Randomness-efficient curve sampling

Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling property: the restriction of low-degree polynomials over the domain to the sampled curve is still low-degree. This property is often used in combination with the sampling property and has found many applications, including PCP constructions, local decoding of codes, and algebraic PRG constructions.

The randomness complexity of curve samplers is a crucial parameter for its applications. It is known that (non-explicit) curve samplers using O(log N + log(1/δ)) random bits exist, where N is the domain size and δ is the confidence error. The question of explicitly constructing randomness-efficient curve samplers was first raised in [TU06] where they obtained curve samplers with near-optimal randomness complexity.

In this thesis, we present an explicit construction of low-degree curve samplers with optimal randomness complexity (up to a constant factor) that sample curves of degree (m log_q(1/δ))^O(1) in F_q^m. Our construction is a delicate combination of several components, including extractor machinery, limited independence, iterated sampling, and list-recoverable codes.

Effects of sintering temperature on morphology and mechanical characteristics of 3D printed porous titanium used as dental implant

Porous titanium samples were manufactured using the 3D printing and sintering method in order to determine the effects of final sintering temperature on morphology and mechanical properties. Cylindrical samples were printed and split into groups according to a final sintering temperature (FST). Irregular geometry samples were also printed and split into groups according to their FST. The cylindrical samples were used to determine part shrinkage, in compressive tests to provide stress-strain data, in microCT scans to provide internal morphology data and for optical microscopy to determine surface morphology. All of the samples were used in microhardness testing to establish the hardness. Below 1100 C FST, shrinkage was in the region of 20% but increased to approximately 30% by a FST of 1300 C. Porosity varied from a maximum of approximately 65% at the surface to the region of 30% internally. Between 97 and 99% of the internal porosity is interconnected. Average pore size varied between 24 µm at the surface and 19 µm internally. Sample hardness increased to in excess of 300 HV0.05 with increasing FST while samples with an FST of below 1250 C produced an elastic-brittle stress/strain curve and samples above this displayed elastic-plastic behaviour. Yield strength increased significantly through the range of sintering temperatures while the Young's modulus remained fairly consistent. © 2013 Elsevier B.V.

Morphology and compression behaviour of biodegradable scaffolds produced by the sintering process

Porous poly(L-lactic acid) (PLA) scaffolds of 85 per cent and 90 per cent porosity are prepared using polymer sintering and porogen leaching method. Different weight fractions of 10 per cent, 30 per cent, and 50 per cent of hydroxyapatite (HA) are added to the PLA to control the acidity and degradation rate. The three-dimensional (3D) morphology and surface porosity are tested using micro-computer tomography (micro-CT), optical microscopy, and scanning electron microscopy (SEM). Results indicate that the surface porosity does not change on the addition of HA. The micro-CT examinations show a slight decrease in the pore size and increase in the wall thickness accompanied by reduced anisotropy for the scaffolds containing HA. Scanning electron micrographs show detectable interconnected pores for the scaffold with pure PLA. Addition of the HA results in agglomeration of the HA particles and reduced leaching of the porogen. Compression tests of the scaffold identify three stages in the stress-strain curve. The addition of HA results in a reduction in the modulus of the scaffold at the first stage of elastic bending of the wall, but this is reversed for the second and third stages of collapse of the wall and densification in the compression tests. In the scaffolds with 85 per cent porosity, the addition of a high percentage of HA could result in 70 per cent decrease in stiffness in the first stage, 200 per cent increase in stiffness in the second stage, and 20 per cent increase in stiffness in the third stage. The results of these tests are compared with the Gibson cellular material model that is proposed for prediction of the behaviour of cellular material under compression. The pH and molecular weight changes are tracked for the scaffolds within a period of 35 days. The addition of HA keeps the pH in the alkaline region, which results in higher rate of degradation at an early period of observation, followed by a reduced rate of degradation later in the process. The final molecular weight is higher for the scaffolds with HA than for scaffolds of pure PLA. The manufactured scaffolds offer acceptable properties in terms of the pore size range and interconnectivity of the pores and porosity for non-load-bearing bone graft substitute; however, improvement to the mixing of the phases of PLA and HA is required to achieve better integrity of the composite scaffolds. © 2008 IMechE.

The elements of the differential calculus, comprehending the general theory of curve surfaces, and of curves of double curvature. Intended for the use of mathematical students in schools and universities.

Available on demand as hard copy or computer file from Cornell University Library.

Sustainable Australia : containing travel in master planned estates

Low density suburban development and excessive use of automobiles are associated with serious urban and environmental problems. These problems include traffic congestion, longer commuting times, high automobile dependency, air and water pollution, and increased depletion of natural resources. Master planned development suggests itself as a possible palliative for the ills of low density and high travel. The following study examines the patterns and dynamics of movement in a selection of master planned estates in Australia. The study develops new approaches for assessing the containment of travel within planned development. Its key aim is to clarify and map the relationships between trip generation and urban form and structure. The initial conceptual framework of the paper is developed in a review of literature related to urban form and travel behaviour. These concepts are tested empirically in a pilot study of suburban travel activity in master planned estates. A geographical information systems methodology is used to determine regional journey-to-work patterns and travel containment rates. Factors that influence selfcontainment patterns are estimated with a regression model. This research is a useful preliminary examination of travel self-containment in Australian master planned estates.