Virtual Reality (VR) is changing how we interact with complex spatial datasets. VR has the potential within forestry to help analyse remotely sensed spatial data for inventory management. However, challenges of scale and legibility of dense forest point clouds must be addressed. To do so, we present three VR Focus+Context (F+C) techniques: Wedgelight, Remote Lantern, and Ray Lantern. These techniques present point cloud data using a constrained highdetail focus within a broader abstracted context representation, manipulated using egocentric and exocentric interactions. We conducted two user studies. The first informed the design of the F+C techniques. The results from the first study indicate that VR significantly outperforms desktop displays in basic analysis of forestry point clouds, with improvements to both time and accuracy. The second study evaluated the performance of the resulting F+C techniques in a task analogous to real-world forestry operations. Our F+C techniques significantly outperformed current approaches, confirming their viability for facilitating detailed and effective forest assessments. These findings indicate that VR has significant advantages for spatial data analysis tasks in forestry, making a strong argument for its adoption in future analytical frameworks. The FF+CC visualisation techniques we introduced show considerable promise for analysis of high density point clouds, opening new avenues for development in immersive analytics. Supplemental materials (code, scans, results) are available at https://osf.io/hqc9u.

Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.