Redundancy and blocking in the spatial domain: A connectionist model.

How can the observations of spatial blocking (Rodrigo, Chamizo, McLaren
 & Mackintosh, 1997) and cue redundancy (OKeefe and Conway, 1978) be
 reconciled within the framework provided by an error-correcting,
 connectionist account of spatial navigation? I show that an implementation
 of McLarens (1995) better beta model can serve this purpose, and examine
 some of the implications for spatial learning and memory

State-trace analysis: dissociable processes in a connectionist network?

Some argue the common practice of inferring multiple processes or systems from a dissociation is flawed (Dunn, 2003). One proposed solution is state-trace analysis (Bamber, 1979), which involves plotting, across two or more conditions of interest, performance measured by either two dependent variables, or two conditions of the same dependent measure. The resulting analysis is considered to provide evidence that either (a) a single process underlies performance (one function is produced) or (b) there is evidence for more than one process (more than one function is produced). This article reports simulations using the simple recurrent network (SRN; Elman, 1990) in which changes to the learning rate produced state-trace plots with multiple functions. We also report simulations using a single-layer error-correcting network that generate plots with a single function. We argue that the presence of different functions on a state-trace plot does not necessarily support a dual-system account, at least as typically defined (e.g. two separate autonomous systems competing to control responding); it can also indicate variation in a single parameter within theories generally considered to be single-system accounts

Birational maps from polarization and the preservation of measure and integrals

The main result of this paper is the discretization of Hamiltonian systems of the form $\ddot x = -K \nabla W(x)$, where $K$ is a constant symmetric matrix and $W\colon\mathbb{R}^n\to \mathbb{R}$ is a polynomial of degree $d\le 4$ in any number of variables $n$. The discretization uses the method of polarization and preserves both the energy and the invariant measure of the differential equation, as well as the dimension of the phase space. This generalises earlier work for discretizations of first order systems with $d=3$, and of second order systems with $d=4$ and $n=1$.Comment: Updated to final pre-publication versio

Volume preservation by Runge–Kutta methods

This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.apnum.2016.06.010It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge–Kutta method will respect this property for such systems, but it has been shown by Iserles, Quispel and Tse and independently by Chartier and Murua that no B-Series method can be volume preserving for all volume preserving vector fields. In this paper, we show that despite this result, symplectic Runge–Kutta methods can be volume preserving for a much larger class of vector fields than Hamiltonian systems, and discuss how some Runge–Kutta methods can preserve a modified measure exactly.This research was supported by the Marie Curie International Research Staff Exchange Scheme, grant number DP140100640, within the 7th European Community Framework Programme; by the Australian Research Council grant number 269281; and by the UK Engineering and Physical Sciences Research Council grant EP/H023348/1 for the Cambridge Centre for Analysis