes were grouped into descriptive categories summarizing the properties of thoughts, their effects, and their relation to suicide. Then, an interpretative synthesis yielded global themes connecting salient meanings on the experience of suicidal thoughts. Results: With a long-term and recurring nature, thoughts of suicide appear in the form of vivid imagery and daydreaming's, initially bringing relief to adverse feelings but eventually becoming conditioned and all-consuming. Rather than a wonderment, they are experienced as intrusive thoughts by people struggling to make meaning of their occurrence. When conciliating the presence of unwanted thoughts, users express intricate relations to wishing or not to die, as well as varying perceptions of control over actions or fear of suicidal behavior. Discussion: With an innovative application of big qualitative data into phenomenological analysis, this study contributes to an initial characterization of suicidal thoughts, uncovering findings that are not contemplated into current conceptualizations of suicidality. The analysis is limited by a restricted context of posts and unknown demographics, and further research with clinical interviews is warranted for in-depth exploration of suicidal thoughts. [ABSTRACT FROM AUTHOR]

This study examined whether sleep disturbance predicted or moderated responses to psychotherapy in participants who participated in STEP-BD, a national, multisite study that examined the effectiveness of different treatment combinations for bipolar disorder. Participants received either a brief psychosocial intervention called collaborative care (CC; n = 130) or intensive psychotherapy (IP; n = 163), with study-based pharmacotherapy. Participants (N = 243) were defined as current (past week) short sleepers (

The aim of this study was to verify the accuracy of predicting oxygen consumption (O2) in predominantly aerobic activities based on net heart rate (netHR), sex, and body mass index (BMI) in active adults. NetHR is the value of the difference between the resting HR (HRrest) and the average HR value obtained during a given session or period of physical activity. These activities must be continuous, submaximal, and of a stabilized intensity. The magnitude of the netHR depends mainly on the intensity of the exercise. The HR is measured in beats per minute (bpm). A total of 156 participants, 52 women and 104 men, between the ages of 18 and 81, had their netHR and net oxygen intake (netVO2) assessed. There were 79 participants in group 1 (prediction sample) (52 males and 27 females). There were 77 people in group 2 (validation sample) (52 males and 25 females). The results of the multiple linear regression showed that netVO2 (R2 = 85.2%, SEE = 3.38) could be significantly predicted by sex (p < 0.001), netHR (p < 0.001), and BMI (p < 0.001). The Bland–Altman plots satisfied the agreement requirements, and the comparison of the measured and estimated netVO2 revealed non-significant differences with a trivial effect size. We calculated the formula NetVO2 (mL/(kg·min)) = 16 + 3.67 (sex) + 0.27 (netHR) − 0.57 (BMI) to predict netVO2, where netVO2 is the amount of oxygen uptake (mL/(kg·min)) above the resting value, netHR is the heart rate (beats per minute) above the resting value measured during exercise, sex is equal to zero for women and one for men, and BMI is the body mass index. In addition, based on the knowledge of VO2, it was possible to estimate the energy expenditure from a particular training session, and to determine or prescribe the exercise intensity in MET (metabolic equivalent of task). [ABSTRACT FROM AUTHOR]

ObjectiveAt least 50% of individuals with bipolar disorder have a lifetime anxiety disorder. Individuals with both bipolar disorder and a co-occurring anxiety disorder experience longer illness duration, greater illness severity, and poorer treatment response. The study explored whether comorbid lifetime anxiety in bipolar patients moderates psychotherapy treatment outcome.MethodIn the Systematic Treatment Enhancement Program randomized controlled trial of psychotherapy for bipolar depression, participants received up to 30 sessions of intensive psychotherapy (family-focused therapy, interpersonal and social rhythm therapy, or cognitive-behavioral therapy) or collaborative care, a three-session comparison treatment, plus pharmacotherapy. Using the number needed to treat, we computed effect sizes to analyze the relationship between lifetime anxiety disorders and rates of recovery across treatment groups after 1 year.ResultsA total of 269 patients (113 women) with a comorbid lifetime anxiety disorder (N=177) or without a comorbid lifetime anxiety disorder (N=92) were included in the analysis. Participants with a lifetime anxiety disorder were more likely to recover with psychotherapy than with collaborative care (66% compared with 49% recovered over 1 year; number needed to treat=5.88, small to medium effect). For patients without a lifetime anxiety disorder, there was no difference between rates of recovery in psychotherapy compared with collaborative care (64% compared with 62% recovered; number needed to treat=50, small effect). Participants with one lifetime anxiety disorder were likely to benefit from intensive psychotherapy compared with collaborative care (84% compared with 53% recovered; number needed to treat=3.22, medium to large effect), whereas patients with multiple anxiety disorders exhibited no difference in response to the two treatments (54% compared with 46% recovered; number needed to treat=12.5, small effect).ConclusionsDepressed patients with bipolar disorder and comorbid anxiety may be in particular need of additional psychotherapy for treating acute depression. These results need to be replicated in studies that stratify bipolar patients to treatments based on their anxiety comorbidity status.

Background: Tobacco use accelerates atherosclerosis and is one of the predictors of death from ischemic heart disease, arrhythmias, heart failure, and sudden death. A new non-invasive parameter, the Index of Cardiac Electrophysiological Balance (iCEB) between depolarization and repolarization of the action potential, was considered a new biomarker for the identification of patients at increased arrhythmic risk. Objectives: We aimed to evaluate the iCEB in apparently healthy Angolans with habitual cigarette smoking compared to non-smokers. Subjects and methods: Data were obtained from the CardioBengo study, a cross-sectional community-based study in which a random sample of individuals aged between 15 and 84 years was selected. In total, 214 apparently healthy subjects, 102 smokers, and 112 non-smokers in the same age group were included in the final analysis. Results: The average age of the participants was 42.17±13.04 years old and 26.6% of the sample was female. Smoking subjects had higher iCEB and corrected Index of Cardiac Electrophysiological Balance (iCEBc) values compared with non-smoking controls (4.39 vs. 4.25; p=0.024, respectively), and (4.74 vs. 4.57; p=0.030, respectively). Conclusions: In summary, iCEB and iCEBc were significantly higher in habitual smokers than in nonsmokers, which represents an increased risk of ventricular arrhythmogenesis in healthy habitual smokers. To the best of our knowledge, this is the first study performed in Africa to evaluate iCEB in smokers, making this type of study very important in low- and middle-income countries in the context of epidemiological transition. [ABSTRACT FROM AUTHOR]