Social media consume an increasing portion of people’s daily lives and are important platforms in the realms of politics and marketing for reaching out to voters and consumers. Describing and predicting the behaviour of users on social media is thus of interest for companies and politicians, as well as researchers studying information diffusion and human behaviour. Twitter is a fast-paced microblog that is host to debates, conversations, and campaigns between users as well as organisations all over the world. As all interactions on Twitter are publicly available, the platform has been used as a data source for many studies. While previous works have mainly focused on interaction dynamics for specific user groups or topics, or on predicting virality, the perspective we take in this thesis is to focus on the level of the individual conversation and to use dynamical models to characterise user interactions. The most prominent characteristic of Twitter conversations is the clear presence of peaks in engagement. We introduce a classification scheme based on peak configurations to quantify the interaction patterns present on Twitter and find that around 70% of conversations exhibit a single peak in user engagement, usually followed by a slower decay. A second order linear model describes the dynamics of the single peak scenario well, indicating that most conversations have two phases - an initial phase of rapid rise and decline in interaction rate, followed by a phase of slowly decreasing interaction rate. We quantify the characteristic life span of Twitter conversations in terms of the second order system time constants. Furthermore, we investigate the impact that users with many followers, so called influencers, have on conversation dynamics, and in particular on the emergence of interaction peaks. The data suggests that influencers do have a noticeable, albeit limited effect on the spreading of conversations to other users.

Recent advances in spaceborne GPS technology have shown significant advantages in many aspects over conventional technologies. For instance, spaceborne GPS can realize autonomous orbit determination with significant savings in spacecraft life cycle, in power, and in mass. At present, the onboard orbit determination in real time or near-real time can typically achieve 3D orbital accuracy of metres to tens metres with Kalman filtering process, but 21st century space engineering requires onboard orbit accuracy of better than 5 metres, and even sub-metre for some space applications. The research focuses on the development of GPS-based autonomous orbit determination techniques for spacecraft. Contributions are made to the field of GPS-based orbit determination in the following five areas: Techniques to simplify the orbital dynamical models for onboard processing have been developed in order to reduce the computional burden while retaining full model accuracy. The Earth gravity acceleration approximation method was established to replace the traditional recursive acceleration computations. Results have demonstrated that with the computation burden for a 55× spherical harmonic gravity model, we achieve the accuracy of a 7070× model. Efforts were made for the simplification of solar & lunar ephemerides, atmosphere density model and orbit integration. All these techniques together enable a more accurate orbit integrator to operate onboard. Efficient algorithms for onboard GPS measurement outlier detection and measurement improvement have been developed. In addition, a closed-form single point position method was implemented to provide an initial orbit solution without any a priori information. The third important contribution was made to the development of sliding-window short-arc orbit filtering techniques for onboard processing. With respect to the existing Kalman recursive filtering, the short-arc method is more stable because more measurements are used. On the other hand, the short-arc method requires less accurate orbit dynamical model information compared to the long-arc method, thus it is suitable for onboard processing. Our results have demonstrated that by using the 1 ~ 2 revolutions of LEO code GPS data we can achieve an orbit accuracy of 1 ~ 2 metres. Sliding-window techniques provide sub-metre level orbit determination solutions with 5~20 minutes delay. A software platform for the GPS orbit determination studies has been established. Methods of orbit determination in near-real time have been developed and tested. The software system includes orbit dynamical modelling, GPS data processing, orbit filtering and result analysis modules, providing an effective technical basis for further studies. Furthermore a ground-based near-real time orbit determination system has been established for FedSat, Australia's first satellite in 30 years. The system generates 10-metre level orbit solution with half-day latency on an operational basis. This system has supported the scientific missions of FedSat such as Ka-band tracking and GPS atmosphere studies within the Cooperative Research Centre for Satellite System (CRCSS) community. Though it is different from the onboard orbit determination, it provides important test-bed for the techniques described in previous section. This thesis focuses on the onboard orbit determination techniques that were discussed in Chapter 2 through Chapter 6. The proposed onboard orbit determination algorithms were successfully validated using real onboard GPS data collected from Topex/Poseidon, CHAMP and SAC-C satellites.

