The latent Markov (LM) model is a popular method for identifying distinct unobserved states and transitions between these states over time in longitudinally observed responses. The bootstrap likelihood-ratio (BLR) test yields the most rigorous test for determining the number of latent states, yet little is known about power analysis for this test. Power could be computed as the proportion of th...

An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved m...

Deep residual networks (ResNets) made a recent breakthrough in deep learning. The core idea of ResNets is to have shortcut connections between layers that allow the network to be much deeper while still being easy to optimize avoiding vanishing gradients. These shortcut connections have interesting properties that make ResNets behave differently from other typical network architectures. In this...

Existing refinery distillation systems are highly energy-intensive, and have complex column configurations that interact strongly with the associated heat exchanger network. An optimisation approach is developed for existing refinery distillation processes. The optimisation framework includes shortcut models developed for the simulation of the existing distillation column, and a retrofit shortc...

An industrial separation system consisting of four pressure-staged distillation columns has been studied to see if multi-effect integration can be applied to any two columns in the sequence. Shortcut equations and Vmin-diagrams have been used for screening purposes to find the columns with the highest potential for energy savings. The most promising case has then been further studied using rigo...

We give a self-contained introduction to the theory of shadows as a tool to study smooth 3 and 4-manifolds. The goal of the present paper twofold: on one side it is intended to be a shortcut to a basic use of the theory of shadows, on the other side it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs ...

Shortcut connections are a popular architectural feature of multi-layer perceptrons. It is generally assumed that by implementing a linear sub-mapping, shortcuts assist the learning process in the remainder of the network. Here we nd that this is not always the case: shortcut weights may also act as distractors that slow down convergence and can lead to inferior solutions. This problem can be a...