698 research outputs found
Editorial for special issue on neurodynamics
No full text“Neurodynamics” is an interdisciplinary area of mathematics where dynamical systems theory (deterministic and stochastic) is the primary tool for elucidating the fundamental mechanisms responsible for the behaviour of neural systems (whether biological or synthetic). A meeting on this topic was held at the International Centre for Mathematical Sciences in Edinburgh from March 5–7 in 2012. In this special issue, we have invited seven of the main contributors to this event to expand on their presentations and highlight the use of mathematics in understanding the dynamics of neural systems
Studies of novel nitro-substituted nitrogen heterocyclic compounds
No full textThis thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The novel candidate high energy insensitive explosive; 2,5-diamino-3,6-dinitropyrazine (ANPZ-i) has been prepared in acceptable overall yield. ANPZ-i was synthesised by the nitration of 2,5-diethoxypyrazine using nitronium tetrafluoroborate (NO2+BF4-) in sulfolane and the subsequent amination of 2,5-diethoxy-3,6-dinitropyrazine, under autoclave conditions. Oxidation studies towards the dioxide derivative of ANPZ-i, 2,5-diamino-3,6-dinitropyrazine-1,4-dioxide (PZDO), were unsuccessful. The synthesis of existing high explosives; 2,6-diamino-3,5-dintropyrazine (ANPZ) and 2,6-diamino-3,5-dinitropyrazine-1-oxide (PZO) has been scaled up to produce approximately 25 g batches of material. A number of novel nitrations using NO2+BF4- have been carried out on a range of chloro-, methyl- and hydroxy-functionalised quinoxalines and quinazolines. A range of novel functionalisations have also been carried out on the platform molecule; 2,4-diamino-6,8-dinitroquinazoline giving rise to 2,4-diamino-6,8-dinitroquinazoline-1,3-dioxide (di-N-oxidation product), 2,4,7-triamino-6,8-dinitroquinazoline (monoamination product) and 2,4,6,8-tetra-aminoquinazoline (dihydrogenation product).
Detonics molecular modelling was carried out on the following target molecules: 2,5-diamino-3,6-dinitropyrazine-1,4-dioxide (PZDO), 2,5,8-triamino-3,6,7-trinitroquinoxaline-1-oxide and 2,5,7-triamino-4,6,8-trinitroquinazoline-1-oxide. The detonation velocity of the new explosive molecule; 2,5-diamino-3,6-dinitropyrazine (ANPZ-i) was calculated and it was found to be a similar value to that obtained experimentally for the existing high explosive RDX. Calculation by molecular modelling of the steric energies of ANPZ, PZO, ANPZ-i and PZDO gave a quantitative assessment of the difficulty in oxidising ANPZ-i to give PZDO. Extensive analysis of carbon-13 NMR spectroscopy shift values was carried out for approximately twenty nitrogen heterocyclic compounds. Comparison of shift values indicated consistency in the interpretations.
On-line literature searches have shown that the following compounds prepared in this project are new: 2,3,6-trichloro-5-nitroquinoxaline, 2,3-dimethoxy-6,7-dinitroquinoxaline, 2,3,6-trichloroquinoxaline-1-oxide, 2,4-diamino-6,8-dinitroquinazoline-1,3-dioxide, 2,4,7-triamino-6,8-dinitroquinazoline and 2,5-diamino-3,6-dinitropyrazine (ANPZ-i). Furthermore, new synthetic routes have been used in the preparation of the following compounds: 2,3-dichloro-5-nitroquinoxaline, 2,3,6,7-tetrachloro-5-nitroquinoxaline, 2-hydroxy-6-nitroquinoxaline, 2-hydroxy-3-methyl-6-nitroquinoxaline and 2,5-diethoxy-3,6-dinitropyrazine
Beyond Lesson Studies and Design Experiments: Using theoretical tools in practice and finding out how they work
No full textThis paper aims to illustrate how fruitful insights into the link between school teaching practice and student learning outcomes can be theoretically grounded by the variation theory from the field of phenomenography; and from this framework demonstrate how a 'pedagogy of awareness' can be implemented in the classroom. In this study, five teachers and 162 students at Primary Four level of school education in Hong Kong participated and the practice of the 'learning study' was adopted. By comparing the results of pre- and posttests, a significant gain was observed in the students learning outcomes.