This research presents three case studies of low temperature anomalies that occurred during the winter–spring seasons and their influence on extreme events and crop production. We investigate causes and effects of each climate event and developed prediction methods for crops based on the climate diagnostic information. The first study diagnosed the driven environmental-factors, including climate pattern, climate change, soils moisture, and sea level height, associated with the 2011 great flood in Thailand and resulting total crop loss. The second study investigated climate circulation and indices that contributed to wet-and-cold (WC) events leading to significant crop damage in Taiwan. We developed empirical–dynamical models based on prominent climate indices to confidently predict WC events as much as 6 months before they occur. The final study extends from the second study and predict chronic damage to rice crops from climate change by using a crop simulation model. The long-term prediction of rice growth and yield effectively illustrated both decreases and increases in yield depending on climate scenarios. The three studies are different in location and circumstances but the methodologies can be applied across Thailand, Taiwan, and other areas with similar agroclimatology.

Using some form of dynamical model in a visual tracking system is a well-known method for increasing robustness and indeed performance in general. Often, quite simple models are used and can be effective, but prior knowledge of the likely motion of the tracking target can often be exploited by using a specially-tailored model. Specifying such a model by hand, while possible, is a time-consuming and error-prone process. Much more desirable is for an automated system to learn a model from training data. A dynamical model learnt in this manner can also be a source of useful information in its own right, and a set of dynamical models can provide discriminatory power for use in classification problems. Methods exist to perform such learning, but are limited in that they assume the availability of 'ground truth' data. In a visual tracking system, this is rarely the case. A learning system must work from visual data alone, and this thesis develops methods for learning dynamical models while explicitly taking account of the nature of the training data --- they are noisy measurements. The algorithms are developed within two tracking frameworks. The Kalman filter is a simple and fast approach, applicable where the visual clutter is limited. The recently-developed Condensation algorithm is capable of tracking in more demanding situations, and can also employ a wider range of dynamical models than the Kalman filter, for instance multi-mode models. The success of the learning algorithms is demonstrated experimentally. When using a Kalman filter, the dynamical models learnt using the algorithms presented here produce better tracking when compared with those learnt using current methods. Learning directly from training data gathered using Condensation is an entirely new technique, and experiments show that many aspects of a multi-mode system can be successfully identified using very little prior information. Significant computational effort is required by the implementation of the methods, and there is scope for improvement in this regard. Other possibilities for future work include investigation of the strong links this work has with learning problems in other areas. Most notable is the study of the 'graphical models' commonly used in expert systems, where the ideas presented here promise to give insight and perhaps lead to new techniques.

We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts [1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.

In this paper, we investigate three particular algorithms: A sto- chastic simulation algorithm (SSA), and explicit and implicit tau-leaping al- gorithms. To compare these methods, we used them to analyze two infection models: A Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunode ciency Virus (HIV) within host in- fection model. While the rst has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative effciency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational effciency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modication of tau-Leaping methods are preferred.

In this thesis we develop a class of nonlinear generative models for high-dimensional time series. The first key property of these models is their distributed, or "componential" latent state, which is characterized by binary stochastic variables which interact to explain the data. The second key property is the use of an undirected graphical model to represent the relationship between latent state (features) and observations. The final key property is composability: the proposed class of models can form the building blocks of deep networks by successively training each model on the features extracted by the previous one. We first propose a model based on the Restricted Boltzmann Machine (RBM) that uses an undirected model with binary latent variables and real-valued "visible" variables. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. This "conditional" RBM (CRBM) makes on-line inference efficient and allows us to use a simple approximate learning procedure. We demonstrate the power of our approach by synthesizing various motion sequences and by performing on-line filling in of data lost during motion capture. We also explore CRBMs as priors in the context of Bayesian filtering applied to multi-view and monocular 3D person tracking. We extend the CRBM in a way that preserves its most important computational properties and introduces multiplicative three-way interactions that allow the effective interaction weight between two variables to be modulated by the dynamic state of a third variable. We introduce a factoring of the implied three-way weight tensor to permit a more compact parameterization. The resulting model can capture diverse styles of motion with a single set of parameters, and the three-way interactions greatly improve its ability to blend motion styles or to transition smoothly among them. In separate but related work, we revisit Products of Hidden Markov Models (PoHMMs). We show how the partition function can be estimated reliably via Annealed Importance Sampling. This enables us to demonstrate that PoHMMs outperform various flavours of HMMs on a variety of tasks and metrics, including log likelihood.

