Pattern formation in electrically coupled pacemaker cells

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Pattern formation in electrically coupled pacemaker cells : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Manawatū, New Zealand

Figures are re-used with permission.In this thesis we study electrical activity in smooth muscle cells in the absence of external stimulation. The main goal is to analyse a reaction-diffusion system that models the dynamical behaviour where adjacent cells are coupled through passive electrical coupling. We first analyse the dynamics of an isolated muscle cell for which the model consists of three first-order ordinary differential equations. The cell is either excitable, nonexcitable, or oscillatory depending on the model parameters. To understand this we reduce the model to two equations, nondimensionalise, then perform a detailed numerical bifurcation analysis of the nondimensionalised model. One parameter bifurcation diagrams reveal that even though there is no external stimulus the cell can exhibit two fundamentally distinct types of excitability. By computing two-parameter bifurcation diagrams we are able to explain how the cell transitions between the two types of excitability as parameters are varied. We then study the full reaction-diffusion system first through numerical integration. We show that the system is capable of exhibiting a wide variety of spatiotemporal behaviours such as travelling pulses, travelling fronts, and spatiotemporal chaos. Through a linear stability analysis we are able to show that the spatiotemporal patterns are not due to diffusion-driven instability as is often the case for reaction-diffusion systems. It is as a consequence of the nonlinear dynamics of the reaction terms and coupling effect of diffusion. The precise mechanism is not yet well understood, this will be subject of future work. We then examine travelling wave solutions in detail. In particular we show how they relate to homoclinic and heteroclinic solutions in travelling wave coordinates. Finally we review spectral stability analysis for travelling waves and compute the essential spectrum of travelling waves in our system

Modelling in ungauged catchments using PyTOPKAPI : a case study of Mhlanga catchment.

Masters Degree. University of KwaZulu-Natal, Durban.Hydrological modeling of rainfall-runoff processes is a powerful tool used in various water resources applications, including the simulation of water yield from ungauged catchments. Many rivers in developing countries are poorly gauged or fully ungauged. This gives rise to a challenge in the calibration and validation of hydrological models. This study investigated the applicability of PyTOPKAPI, a physically based distributed hydrological model, in simulating runoff in ungauged catchments, using the Mhlanga River as a case study. This study is the first application of the PyTOPKAPI model to simulate daily runoff on an ungauged catchment in South Africa. The PyTOPKAPI model was parameterised using globally available digital elevation data (DEM), satellite-derived land cover, soil type data and processed hydro-meteorological data collected from various sources. Historical 30-year (1980-2009) quaternary monthly streamflow (from a well-tested and calibrated model) and daily meteorological variables (rainfall, temperature, humidity and so on) were obtained. The rainfall data were subjected to double mass curve test to check for consistency. The monthly streamflow was transposed to the catchment and disaggregated to daily streamflow time step. The PyTOPKAPI model was calibrated using an average runoff ratio as an alternative to matching streamflow data that is usually used for model calibrations. The simulated results were thereafter compared with the disaggregated monthly quaternary data. The model results show good overall performance when compared with the average runoff ratio, monthly disaggregated streamflow and the expected mean annual runoff in the catchment. In general, PyTOPKAPI can be used to predict runoff response in ungauged catchments, and thus may be adopted for water resources management applications

ETHNIC PLURALISM, SOCIAL JUSTICE AND INTEGRATION POLICY IN POST CONFLICT RWANDA

Like every war ravaged country, the Republic of Rwanda is reawakening to grapple with the challenges of post-conflict reintegration and transformation. To scholars and observers of the trend, Rwanda is recuperating at a very high speed due to socio-economic reforms and the apparent commitment of the Government of the country to rebuild a new Rwanda from the rubbles of the devastation that greeted the 1994 genocide. Expectedly, the Rwandan government generated laws and codes which govern social interaction – former ‘enemies’ that must co-habit. There is public ban on all divisionism tendencies. In Rwanda there should be no ‘Hutu’, ‘Tutsi’ or ‘Twa’. All are Rwandans. Indeed, there are sanctions against defaulters irrespective of their nationalities. The drive for identity reconstruction is fierce and the government of Rwanda is determined to obliterate the ethnic ideologies which it believes, reinforced the 1994 Genocide against the Tutsi in Rwanda. However, the questions to ask are: will suppression of ethnic identity effectively obliterate natural affinity for group relations and the right to cultural identification and association? How does the government policy against sectarianism help in the reintegration programmes in Rwanda particularly the traditional judicial option called the Gacaca? This paper seeks to address these questions based on the data collected from a field-work conducted in Rwanda in 2011 and from the observations of scholars of ethnicity and the Rwandan Crisis. &nbsp

Understanding how Temperature influences European Starling’s Reproductive Success

Many habitats face fluctuating temperatures year round. The animals that live there are typically able to adjust their behaviors to match these conditions. When temperatures become too extreme, however, it could potentially start having a negative effect on the animal’s reproductive success. In birds, for example, severe climate can affect their eggs and nestlings due to nestlings lacking the ability to thermoregulate. The parents then have to bear the responsibility of thermoregulation for their young, through a behavior called incubation or brooding. European starlings (Sturnus vulgaris) are a species of birds common across the United States where both parents incubate their eggs and or brood their nestlings. In order to understand how the weather could impact these birds, we used nest cameras to record the behaviors of starling parents from March to June of 2020. We then used NOAA historical weather data to assess whether temperatures during the daytime shaped the number of eggs these starlings laid (clutch size). We also checked to see if weather temperatures effected the incubation and brooding behaviors of parents when they were keeping their nestlings warm (thermoregulation). We hypothesized that extreme temperatures (too warm or too cold) would results in less eggs at the nest, and more parental care from the parents

