Robust Localization of the Best Error with Finite Elements in the Reaction-Diffusion Norm

We consider the approximation in the reaction-diffusion norm with continuous finite elements and prove that the best error is equivalent to a sum of the local best errors on pairs of elements. The equivalence constants do not depend on the ratio of diffusion to reaction. As application, we derive local error functionals that ensure robust performance of adaptive tree approximation in the reaction-diffusion norm.Comment: 21 pages, 1 figur

Comparing methods for comparing networks

With the impressive growth of available data and the flexibility of network modelling, the problem of devising effective quantitative methods for the comparison of networks arises. Plenty of such methods have been designed to accomplish this task: most of them deal with undirected and unweighted networks only, but a few are capable of handling directed and/or weighted networks too, thus properly exploiting richer information. In this work, we contribute to the effort of comparing the different methods for comparing networks and providing a guide for the selection of an appropriate one. First, we review and classify a collection of network comparison methods, highlighting the criteria they are based on and their advantages and drawbacks. The set includes methods requiring known node-correspondence, such as DeltaCon and Cut Distance, as well as methods not requiring a priori known node-correspondence, such as alignment-based, graphlet-based, and spectral methods, and the recently proposed Portrait Divergence and NetLSD. We test the above methods on synthetic networks and we assess their usability and the meaningfulness of the results they provide. Finally, we apply the methods to two real-world datasets, the European Air Transportation Network and the FAO Trade Network, in order to discuss the results that can be drawn from this type of analysis

Privacy Concerns and Purchase of Travel Product Online

The travel and tourism industry has come to rely heavily on information and communication technologies to facilitate relations with consumers. Compiling consumer data profiles has become easier and it is widely thought that consumers place great importance on how that data is handled by firms. Lack of trust may cause consumers to have privacy concerns and may, in turn, have an adverse impact on consumers' willingness to purchase online. Three specific aspects of privacy that have received attention from researchers are unauthorized use of secondary data, invasion of privacy, and errors. A survey study was undertaken to examine the effects of these factors on both prior purchase of travel products via the Internet and future purchase probability. Surprisingly, no significant relationships were found to indicate that such privacy concerns affect online purchase behavior within the travel industry. Implications for managers are discussed

Blood cell differential count discretisation modelling to predict survival in adults reporting to the emergency room: a retrospective cohort study

OBJECTIVES: To assess the survival predictivity of baseline blood cell differential count (BCDC), discretised according to two different methods, in adults visiting an emergency room (ER) for illness or trauma over 1 year. DESIGN: Retrospective cohort study of hospital records. SETTING: Tertiary care public hospital in northern Italy. PARTICIPANTS: 11 052 patients aged >18 years, consecutively admitted to the ER in 1 year, and for whom BCDC collection was indicated by ER medical staff at first presentation. PRIMARY OUTCOME: Survival was the referral outcome for explorative model development. Automated BCDC analysis at baseline assessed haemoglobin, mean cell volume (MCV), red cell distribution width (RDW), platelet distribution width (PDW), platelet haematocrit (PCT), absolute red blood cells, white blood cells, neutrophils, lymphocytes, monocytes, eosinophils, basophils and platelets. Discretisation cut-offs were defined by benchmark and tailored methods. Benchmark cut-offs were stated based on laboratory reference values (Clinical and Laboratory Standards Institute). Tailored cut-offs for linear, sigmoid-shaped and U-shaped distributed variables were discretised by maximally selected rank statistics and by optimal-equal HR, respectively. Explanatory variables (age, gender, ER admission during SARS-CoV2 surges and in-hospital admission) were analysed using Cox multivariable regression. Receiver operating curves were drawn by summing the Cox-significant variables for each method. RESULTS: Of 11 052 patients (median age 67 years, IQR 51-81, 48% female), 59% (n=6489) were discharged and 41% (n=4563) were admitted to the hospital. After a 306-day median follow-up (IQR 208-417 days), 9455 (86%) patients were alive and 1597 (14%) deceased. Increased HRs were associated with age >73 years (HR=4.6, 95% CI=4.0 to 5.2), in-hospital admission (HR=2.2, 95% CI=1.9 to 2.4), ER admission during SARS-CoV2 surges (Wave I: HR=1.7, 95% CI=1.5 to 1.9; Wave II: HR=1.2, 95% CI=1.0 to 1.3). Gender, haemoglobin, MCV, RDW, PDW, neutrophils, lymphocytes and eosinophil counts were significant overall. Benchmark-BCDC model included basophils and platelet count (area under the ROC (AUROC) 0.74). Tailored-BCDC model included monocyte counts and PCT (AUROC 0.79). CONCLUSIONS: Baseline discretised BCDC provides meaningful insight regarding ER patients' survival

Blood cell differential count discretization modeling predicts survival in adults reporting to the emergency room: a retrospective cohort study

Objectives: to assess survival predictivity of baseline blood cell differential count (BCDC), discretized according to two different methods, in adults visiting the Emergency Room (ER) for illness or trauma over one-year. Design: Retrospective cohort study of hospital records. Setting: Tertiary care public hospital in northern Italy. Participants: 11052 patients aged > 18 years, consecutively admitted to the ER in one year, and for whom BCDC collection was indicated by ER medical staff at first presentation. Primary outcome: Survival was the referral outcome for explorative model development. Automated BCDC analysis at baseline assessed hemoglobin, red cell mean volume (MCV) and distribution-width (RDW), platelet distribution-width (PDW), plateletcrit (PCT), absolute red blood cells, white blood cells, neutrophils, lymphocytes, monocytes, eosinophils, basophils, and platelets. Discretization cutoffs were defined by Benchmark and Tailored methods. Benchmark cutoffs were stated on laboratory reference values (CLSI). Tailored cutoffs for linear, sigmoid-shaped and for U-shaped distributed variables were discretized by Maximally Selected Rank Statistics and by Optimal-Equal Hazard Ratio respectively. Explanatory variables (age, gender, ER admission during SARS-CoV2 surges, in-hospital admission) were analyzed using Cox multivariable regression. ROC curves were drawn by sum of Cox-significant variables for each method. Results: Of 11052 patients (median age 67 years, IQR 51–81, 48% female), 59% (n=6489) were discharged and 41% (n=4563) were admitted in hospital. After a 306-day median follow up (IQR 208–417 days), 9455 (86%) patients were alive and 1597 (14%) deceased. Increased HRs were associated with age >73-years (HR=4.6 CI=4.0–5.2), in-hospital admission (HR=2.2 CI=1.9–2.4), ER admission during SARS-CoV2 surges (Wave-I HR=1.7 CI=1.5–1.9); Wave-II HR=1.2 CI=1.0–1.3). Gender, hemoglobin, MCV, RDW, PDW, neutrophils, lymphocytes and eosinophils counts were significant in overall. Benchmark-BCDC model included basophils and platelet count (AUROC 0.74). Tailored-BCDC model included monocyte counts and plateletcrit (AUROC 0.79). Conclusions: baseline discretized BCDC provides meaningful insight regarding Emergency Room patients survival.Complete blood cell differential count (BCDC) was performed using the automated Sysmex XN-9000 analyzer on peripheral blood samples taken at baseline and stored in hospital Lab electronic archives by dates (starting 2020-01-01 ending 2020-12-31) and by dept (Pronto Soccorso). Data were handled in CSV format by RStudio. Survival was the referral outcome for explorative model development and was assessed on June 30th, 2021, by a population registry office query through the NHS territorial service. Lab data were converted from tong to wide and dataframe was joined with the survival dataframe by unique personal alphanumeric code assigned by Italian authorities to each citizen. Being under category of sensitive information, although codified and not overt, personal alphanumeric codes were then deleted by assigning each patient a sequential coding number in dataframe. Duplicates were deleted. Predictors were searched among the BCDC first automated analysis assessment at presentation of hemoglobin (Hb), mean red cell volume (MCV), red cell distribution width (RDW), platelet distribution width (PDW), platelet hematocrit (piastrinocrit) (PCT) and absolute count of red blood cells (RBC), white blood cells (WBC), neutrophils (Neu), lymphocytes (Lym), monocytes (Mon), eosinophils (Eos), basophils (Bas), and platelets (PLT). Missing data were excluded, as only patients having BCDC records were evaluated. Analysis was performed by R studio and by Jamovi free R-based software (The jamovi project (2021). jamovi. [Computer Software]. Retrieved from https://www.jamovi.org). The "Benchmark" reference model was set by discretization of BCDC continuous values on our laboratory reference interval, established according to the C28-A3 guideline by the Clinical and Laboratory Standards Institute (CLSI). The "Tailored" discretization was set as follows. The relationship between each continuous variable and log relative hazard was plotted using the penalized B-splines (psplines) technique] for fitting the nonlinear effect of covariate in Cox models, by minimizing pitfalls associated with dichotomization of biological variables.Variables were treated differently according to their respective distribution profile. Linear and sigmoid-shaped variables were dichotomized by the maximally selected rank statistic method (MSRS). U-shaped variables were univariately discretized by cutoff point determination using the optimal-equal hazard ratio method (OEHR) (Chen Y, Huang J, He X, et al. BMC Med Res Methodol. 2019 May 9;19(1):96. doi: 10.1186/s12874-019-0738-4