Fractional differential equations and numerical methods

The increasing use of Fractional Calculus demands more accurate arid efficient methods for the numerical solution of fractional differential equations. We introduce the concepts of Fractional Calculus and give the definitions of fractional integrals and derivatives in the Riemann-Liouville and Caputo forms. We explore three existing Numerical Methods of solution of Fractional Differential Equations. 1. Diethelm's Backward Difference Form (BDF) method. 2. Lubich's Convolution Quadrature method. 3. Luchko and Diethelm's Operational Calculus (using the Mittag-Lefner function) method. We present useful recursive expressions we developed to compute the Taylor Series coefficients in the Operational Calculus method. These expressions are used in the calculation of the convolution and starting weights. We compare their accuracy and performance of the numerical methods, and conclude that the more complex methods produce the more accurate results

Long-Range Autocorrelations of CpG Islands in the Human Genome

In this paper, we use a statistical estimator developed in astrophysics to study the distribution and organization of features of the human genome. Using the human reference sequence we quantify the global distribution of CpG islands (CGI) in each chromosome and demonstrate that the organization of the CGI across a chromosome is non-random, exhibits surprisingly long range correlations (10 Mb) and varies significantly among chromosomes. These correlations of CGI summarize functional properties of the genome that are not captured when considering variation in any particular separate (and local) feature. The demonstration of the proposed methods to quantify the organization of CGI in the human genome forms the basis of future studies. The most illuminating of these will assess the potential impact on phenotypic variation of inter-individual variation in the organization of the functional features of the genome within and among chromosomes, and among individuals for particular chromosomes

Impact of opioid-free analgesia on pain severity and patient satisfaction after discharge from surgery: multispecialty, prospective cohort study in 25 countries

Background: Balancing opioid stewardship and the need for adequate analgesia following discharge after surgery is challenging. This study aimed to compare the outcomes for patients discharged with opioid versus opioid-free analgesia after common surgical procedures.Methods: This international, multicentre, prospective cohort study collected data from patients undergoing common acute and elective general surgical, urological, gynaecological, and orthopaedic procedures. The primary outcomes were patient-reported time in severe pain measured on a numerical analogue scale from 0 to 100% and patient-reported satisfaction with pain relief during the first week following discharge. Data were collected by in-hospital chart review and patient telephone interview 1 week after discharge.Results: The study recruited 4273 patients from 144 centres in 25 countries; 1311 patients (30.7%) were prescribed opioid analgesia at discharge. Patients reported being in severe pain for 10 (i.q.r. 1-30)% of the first week after discharge and rated satisfaction with analgesia as 90 (i.q.r. 80-100) of 100. After adjustment for confounders, opioid analgesia on discharge was independently associated with increased pain severity (risk ratio 1.52, 95% c.i. 1.31 to 1.76; P < 0.001) and re-presentation to healthcare providers owing to side-effects of medication (OR 2.38, 95% c.i. 1.36 to 4.17; P = 0.004), but not with satisfaction with analgesia (beta coefficient 0.92, 95% c.i. -1.52 to 3.36; P = 0.468) compared with opioid-free analgesia. Although opioid prescribing varied greatly between high-income and low- and middle-income countries, patient-reported outcomes did not.Conclusion: Opioid analgesia prescription on surgical discharge is associated with a higher risk of re-presentation owing to side-effects of medication and increased patient-reported pain, but not with changes in patient-reported satisfaction. Opioid-free discharge analgesia should be adopted routinely

Proceedings of the 3rd Biennial Conference of the Society for Implementation Research Collaboration (SIRC) 2015: advancing efficient methodologies through community partnerships and team science

It is well documented that the majority of adults, children and families in need of evidence-based behavioral health interventionsi do not receive them [1, 2] and that few robust empirically supported methods for implementing evidence-based practices (EBPs) exist. The Society for Implementation Research Collaboration (SIRC) represents a burgeoning effort to advance the innovation and rigor of implementation research and is uniquely focused on bringing together researchers and stakeholders committed to evaluating the implementation of complex evidence-based behavioral health interventions. Through its diverse activities and membership, SIRC aims to foster the promise of implementation research to better serve the behavioral health needs of the population by identifying rigorous, relevant, and efficient strategies that successfully transfer scientific evidence to clinical knowledge for use in real world settings [3]. SIRC began as a National Institute of Mental Health (NIMH)-funded conference series in 2010 (previously titled the “Seattle Implementation Research Conference”; $150,000 USD for 3 conferences in 2011, 2013, and 2015) with the recognition that there were multiple researchers and stakeholdersi working in parallel on innovative implementation science projects in behavioral health, but that formal channels for communicating and collaborating with one another were relatively unavailable. There was a significant need for a forum within which implementation researchers and stakeholders could learn from one another, refine approaches to science and practice, and develop an implementation research agenda using common measures, methods, and research principles to improve both the frequency and quality with which behavioral health treatment implementation is evaluated. SIRC’s membership growth is a testament to this identified need with more than 1000 members from 2011 to the present.ii SIRC’s primary objectives are to: (1) foster communication and collaboration across diverse groups, including implementation researchers, intermediariesi, as well as community stakeholders (SIRC uses the term “EBP champions” for these groups) – and to do so across multiple career levels (e.g., students, early career faculty, established investigators); and (2) enhance and disseminate rigorous measures and methodologies for implementing EBPs and evaluating EBP implementation efforts. These objectives are well aligned with Glasgow and colleagues’ [4] five core tenets deemed critical for advancing implementation science: collaboration, efficiency and speed, rigor and relevance, improved capacity, and cumulative knowledge. SIRC advances these objectives and tenets through in-person conferences, which bring together multidisciplinary implementation researchers and those implementing evidence-based behavioral health interventions in the community to share their work and create professional connections and collaborations