In this thesis we develop a class of nonlinear generative models for high-dimensional time series. The first key property of these models is their distributed, or "componential" latent state, which is characterized by binary stochastic variables which interact to explain the data. The second key property is the use of an undirected graphical model to represent the relationship between latent state (features) and observations. The final key property is composability: the proposed class of models can form the building blocks of deep networks by successively training each model on the features extracted by the previous one. We first propose a model based on the Restricted Boltzmann Machine (RBM) that uses an undirected model with binary latent variables and real-valued "visible" variables. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. This "conditional" RBM (CRBM) makes on-line inference efficient and allows us to use a simple approximate learning procedure. We demonstrate the power of our approach by synthesizing various motion sequences and by performing on-line filling in of data lost during motion capture. We also explore CRBMs as priors in the context of Bayesian filtering applied to multi-view and monocular 3D person tracking. We extend the CRBM in a way that preserves its most important computational properties and introduces multiplicative three-way interactions that allow the effective interaction weight between two variables to be modulated by the dynamic state of a third variable. We introduce a factoring of the implied three-way weight tensor to permit a more compact parameterization. The resulting model can capture diverse styles of motion with a single set of parameters, and the three-way interactions greatly improve its ability to blend motion styles or to transition smoothly among them. In separate but related work, we revisit Products of Hidden Markov Models (PoHMMs). We show how the partition function can be estimated reliably via Annealed Importance Sampling. This enables us to demonstrate that PoHMMs outperform various flavours of HMMs on a variety of tasks and metrics, including log likelihood.

The vital signs monitoring data of an infant receiving intensive care are a rich source of information about its health condition. One major concern about the state of health of such patients is the onset of neonatal sepsis, a life-threatening bloodstream infection. As early signs are subtle and current diagnosis procedures involve slow laboratory testing, sepsis detection based on the monitored physiological dynamics is a clinically significant task. This challenging problem can be thoroughly modelled as real-time inference within a machine learning framework. In this thesis, we develop probabilistic dynamical models centred around the goal of providing useful predictions about the onset of neonatal sepsis. This research is characterised by the careful incorporation of domain knowledge for the purpose of extracting the infant’s true physiology from the monitoring data. We make two main contributions. The first one is the formulation of sepsis detection as learning and inference in an Auto-Regressive Hidden Markov Model (AR-HMM). The model investigates the extent to which physiological events observed in the patient’s monitoring traces could be used for the early detection of neonatal sepsis. In addition, the proposed approach involves exact marginalisation over missing data at inference time. When applying the ARHMM on a real-world dataset, we found that it can produce effective predictions about the onset of sepsis. Second, both sepsis and clinical event detection are formulated as learning and inference in a Hierarchical Switching Linear Dynamical System (HSLDS). The HSLDS models dynamical systems where complex interactions between modes of operation can be represented as a twolevel hidden discrete hierarchical structure. For neonatal condition monitoring, the lower layer models clinical events and is controlled by upper layer variables with semantics sepsis/nonsepsis. The model parameterisation and estimation procedures are adapted to the specifics of physiological monitoring data. We demonstrate that the performance of the HSLDS for the detection of sepsis is not statistically different from the AR-HMM, despite the fact that the latter model is given “ground truth” annotations of the patient’s physiology.

