Dynamic Transitions of Pediatric Sepsis: A Markov Chain Analysis

Pediatric sepsis is a heterogeneous disease with varying physiological dynamics associated with recovery, disability, and mortality. Using risk scores generated from a sepsis prediction model to define illness states, we used Markov chain modeling to describe disease dynamics over time by describing how children transition among illness states. We analyzed 18,666 illness state transitions over 157 pediatric intensive care unit admissions in the 3 days following blood cultures for suspected sepsis. We used Shannon entropy to quantify the differences in transition matrices stratified by clinical characteristics. The population-based transition matrix based on the sepsis illness severity scores in the days following a sepsis diagnosis can describe a sepsis illness trajectory. Using the entropy based on Markov chain transition matrices, we found a different structure of dynamic transitions based on ventilator use but not age group. Stochastic modeling of transitions in sepsis illness severity scores can be useful in describing the variation in transitions made by patient and clinical characteristics.

Sterne

Laurence Sterne’s masterpiece Tristram Shandy experiments with dynamics in nonverbal communication. Tonic shifts and variations in pace are systematically narrated in the interactions between characters. This chapter focuses on the moment when Walter Shandy, emotionally shocked, throws himself across his bed and lies on his stomach for a long time, Uncle Toby patiently waiting next to him. The kinesic dialogue taking place between the two men is echoed by the relationship Sterne establishes with his readers through his work. In both instances, the novel shows that making inferences about the mental states of others is practiced on the basis of unstable kinesic data. In this section of Tristram Shandy, Sterne theorizes that the meaning of movements and gestures comes from the transitions between attitudes, rather than from fixed facial or postural representations. The text prompts perceptual simulations of such dynamic transitions, leading to humorous effects involving readers.

Mathematical modeling of commissioning activities using differential equations of dynamic transitions and the Monte Carlo method

The article defines and highlights the tasks of commissioning, describes mathematical methods that can be used to obtain various models of commissioning in construction. Mathematical modeling of commissioning can be described by differential equations of dynamic transitions and the Monte Carlo method. To simulate the commissioning process using differential equations of dynamic transitions, it must be split into separate elements.

Reviving a failed network via microscopic interventions

From mass extinction to cell death, complex networked systems often exhibit abrupt dynamic transitions between desirable and undesirable states. Such transitions are often caused by topological perturbations, such as node or link removal, or decreasing link strengths. The problem is that reversing the topological damage, namely retrieving the lost nodes/links or reinforcing the weakened interactions, does not guarantee the spontaneous recovery to the desired functional state. Indeed, many of the relevant systems exhibit a hysteresis phenomenon, remaining in the dysfunctional state, despite reconstructing their damaged topology. To address this challenge, we develop a two-step recovery scheme: first - topological reconstruction to the point where the system can be revived, then dynamic interventions, to reignite the system's lost functionality. Applied to a range of nonlinear network dynamics, we identify a complex system's recoverable phase, a state in which the system can be reignited by a microscopic intervention, i.e. controlling just a single node. Mapping the boundaries of this newly discovered phase, we obtain guidelines for our two-step recovery.