Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

Predicting Infectious ComplicatioNs in Children with Cancer : an external validation study

Background:The aim of this study was to validate the 'Predicting Infectious ComplicatioNs in Children with Cancer' (PICNICC) clinical decision rule (CDR) that predicts microbiologically documented infection (MDI) in children with cancer and fever and neutropenia (FN). We also investigated costs associated with current FN management strategies in Australia.Methods:Demographic, episode, outcome and cost data were retrospectively collected on 650 episodes of FN. We assessed the discrimination, calibration, sensitivity and specificity of the PICNICC CDR in our cohort compared with the derivation data set.Results:Using the original variable coefficients, the CDR performed poorly. After recalibration the PICNICC CDR had an area under the receiver operating characteristic (AUC-ROC) curve of 0.638 (95% CI 0.590-0.685) and calibration slope of 0.24. The sensitivity, specificity, positive predictive value and negative predictive value of the PICNICC CDR at presentation was 78.4%, 39.8%, 28.6% and 85.7%, respectively. For bacteraemia, the sensitivity improved to 85.2% and AUC-ROC to 0.71. Application at day 2, taking into consideration the proportion of MDI known (43%), further improved the sensitivity to 87.7%. Length of stay is the main contributor to cost of FN treatment, with an average cost per day of AUD 2183 in the low-risk group.Conclusions:For prediction of any MDI, the PICNICC rule did not perform as well at presentation in our cohort as compared with the derivation study. However, for bacteraemia, the predictive ability was similar to that of the derivation study, highlighting the importance of recalibration using local data. Performance also improved after an overnight period of observation. Implementation of a low-risk pathway, using the PICNICC CDR after a short period of inpatient observation, is likely to be safe and has the potential to reduce health-care expenditure

Individual participant data validation of the PICNICC prediction model for febrile neutropenia

BACKGROUND: Risk-stratified approaches to managing cancer therapies and their consequent complications rely on accurate predictions to work effectively. The risk-stratified management of fever with neutropenia is one such very common area of management in paediatric practice. Such rules are frequently produced and promoted without adequate confirmation of their accuracy. METHODS: An individual participant data meta-analytic validation of the 'Predicting Infectious ComplicatioNs In Children with Cancer' (PICNICC) prediction model for microbiologically documented infection in paediatric fever with neutropenia was undertaken. Pooled estimates were produced using random-effects meta-analysis of the area under the curve-receiver operating characteristic curve (AUC-ROC), calibration slope and ratios of expected versus observed cases (E/O). RESULTS: The PICNICC model was poorly predictive of microbiologically documented infection (MDI) in these validation cohorts. The pooled AUC-ROC was 0.59, 95% CI 0.41 to 0.78, tau2=0, compared with derivation value of 0.72, 95% CI 0.71 to 0.76. There was poor discrimination (pooled slope estimate 0.03, 95% CI -0.19 to 0.26) and calibration in the large (pooled E/O ratio 1.48, 95% CI 0.87 to 2.1). Three different simple recalibration approaches failed to improve performance meaningfully. CONCLUSION: This meta-analysis shows the PICNICC model should not be used at admission to predict MDI. Further work should focus on validating alternative prediction models. Validation across multiple cohorts from diverse locations is essential before widespread clinical adoption of such rules to avoid overtreating or undertreating children with fever with neutropenia

Representing Dependencies in Event Structures

Event structures where the causality may explicitly change during a computation have recently gained the stage. In this kind of event structures the changes in the set of the causes of an event are triggered by modifiers that may add or remove dependencies, thus making the happening of an event contextual. Still the focus is always on the dependencies of the event. In this paper we promote the idea that the context determined by the modifiers plays a major role, and the context itself determines not only the causes but also what causality should be. Modifiers are then used to understand when an event (or a set of events) can be added to a configuration, together with a set of events modeling dependencies, which will play a less important role. We show that most of the notions of Event Structure presented in literature can be translated into this new kind of event structure, preserving the main notion, namely the one of configuration

Predicting microbiologically defined infection in febrile neutropenic episodes in children : global individual participant data multivariable meta-analysis

BACKGROUND: Risk-stratified management of fever with neutropenia (FN), allows intensive management of high-risk cases and early discharge of low-risk cases. No single, internationally validated, prediction model of the risk of adverse outcomes exists for children and young people. An individual patient data (IPD) meta-analysis was undertaken to devise one. METHODS: The 'Predicting Infectious Complications in Children with Cancer' (PICNICC) collaboration was formed by parent representatives, international clinical and methodological experts. Univariable and multivariable analyses, using random effects logistic regression, were undertaken to derive and internally validate a risk-prediction model for outcomes of episodes of FN based on clinical and laboratory data at presentation. RESULTS: Data came from 22 different study groups from 15 countries, of 5127 episodes of FN in 3504 patients. There were 1070 episodes in 616 patients from seven studies available for multivariable analysis. Univariable analyses showed associations with microbiologically defined infection (MDI) in many items, including higher temperature, lower white cell counts and acute myeloid leukaemia, but not age. Patients with osteosarcoma/Ewings sarcoma and those with more severe mucositis were associated with a decreased risk of MDI. The predictive model included: malignancy type, temperature, clinically 'severely unwell', haemoglobin, white cell count and absolute monocyte count. It showed moderate discrimination (AUROC 0.723, 95% confidence interval 0.711-0.759) and good calibration (calibration slope 0.95). The model was robust to bootstrap and cross-validation sensitivity analyses. CONCLUSIONS: This new prediction model for risk of MDI appears accurate. It requires prospective studies assessing implementation to assist clinicians and parents/patients in individualised decision making

EGRINs (Environmental Gene Regulatory Influence Networks) in Rice That Function in the Response to Water Deficit, High Temperature, and Agricultural Environments

