Biomathematics

Interplay between Network Topology and Dynamics in Neural Systems

by Samuel Johnson

PhD thesis
Homepage: http://www.ugr.es/~sam/index_archivos/thesis.pdf
TESEO: https://www.educacion.gob.es/teseo/mostrarSeleccion.do

This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and... more This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems:

1) How the activity of neurons, via synaptic changes, can shape the topology of the network they form part of, and

2) How the resulting network structure, in its turn, might condition aspects of brain behaviour.

Although the emphasis is on neural networks, several theoretical findings which are relevant for complex networks in general are presented - such as a method for studying network evolution as a stochastic process, or a theory that allows for ensembles of correlated networks, and sets of dynamical elements thereon, to be treated mathematically and computationally in a model-independent manner. Some of the results are used to explain experimental data - certain properties of brain tissue, the spontaneous emergence of correlations in
all kinds of networks... - and predictions regarding statistical aspects of the central nervous system are made. The mechanism of Cluster Reverberation is proposed to account for the near-instant storage of novel information the brain is capable of.

Competitive Coexistence In Stoichiometric Chaos

by Irakli Loladze

Stoichiometric Exception to the Competitive Exclusion Principle

by Irakli Loladze

Submitted to Theoretical Population Biology on 14 October 2001


The above paper eventually was published as:

Loladze, I., Kuang, Y., Elser, J. J., & Fagan, W. F. (2004). Competition and stoichiometry: coexistence of two predators on one prey. Theoretical Population Biology, 65(1), 1-15.

The competitive exclusion principle (CEP) states that no equilibrium is possible if n species exploit fewer than n... more The competitive exclusion principle (CEP) states that no equilibrium is possible if n species exploit fewer than n resources. This principle does not appear to hold in nature, where high biodiversity is commonly observed, even in seemingly homogenous habitats. Here we analyze the competition of two predators for one prey in a spatially homogeneous model that captures the fundamental stoichiometric fact - any prey always provides multiple essential chemical elements to its predators. We prove that the two competitors can stably coexist on one prey while being simultaneously limited by the same chemical element (e.g. phosphorus) in the prey.