Identifying the critical parameters of a cyanobacterial growth and movement model by using generalised sensitivity analysis

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes and rivers. A new deterministic-mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including, light, nutrients and temperature. A technique called generalised sensitivity analysis was applied to the model to identify the critical parameter uncertainties in the model and investigates the interaction between the chosen parameters of the model. The result of the analysis suggested that 8 out of 12 parameters were significant in obtaining the observed cyanobacterial behaviour in a simulation. It was found that there was a high degree of correlation between the half-saturation rate constants used in the model.

Sensitivity analysis of a cyanobacterial growth and movement model under two different flow regimes

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling cyanobacterial behaviour in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes, reservoirs and rivers. A new deterministic–mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including light, nutrients and temperature. A parameter sensitivity analysis using a one-at-a-time approach was carried out. There were two objectives of the sensitivity analysis presented in this paper: to identify the key parameters controlling the growth and movement patterns of cyanobacteria and to provide a means for model validation. The result of the analysis suggested that maximum growth rate and day length period were the most significant parameters in determining the population growth and colony depth, respectively.

An animal movement model incorporating home range and habitat selection

Wildlife biologists are often interested in how an animal uses space and the habitat resources within that space. We propose a single model that estimates an animal’s home range and habitat selection parameters within that range while accounting for the inherent autocorrelation in frequently sampled telemetry data. The model is applied to brown bear telemetry data in southeast Alaska.

Using data from an encounter sampler to model fish dispersal

A method to estimate speed of free-ranging fishes using a passive sampling device is described and illustrated with data from the Everglades, U.S.A. Catch per unit effort (CPUE) from minnow traps embedded in drift fences was treated as an encounter rate and used to estimate speed, when combined with an independent estimate of density obtained by use of throw traps that enclose 1 m2 of marsh habitat. Underwater video was used to evaluate capture efficiency and species-specific bias of minnow traps and two sampling studies were used to estimate trap saturation and diel-movement patterns; these results were used to optimize sampling and derive correction factors to adjust species-specific encounter rates for bias and capture efficiency. Sailfin mollies Poecilia latipinna displayed a high frequency of escape from traps, whereas eastern mosquitofish Gambusia holbrooki were most likely to avoid a trap once they encountered it; dollar sunfish Lepomis marginatus were least likely to avoid the trap once they encountered it or to escape once they were captured. Length of sampling and time of day affected CPUE; fishes generally had a very low retention rate over a 24 h sample time and only the Everglades pygmy sunfish Elassoma evergladei were commonly captured at night. Dispersal speed of fishes in the Florida Everglades, U.S.A., was shown to vary seasonally and among species, ranging from 0· 05 to 0· 15 m s−1 for small poeciliids and fundulids to 0· 1 to 1· 8 m s−1 for L. marginatus. Speed was generally highest late in the wet season and lowest in the dry season, possibly tied to dispersal behaviours linked to finding and remaining in dry-season refuges. These speed estimates can be used to estimate the diffusive movement rate, which is commonly employed in spatial ecological models.

Effects of Externally Applied, Cyclical, Low Magnitude Forces on Orthodontic Tooth Movement in Rats

