"Not one word of it made any sense" : Hyperbolic Synecdoche in the British National Corpus

A distinct metonymic pattern was discovered in the course of conducting a corpus-based study of figurative uses of WORD. The pattern involved examples such as Not one word of it made any sense and I agree with every word. It was labelled ‘hyperbolic synecdoche’, defined as a case in which a lexeme which typically refers to part of an entity (a) is used to stand for the whole entity and (b) is described with reference to the end point on a scale. Specifically, the speaker/writer selects the perspective of a lower-level unit (such as word for ‘utterance’), which is quantified as NOTHING or ALL, thus forming a subset of ‘extreme case formulations’. Hyperbolic synecdoche was found to exhibit a restricted range of lexicogrammatical patterns involving word, with the negated NOTHING patterns being considerably more common than the ALL patterns. The phenomenon was shown to be common in metonymic uses in general, constituting one-fifth of all cases of metonymy in word. The examples of hyperbolic synecdoche were found not to be covered by the oftquoted ‘abbreviation’ rationale for metonymy; instead, they represent a more roundabout way of expression. It is shown that other cases of hyperbolic synecdoche exist outside of word and the domain of communication (such as ‘time’ and ‘money’).

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Axisymmetric shell structures for multi-use

Shell structures find use in many fields of engineering, notably structural, mechanical, aerospace and nuclear-reactor disciplines. Axisymmetric shell structures are used as dome type of roofs, hyperbolic cooling towers, silos for storage of grain, oil and industrial chemicals and water tanks. Despite their thin walls, strength is derived due to the curvature. The generally high strength-to-weight ratio of the shell form, combined with its inherent stiffness, has formed the basis of this vast application. With the advent in computation technology, the finite element method and optimisation techniques, structural engineers have extremely versatile tools for the optimum design of such structures. Optimisation of shell structures can result not only in improved designs, but also in a large saving of material. The finite element method being a general numerical procedure that could be used to treat any shell problem to any desired degree of accuracy, requires several runs in order to obtain a complete picture of the effect of one parameter on the shell structure. This redesign I re-analysis cycle has been achieved via structural optimisation in the present research, and MSC/NASTRAN (a commercially available finite element code) has been used in this context for volume optimisation of axisymmetric shell structures under axisymmetric and non-axisymmetric loading conditions. The parametric study of different axisymmetric shell structures has revealed that the hyperbolic shape is the most economical solution of shells of revolution. To establish this, axisymmetric loading; self-weight and hydrostatic pressure, and non-axisymmetric loading; wind pressure and earthquake dynamic forces have been modelled on graphical pre and post processor (PATRAN) and analysis has been performed on two finite element codes (ABAQUS and NASTRAN), numerical model verification studies are performed, and optimum material volume required in the walls of cylindrical, conical, parabolic and hyperbolic forms of axisymmetric shell structures are evaluated and reviewed. Free vibration and transient earthquake analysis of hyperbolic shells have been performed once it was established that hyperbolic shape is the most economical under all possible loading conditions. Effect of important parameters of hyperbolic shell structures; shell wall thickness, height and curvature, have been evaluated and empirical relationships have been developed to estimate an approximate value of the lowest (first) natural frequency of vibration. The outcome of this thesis has been the generation of new research information on performance characteristics of axisymmetric shell structures that will facilitate improved designs of shells with better choice of shapes and enhanced levels of economy and performance. Key words; Axisymmetric shell structures, Finite element analysis, Volume Optimisation_ Free vibration_ Transient response.

Fault diagnostics and supervised testing : How fault diagnostic tools can be proactive?

The topic of fault detection and diagnostics (FDD) is studied from the perspective of proactive testing. Unlike most research focus in the diagnosis area in which system outputs are analyzed for diagnosis purposes, in this paper the focus is on the other side of the problem: manipulating system inputs for better diagnosis reasoning. In other words, the question of how diagnostic mechanisms can direct system inputs for better diagnosis analysis is addressed here. It is shown how the problem can be formulated as decision making problem coupled with a Bayesian Network based diagnostic mechanism. The developed mechanism is applied to the problem of supervised testing in HVAC systems.

