A reaction-diffusion model of cholinergic retinal waves

Prior to receiving visual stimuli, spontaneous, correlated activity called retinal waves drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their extended inter-wave intervals and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In contrast with previous, simulation-based models, we are able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how the noise rate and sAHP refractory period contributes to critical wave size variability.Comment: 38 pages, 10 figure

A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

A PHYSICS-BASED APPROACH TO MODELING WILDLAND FIRE SPREAD THROUGH POROUS FUEL BEDS

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model is derived and implemented to investigate transport properties of flow through porous fuel beds. Note that these two developed models can also be applied to other situations for flow through porous media. Simulations of both grassland and forest fire spread are performed via an implicit LES code parallelized with OpenMP; the parallel performance of the algorithms are presented and discussed. The current model and numerical scheme produce reasonably correct wildfire results compared with previous wildfire experiments and simulations, but using coarser grids, and presenting complicated subgrid-scale behaviors. It is concluded that this physics-based wildfire model can be a good learning tool to examine some of the more complex wildfire behaviors, and may be predictive in the near future

Deep Learning in Cardiology

The medical field is creating large amount of data that physicians are unable to decipher and use efficiently. Moreover, rule-based expert systems are inefficient in solving complicated medical tasks or for creating insights using big data. Deep learning has emerged as a more accurate and effective technology in a wide range of medical problems such as diagnosis, prediction and intervention. Deep learning is a representation learning method that consists of layers that transform the data non-linearly, thus, revealing hierarchical relationships and structures. In this review we survey deep learning application papers that use structured data, signal and imaging modalities from cardiology. We discuss the advantages and limitations of applying deep learning in cardiology that also apply in medicine in general, while proposing certain directions as the most viable for clinical use.Comment: 27 pages, 2 figures, 10 table

e-Sanctuary: open multi-physics framework for modelling wildfire urban evacuation

The number of evacuees worldwide during wildfire keep rising, year after year. Fire evacuations at the wildland-urban interfaces (WUI) pose a serious challenge to fire and emergency services and are a global issue affecting thousands of communities around the world. But to date, there is a lack of comprehensive tools able to inform, train or aid the evacuation response and the decision making in case of wildfire. The present work describes a novel framework for modelling wildfire urban evacuations. The framework is based on multi-physics simulations that can quantify the evacuation performance. The work argues that an integrated approached requires considering and integrating all three important components of WUI evacuation, namely: fire spread, pedestrian movement, and traffic movement. The report includes a systematic review of each model component, and the key features needed for the integration into a comprehensive toolkit