Exotic dynamics in a firing rate model of neural tissue with threshold accommodation
No full textMany of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems.
A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4)
Spots: breathing, drifting and scattering in a neural field model
No full textTwo dimensional neural field models with short range excitation and long range inhibition can exhibit localised solutions in the form of spots. Moreover, with the inclusion of a spike frequency adaptation current, these models can also support breathers and travelling spots. In this chapter we show how to analyse the proper- ties of spots in a neural field model with linear spike frequency adaptation. For a Heaviside firing rate function we use an interface description to derive a set of four nonlinear ordinary differential equations to describe the width of a spot, and show how a stationary solution can undergo a Hopf instability leading to a branch of pe- riodic solutions (breathers). For smooth firing rate functions we develop numerical codes for the evolution of the full space-time model and perform a numerical bifur- cation analysis of radially symmetric solutions. An amplitude equation for analysing breathing behaviour in the vicinity of the bifurcation point is determined. The con- dition for a drift instability is also derived and a center manifold reduction is used to describe a slowly moving spot in the vicinity of this bifurcation. This analysis is extended to cover the case of two slowly moving spots, and establishes that these will reflect from each other in a head-on collision
Gap junctions, dendrites and resonances : a recipe for tuning network dynamics
No full textGap junctions, also referred to as electrical synapses, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. These connections can form between the dendritic trees of individual cells. Many dendrites express membrane channels that confer on them a form of sub-threshold resonant dynamics. To obtain insight into the modulatory role of gap junctions in tuning networks of resonant dendritic trees, we generalise the “sum-over-trips” formalism for calculating the response function of a single branching dendrite to a gap junctionally coupled network. Each cell in the network is modelled by a soma connected to an arbitrary structure of dendrites with resonant membrane. The network is treated as a single extended tree structure with dendro-dendritic gap junction coupling. We present the generalised “sum-over-trips” rules for constructing the network response function in terms of a set of coefficients defined at special branching, somatic and gap-junctional nodes. Applying this framework to a two-cell network, we construct compact closed form solutions for the network response function in the Laplace (frequency) domain and study how a preferred frequency in each soma depends on the location and strength of the gap junction
Stamford group extending Cowboy Reunion invitations to Amon Carter and Paul Whiteman
No full textGroup from Stamford, Texas, extending Cowboy Reunion invitations to Amon Carter and Paul Whiteman. Mrs. Joe Benton (far left) is pinning a badge on Paul Whiteman. Mrs. C. B. Gray is pinning a badge on Amon Carter, at the right. Charles E. Coombes is standing between the two horses to be ridden by Whiteman and Carter in the opening parade of the reunion. W. G. Swenson, of Stamford, is standing beside Mrs. Gray. Others in the group are Mrs. L. I. Bennett, Miss Lou Lou Williams, Stephen Bennet, Mr. and Mrs. Lawrence Crider, Mr. and Mrs. John Braswell, Joe Benton, C. B. Gray, Mrs. Fannie Williams and Mrs. Charles E. Coombes. Several people in the background are holding up their cowboy hats.https://mavmatrix.uta.edu/specialcollections_startelegram1930s/5410/thumbnail.jp
Evolution of resistance in ecological and epidemiological contexts.