Orthodontic tooth movement requires external orthodontic forces to be converted to cellular signals that result in the coordinated removal of bone on one side of the tooth (compression side) by osteoclasts, and the formation of new bone by osteoblasts on the other side (tension side). The length of orthodontic treatment can take several years, leading to problems of caries, periodontal disease, root resorption, and patient dissatisfaction. It appears that the velocity of tooth movement is largely dependent on the rate of alveolar bone remodeling. Pharmacological approaches to increase the rate of tooth movement are limited due to patient discomfort, severe root resorption, and drug-induced side effects. Recently, externally applied, cyclical, low magnitude forces (CLMF) have been shown to cause an increase in the bone mineral density of long bones, and in the growth of craniofacial structures in a variety of animal models. In addition, CLMF is well tolerated by the patient and produces no known adverse effects. However, its application in orthodontic tooth movement has not been specifically determined. Since factors that increase alveolar bone remodeling enhance the rate of orthodontic tooth movement, we hypothesized that externally applied, cyclical, low magnitude forces (CLMF) will increase the rate of orthodontic tooth movement. In order to test this hypothesis we used an in vivo rat orthodontic tooth movement model. Our specific aims were: Specific Aim 1: To develop an in vivo rat model for tooth movement. We developed a tooth movement model based upon two established rodent models (Ren and Yoshimatsu et al, See Figure 1.). The amount of variation of tooth movement in rats exposed to 25-60 g of mesial force activated viii from the first molar to the incisor for 4 weeks was calculated. Specific Aim 2: To determine the frequency dose response of externally applied, cyclical, low magnitude forces (CLMF) for maximal tooth movement and osteoclast numbers. Our working hypothesis for this aim was that the amount of tooth movement would be dose dependent on the frequency of application of the CLMF. In order to test this working hypothesis, we varied the frequency of the CLMF from 30, 60, 100, and 200 Hz, 0.4N, two times per week, for 10 minutes for 4 weeks, and measured the amount of tooth movement. We also looked at the number of osteoclasts for the different frequencies; we hypothesized an increase in osteoclasts for the dose respnse of different frequencies. Specific Aim 3: To determine the effects of externally applied, cyclical, low magnitude forces (CLMF) on PDL proliferation. Our working hypothesis for this aim was that PDL proliferation would increase with CLMF. In order to test this hypothesis we compared CLMF (30 Hz, 0.4N, two times per week, for 10 minutes for 4 weeks) performed on the left side (experimental side), to the non-CLMF side, on the right (control side). This was an experimental study with 24 rats in total. The experimental group contained fifteen (15) rats in total, and they all received a spring plus a different frequency of CLMF. Three (3) received a spring and CLMF at 30 Hz, 0.4N for 10 minutes. Six (6) received a spring and CLMF at 60 Hz, 0.4N for 10 minutes. Three (3) received a spring and CLMF at 100 Hz, 0.4N for 10 minutes. Three (3) received a spring and CLMF at 200 Hz, 0.4N for 10 minutes. The control group contained six (6) rats, and received only a spring. An additional ix three (3) rats received CLMF (30 Hz, 0.4N, two times per week, for 10 minutes for 4 weeks) only, with no spring, and were used only for histological purposes. Rats were subjected to the application of orthodontic force from their maxillary left first molar to their left central incisor. In addition some of the rats received externally applied, cyclical, low magnitude force (CLMF) on their maxillary left first molar. micro-CT was used to measure the amount of orthodontic tooth movement. The distance between the maxillary first and second molars, at the most mesial point of the second molar and the most distal point of the first molar (1M-2M distance) were used to evaluate the distance of tooth movement. Immunohistochemistry was performed with TRAP staining and BrdU quantification. Externally applied, cyclical, low magnitude forces (CLMF) do appear to have an effect on the rate, while not significant, of orthodontic tooth movement in rats. It appears that lower CLMF decreases the rate of tooth movement, while higher CLMF increases the rate of tooth movement. Future studies with larger sample sizes are needed to clarify this issue. CLMF does not appear to affect the proliferation in PDL cells, and has no effect on the number of osteoclasts.

Parameterization of the atmospheric boundary layer for offshore wind resource assessment with a limited length-scale k-ε model

The structure of the atmospheric boundary layer (ABL) is modelled with the limited- length-scale k-ε model of Apsley and Castro. Contrary to the standard k-ε model, the limited-length-scale k-ε model imposes a maximum mixing length which is derived from the boundary layer height, for neutral and unstable atmospheric situations, or by Monin-Obukhov length when the atmosphere is stably stratified. The model is first verified reproducing the famous Leipzig wind profile. Then the performance of the model is tested with measurements from FINO-1 platform using sonic anemometers to derive the appropriate maximum mixing length.