Computer controlled stereotaxic radiotherapy system

A computer-controlled stereotaxic radiotherapy system based on a low-frequency magnetic field technology integrated with a single fixation point stereotaxic guide has been designed and instituted. The magnetic field, generated in space by a special field source located in the accelerator gantry, is digitized in real time by a field sensor that is a six degree-of-freedom measurement device. As this sensor is an integral part of the patient stereotaxic halo, the patient position (x, y, z) and orientation (azimuth, elevation, roll) within the accelerator frame of reference are always known. Six parameters — three coordinates and three Euler space angles — are continuously transmitted to a computer where they are analyzed and compared with the stereotaxic parameters of the target point. Hence, the system facilitates rapid and accurate patient set-up for stereotaxic treatment as well as monitoring of patient during the subsequent irradiation session. The stereotaxic system has been developed to promote the integration of diagnostic and therapeutic procedures, with the specific aim of integrating CT and/or MR aided tumor localization and long term (4- to 7-week) fractionated radiotherapy of small intracranial and ocular lesions

Risk-adjusted models for adverse obstetric outcomes and variation in risk-adjusted outcomes across hospitals

OBJECTIVE: Regulatory bodies and insurers evaluate hospital quality using obstetrical outcomes, however meaningful comparisons should take pre-existing patient characteristics into account. Furthermore, if risk-adjusted outcomes are consistent within a hospital, fewer measures and resources would be needed to assess obstetrical quality. Our objective was to establish risk-adjusted models for five obstetric outcomes and assess hospital performance across these outcomes. STUDY DESIGN: A cohort study of 115,502 women and their neonates born in 25 hospitals in the United States between March 2008 and February 2011. Hospitals were ranked according to their unadjusted and risk-adjusted frequency of venous thromboembolism, postpartum hemorrhage, peripartum infection, severe perineal laceration, and a composite neonatal adverse outcome. Correlations between hospital risk-adjusted outcome frequencies were assessed. RESULTS: Venous thromboembolism occurred too infrequently (0.03%, 95% CI 0.02% – 0.04%) for meaningful assessment. Other outcomes occurred frequently enough for assessment (postpartum hemorrhage 2.29% (95% CI 2.20–2.38), peripartum infection 5.06% (95% CI 4.93–5.19), severe perineal laceration at spontaneous vaginal delivery 2.16% (95% CI 2.06–2.27), neonatal composite 2.73% (95% CI 2.63–2.84)). Although there was high concordance between unadjusted and adjusted hospital rankings, several individual hospitals had an adjusted rank that was substantially different (as much as 12 rank tiers) than their unadjusted rank. None of the correlations between hospital adjusted outcome frequencies was significant. For example, the hospital with the lowest adjusted frequency of peripartum infection had the highest adjusted frequency of severe perineal laceration. CONCLUSIONS: Evaluations based on a single risk-adjusted outcome cannot be generalized to overall hospital obstetric performance

The integration of motion and disparity cues to depth in dorsal visual cortex.

Humans exploit a range of visual depth cues to estimate three-dimensional (3D) structure. For example, the slant of a nearby tabletop can be judged by combining information from binocular disparity, texture and perspective. Behavioral tests show humans combine cues near-optimally, a feat that could depend on: (i) discriminating the outputs from cue-specific mechanisms, or (ii) fusing signals into a common representation. While fusion is computationally attractive, it poses a significant challenge, requiring the integration of quantitatively different signals. We used functional magnetic resonance imaging (fMRI) to provide evidence that dorsal visual area V3B/KO meets this challenge. Specifically, we found that fMRI responses are more discriminable when two cues (binocular disparity and relative motion) concurrently signal depth, and that information provided by one cue is diagnostic of depth indicated by the other. This suggests a cortical node important when perceiving depth, and highlights computations based on fusion in the dorsal stream