Environmental gene regulatory influence networks (EGRINs) coordinate the timing and rate of gene expression in response to environmental signals. EGRINs encompass many layers of regulation, which culminate in changes in accumulated transcript levels. Here, we inferred EGRINs for the response of five tropical Asian rice (Oryza sativa) cultivars to high temperatures, water deficit, and agricultural field conditions by systematically integrating time-series transcriptome data, patterns of nucleosome-free chromatin, and the occurrence of known cis-regulatory elements. First, we identified 5447 putative target genes for 445 transcription factors (TFs) by connecting TFs with genes harboring known cis-regulatory motifs in nucleosome-free regions proximal to their transcriptional start sites. We then used network component analysis to estimate the regulatory activity for each TF based on the expression of its putative target genes. Finally, we inferred an EGRIN using the estimated transcription factor activity (TFA) as the regulator. The EGRINs include regulatory interactions between 4052 target genes regulated by 113 TFs. We resolved distinct regulatory roles for members of the heat shock factor family, including a putative regulatory connection between abiotic stress and the circadian clock. TFA estimation using network component analysis is an effective way of incorporating multiple genome-scale measurements into network inference

Physical activity and fitness in women with metastatic breast cancer.

PURPOSE: This study aimed to explore differences in physical activity and fitness between women with metastatic breast cancer compared to healthy controls and factors associated with their physical activity levels. METHODS: Seventy-one women with metastatic breast cancer, aged (mean (SD)) 57.7 (9.5) and 2.9 (3.1) years after the onset of metastatic disease, and 71 healthy controls aged 55.0 (9.4) years participated. Of those with metastatic disease, 27% had bone-only metastases, 35% visceral-only metastases and 38% bone and visceral metastases. Patient-reported outcomes and physical measures of muscle strength and aerobic fitness assessments were obtained. Participants wore a SenseWear® physical activity monitor over 7 days, and the average steps/day and the time spent in moderate-to-vigorous intensity physical activity were determined. RESULTS: Women with metastases were significantly (i) less aerobically fit than the control group (25.3 (5.4) vs. 31.9 (6.1) mL • kg(-1) • min(-1); P < 0.001); (ii) weaker (e.g. lower limb strength for the metastatic and control groups was 53.5 (23.7) vs. 76.0 (27.4) kg, respectively; P < 0.001); (iii) less active, with the metastatic group attaining only 56% of the mean daily step counts of the healthy women; and (iv) more symptomatic, reporting higher levels of fatigue and dyspnoea (P < 0.001). CONCLUSION: Women living in the community with metastatic breast cancer possessed lower aerobic fitness, reduced muscular strength and less daily physical activity compared to healthy counterparts. They also experienced poorer functioning and higher symptom burden. IMPLICATIONS FOR CANCER SURVIVORS: Women living with metastatic breast cancer may benefit from a physical activity programme to address their physical impairments

Re-evaluating and recalibrating predictors of bacterial infection in children with cancer and febrile neutropenia

Background Numerous paediatric febrile neutropenia (FN) clinical decision rules (CDRs) have been derived. Validation studies show reduced performance in external settings. We evaluated the association between variables common across published FN CDRs and bacterial infection and recalibrated existing CDRs using these data. Methods Prospective data from the Australian-PICNICC study which enrolled 858 FN episodes in children with cancer were used. Variables shown to be significant predictors of infection or adverse outcome in >1 CDR were analysed using multivariable logistic regression. Recalibration included re-evaluation of beta-coefficients (logistic model) or recursive-partition analysis (tree-based models). Findings Twenty-five unique variables were identified across 17 FN CDRs. Fourteen were included in >1 CDR and 10 were analysed in our dataset. On univariate analysis, location, temperature, hypotension, rigors, severely unwell and decreasing platelets, white cell count, neutrophil count and monocyte count were significantly associated with bacterial infection. On multivariable analysis, decreasing platelets, increasing temperature and the appearance of being clinically unwell remained significantly associated. Five rules were recalibrated. Across all rules, recalibration increased the AUC-ROC and low-risk yield as compared to non-recalibrated data. For the SPOG-adverse event CDR, recalibration also increased sensitivity and specificity and external validation showed reproducibility. Interpretation Degree of marrow suppression (low platelets), features of inflammation (temperature) and clinical judgement (severely unwell) have been consistently shown to predict infection in children with FN. Recalibration of existing CDRs is a novel way to improve diagnostic performance of CDRs and maintain relevance over time

Household Transmission of Rotavirus in a Community with Rotavirus Vaccination in Quininde, Ecuador

Background: We studied the transmission of rotavirus infection in households in peri-urban Ecuador in the vaccination era. Methods: Stool samples were collected from household contacts of child rotavirus cases, diarrhea controls and healthy controls following presentation of the index child to health facilities. Rotavirus infection status of contacts was determined by RT-qPCR. We examined factors associated with transmissibility (index-case characteristics) and susceptibility (householdcontact characteristics). Results: Amongst cases, diarrhea controls and healthy control household contacts, infection attack rates (iAR) were 55%, 8% and 2%, (n = 137, 130, 137) respectively. iARs were higher from index cases with vomiting, and amongst siblings. Disease ARs were higher when the index child was ,18 months and had vomiting, with household contact ,10 years and those sharing a room with the index case being more susceptible. We found no evidence of asymptomatic infections leading to disease transmission. Conclusion: Transmission rates of rotavirus are high in households with an infected child, while background infections are rare. We have identified factors associated with transmission (vomiting/young age of index case) and susceptibility (young age/sharing a room/being a sibling of the index case). Vaccination may lead to indirect benefits by averting episodes or reducing symptoms in vaccinees