Le travail de thèse présenté ici vise à caractériser et simuler les forces mécaniques impliquées dans le processus de fermeture dorsale chez l’organisme Drosophila melanogaster. Ce processus participe à l’acquisition par l’embryon de sa forme finale. Ainsi, l’objectif du travail présenté ici est d’approfondir nos connaissances sur la mécanique des tissus,ainsi que sur leur rôle dans l’embryogenèse.La fermeture dorsale est un processus similaire à la cicatrisation, dans lequel la fermeture du trou dorsal est réalisée par l'amnioséreuse, qui couvre le trou dorsal, et la rangée la plus dorsale des cellules de l'épiderme: les leading edge cells.Une partie du travail présenté ici étudie aussi les mouvements des cellules du leading edge,dans le but de comprendre l’effet du câble d’actine sur la dynamique de la fermeture dorsale.Un algorithme permettant de détecter les contours des cellules, leur position ainsi que celle de leurs jonctions multiples a été développé, ainsi qu'un interface utilisateur.Différents modèles dynamiques ont ensuite été construits, prenant en compte différents comportements mécaniques, selon l’approche lagrangienne. Les systèmes d’équations ont été résolus numériquement, et leurs prédictions comparées aux données biologiques selon l’approche des moindres carrés. Les résultats ont été validés par le test de la fonction d’auto corrélation.Les résultats présentés dans cette thèse nous permettent de mieux comprendre les processus mécaniques impliqués dans les oscillations des cellules de l’amnioséreuse. Ils nous donnent aussi des indices sur leurs caractéristiques biologiques. Ils nous permettent enfin de mieux appréhender le rôle du cabled’actine dans ce processus. / The work presented here aims at characterizing and simulating the mechanical forces involved in the process of Dorsal Closure in the organism Drosophila melanogaster, an embryonic process. In particular, Dorsal Closure participates in the acquisition of the final form of the embryo. Therefore, the work presented here aims at fathoming our knowledge on tissues mechanics, as well as their role in the acquisition of shape. The tissues involved in Dorsal Closure are the epidermis and the amnioserosa. At this stage of development, the epidermis surrounds almost all the embryo. Nevertheless, the amnioserosa still covers a large area of the dorsal side called dorsal hole. Hence, Dorsal Closure aims at shutting this hole and joining the lateral sides of the epidermis, in a process similar to wound healing. In order to fuse the two sides of the epidermis on the dorsal line, the epidermis must be drawn dorsalward. This movement is driven by the amnioserosa on the one hand, and by the dorsalmost row of the epidermis (called Leading Edge cells) on the other hand. The latter first form a transcellular Actin Cable around the dorsal hole. The cable, contracting, will reduce the area of the dorsal hole, covered by the amnioserosa. Second, the Leading Edge cells emit protrusions that will attach to the opposite Leading Edge and drag it toward themselves, untill the two sides of the epidermis fuse. These protrusions have a limited range, hence the dragging and fusion only take place at the ends of the dorsal hole (called canthi), where the distance between the two Leading Edges is small enough. The Amnioserosa also drags the epidermis toward the dorsal line. Its cells produce a contractile network. Interstingly, Amnioserosa cells see the area of their top side (apical side) vary in a periodic way. Although these variations have been widely studied, their role in Dorsal Closure remains unknown. This PhD aims at improving our knowledge of the mechanical concepts involved in these oscillations, and to build a physical model representing these movements. The work presented here also studies the movements of the Leading Edge cells, in order to understand the effect of the Actin Cableon the dynamics of Dorsal Closure. In order to study the cells movements and the role of the tissues involved in Dorsal Closure, an algorithm was developped, allowing to detect the cells edges, their position, as well as those of their vertices (multiple junction between three or four cells) and to track them over time. A user interface was also developped, in order to facilitate the adjustment of the parameters allowing the detection, as well as the correction of possible errors. Various dynamical models were then built following the lagrangian approach. The systems of equations deriving from the Euler-Lagrange equations were numerically solved, and their predictions compared to the biological data extracted thanks to the algorithm presented earlier, following the least square approach. The model validation was performed thanks to the autocorrelation function test. Finally, the Leading Edge dynamics was studied characterising the cellular movements at the interface between the epidermis and the amnioserosa. Wild type embryos dynamics were compared to those of mutated embryos showing specific defects in the Actin Cable formation. The results presented in this manuscript allow a better understanding of the processes involved in in Amnioserosa cells oscicllations. They also give clues on their biological characteristics. Finally, they assess the role of the actin cable in this process similar to wound healing.