Computational convergence of the path integral for real dendritic morphologies

Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures

The Functional Dendritic Cell Algorithm: A Formal Specification With Haskell

The Dendritic Cell Algorithm (DCA) has been described in a number of different ways, sometimes resulting in incorrect implementations. We believe this is due to previous, imprecise attempts to describe the algorithm. The main contribution of this paper is to remove this imprecision through a new approach inspired by purely functional programming. We use new specification to implement the deterministic DCA in Haskell - the hDCA. This functional variant will also serve to introduce the DCA to a new audience within computer science. We hope that our functional specification will help improve the quality of future DCA related research and to help others understand further its algorithmic properties

Supervised Learning in Spiking Neural Networks for Precise Temporal Encoding

Precise spike timing as a means to encode information in neural networks is biologically supported, and is advantageous over frequency-based codes by processing input features on a much shorter time-scale. For these reasons, much recent attention has been focused on the development of supervised learning rules for spiking neural networks that utilise a temporal coding scheme. However, despite significant progress in this area, there still lack rules that have a theoretical basis, and yet can be considered biologically relevant. Here we examine the general conditions under which synaptic plasticity most effectively takes place to support the supervised learning of a precise temporal code. As part of our analysis we examine two spike-based learning methods: one of which relies on an instantaneous error signal to modify synaptic weights in a network (INST rule), and the other one on a filtered error signal for smoother synaptic weight modifications (FILT rule). We test the accuracy of the solutions provided by each rule with respect to their temporal encoding precision, and then measure the maximum number of input patterns they can learn to memorise using the precise timings of individual spikes as an indication of their storage capacity. Our results demonstrate the high performance of FILT in most cases, underpinned by the rule's error-filtering mechanism, which is predicted to provide smooth convergence towards a desired solution during learning. We also find FILT to be most efficient at performing input pattern memorisations, and most noticeably when patterns are identified using spikes with sub-millisecond temporal precision. In comparison with existing work, we determine the performance of FILT to be consistent with that of the highly efficient E-learning Chronotron, but with the distinct advantage that FILT is also implementable as an online method for increased biological realism.Comment: 26 pages, 10 figures, this version is published in PLoS ONE and incorporates reviewer comment

The identification of cellular automata

Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid CA is introduced

Growth in non-Laplacian fields

We develop a formal method for assigning rules to lattice-based walkers which allows the modeling of irreversible growth in systems governed by non-Laplacian partial differential equations. The method is used to study diffusive growth in finite concentration fields. Good agreement with analytic results is obtained. The method is subsequently applied to study electrochemical deposition and investigate the interplay between the electrostatic and diffusion fields. We examine the effect of a local (nonuniform) flow field on deposition on a substrate