Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory

In this dissertation, we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph theory

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Association of Architecture Schools in Australasia

"Techniques and Technologies: Transfer and Transformation", proceedings of the 2007 AASA Conference held September 27-29, 2007, at the School of Architecture, UTS

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

Characterisation and computational modelling of retinal stem cells in medaka (Oryzias latipes)

The central functional unit of the vertebrate eye is the retina, composed of neural retina (NR), retinal pigmented epithelium (RPE), and non-visual retina (NVR). In amphibians and fish, the retina grows throughout life via different pools of stem cells (SCs). In this work, I combined experimental and computational approaches to elucidate SC dynamics in the three retinal tissues of the teleost fish medaka (Oryzias latipes). I developed a cell centred agent based model to recapitulate post-embryonic growth of the NR and RPE. By accounting for 3D tissue geometry and continuous growth, the model reconciled conflicting hypotheses, demonstrating that competition between SCs is not mutually exclusive with lifelong coexistence of multiple SC lineages. To understand how NR and RPE regulate their proliferative output to coordinate growth rates, I developed quantitative methods to compare experiment and simulation. I tested the experimental data against simulations implementing two modes of feedback between cell proliferation and organ growth. Thus, I identified that the NR acts upstream to set the growth pace by sending an inductive growth signal, while the RPE responds downstream to this signal. Leveraging the model, I showed that NR SCs compete for niche space, but tissue geometry biases cells at certain positions to win this competition. Further, NR SCs modulate division axes and proliferation rate to change organ shape and retinal topology. Motivated by model predictions, I experimentally characterised the large SC population of the RPE, which consisted of both cycling and non-cycling quiescent cells. Putative sister cells exhibited similar temporal dynamics in local clusters, indicating that quiescence was the major mechanism for regulating proliferative output in the RPE. Finally, I experimentally showed that the NVR grows post-embryonically from a primordium, and shared all known markers for NR SCs in the same spatial distribution. Unlike NR and RPE, the NVR lacked a dedicated niche, instead proliferative cells were distributed throughout the tissue. Lineage tracing revealed a continuous relationship between RPE, NVR, and NR. Thus, the SCs of NR and RPE, and all cells of the NVR displayed plastic multipotency capable of generating all retinal tissues. By taking advantage of the positive feedback loop between experiment and simulation, this work shines a new light into a fundamental problem – growth coordination of different SC populations in a complex vertebrate organ

The Proceedings of the Fourth International Conference of the Association of Architecture Schools of Australasia

The Proceedings of the Fourth International Conference of the Association of Architecture Schools of Australasia. Each paper in the Proceedings has been double refereed by members of an independent panel of academic peers appointed by the Conference Committee. Papers were matched, where possible, to referees in the same field and with similar interests to the authors

Towards realistic interactive sand : a GPU-based framework

Includes bibliographical references (leaves 147-160).Many real-time computer games contain virtual worlds built upon terrestrial landscapes, in particular, "sandy" terrains, such as deserts and beaches. These terrains often contain large quantities of granular material, including sand, soil, rubble, and gravel. Allowing other environmental elements, such as trees or bodies of water, as well as players, to interact naturally and realistically with sand, is an important milestone for achieving realism in games. In the past, game developers have resorted to approximating sand with flat. textured surfaces that are static, non-granular, and do not behave like the physical material they model. A reasonable expectation is that sand be granular in its composition and governed by the laws of physics in its behaviour. However, for a single PC user, physics-based models are too computationally expensive to simulate and animate in real-time. An alternative is to use computer clusters to handle numerically intensive simulation, but at the loss of single-user affordability and real-time interactivity. Instead, we propose a GPU-based simulation framework that exploits the massive computational parallelism of a modern GPU to achieve interactive frame rates, on a single PC. We base our method on a discrete elements approach that represents each sand granule as a rigid arrangement of particles. Our model shows highly dynamic phenomena, such as splashing and avalanching, as well as static dune formation. Moreover, by utilising standard metrics taken from granular material science, we show that the simulated sand behaves in accordance with previous numerical and experimental research. We also support general rigid bodies in the simulation by automated particle-based sampling of their surfaces. This allows sand to interact naturally with its environment without extensive modification to underlying physics engine. The generality of our physics framework also allows for real-time physically-based rigid body simulation sans sand, as demonstrated in our testing. Finally, we describe an accelerated real-time method for lighting sand that supports both self-shadowing and environmental shadowing effects