Network resilience

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.Comment: Review chapter

Predicting and identifying signs of criticality near neuronal phase transition

This thesis examines the critical transitions between distinct neural states associated with the transition to neuron spiking and with the induction of anaesthesia. First, mathematical and electronic models of a single spiking neuron are investigated, focusing on stochastic subthreshold dynamics on close approach to spiking and to depolarisation-blocked quiescence (spiking death) transition points. Theoretical analysis of subthreshold neural behaviour then shifts to the anaesthetic-induced phase transition into unconsciousness using a mean-field model for interacting populations of excitatory and inhibitory neurons. The anaesthetic-induced changes are validated experimentally using published electrophysiological data recorded in anaesthetised rats. The criticality hypothesis associated with brain state change is examined using neuronal avalanches for experimentally recorded rat local field potential (LFP) data and mean-field pseudoLFP simulation data. We compare three different implementations of the FitzHugh--Nagumo single spiking neuron model: a mathematical model by H. R. Wilson, an alternative due to Keener and Sneyd, and an op-amp based nonlinear oscillator circuit. Although all three models can produce nonlinear ``spiking" oscillations, our focus is on the altering characteristics of noise-induced fluctuations near spiking onset and death via Hopf bifurcation. We introduce small-amplitude white noise to enable a linearised stochastic analyses using Ornstein--Uhlenbeck theory to predict variance, power spectrum and correlation of voltage fluctuations during close approach to the critical point, identified as the point at which the real part of the dominant eigenvalue becomes zero. We validate the theoretical predictions with numerical simulations and show that the fluctuations exhibit critical slowing down divergences when approaching the critical point: power-law increases in the variance of the fluctuations simultaneous with prolongation of the system response. We expand the study of stochastic behaviour to two spatial dimensions using the Waikato mean-field model operating near phase transition points controlled by the infusion or elimination of anaesthetic inhibition. Specifically, we investigate close approach to the critical point (CP), and to the points of loss of consciousness (LOC) and recovery of consciousness (ROC). We select the equilibrium states using $\lambda$ anaesthetic inhibition and $\Delta V^{\text{rest}}_e$ cortical excitation as control parameters, then analyse the voltage fluctuations evoked by small-amplitude spatiotemporal white noise. We predict the variance and power spectrum of voltage fluctuations near the marginally stable LOC and ROC transition points, then validate via numerical simulation. The results demonstrate a marked increase in voltage fluctuations and spectral power near transition points. This increased susceptibility to low-intensity white noise stimulation provides an early warning of impending phase transition. Effects of anaesthetic agents on cortical activity are reflected in local field potentials (LFPs) by the variation of amplitude and frequency in voltage fluctuations. To explore these changes, we investigate LFPs acquired from published electrophysiological experiments of anaesthetised rats to extract amplitude distribution, variance and time-correlation statistics. The analysis is broadened by applying detrended fluctuation analysis (DFA) to detect long-range dependencies in the time-series, and we compare DFA results with power spectral density (PSD). We find that the DFA exponent increases with anaesthetic concentration, but is always close to 1. The penultimate chapter investigates the evidence of criticality in anaesthetic induced phase-transitions using avalanche analysis. Rat LFP data reveal an avalanche power-law exponent close to $\alpha = 1.5$, but this value depends on both the time-bin width chosen to separate the events and the \textit{z}-score threshold used to detect these events. Power-law behaviour is only evident at lower anaesthetic concentrations; at higher concentrations the avalanche size distribution fails to align with a power-law nature. Criticality behaviour is also indicated in the Waikato mean-field model for anaesthetic-induced phase-transition using avalanches detected from the pseudoLFP time-series, but only at the critical point (CP) and at the secondary phase-transition points of LOC and ROC. In summary, this thesis unveils evidence of characteristic changes near phase transition points using computer-based mathematical modelling and electrophysiological data analysis. We find that noise-driven fluctuations become larger and persist for longer as the critical point is closely approached, with similar properties being seen not only in single-neuron and neural population models, but also in biological LFP signals. These results consistent with an increase of susceptibility to noise perturbations near phase transition point. Identification of neuronal avalanches in rat LFP data for low anaesthetic concentrations provides further support for the criticality hypothesis

Tipping Points and Early Warning Signals in the Climate-Carbon System

This is a thesis about tipping points and early warning signals. The tipping points investigated are related to various components of the climate-carbon system. In contrast, the work on early warning signals has more generic applications, however in this thesis they are analysed in the context of the climate-carbon system. The thesis begins with an introduction to the climate-carbon system as well as a discussion of tipping points in the Earth system. Then a more mathematical summary of tipping points and early warning signals is given. An investigation into the ‘compost bomb’ is undertaken, in which the spatial structure of soils is accounted for. It is found that a hot summer could cause a compost bomb. The effect of biogeochemical heating on the stability of the global carbon cycle is investigated and it is found to play only a small role. The potential for instabilities in the climate-carbon cycle is further investigated when the dynamic behaviour of the ocean carbon cycle is accounted for. It is found that some CMIP6 models may be close to having an unstable carbon cycle. Spatial early warning signals are investigated in the context of more rapidly forced systems. It is found that spatial early warning signals perform better when the system is rapidly forced compared with time series based early warning signals. The typical assumptions about white noise made when using early warning signals are also studied. It is found that time correlated noise may mask the early warning signal. It is shown that a spectral analysis can avoid this problem.European Commissio