Broad direction bandwidths for complex motion mechanisms

Growing evidence from psychophysics and single-unit recordings suggests specialised mechanisms in the primate visual system for the detection of complex motion patterns such as expansion and rotation. Here we used a subthreshold summation technique to determine the direction tuning functions of the detecting mechanisms. We measured thresholds for discriminating noise and signal + noise for pairs of superimposed complex motion patterns (signal A and B) carried by random-dot stimuli in a circular 5° field. For expansion, rotation, deformation and translation we found broad tuning functions approximated by cos(d), where d is the difference in dot directions for signal A and B. These data were well described by models in which either: (a) cardinal mechanisms had direction bandwidths (half-widths) of around 60° or (b) the number of mechanisms was increased and their half-width was reduced to about 40°. When d = 180° we found summation to be greater than probability summation for expansion, rotation and translation, consistent with the idea that mechanisms for these stimuli are constructed from subunits responsive to relative motion. For deformation, however, we found sensitivity declined when d = 180°, suggesting antagonistic input from directional subunits in the deformation mechanism. This is a necessary property for a mechanism whose job is to extract the deformation component from the optic flow field. © 2001 Elsevier Science Ltd.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

The amyloid precursor protein (APP) binds the PIKfyve complex and modulates its function

Phosphoinositides are important components of eukaryotic membranes that are required for multiple forms of membrane dynamics. Phosphoinositides are involved in defining membrane identity, mediate cell signalling and control membrane trafficking events. Due to their pivotal role in membrane dynamics, phosphoinositide de-regulation contributes to various human diseases. In this review, we will focus on the newly emerging regulation of the PIKfyve complex, a phosphoinositide kinase that converts the endosomal phosphatidylinositol-3-phosphate [PI(3)P] to phosphatidylinositol-3,5-bisphosphate [PI(3,5)P2)], a low abundance phosphoinositide of outstanding importance for neuronal integrity and function. Loss of PIKfyve function is well known to result in neurodegeneration in both mousemodels and human patients. Our recent work has surprisingly identified the amyloid precursor protein (APP), the central molecule in Alzheimer s disease aetiology, as a novel interaction partner of a subunit of the PIKfyve complex, Vac14. Furthermore, it has been shown that APP modulates PIKfyve function and PI(3,5)P2 dynamics, suggesting that the APP gene family functions as regulator of PI(3,5)P2 metabolism. The recent advances discussed in this review suggest a novel, unexpected, â-amyloid-independent mechanism for neurodegeneration in Alzheimer s disease.