Mapping Mangrove Extent and Change: A Globally Applicable Approach

This study demonstrates a globally applicable method for monitoring mangrove forest extent at high spatial resolution. A 2010 mangrove baseline was classified for 16 study areas using a combination of ALOS PALSAR and Landsat composite imagery within a random forests classifier. A novel map-to-image change method was used to detect annual and decadal changes in extent using ALOS PALSAR/JERS-1 imagery. The map-to-image method presented makes fewer assumptions of the data than existing methods, is less sensitive to variation between scenes due to environmental factors (e.g., tide or soil moisture) and is able to automatically identify a change threshold. Change maps were derived from the 2010 baseline to 1996 using JERS-1 SAR and to 2007, 2008 and 2009 using ALOS PALSAR. This study demonstrated results for 16 known hotspots of mangrove change distributed globally, with a total mangrove area of 2,529,760 ha. The method was demonstrated to have accuracies consistently in excess of 90% (overall accuracy: 92.293.3%, kappa: 0.86) for mapping baseline extent. The accuracies of the change maps were more variable and were dependent upon the time period between images and number of change features. Total change from 1996 to 2010 was 204,850 ha (127,990 ha gain, 76,860 ha loss), with the highest gains observed in French Guiana (15,570 ha) and the highest losses observed in East Kalimantan, Indonesia (23,003 ha). Changes in mangrove extent were the consequence of both natural and anthropogenic drivers, yielding net increases or decreases in extent dependent upon the study site. These updated maps are of importance to the mangrove research community, particularly as the continual updating of the baseline with currently available and anticipated spaceborne sensors. It is recommended that mangrove baselines are updated on at least a 5-year interval to suit the requirements of policy makers

Flood Extent Mapping for Namibia Using Change Detection and Thresholding with SAR

A new method for flood detection change detection and thresholding (CDAT) was used with synthetic aperture radar (SAR) imagery to delineate the extent of flooding for the Chobe floodplain in the Caprivi region of Namibia. This region experiences annual seasonal flooding and has seen a recent renewal of severe flooding after a long dry period in the 1990s. Flooding in this area has caused loss of life and livelihoods for the surrounding communities and has caught the attention of disaster relief agencies. There is a need for flood extent mapping techniques that can be used to process images quickly, providing near real-time flooding information to relief agencies. ENVISAT/ASAR and Radarsat-2 images were acquired for several flooding seasons from February 2008 to March 2013. The CDAT method was used to determine flooding from these images and includes the use of image subtraction, decision based classification with threshold values, and segmentation of SAR images. The total extent of flooding determined for 2009, 2011 and 2012 was about 542 km2, 720 km2, and 673 km2 respectively. Pixels determined to be flooded in vegetation were typically <0.5 % of the entire scene, with the exception of 2009 where the detection of flooding in vegetation was much greater (almost one third of the total flooded area). The time to maximum flooding for the 2013 flood season was determined to be about 27 days. Landsat water classification was used to compare the results from the new CDAT with SAR method; the results show good spatial agreement with Landsat scenes

Height and Biomass of Mangroves in Africa from ICEsat/GLAS and SRTM

The accurate quantification of forest 3-D structure is of great importance for studies of the global carbon cycle and biodiversity. These studies are especially relevant in Africa, where deforestation rates are high and the lack of background data is great. Mangrove forests are ecologically significant and it is important to measure mangrove canopy heights and biomass. The objectives of this study are to estimate: 1. The total area, 2. Canopy height distributions and 3. Aboveground biomass of mangrove forests in Africa. To derive mangrove 3-D structure and biomass maps, we used a combination of mangrove maps derived from Landsat ETM+, LiDAR canopy height estimates from ICEsat/GLAS (Ice, Cloud, and land Elevation Satellite/Geoscience Laser Altimeter System) and elevation data from SRTM (Shuttle Radar Topography Mission) for the African continent. More specifically, we extracted mangrove forest areas on the SRTM DEM using Landsat based landcover maps. The LiDAR (Light Detection and Ranging) measurements from the large footprint GLAS sensor were used to derive local estimates of canopy height and calibrate the Interferometric Synthetic Aperture Radar (InSAR) data from SRTM. We then applied allometric equations relating canopy height to biomass in order to estimate above ground biomass (AGB) from the canopy height product. The total mangrove area of Africa was estimated to be 25 960 square kilometers with 83% accuracy. The largest mangrove areas and greatest total biomass was 29 found in Nigeria covering 8 573 km2 with 132 x10(exp 6) Mg AGB. Canopy height across Africa was estimated with an overall root mean square error of 3.55 m. This error also includes the impact of using sensors with different resolutions and geolocation error which make comparison between measurements sensitive to canopy heterogeneities. This study provides the first systematic estimates of mangrove area, height and biomass in Africa. Our results showed that the combination of ICEsat/GLAS and SRTM data is well suited for vegetation 3-D mapping on a continental scale

A synopsis of the non-invertible, two-dimensional, border-collision normal form with applications to power converters

The border-collision normal form is a canonical form for two-dimensional, continuous maps comprised of two affine pieces. In this paper we provide a guide to the dynamics of this family of maps in the non-invertible case where the two pieces fold onto the same half-plane. We identify parameter regimes for the occurrence of key bifurcation structures, such as period-incrementing, period-adding, and robust chaos. We then apply the results to a classic model of a boost converter for adjusting the voltage of direct current. It is known that for one combination of circuit parameters the model exhibits a border-collision bifurcation that mimics supercritical period-doubling and is non-invertible due to the switching mechanism of the converter. We find that over a wide range of parameter values, even though the dynamics created in border-collision bifurcations is in general extremely diverse, the bifurcation in the boost converter can only mimic period-doubling, although it can be subcritical.Comment: 11 figure