Overcoming the complexity of diagnostic problems due to sensor network architecture

In fault detection and diagnostics, limitations coming from the sensor network architecture are one of the main challenges in evaluating a system’s health status. Usually the design of the sensor network architecture is not solely based on diagnostic purposes, other factors like controls, financial constraints, and practical limitations are also involved. As a result, it quite common to have one sensor (or one set of sensors) monitoring the behaviour of two or more components. This can significantly extend the complexity of diagnostic problems. In this paper a systematic approach is presented to deal with such complexities. It is shown how the problem can be formulated as a Bayesian network based diagnostic mechanism with latent variables. The developed approach is also applied to the problem of fault diagnosis in HVAC systems, an application area with considerable modeling and measurement constraints.

Application of machine learning in fault diagnostics of mechanical systems

A diagnostic method based on Bayesian Networks (probabilistic graphical models) is presented. Unlike conventional diagnostic approaches, in this method instead of focusing on system residuals at one or a few operating points, diagnosis is done by analyzing system behavior patterns over a window of operation. It is shown how this approach can loosen the dependency of diagnostic methods on precise system modeling while maintaining the desired characteristics of fault detection and diagnosis (FDD) tools (fault isolation, robustness, adaptability, and scalability) at a satisfactory level. As an example, the method is applied to fault diagnosis in HVAC systems, an area with considerable modeling and sensor network constraints.

Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

Spin

“Spin” borrows idioms and metaphors from sports commentary and squeezes them into a single emotional rollercoaster. Accompanied by a driving soundtrack, text appears and disappears one word at a time. As the work progresses, multiple words fade in and out at the same time, filling the screen and testing our ability to read and assimilate these well-worn phrases. On the one hand, the work mimes some of what we enjoy about sport – its ability to take us to another place, to incite passion and emotion, and to enable us to share in common experiences, goals and desires. On the other hand, it plays up the hyperbolic language often associated with sports broadcasting. The very language that helps take us to another place, incite passion and make us feel part of something bigger than ourselves, is pushed to its extreme and starts to burst at the seams. This work was commissioned for “Kick Off: contemporary video art program” at Metricon Stadium, Gold Coast, and supported by Project Services, Department of Public Works, Queensland Government.

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Axial capacity of barrette piles embedded in gravel layer

In this paper, the axial performance of two heavily instrumented barrette piles, with and without grouting, socket into gravel layer in Taipei are evaluated based on the results of pile load tests. Both piles are 44 m long with the same dimension of 0.8 by 2.7 m, installed by hydraulic long bucket. One of the piles with toe grouting was socket 6 m into gravel layer and the other pile without toe grouting was socket 3 m into gravel layer. The load versus displacement relationships at pile head, the t-z curves of upper soil layers and of bottom gravel layer, and the tip resistance versus displacement relationships are important concerns and are presented in the paper. The t-z curves interpreted from the measured data along depth are also simulated by the hyperbolic model.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

How does angular resolution affect diffusion imaging measures?

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 ≤ N ≤ 94) that optimized a spherical angular distribution energy, we created SNR plots (versus gradient numbers) for seven common diffusion anisotropy indices: fractional and relative anisotropy (FA, RA), mean diffusivity (MD), volume ratio (VR), geodesic anisotropy (GA), its hyperbolic tangent (tGA), and generalized fractional anisotropy (GFA). SNR, defined in a region of interest in the corpus callosum, was near-maximal with 58, 66, and 62 gradients for MD, FA, and RA, respectively, and with about 55 gradients for GA and tGA. For VR and GFA, SNR increased rapidly with more gradients. SNR was optimized when the ratio of diffusion-sensitized to non-sensitized images was 9.13 for GA and tGA, 10.57 for FA, 9.17 for RA, and 26 for MD and VR. In orientation density functions modeling the HARDI signal as a continuous mixture of tensors, the diffusion profile reconstruction accuracy rose rapidly with additional gradients. These plots may help in making trade-off decisions when designing diffusion imaging protocols.

Swelling behaviour of soil-bentonite mixtures

Studies on the swelling behaviour of mixtures of bentonite clay and nonswelling coarser fractions of different sizes and shapes reveal that observed swelling occurs only after the voids of the nonswelling particles are filled up with swollen clay particles. The magnitude of the swell within the voids, called intervoid swelling is large when the size and percentage of the nonswelling coarser fraction is large. The observable swell, after intervoid swelling, is called primary swelling and follows a rectangular hyperbolic relationship with time. The total swell per gram of the clay decreases with an increase in the size of the nonswelling fraction and with a decrease in the percentage of swelling clay. Time-swell relationships show that swelling continues to occur for a long time after the primary swelling, and this is called secondary swelling.