Cable Tree Wiring -- Benchmarking Solvers on a Real-World Scheduling Problem with a Variety of Precedence Constraints

Cable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring Problem (CTW) as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP) solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and is accepted for inclusion in the MiniZinc challenge 2020

Classes of graphs embeddable in order-dependent surfaces

Given a function $g=g(n)$ we let $\mathcal{E}^g$ be the class of all graphs $G$ such that if $G$ has order $n$ (that is, has $n$ vertices) then it is embeddable in some surface of Euler genus at most $g(n)$, and let $\widetilde{\mathcal E}^g$ be the corresponding class of unlabelled graphs. We give estimates of the sizes of these classes. For example we show that if $g(n)=o(n/\log^3n)$ then the class $\mathcal{E}^{g}$ has growth constant $\gamma_{\mathcal{P}}$, the (labelled) planar graph growth constant; and when $g(n) = O(n)$ we estimate the number of n-vertex graphs in $\mathcal{E}^{g}$ and $\widetilde{\mathcal E}^g$ up to a factor exponential in $n$. From these estimates we see that, if $\mathcal{E}^g$ has growth constant $\gamma_{\mathcal{P}}$ then we must have $g(n)=o(n/\log n)$, and the generating functions for $\mathcal{E}^g$ and $\widetilde{\mathcal E}^g$ have strictly positive radius of convergence if and only if $g(n)=O(n/\log n)$. Such results also hold when we consider orientable and non-orientable surfaces separately. We also investigate related classes of graphs where we insist that, as well as the graph itself, each subgraph is appropriately embeddable (according to its number of vertices); and classes of graphs where we insist that each minor is appropriately embeddable. In a companion paper, these results are used to investigate random $n$-vertex graphs sampled uniformly from $\mathcal{E}^g$ or from similar classes.Mathematics Subject Classifications: 05C10, 05C30Keywords: Embeddable graphs, order-dependent surfaces, approximate counting, labelled graph

Functional Testing for Tranexamic Acid Duration of Action Using Modified Viscoelastometry

Introduction: Tranexamic acid (TXA) is the standard medication to prevent or treat hyperfibrinolysis. However, prolonged inhibition of lysis (so-called fibrinolytic shutdown) correlates with increased mortality. A new viscoelastometric test enables bedside quantification of the antifibrinolytic activity of TXA using tissue plasminogen activator (TPA). Materials and Methods: Twenty-five cardiac surgery patients were included in this prospective observational study. In vivo, the viscoelastometric TPA test was used to determine lysis time (LT) and maximum lysis (ML) over 96 h after TXA bolus. Additionally, plasma concentrations of TXA and plasminogen activator inhibitor 1 (PAI-1) were measured. Moreover, dose effect curves from the blood of healthy volunteers were performed in vitro. Data are presented as median (25-75th percentile). Results: In vivo TXA plasma concentration correlated with LT (r = 0.55; p < 0.0001) and ML (r = 0.62; p < 0.0001) at all time points. Lysis was inhibited up to 96 h (LTTPA-test: baseline: 398 s [229-421 s] vs. at 96 h: 886 s [626-2,175 s]; p = 0.0013). After 24 h, some patients (n = 8) had normalized lysis, but others (n = 17) had strong lysis inhibition (ML p < 0.001). The high- and low-lysis groups differed regarding kidney function (cystatin C: 1.64 [1.42-2.02] vs. 1.28 [1.01-1.52] mg/L; p = 0.002) in a post hoc analysis. Of note, TXA plasma concentration after 24 h was significantly higher in patients with impaired renal function (9.70 [2.89-13.45] vs.1.41 [1.30-2.34] mu g/mL; p < 0.0001). In vitro, TXA concentrations of 10 mu g/mL effectively inhibited fibrinolysis in all blood samples. Conclusions: Determination of antifibrinolytic activity using the TPA test is feasible, and individual fibrinolytic capacity, e.g., in critically ill patients, can potentially be measured. This is of interest since TXA-induced lysis inhibition varies depending on kidney function