Computing and Visualizing Solution Sets of Interval Linear Systems

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Studies on the propagation of errors in physical oceanographic computations

The results of an investigation on the limits of the random errors contained in the basic data of Physical Oceanography and their propagation through the computational procedures are presented in this thesis. It also suggest a method which increases the reliability of the derived results. The thesis is presented in eight chapters including the introductory chapter. Chapter 2 discusses the general theory of errors that are relevant in the context of the propagation of errors in Physical Oceanographic computations. The error components contained in the independent oceanographic variables namely, temperature, salinity and depth are deliniated and quantified in chapter 3. Chapter 4 discusses and derives the magnitude of errors in the computation of the dependent oceanographic variables, density in situ, gt, specific volume and specific volume anomaly, due to the propagation of errors contained in the independent oceanographic variables. The errors propagated into the computed values of the derived quantities namely, dynamic depth and relative currents, have been estimated and presented chapter 5. Chapter 6 reviews the existing methods for the identification of level of no motion and suggests a method for the identification of a reliable zero reference level. Chapter 7 discusses the available methods for the extension of the zero reference level into shallow regions of the oceans and suggests a new method which is more reliable. A procedure of graphical smoothening of dynamic topographies between the error limits to provide more reliable results is also suggested in this chapter. Chapter 8 deals with the computation of the geostrophic current from these smoothened values of dynamic heights, with reference to the selected zero reference level. The summary and conclusion are also presented in this chapter.

Synthesis of computations and experiments for obtaining pulsatile gas flow rates from dynamic pressure difference measurements across an orifice-plate meter

The use of conventional orifice-plate meter is typically restricted to measurements of steady flows. This study proposes a new and effective computational-experimental approach for measuring the time-varying (but steady-in-the-mean) nature of turbulent pulsatile gas flows. Low Mach number (effectively constant density) steady-in-the-mean gas flows with large amplitude fluctuations (whose highest significant frequency is characterized by the value fF) are termed pulsatile if the fluctuations have a direct correlation with the time-varying signature of the imposed dynamic pressure difference and, furthermore, they have fluctuation amplitudes that are significantly larger than those associated with turbulence or random acoustic wave signatures. The experimental aspect of the proposed calibration approach is based on use of Coriolis-meters (whose oscillating arm frequency fcoriolis >> fF) which are capable of effectively measuring the mean flow rate of the pulsatile flows. Together with the experimental measurements of the mean mass flow rate of these pulsatile flows, the computational approach presented here is shown to be effective in converting the dynamic pressure difference signal into the desired dynamic flow rate signal. The proposed approach is reliable because the time-varying flow rate predictions obtained for two different orifice-plate meters exhibit the approximately same qualitative, dominant features of the pulsatile flow.

Distributed, layered and reliable computing nets to represent neuronal receptive fields

Abstract. Receptive fields of retinal and other sensory neurons show a large variety of spatiotemporal linear and non linear types of responses to local stimuli. In visual neurons, these responses present either asymmetric sensitive zones or center-surround organization. In most cases, the nature of the responses suggests the existence of a kind of distributed computation prior to the integration by the final cell which is evidently supported by the anatomy. We describe a new kind of discrete and continuous filters to model the kind of computations taking place in the receptive fields of retinal cells. To show their performance in the analysis of diferent non-trivial neuron-like structures, we use a computer tool specifically programmed by the authors to that efect. This tool is also extended to study the efect of lesions on the whole performance of our model nets.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

ICTM: an interval tessellation-based model for reliable topographic segmentation

This work introduces a tessellation-based model for the declivity analysis of geographic regions. The analysis of the relief declivity, which is embedded in the rules of the model, categorizes each tessellation cell, with respect to the whole considered region, according to the (positive, negative, null) sign of the declivity of the cell. Such information is represented in the states assumed by the cells of the model. The overall configuration of such cells allows the division of the region into subregions of cells belonging to a same category, that is, presenting the same declivity sign. In order to control the errors coming from the discretization of the region into tessellation cells, or resulting from numerical computations, interval techniques are used. The implementation of the model is naturally parallel since the analysis is performed on the basis of local rules. An immediate application is in geophysics, where an adequate subdivision of geographic areas into segments presenting similar topographic characteristics is often convenient.

Dense Correspondence Extraction in Difficult Uncalibrated Scenarios

The relationship between multiple cameras viewing the same scene may be discovered automatically by finding corresponding points in the two views and then solving for the camera geometry. In camera networks with sparsely placed cameras, low resolution cameras or in scenes with few distinguishable features it may be difficult to find a sufficient number of reliable correspondences from which to compute geometry. This paper presents a method for extracting a larger number of correspondences from an initial set of putative correspondences without any knowledge of the scene or camera geometry. The method may be used to increase the number of correspondences and make geometry computations possible in cases where existing methods have produced insufficient correspondences.

A Reliable Basis for Approximate Association Rules

For most of the work done in developing association rule mining, the primary focus has been on the efficiency of the approach and to a lesser extent the quality of the derived rules has been emphasized. Often for a dataset, a huge number of rules can be derived, but many of them can be redundant to other rules and thus are useless in practice. The extremely large number of rules makes it difficult for the end users to comprehend and therefore effectively use the discovered rules and thus significantly reduces the effectiveness of rule mining algorithms. If the extracted knowledge can’t be effectively used in solving real world problems, the effort of extracting the knowledge is worth little. This is a serious problem but not yet solved satisfactorily. In this paper, we propose a concise representation called Reliable Approximate basis for representing non-redundant approximate association rules. We prove that the redundancy elimination based on the proposed basis does not reduce the belief to the extracted rules. We also prove that all approximate association rules can be deduced from the Reliable Approximate basis. Therefore the basis is a lossless representation of approximate association rules.

