arXiv subjects

Jon Borresen

Publications and source records attributed to Jon Borresen.

3 recordsLinked to original sources

arXiv2019

An Upper Bound on the Number of Discrete States Possible for the Human Brain

Human brains are arguably the most complex entities known. Composed of billions of neurons, connected via a highly detailed structure where the underlying method by which functionality occurs is still debated. Here we consider one theory for neural coding, synchronization coding, which gives rise to the highest possible number of discrete states that a brain could exist in. A strict upper bound on the number of these states is determined. We conclude that the theoretical upper limit on the capacity of one human brain is almost inconceivably large and massively larger than the corresponding theoretical limit that could be obtained using every transistor ever built.

q-bio.NC↗

arXiv2016

Bifurcation and Stability Analysis of Bistable Neuromodules

This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and periodic bifurcations). For the first time, bifurcation diagrams are plotted using a feedback mechanism. It is shown that the stability curves and bifurcation diagrams must be dealt with simultaneously in order to fully understand the dynamics of the systems involved. Synaptic weights, biases and gradients of transfer functions are varied and the system is shown to be history dependent. The work can be applied to artificial neural networks and developing brains and gives a very important generalization of previous work in this field.

math.DS↗

arXiv2004

How to compute using globally coupled oscillators

Synchronization is known to play a vital role within many highly connected neural systems such as the olfactory systems of fish and insects. In this paper we show how one can robustly and effectively perform practical computations using small perturbations to a very simple globally coupled network of coupled oscillators. Computations are performed by exploiting the spatio-temporal dynamics of a robust attracting heteroclinic network (also referred to as `winnerless competition' dynamics). We use different cluster synchronization states to encode memory states and use this to design a simple multi-base counter. The simulations indicate that this gives a robust computational system exploiting the natural dynamics of the system.

q-bio.NC↗