New evidence for the zoom lens model using the RSVP technique

A main prediction from the zoom lens model for visual attention is that performance is an inverse function of the size of the attended area. The "attention shift paradigm" developed by Sperling and Reeves (1980) was adapted here to study predictions from the zoom lens model. In two experiments two lists of items were simultaneously presented using the rapid serial visual presentation technique. Subjects were to report the first item he/she was able to identify in the series that did not include the target (the letter T) after he/she saw the target. In one condition, subjects knew in which list the target would appear, in another condition, they did not have this knowledge, having to attend to both positions in order to detect the target. The zoom lens model predicts an interaction between this variable and the distance separating the two positions where the lists are presented. In both experiments, this interaction was observed. The results are also discussed as a solution to the apparently contradictory results with regard to the analog movement model.

A Heuristic algorithm for fixed train runtime

This paper proposes a train movement model with fixed runtime that can be employed to find feasible control strategies for a single train along an inter-city railway line. The objective of the model is to minimize arrival delays at each station along railway lines. However, train movement is a typical nonlinear problem for complex running environments and different requirements. A heuristic algorithm is developed to solve the problem in this paper and the simulation results show that the train could overcome the disturbance from train delay and coordinates the operation strategies to sure punctual arrival of trains at the destination. The developed algorithm can also be used to evaluate the running reliability of trains in scheduled timetables.

Representative learning design in dynamic interceptive actions

The overarching aim of this thesis was to investigate how processes of perception and action emerge under changing informational constraints during performance of multi-articular interceptive actions. Interceptive actions provide unique opportunities to study processes of perception and action in dynamic performance environments. The movement model used to exemplify the functionally coupled relationship between perception and action, from an ecological dynamics perspective, was cricket batting. Ecological dynamics conceptualises the human body as a complex system composed of many interacting sub-systems, and perceptual and motor system degrees of freedom, which leads to the emergence of patterns of behaviour under changing task constraints during performance. The series of studies reported in the Chapters of this doctoral thesis contributed to understanding of human behaviour by providing evidence of key properties of complex systems in human movement systems including self-organisation under constraints and meta-stability. Specifically, the studies: i) demonstrated how movement organisation (action) and visual strategies (perception) of dynamic human behaviour are constrained by changing ecological (especially informational) task constraints; (ii) provided evidence for the importance of representative design in experiments on perception and action; and iii), provided a principled theoretical framework to guide learning design in acquisition of skill in interceptive actions like cricket batting.

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.

Magnetostatic equilibrium of isolated magnetic-flux tube

In the present paper, an isolated axisymmetric flux tube is discussed for slender magnetic configuration. The magnetostatic model and the stratified atmospheric model are applied, respectively, to the regions inside and outside the flux tube. The problem is described mathematically by the nonlinear partial differential equations under the nonlinear boundary condition at the free boundary of flux tube. According to the approximation of a small expansive angle, the solutions of series expressions are obtained formally. The model of polytropic plasma is discussed in detail especially. The results show the distributions of thermodynamic quantities and magnetic field extending from the high β region to the low β region, and the flux tube may be either divergent or convergent according to the pressure difference outside and inside the flux tube.

Fish production, catches and the carrying capacity of the world oceans

A brief review of the status of the world fisheries is presented with emphasis on the differences between catches (= landings + bycatch), biological production of fish, and predation (= production - catches). The ECOPATH II approach implemented as a new, Windows-based software is then shown to allow construction of a stratified world model accoutinng for global catches, production of and predation on fishes, and thus improved estimates of global potentials. A newly initiated, cooperative project is described through which the foundation for such a global model could be constructed, based on a stratified database with more than 100 trophic models. Collaborators are invited to join in this, and will be assisted in constructing models covering their areas of interest.