Osteoarthritis Index delivered by mobile phone (m-WOMAC) is valid, reliable, and responsive

Objectives: To evaluate the validity, reliability and responsiveness of EDC using the WOMAC® NRS 3.1 Index on Motorola V3 mobile phones. ---------- Methods: Patients with osteoarthritis (OA) undergoing primary unilateral hip or knee joint replacement surgery were assessed pre-operatively and 3-4 months post-operatively. Patients completed the WOMAC® Index in paper (p-WOMAC®) and electronic (m-WOMAC®) format in random order. ---------- Results: 24 men and 38 women with hip and knee OA participated and successfully completed the m-WOMAC® questionnaire. Pearson correlations between the summated total index scores for the p-WOMAC® and m-WOMAC® pre- and post-surgery were 0.98 and 0.99 (p<0.0001). There was no clinically important or statistically significant between-method difference in the adjusted total summated scores, pre- and post-surgery (adjusted mean difference = 4.44, p = 0.474 and 1.73, p = 0.781). Internal consistency estimates of m-WOMAC® reliability were 0.87 – 0.98. The m-WOMAC® detected clinically important, statistically significant (p<0.0001) improvements in pain, stiffness, function and total index score. ---------- Conclusions: Sixty-two patients with hip and knee OA successfully completed EDC by Motorola V3 mobile phone using the m-WOMAC® NRS3.1 Index; completion times averaging only 1-1.5 minutes longer than the p-WOMAC® Index. Data were successfully and securely transmitted from patients in Australia to a server in the USA. There was close agreement and no significant differences between m-WOMAC® and p-WOMAC® scores. This study confirms the validity, reliability and responsiveness of the Exco InTouch engineered, Java-based m-WOMAC® Index application. EDC with the m-WOMAC® Index provides unique opportunities for using quantitative measurement in clinical research and practice.

ERTP : Energy-efficient and reliable transport protocol for data streaming in wireless sensor networks

Emerging data streaming applications in Wireless Sensor Networks require reliable and energy-efficient Transport Protocols. Our recent Wireless Sensor Network deployment in the Burdekin delta, Australia, for water monitoring [T. Le Dinh, W. Hu, P. Sikka, P. Corke, L. Overs, S. Brosnan, Design and deployment of a remote robust sensor network: experiences from an outdoor water quality monitoring network, in: Second IEEE Workshop on Practical Issues in Building Sensor Network Applications (SenseApp 2007), Dublin, Ireland, 2007] is one such example. This application involves streaming sensed data such as pressure, water flow rate, and salinity periodically from many scattered sensors to the sink node which in turn relays them via an IP network to a remote site for archiving, processing, and presentation. While latency is not a primary concern in this class of application (the sampling rate is usually in terms of minutes or hours), energy-efficiency is. Continuous long-term operation and reliable delivery of the sensed data to the sink are also desirable. This paper proposes ERTP, an Energy-efficient and Reliable Transport Protocol for Wireless Sensor Networks. ERTP is designed for data streaming applications, in which sensor readings are transmitted from one or more sensor sources to a base station (or sink). ERTP uses a statistical reliability metric which ensures the number of data packets delivered to the sink exceeds the defined threshold. Our extensive discrete event simulations and experimental evaluations show that ERTP is significantly more energyefficient than current approaches and can reduce energy consumption by more than 45% when compared to current approaches. Consequently, sensor nodes are more energy-efficient and the lifespan of the unattended WSN is increased.

Animal Control - What constitutes a reliable cue to stop animal movement ?

Controlling free-ranging livestock requires low-stress cues to alter animal behaviour. Recently modulated sound and electric shock were demonstrated to be effective in controlling free-ranging cattle. In this study the behaviour of 60, 300 kg Belmont Red heifers were observed for behavioural changes when presented cues designed to impede their movement through an alley. The heifers were given an overnight drylot shrink off feed but not drinking water prior to being tested. Individual cattle were allowed to move down a 6.5 m wide alley towards a pen of peers and feed located 71 m from their point of release. Each animal was allowed to move through the alley unimpeded five times to establish a basal behavioural pattern. Animals were then randomly assigned to treatments consisting of sound plus shock, vibration plus shock, a visual cue plus shock, shock by itself and a control. The time each animal required to reach the pen of peers and feed was recorded. If the animal was prevented from reaching the pen of peers and feed by not penetrating through the cue barrier at set points along the alley for at least 60 sec the test was stopped and the animal was returned to peers located behind the release pen. Cues and shock were manually applied from a laptop while animals were observed from a 3.5 m tower located outside the alley. Electric shock, sound, vibration and Global Position System (GPS) hardware were housed in a neck collar. Results and implications will be discussed.

Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

Faster pairing computations on curves with high-degree twists

Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high- degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Delaying mismatched field multiplications in pairing computations

Miller’s algorithm for computing pairings involves perform- ing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field Fpk are multiplied by elements contained in proper subfields F pk/d , and by elements in the base field Fp . We show that significant speedups in pairing computations can be achieved by delaying these “mismatched” multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.