Validation and Analysis of Numerical Methods for Solving Fractional-Order Differential Equations

Fractional-order differential equations have been very effective in modeling the behavior of various phenomena that have been otherwise difficult to accurately simulate. A new class of predictor-corrector schemes for solving nonlinear fractional-order differential equations has been proposed with claims of both increased accuracy and decreased computational cost. The purpose of this research is to test and attempt to validate these claims through both an independent replication of the results reported for the new method, as well as a comparison against the performance of an existing standard. Additionally, an operational software package that implements this new method will result as a byproduct of this research. Independent simulations are run for this new method, and compared against the findings of this new method’s author. This research is broken down into three main areas of interest: (1) Independently develop software for the newly proposed and existing methods, (2) Conduct an error analysis on the methods’ order of accuracy, and (3) Conduct a computational cost analysis of the two methods in their pure form. This research has successfully created a tool for solving fractional-order differential equations with greater accuracy than the existing method, with replicated findings in regard to order of accuracy. The claims of decreased computational cost were neither confirmed or disproved, and require further study. The results of this research have not only increased the validity and usage-case understanding of the newly proposed method, but also raised new areas for future work with respect to optimization and run speed

Validation and Analysis of Numerical Methods for Solving Fractional-Order Differential Equations

Fractional-order differential equations have been very effective in modeling the behavior of various phenomena that have been otherwise difficult to accurately simulate. A new class of predictor-corrector schemes for solving nonlinear fractional-order differential equations has been proposed with claims of both increased accuracy and decreased computational cost. The purpose of this research is to test and attempt to validate these claims through both an independent replication of the results reported for the new method, as well as a comparison against the performance of an existing standard. Additionally, an operational software package that implements this new method will result as a byproduct of this research. Independent simulations are run for this new method, and compared against the findings of this new method’s author. This research is broken down into three main areas of interest: (1) Independently develop software for the newly proposed and existing methods, (2) Conduct an error analysis on the methods’ order of accuracy, and (3) Conduct a computational cost analysis of the two methods in their pure form. This research has successfully created a tool for solving fractional-order differential equations with greater accuracy than the existing method, with replicated findings in regard to order of accuracy. The claims of decreased computational cost were neither confirmed or disproved, and require further study. The results of this research have not only increased the validity and usage-case understanding of the newly proposed method, but also raised new areas for future work with respect to optimization and run speed

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Procalcitonin Is Not a Reliable Biomarker of Bacterial Coinfection in People With Coronavirus Disease 2019 Undergoing Microbiological Investigation at the Time of Hospital Admission

Abstract Admission procalcitonin measurements and microbiology results were available for 1040 hospitalized adults with coronavirus disease 2019 (from 48 902 included in the International Severe Acute Respiratory and Emerging Infections Consortium World Health Organization Clinical Characterisation Protocol UK study). Although procalcitonin was higher in bacterial coinfection, this was neither clinically significant (median [IQR], 0.33 [0.11–1.70] ng/mL vs 0.24 [0.10–0.90] ng/mL) nor diagnostically useful (area under the receiver operating characteristic curve, 0.56 [95% confidence interval, .51–.60]).</jats:p

Implementation of corticosteroids in treating COVID-19 in the ISARIC WHO Clinical Characterisation Protocol UK:prospective observational cohort study

