Arguments for Nested Patterns in Neural Ensembles

This paper describes a relatively simple way of allowing a brain model to self-organise its concept patterns through nested structures. Time is a key element and a simulator would be able to show how patterns may form and then fire in sequence, as part of a search or thought process. It uses a very simple equation to show how the inhibitors in particular, can switch off certain areas, to allow other areas to become the prominent ones and thereby define the current brain state. This allows for a small amount of control over what appears to be a chaotic structure inside of the brain. It is attractive because it is still mostly mechanical and therefore can be added as an automatic process, or the modelling of that. The paper also describes how the nested pattern structure can be used as a basic counting mechanism.Comment: Preprin

New Ideas for Brain Modelling

This paper describes some biologically-inspired processes that could be used to build the sort of networks that we associate with the human brain. New to this paper, a 'refined' neuron will be proposed. This is a group of neurons that by joining together can produce a more analogue system, but with the same level of control and reliability that a binary neuron would have. With this new structure, it will be possible to think of an essentially binary system in terms of a more variable set of values. The paper also shows how recent research associated with the new model, can be combined with established theories, to produce a more complete picture. The propositions are largely in line with conventional thinking, but possibly with one or two more radical suggestions. An earlier cognitive model can be filled in with more specific details, based on the new research results, where the components appear to fit together almost seamlessly. The intention of the research has been to describe plausible 'mechanical' processes that can produce the appropriate brain structures and mechanisms, but that could be used without the magical 'intelligence' part that is still not fully understood. There are also some important updates from an earlier version of this paper

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal’s position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial “tuning curves” for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons

Random graph ensembles with many short loops

Networks observed in the real world often have many short loops. This violates the tree-like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible research routes to be explored in order to make progress on networks with many short loops, involving old and new random graph models and ideas for novel mathematical methods. We do not present conclusive solutions of problems, but aim to encourage and stimulate new activity and in what we believe to be an important but under-exposed area of research. We discuss in more detail the Strauss model, which can be seen as the `harmonic oscillator' of `loopy' random graphs, and a recent exactly solvable immunological model that involves random graphs with extensively many cliques and short loops.Comment: 18 pages, 10 figures,Mathematical Modelling of Complex Systems (Paris 2013) conferenc

Reductionism ad absurdum: Attneave and Dennett cannot reduce Homunculus (and hence the mind)

Purpose – Neuroscientists act as proxies for implied anthropomorphic signal- processing beings within the brain, Homunculi. The latter examine the arriving neuronal spike-trains to infer internal and external states. But a Homunculus needs a brain of its own, to coordinate its capabilities – a brain that necessarily contains a Homunculus and so on indefinitely. Such infinity is impossible – and in well-cited papers, Attneave and later Dennett claim to eliminate it. How do their approaches differ and do they (in fact) obviate the Homunculi? Design/methodology/approach – The Attneave and Dennett approaches are carefully scrutinized. To Attneave, Homunculi are effectively “decision-making” neurons that control behaviors. Attneave presumes that Homunculi, when successively nested, become successively “stupider”, limiting their numbers by diminishing their responsibilities. Dennett likewise postulates neuronal Homunculi that become “stupider” – but brain-wards, where greater sophistication might have been expected. Findings – Attneave’s argument is Reductionist and it simply assumes-away the Homuncular infinity. Dennett’s scheme, which evidently derives from Attneave’s, ultimately involves the same mistakes. Attneave and Dennett fail, because they attempt to reduce intentionality to non-intentionality. Research limitations/implications – Homunculus has been successively recognized over the centuries by philosophers, psychologists and (some) neuroscientists as a crucial conundrum of cognitive science. It still is. Practical implications – Cognitive-science researchers need to recognize that Reductionist explanations of cognition may actually devolve to Homunculi, rather than eliminating them. Originality/value – Two notable Reductionist arguments against the infinity of Homunculi are proven wrong. In their place, a non-Reductionist treatment of the mind, “Emergence”, is discussed as a means of rendering Homunculi irrelevant