Dynamics of intraseasonal sea level and thermocline variability in the equatorial Atlantic during 2002-03

Satellite and in situ observations in the equatorial Atlantic Ocean during 2002-03 show dominant spectral peaks at 40-60 days and secondary peaks at 10-40 days in sea level and thermocline within the intraseasonal period band (10-80 days). A detailed investigation of the dynamics of the intraseasonal variations is carried out using an ocean general circulation model, namely, the Hybrid Coordinate Ocean Model (HYCOM). Two parallel experiments are performed in the tropical Atlantic Ocean basin for the period 2000-03: one is forced by daily scatterometer winds from the Quick Scatterometer (QuikSCAT) satellite together with other forcing fields, and the other is forced by the low-passed 80-day version of the above fields. To help in understanding the role played by the wind-driven equatorial waves, a linear continuously stratified ocean model is also used. Within 3 degrees S-3 degrees N of the equatorial region, the strong 40-60-day sea surface height anomaly (SSHA) and thermocline variability result mainly from the first and second baroclinic modes equatorial Kelvin waves that are forced by intraseasonal zonal winds, with the second baroclinic mode playing a more important role. Sharp 40-50-day peaks of zonal and meridional winds appear in both the QuikSCAT and Pilot Research Moored Array in the Tropical Atlantic (PIRATA) data for the period 2002-03, and they are especially strong in 2002. Zonal wind anomaly in the central-western equatorial basin for the period 2000-06 is significantly correlated with SSHA across the equatorial basin, with simultaneous/ lag correlation ranging from-0.62 to 0.74 above 95% significance. Away from the equator (3 degrees-5 degrees N), however, sea level and thermocline variations in the 40-60-day band are caused largely by tropical instability waves (TIWs). On 10-40-day time scales and west of 10 degrees W, the spectral power of sea level and thermocline appears to be dominated by TIWs within 5 degrees S-5 degrees N of the equatorial region. The wind-driven circulation, however, also provides a significant contribution. Interestingly, east of 10 W, SSHA and thermocline variations at 10 40- day periods result almost entirely from wind-driven equatorial waves. During the boreal spring of 2002 when TIWs are weak, Kelvin waves dominate the SSHA across the equatorial basin (2 degrees S-2 degrees N). The observed quasi-biweekly Yanai waves are excited mainly by the quasi-biweekly meridional winds, and they contribute significantly to the SSHA and thermocline variations in 1 degrees-5 degrees N and 1 degrees-5 degrees S regions.

利用接收函数方位变化研究地壳各向异性

Because of its sensitivity to the velocity discontinuity of the earth, receiver function technique has become a routine procedure used to probe interior structure of the earth. Receiver functions contain anisotropic information of the earth’s interior, however, traditional receiver function techniques such as migration imaging and waveform inversion method, which are based on isotropic media assumption, can not effectively extract the anisotropy information contained in the azimuth variation pattern. Only by using the anisotropic media, e.g. a model with symmetric axis of arbitrary orientation, computing the response, can we obtain the detailed anisotropy information hidden in the radial and transversal receiver function. Focusing on the receiver function variation pattern changing wtih different back azimuths, we introduced different kinds of symmetric systems of seismic anisotropy used often, and summarized some possible causes of anisotropy formation. We show details about how to calculate the response of a stratified anisotropy model with symmetric axis of arbitrary orientation. We also simulated receiver functions among different models and analyzed how the changing of anisotropic parameters influence the azimuth variation pattern of receiver functions. The anisotropy study by receiver function analysis was applied to Taihang Mountain Range (TMR) in North China in this thesis. The maximum entropy spectrum deconvolution technique was used to extract radial and transversal receiver functions from the waveforms of 20 portable seismic stations deployed in TMR. Considering the signal-to-noise ratio and the azimuth coverage, we got the variation pattern of receiver functions for 11 stations. After carefully analyzing the pattern of the receiver functions that we got, we obtained the reliable evidence on the existence of anisotropy in the shallow crust in TMR. Our results show that, although the thickness of the upper crustal layer is only about 1 km, the layer shows a strong anisotropy with magnitude of 8~15%; in the deeper of crust, the magnitudes of anisotropy is about 3%~5%, showing a pattern with fast-symmetric-axis. The crust anisotropy beneath TMR in North China obtained in this study also shows a significant difference in both the lateral and vertical scale, which might imply a regional anisotropy characteristic in the studied region.