BACKGROUND: Dexamethasone was the first intervention proven to reduce mortality in patients with COVID-19 being treated in hospital. We aimed to evaluate the adoption of corticosteroids in the treatment of COVID-19 in the UK after the RECOVERY trial publication on June 16, 2020, and to identify discrepancies in care. METHODS: We did an audit of clinical implementation of corticosteroids in a prospective, observational, cohort study in 237 UK acute care hospitals between March 16, 2020, and April 14, 2021, restricted to patients aged 18 years or older with proven or high likelihood of COVID-19, who received supplementary oxygen. The primary outcome was administration of dexamethasone, prednisolone, hydrocortisone, or methylprednisolone. This study is registered with ISRCTN, ISRCTN66726260. FINDINGS: Between June 17, 2020, and April 14, 2021, 47 795 (75·2%) of 63 525 of patients on supplementary oxygen received corticosteroids, higher among patients requiring critical care than in those who received ward care (11 185 [86·6%] of 12 909 vs 36 415 [72·4%] of 50 278). Patients 50 years or older were significantly less likely to receive corticosteroids than those younger than 50 years (adjusted odds ratio 0·79 [95% CI 0·70–0·89], p=0·0001, for 70–79 years; 0·52 [0·46–0·58], p80 years), independent of patient demographics and illness severity. 84 (54·2%) of 155 pregnant women received corticosteroids. Rates of corticosteroid administration increased from 27·5% in the week before June 16, 2020, to 75–80% in January, 2021. INTERPRETATION: Implementation of corticosteroids into clinical practice in the UK for patients with COVID-19 has been successful, but not universal. Patients older than 70 years, independent of illness severity, chronic neurological disease, and dementia, were less likely to receive corticosteroids than those who were younger, as were pregnant women. This could reflect appropriate clinical decision making, but the possibility of inequitable access to life-saving care should be considered. FUNDING: UK National Institute for Health Research and UK Medical Research Council

Dissecting the Shared Genetic Architecture of Suicide Attempt, Psychiatric Disorders, and Known Risk Factors

Background Suicide is a leading cause of death worldwide, and nonfatal suicide attempts, which occur far more frequently, are a major source of disability and social and economic burden. Both have substantial genetic etiology, which is partially shared and partially distinct from that of related psychiatric disorders. Methods We conducted a genome-wide association study (GWAS) of 29,782 suicide attempt (SA) cases and 519,961 controls in the International Suicide Genetics Consortium (ISGC). The GWAS of SA was conditioned on psychiatric disorders using GWAS summary statistics via multitrait-based conditional and joint analysis, to remove genetic effects on SA mediated by psychiatric disorders. We investigated the shared and divergent genetic architectures of SA, psychiatric disorders, and other known risk factors. Results Two loci reached genome-wide significance for SA: the major histocompatibility complex and an intergenic locus on chromosome 7, the latter of which remained associated with SA after conditioning on psychiatric disorders and replicated in an independent cohort from the Million Veteran Program. This locus has been implicated in risk-taking behavior, smoking, and insomnia. SA showed strong genetic correlation with psychiatric disorders, particularly major depression, and also with smoking, pain, risk-taking behavior, sleep disturbances, lower educational attainment, reproductive traits, lower socioeconomic status, and poorer general health. After conditioning on psychiatric disorders, the genetic correlations between SA and psychiatric disorders decreased, whereas those with nonpsychiatric traits remained largely unchanged. Conclusions Our results identify a risk locus that contributes more strongly to SA than other phenotypes and suggest a shared underlying biology between SA and known risk factors that is not mediated by psychiatric disorders.Peer reviewe

The Science Performance of JWST as Characterized in Commissioning

This paper characterizes the actual science performance of the James Webb Space Telescope (JWST), as determined from the six month commissioning period. We summarize the performance of the spacecraft, telescope, science instruments, and ground system, with an emphasis on differences from pre-launch expectations. Commissioning has made clear that JWST is fully capable of achieving the discoveries for which it was built. Moreover, almost across the board, the science performance of JWST is better than expected; in most cases, JWST will go deeper faster than expected. The telescope and instrument suite have demonstrated the sensitivity, stability, image quality, and spectral range that are necessary to transform our understanding of the cosmos through observations spanning from near-earth asteroids to the most distant galaxies.Comment: 5th version as accepted to PASP; 31 pages, 18 figures; https://iopscience.iop.org/article/10.1088/1538-3873/acb29

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Background: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. Methods: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). Findings: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29–146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0– 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25–1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39–1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65–1·60]; p=0·92). Interpretation: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Background: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. Methods: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). Findings: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29–146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0– 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25–1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39–1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65–1·60]; p=0·92). Interpretation: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention