Scheduling periodic tasks in a hard real-time environment

We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks $au_i=(c_i,p_i)$ on a minimum number of identical machines and to compute offsets $a_i$ for the tasks such that no collision occurs. A task $au_i$ releases a job of running time $c_i$ at each time $a_i + kcdot p_i,k in mathbb{N}_0$ and a collision occurs if two jobs are simultaneously active on the same machine. We shed some light on the complexity and approximability landscape of this problem. Although the problem cannot be approximated within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i | p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads to a 2-approximation. This result is tight, even asymptotically

Solving an Avionics Real-Time Scheduling Problem by Advanced IP-Methods

We report on the solution of a real-time scheduling problem that arises in the design of software-based operation control of aircraft. A set of tasks has to be distributed on a minimum number of machines and offsets of the tasks have to be computed. The tasks emit jobs periodically starting at their offset and then need to be executed on the machines without any delay. Also, further constraints in terms of memory usage and redundancy requirements have to be met. Approaches based on standard integer programming formulations fail to solve our real-world instances. By exploiting structural insights of the problem we obtain an IP-formulation and primal heuristics that together solve the real-world instances to optimality and outperform text-book approaches by several orders of magnitude. Our methods lead, for the first time, to an industry strength tool to optimally schedule aircraft sized problems

Machine learning algorithms performed no better than regression models for prognostication in traumatic brain injury

Objective: We aimed to explore the added value of common machine learning (ML) algorithms for prediction of outcome for moderate and severe traumatic brain injury. Study Design and Setting: We performed logistic regression (LR), lasso regression, and ridge regression with key baseline predictors in the IMPACT-II database (15 studies, n = 11,022). ML algorithms included support vector machines, random forests, gradient boosting machines, and artificial neural networks and were trained using the same predictors. To assess generalizability of predictions, we performed internal, internal-external, and external validation on the recent CENTER-TBI study (patients with Glasgow Coma Scale <13, n = 1,554). Both calibration (calibration slope/intercept) and discrimination (area under the curve) was quantified. Results: In the IMPACT-II database, 3,332/11,022 (30%) died and 5,233(48%) had unfavorable outcome (Glasgow Outcome Scale less than 4). In the CENTER-TBI study, 348/1,554(29%) died and 651(54%) had unfavorable outcome. Discrimination and calibration varied widely between the studies and less so between the studied algorithms. The mean area under the curve was 0.82 for mortality and 0.77 for unfavorable outcomes in the CENTER-TBI study. Conclusion: ML algorithms may not outperform traditional regression approaches in a low-dimensional setting for outcome prediction after moderate or severe traumatic brain injury. Similar to regression-based prediction models, ML algorithms should be rigorously validated to ensure applicability to new populations

Analysis of segregated boundary-domain integral equations for BVPs with non-smooth coefficients on Lipschitz domains

Segregated direct boundary-domain integral equations (BDIEs) based on a parametrix and associated with the Dirichlet and Neumann boundary value problems for the linear stationary diffusion partial differential equation with a variable Hölder-continuous coefficients on Lipschitz domains are formulated. The PDE right-hand sides belong to the Sobolev (Bessel potential) space Hs−2(Ω ) or H˜s−2(Ω ) , 12<s<32, when neither strong classical nor weak canonical co-normal derivatives are well defined. Equivalence of the BDIEs to the original BVP, BDIE solvability, solution uniqueness/non-uniqueness, and the Fredholm property and invertibility of the BDIE operators are analysed in appropriate Sobolev spaces. It is shown that the BDIE operators for the Neumann BVP are not invertible; however, some finite-dimensional perturbations are constructed leading to invertibility of the perturbed (stabilised) operators.EPSR

Clustering identifies endotypes of traumatic brain injury in an intensive care cohort: a CENTER-TBI study

Background While the Glasgow coma scale (GCS) is one of the strongest outcome predictors, the current classification of traumatic brain injury (TBI) as ‘mild’, ‘moderate’ or ‘severe’ based on this fails to capture enormous heterogeneity in pathophysiology and treatment response. We hypothesized that data-driven characterization of TBI could identify distinct endotypes and give mechanistic insights. Methods We developed an unsupervised statistical clustering model based on a mixture of probabilistic graphs for presentation (< 24 h) demographic, clinical, physiological, laboratory and imaging data to identify subgroups of TBI patients admitted to the intensive care unit in the CENTER-TBI dataset (N = 1,728). A cluster similarity index was used for robust determination of optimal cluster number. Mutual information was used to quantify feature importance and for cluster interpretation. Results Six stable endotypes were identified with distinct GCS and composite systemic metabolic stress profiles, distinguished by GCS, blood lactate, oxygen saturation, serum creatinine, glucose, base excess, pH, arterial partial pressure of carbon dioxide, and body temperature. Notably, a cluster with ‘moderate’ TBI (by traditional classification) and deranged metabolic profile, had a worse outcome than a cluster with ‘severe’ GCS and a normal metabolic profile. Addition of cluster labels significantly improved the prognostic precision of the IMPACT (International Mission for Prognosis and Analysis of Clinical trials in TBI) extended model, for prediction of both unfavourable outcome and mortality (both p < 0.001). Conclusions Six stable and clinically distinct TBI endotypes were identified by probabilistic unsupervised clustering. In addition to presenting neurology, a profile of biochemical derangement was found to be an important distinguishing feature that was both biologically plausible and associated with outcome. Our work motivates refining current TBI classifications with factors describing metabolic stress. Such data-driven clusters suggest TBI endotypes that merit investigation to identify bespoke treatment strategies to improve care

Serum metabolome associated with severity of acute traumatic brain injury

Complex metabolic disruption is a crucial aspect of the pathophysiology of traumatic brain injury (TBI). Associations between this and systemic metabolism and their potential prognostic value are poorly understood. Here, we aimed to describe the serum metabolome (including lipidome) associated with acute TBI within 24 h post-injury, and its relationship to severity of injury and patient outcome. We performed a comprehensive metabolomics study in a cohort of 716 patients with TBI and non-TBI reference patients (orthopedic, internal medicine, and other neurological patients) from the Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) cohort. We identified panels of metabolites specifically associated with TBI severity and patient outcomes. Choline phospholipids (lysophosphatidylcholines, ether phosphatidylcholines and sphingomyelins) were inversely associated with TBI severity and were among the strongest predictors of TBI patient outcomes, which was further confirmed in a separate validation dataset of 558 patients. The observed metabolic patterns may reflect different pathophysiological mechanisms, including protective changes of systemic lipid metabolism aiming to maintain lipid homeostasis in the brain

Frequency of fatigue and its changes in the first 6 months after traumatic brain injury: results from the CENTER-TBI study

Background: Fatigue is one of the most commonly reported subjective symptoms following traumatic brain injury (TBI). The aims were to assess frequency of fatigue over the first 6 months after TBI, and examine whether fatigue changes could be predicted by demographic characteristics, injury severity and comorbidities. Methods: Patients with acute TBI admitted to 65 trauma centers were enrolled in the study Collaborative European NeuroTrauma Effectiveness Research in TBI (CENTER-TBI). Subj

Tracheal intubation in traumatic brain injury

Background: We aimed to study the associations between pre- and in-hospital tracheal intubation and outcomes in traumatic brain injury (TBI), and whether the association varied according to injury severity. Methods: Data from the international prospective pan-European cohort study, Collaborative European NeuroTrauma Effectiveness Research for TBI (CENTER-TBI), were used (n=4509). For prehospital intubation, we excluded self-presenters. For in-hospital intubation, patients whose tracheas were intubated on-scene were excluded. The association between intubation and outcome was analysed with ordinal regression with adjustment for the International Mission for Prognosis and Analysis of Clinical Trials in TBI variables and extracranial injury. We assessed whether the effect of intubation varied by injury severity by testing the added value of an interaction term with likelihood ratio tests. Results: In the prehospital analysis, 890/3736 (24%) patients had their tracheas intubated at scene. In the in-hospital analysis, 460/2930 (16%) patients had their tracheas intubated in the emergency department. There was no adjusted overall effect on functional outcome of prehospital intubation (odds ratio=1.01; 95% confidence interval, 0.79–1.28; P=0.96), and the adjusted overall effect of in-hospital intubation was not significant (odds ratio=0.86; 95% confidence interval, 0.65–1.13; P=0.28). However, prehospital intubation was associated with better functional outcome in patients with higher thorax and abdominal Abbreviated Injury Scale scores (P=0.009 and P=0.02, respectively), whereas in-hospital intubation was associated with better outcome in patients with lower Glasgow Coma Scale scores (P=0.01): in-hospital intubation was associated with better functional outcome in patients with Glasgow Coma Scale scores of 10 or lower. Conclusion: The benefits and harms of tracheal intubation should be carefully evaluated in patients with TBI to optimise benefit. This study suggests that extracranial injury should influence the decision in the prehospital setting, and level of consciousness in the in-hospital setting. Clinical trial registration: NCT02210221