No full textUnderstanding the dynamics of an infectious disease, such as malaria, helps us to reduce the number of deaths and to achieve better control of its spread. Mathematical models can help to predict the outcomes of new ideas for containing disease spread. This thesis constitutes an extension of previous attempts to understand, via mathematical modelling, the dynamics of mosquito populations and malaria. We propose 5 distinct non-linear age dependent mathematical models. The first model uses, as a starting point, an approach to modelling nonlinear effects in agestructured models due to Gurtin and MacCamy [31]. However, the model we derive (which takes the form of a system of delay differential equations) is much more complex. We demonstrate analytical results on linear stability of both zero and positive equilibria in various cases. We then examine a more complex equation which incorporates competition among larval mosquitoes. Furthermore, results on boundedness of solutions and on the existence of positive equilibria are proved. Numerical simulations show that for specific values of several parameters three equilibrium points can be achieved as well as that the equilibria decrease as we increase the larval competition coefficient. In the second mathematical model, we examine a neutral delay differential equation. This specific type of equation is consequent upon the assumption that an adult mosquito lays a batch of eggs immediately upon maturation, followed possibly by further batches (not necessarily containing the same number of eggs) on reaching the particular ages τi + nτ, n = 1,2,..., with no egg laying in between these ages. This models the idea that egg laying follows blood meals. A particular case is the case when adult mosquito lays all of its eggs immediately on maturation, and none at all later in life. In that case the non-trivial equilibrium is locally stable but the roots of the characteristic equation are not bounded away from the imaginary axis. More generally, with adults laying eggs at ages τi +nτ, we may show under some conditions that the unique positive equilibria is linearly stable. Results on the existence of positive equilibria and boundedness of solutions are proved in this general case. Moving to the third mathematical model of the thesis, in Chapter 4, we examine two strains for the mosquito population, the vulnerable and the resistant strain. This model is based on the assumption that mosquitoes may become resistant to insecticides. One particular idea that we examine is the possibility that the parameter values such as the per-capita death rate, maturation time and the kernel g(a) which describes the adult mosquito egg laying activity are different in the two strains. We present analytical results on the global stability of the zero equilibrium and the linear stability of the boundary equilibrium. Numerical simulations show that for several parameter values either of the two strains can win the competition and drive the other one to extinction. In Chapter 5, the fourth mathematical model that we propose has similarities to the model of Chapter 4 but also allows the possibility of an adult vulnerable mosquito to die due to the insecticide. We propose a model for the case of an insecticide that attacks a mosquito with increasing potency as it ages, eventually giving us a system of four-integral equations. We compare two kinds of insecticides, late-life acting (LLA) insecticides and conventional insecticides, and try to find under what circumstances the LLA insecticide will slow down the evolution of insecticide resistance. The final part of the thesis examines the interaction between the host (human) and the vector (mosquito). Our fifth model provides analytical and numerical results for an eight-dimensional system of equations, consisting of two differential equations and six integral equations. For this model we find a set of conditions sufficient for the eradication of malaria
Simulating brain resting-state activity: what matters?
No full textIn the field of computational neuroscience, large-scale biophysical modelling is a bottom-up approach to study the interaction between brain structure and function. In this thesis, we propose two models of varying biophysical plausibility as a mechanistic explanations for spontaneous brain activity, as measured with magnetoencephalography (MEG).
Mathematically, these models take the form of large systems of non-linear coupled delay-differential equations, and we implement software to numerically solve such systems efficiently. After analysing the empirical data and extracting key features of interest (relating to the temporal dynamics of measured signals), we use Bayesian optimisation to fit our models with two different parameterisation of increasing complexity: first assuming a spatially uniform brain in which the pattern of connections between cortical regions is the only source of temporal structure in the simulations; and second allowing smooth variations of intrinsic parameters across the cortical surface. Our results outperform those published in the scientific literature to date.
We contribute an original derivation of a conductance-based model, and an in-depth analysis of the effects of intrinsic model parameters; software to build and simulate large models of delay-networks efficiently; a new approach to the exploration of high-dimensional spaces in the context of Bayesian optimisation (using space-partitioning); an original parameterisation allowing smooth spatial variations of intrinsic parameters across the cortical surface (using spherical harmonics); a novel analysis of structural brain data (from tractography), and several original methods to analyse MEG data (e.g. exploiting the Hilbert phase and extending Riemannian metrics).</p
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