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Sepsis is one of the biggest risks to patient safety, with a natural mortality rate between 25% and 50%. It is difficult to diagnose, and no validated standard for diagnosis currently exists. A commonly used scoring criteria is the quick sequential organ failure assessment (qSOFA). It demonstrates very low specificity in ICU populations, however. We develop a method to personalize thresholds in qSOFA that incorporates easily to measure patient baseline characteristics. We compare the personalized threshold method to qSOFA, five previously published methods that obtain an optimal constant threshold for a single biomarker, and to the machine learning algorithms based on logistic regression and AdaBoosting using patient data in the MIMIC-III database. The personalized threshold method achieves higher accuracy than qSOFA and the five published methods and has comparable performance to machine learning methods. Personalized thresholds, however, are much easier to adopt in real-life monitoring than machine learning methods as they are computed once for a patient and used in the same way as qSOFA, whereas the machine learning methods are hard to implement and interpret.

This paper considers the sequencing of n jobs in a single-machine shop in which each job is assigned a constant flow allowance. The objective is to determine the optimal value of the flow allowance and the optimal job sequence to minimize a cost function based on the flow allowance and the job earliness and tardiness values. We first propose a linear programming (LP) formulation of the problem. We then derive the optimal constant flow allowance via considering the LP dual problem and show that it is independent of the job sequence. After the theoretical treatment, a numerical example is presented for discussion.

This paper considers the problem of determining the optimal constant flow allowance for the CON due-date assignment method. A linear programming formulation of the problem is proposed and the optimal due-date is obtained by solving the LP dual problem.

We consider a class of ecosystems subjected to optimal constant harvesting effort and continual, unpredictable, but bounded disturbances. If certain conditions are satisfied, a state feedback control can be used to guarantee uniform ultimate bounded-ness of every system response within an arbitrarily small neighbourhood of the unique non-trivial equilibrium state of the undisturbed exploited ecosystem. The result is demonstrated with the aid of some examples

A dual version of the Levine-Athans algorithm for solving the optimal constant output feedback gain for continuous-time systems is studied. Global convergence of the procedure to a stationary point of the loss function is proved. A global convergence property of the Levine-Athans algorithm is also obtained.

Necessary and sufficient globally optimal conditions—a matrix equation and a matrix inequality—are given for the existence of the optimal constant output feedback gain. Furthermore, it is shown that if the optimal output law L0 exists, it must be a solution derived from the corresponding optimal state-variable feedback problem, that is L0C = K0, where K0 is the optimal state-variable feedback law. An example is given to show that a globally optimal output law may not be found even if the system is stabilizable by output feedback. These results are helpful for the understanding of the fundamental problems of output feedback and give the reasons for suboptimal approaches as adopted by Levine and Athans (1970) and other authors.

This paper considers an application of control theory to management decision problems. The formulation of optimal periodic control is employed in studying the so-called intertemporal price discrimination problem. Previous static analyses of this problem have shown that the policy of switching between two certain price levels is more profitable than the optimal constant price. In the present paper the dynamics of the demand is modelled explicitly. Using this formulation the optimal dynamic solution to this problem can be found. A numerical example with three consumer groups is considered. The solution to this example shows that the optimal price patterns need not necessarily consist of only two price levels.