Neocortical layer 5 thick-tufted pyramidal cells are prone to exhibiting burst firing on receipt of coincident basal and apical dendritic inputs. These inputs carry different information, with basal inputs coming from feedforward sensory pathways and apical inputs coming from diverse sources that provide context in the cortical hierarchy. We explore the information processing possibilities of this burst firing using computer simulations of a noisy compartmental cell model. Simulated data on stochastic burst firing due to brief, simultaneously injected basal and apical currents allow estimation of burst firing probability for different stimulus current amplitudes. Information-theory-based partial information decomposition (PID) is used to quantify the contributions of the apical and basal input streams to the information in the cell output bursting probability. Four different operating regimes are apparent, depending on the relative strengths of the input streams, with output burst probability carrying more or less information that is uniquely contributed by either the basal or apical input, or shared and synergistic information due to the combined streams. We derive and fit transfer functions for these different regimes that describe burst probability over the different ranges of basal and apical input amplitudes. The operating regimes can be classified into distinct modes of information processing, depending on the contribution of apical input to output bursting: apical cooperation, in which both basal and apical inputs are required to generate a burst; apical amplification, in which basal input alone can generate a burst but the burst probability is modulated by apical input; apical drive, in which apical input alone can produce a burst; and apical integration, in which strong apical or basal inputs alone, as well as their combination, can generate bursting. In particular, PID and the transfer function clarify that the apical amplification mode has the features required for contextually modulated information processing.

Information about context can enable local processors to discover latent variables that are relevant to the context within which they occur, and it can also guide short-term processing. For example, Becker and Hinton (1992) have shown how context can guide learning, and Hummel and Biederman (1992) have shown how it can guide processing in a large neural net for object recognition. This article studies the basic capabilities of a local processor with two distinct classes of inputs: receptive field inputs that provide the primary drive and contextual inputs that modulate their effects. The contextual predictions are used to guide processing without confusing them with receptive field inputs. The processor's transfer function must therefore distinguish these two roles. Given these two classes of input, the information in the output can be decomposed into four disjoint components to provide a space of possible goals in which the unsupervised learning of Linsker (1988) and the internally supervised learning of Becker and Hinton (1992) are special cases. Learning rules are derived from an information-theoretic objective function, and simulations show that a local processor trained with these rules and using an appropriate activation function has the elementary properties required.

This note discusses the inferential procedure used by Esposito et al. [1] to compare the performance of methods of classification, makes some links with recent research on resampling methodology, and mentions some alternative approaches.

Markov random fields are typically used as priors in Bayesian image restoration methods to represent spatial information in the image. Commonly used Markov random fields are not in fact capable of representing the moderate-to-large scale clustering present in naturally occurring images and can also be time consuming to simulate, requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge. Markov mesh models, a causal subclass of Markov random fields, are, however, readily simulated. We describe an empirical study of simulated realizations from various models used in the literature, and we introduce some new mesh-type models. We conclude, however, that while large-scale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations. It is emphasized that the results do not detract from the use of Markov random fields as representers of local spatial properties, which is their main purpose in the implementation of Bayesian statistical approaches to image analysis. Brief allusion is made to the issue of parameter estimation.>

The method of regularization is portrayed as providing a compromise between fidelity to the data and smoothness, with the tradeoff being determined by a scalar smoothing parameter. Various ways of choosing this parameter are discussed in the case of quadratic regularization criteria. They are compared algebraically, and their statistical properties are comparatively assessed from the results of all extensive simulation study based on simple images.>