Fitting the Cusp Catastrophe in R: A cusp Package Primer

Of the seven elementary catastrophes in catastrophe theory, the âÂÂcuspâ model is the most widely applied. Most applications are however qualitative. Quantitative techniques for catastrophe modeling have been developed, but so far the limited availability of flexible software has hindered quantitative assessment. We present a package that implements and extends the method of Cobb (Cobb and Watson'80; Cobb, Koppstein, and Chen'83), and makes it easy to quantitatively fit and compare different cusp catastrophe models in a statistically principled way. After a short introduction to the cusp catastrophe, we demonstrate the package with two instructive examples.

Fitting the Cusp Catastrophe in R: A cusp Package Primer

Of the seven elementary catastrophes in catastrophe theory, the "cusp" model is the most widely applied. Most applications are however qualitative. Quantitative techniques for catastrophe modeling have been developed, but so far the limited availability of flexible software has hindered quantitative assessment. We present a package that implements and extends the method of Cobb (Cobb and Watson 1980; Cobb, Koppstein, and Chen 1983), and makes it easy to quantitatively fit and compare different cusp catastrophe models in a statistically principled way. After a short introduction to the cusp catastrophe, we demonstrate the package with two instructive examples

Modelling and Simulation of Spontaneous Perception Switching with Ambiguous Visual Stimuli in Augmented Vision Systems

A behavioral nonlinear dynamics model of multistable perception due to ambiguous visual stimuli is presented. The perception state is formalized as the phase variable (order parameter) of a recursive cosinuidal map with the two control parameters μ= difference of meaning and G ~ attention. μ controls the transition between unambiguous and ambiguous stimuli, e.g. from stimulus off to stimulus on, by means of a node bifurcation. Neuronal mean field interference with delayed phase feedback, with gain G, delay T, and damping time τ enables transitions between chaotic and limit cycle attractors representing the perception states. Quasiperiodic perceptual reversals are induced by attention satiation (fatigue) G(t) with time constant γ and attention bias which determines the relative duration of the different percepts. The coupled attention – percep-tion dynamics with an additive stochastic attention noise term reproduces the experimentally observed Γ-distribution of the reversal time statistics. Mean reversal times of typically 3 – 5 s as reported in the literature, are correctly predicted if T is associated with the delay of 40 ms between stimulus onset and primary visual cortex (V1) response. Numerically determined perceptual transition times of 3 – 5 T are in reasonable agreement with stimulus – conscious perception delay of 150 – 200 ms [11]. Eigenfrequencies of the limit cycle oscillations are in the range of 10 – 100 Hz, in agreement with typical EEG frequencies

Modelling and Simulation of Spontaneous Perception Switching with Ambiguous Visual Stimuli in Augmented Vision Systems

A behavioral nonlinear dynamics model of multistable perception due to ambiguous visual stimuli is presented. The perception state is formalized as the dynamic phase variable v(t) of a recursive process with cosinuidal transfer characteristic which is created by superposition (interference) of neuronal mean fields. The two parameters μ = difference of meaning of alternative percepts and G = attention parameter, control the transition between unambiguous and ambiguous stimuli, e.g. from stimulus off to stimulus on, and attention fatigue respectively. Mean field interference with delayed phase feedback enables transitions between chaotic and limit cycle attractors v(t) representing the perception states. Perceptual reversals are induced by attention fatigue G(t) ( ~ adaptive gain g(v)) with time constant γ, and attention bias which determines the relative duration of the percepts. The coupled attention – perception dynamics with an additive stochastic noise term reproduces the experimentally observed Γ-distribution of the reversal time statistics. Mean reversal times of typically 3 – 5 s as reported in the literature, are correctly predicted if delay T is associated with the delay of 40 ms between stimulus onset and primary visual cortex (V1) response. Numerically determined perceptual transition times of 3 – 5 T are in reasonable agreement with stimulus – conscious perception delay of 150 – 200 ms [11]. Eigenfrequencies of the limit cycle oscillations are in the range of 10 – 100 Hz, in agreement with typical EEG frequencies.

3D-in-2D Displays for ATC.

This paper reports on the efforts and accomplishments of the 3D-in-2D Displays for ATC project at the end of Year 1. We describe the invention of 10 novel 3D/2D visualisations that were mostly implemented in the Augmented Reality ARToolkit. These prototype implementations of visualisation and interaction elements can be viewed on the accompanying video. We have identified six candidate design concepts which we will further research and develop. These designs correspond with the early feasibility studies stage of maturity as defined by the NASA Technology Readiness Level framework. We developed the Combination Display Framework from a review of the literature, and used it for analysing display designs in terms of display technique used and how they are combined. The insights we gained from this framework then guided our inventions and the human-centered innovation process we use to iteratively invent. Our designs are based on an understanding of user work practices. We also developed a simple ATC simulator that we used for rapid experimentation and evaluation of design ideas. We expect that if this project continues, the effort in Year 2 and 3 will be focus on maturing the concepts and employment in a operational laboratory settings