Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Characterising anomalous events using change point correlation on unsolicited network traffic

Monitoring unused or dark IP addresses offers opportunities to extract useful information about both on-going and new attack patterns. In recent years, different techniques have been used to analyze such traffic including sequential analysis where a change in traffic behavior, for example change in mean, is used as an indication of malicious activity. Change points themselves say little about detected change; further data processing is necessary for the extraction of useful information and to identify the exact cause of the detected change which is limited due to the size and nature of observed traffic. In this paper, we address the problem of analyzing a large volume of such traffic by correlating change points identified in different traffic parameters. The significance of the proposed technique is two-fold. Firstly, automatic extraction of information related to change points by correlating change points detected across multiple traffic parameters. Secondly, validation of the detected change point by the simultaneous presence of another change point in a different parameter. Using a real network trace collected from unused IP addresses, we demonstrate that the proposed technique enables us to not only validate the change point but also extract useful information about the causes of change points.

Intrusion detection techniques in wireless local area networks

This research investigates wireless intrusion detection techniques for detecting attacks on IEEE 802.11i Robust Secure Networks (RSNs). Despite using a variety of comprehensive preventative security measures, the RSNs remain vulnerable to a number of attacks. Failure of preventative measures to address all RSN vulnerabilities dictates the need for a comprehensive monitoring capability to detect all attacks on RSNs and also to proactively address potential security vulnerabilities by detecting security policy violations in the WLAN. This research proposes novel wireless intrusion detection techniques to address these monitoring requirements and also studies correlation of the generated alarms across wireless intrusion detection system (WIDS) sensors and the detection techniques themselves for greater reliability and robustness. The specific outcomes of this research are: A comprehensive review of the outstanding vulnerabilities and attacks in IEEE 802.11i RSNs. A comprehensive review of the wireless intrusion detection techniques currently available for detecting attacks on RSNs. Identification of the drawbacks and limitations of the currently available wireless intrusion detection techniques in detecting attacks on RSNs. Development of three novel wireless intrusion detection techniques for detecting RSN attacks and security policy violations in RSNs. Development of algorithms for each novel intrusion detection technique to correlate alarms across distributed sensors of a WIDS. Development of an algorithm for automatic attack scenario detection using cross detection technique correlation. Development of an algorithm to automatically assign priority to the detected attack scenario using cross detection technique correlation.

Science and subjectivity

Science has been under attack in the last thirty years, and recently a number of prominent scientists have been busy fighting back. Here, an argument is presented that the `science wars' stem from an unreasonably strict adherence to the reductive method on the part of science, but that weakening this stance need not imply a lapse into subjectivity. One possible method for formalising the description of non-separable, contextually dependent complex systems is presented. This is based upon a quantum-like approach.

Telcagepant is a new oral treatment for migraine

Background : Migraine is a common cause of disability. Many subjects (30 – 40%) do not respond to the 5-HT 1B/1D agonists (the triptans) commonly used in the treatment of migraine attacks. Calcitonin gene-related protein (CGRP) receptor antagonism is a new approach to the treatment of migraine attacks. Objectives/methods : This evaluation is of a Phase III clinical trial comparing telcagepant, an orally active CGRP receptor antagonist, with zolmitriptan in subjects during an attack of migraine. Results : Telcagepant 300 mg has a similar efficacy to zolmitriptan in relieving pain, phonophobia, photophobia, and nausea. Telcagepant was better tolerated than zolmitriptan. Conclusions : The initial Phase III clinical trial results with telcagepant are promising but several further clinical trials are needed to determine the place of telcagepant in the treatment of migraine attacks

Detecting and characterising malicious executable payloads

Buffer overflow vulnerabilities continue to prevail and the sophistication of attacks targeting these vulnerabilities is continuously increasing. As a successful attack of this type has the potential to completely compromise the integrity of the targeted host, early detection is vital. This thesis examines generic approaches for detecting executable payload attacks, without prior knowledge of the implementation of the attack, in such a way that new and previously unseen attacks are detectable. Executable payloads are analysed in detail for attacks targeting the Linux and Windows operating systems executing on an Intel IA-32 architecture. The execution flow of attack payloads are analysed and a generic model of execution is examined. A novel classification scheme for executable attack payloads is presented which allows for characterisation of executable payloads and facilitates vulnerability and threat assessments, and intrusion detection capability assessments for intrusion detection systems. An intrusion detection capability assessment may be utilised to determine whether or not a deployed system is able to detect a specific attack and to identify requirements for intrusion detection functionality for the development of new detection methods. Two novel detection methods are presented capable of detecting new and previously unseen executable attack payloads. The detection methods are capable of identifying and enumerating the executable payload’s interactions with the operating system on the targeted host at the time of compromise. The detection methods are further validated using real world data including executable payload attacks.

Using honeypots to analyse anomalous Internet activities

Monitoring Internet traffic is critical in order to acquire a good understanding of threats to computer and network security and in designing efficient computer security systems. Researchers and network administrators have applied several approaches to monitoring traffic for malicious content. These techniques include monitoring network components, aggregating IDS alerts, and monitoring unused IP address spaces. Another method for monitoring and analyzing malicious traffic, which has been widely tried and accepted, is the use of honeypots. Honeypots are very valuable security resources for gathering artefacts associated with a variety of Internet attack activities. As honeypots run no production services, any contact with them is considered potentially malicious or suspicious by definition. This unique characteristic of the honeypot reduces the amount of collected traffic and makes it a more valuable source of information than other existing techniques. Currently, there is insufficient research in the honeypot data analysis field. To date, most of the work on honeypots has been devoted to the design of new honeypots or optimizing the current ones. Approaches for analyzing data collected from honeypots, especially low-interaction honeypots, are presently immature, while analysis techniques are manual and focus mainly on identifying existing attacks. This research addresses the need for developing more advanced techniques for analyzing Internet traffic data collected from low-interaction honeypots. We believe that characterizing honeypot traffic will improve the security of networks and, if the honeypot data is handled in time, give early signs of new vulnerabilities or breakouts of new automated malicious codes, such as worms. The outcomes of this research include: • Identification of repeated use of attack tools and attack processes through grouping activities that exhibit similar packet inter-arrival time distributions using the cliquing algorithm; • Application of principal component analysis to detect the structure of attackers’ activities present in low-interaction honeypots and to visualize attackers’ behaviors; • Detection of new attacks in low-interaction honeypot traffic through the use of the principal component’s residual space and the square prediction error statistic; • Real-time detection of new attacks using recursive principal component analysis; • A proof of concept implementation for honeypot traffic analysis and real time monitoring.

Mitigating sandwich attacks against a secure key management scheme in wireless sensor networks for PCS/SCADA

Alzaid et al. proposed a forward & backward secure key management scheme in wireless sensor networks for Process Control Systems (PCSs) or Supervisory Control and Data Acquisition (SCADA) systems. The scheme, however, is still vulnerable to an attack called the sandwich attack that can be launched when the adversary captures two sensor nodes at times t1 and t2, and then reveals all the group keys used between times t1 and t2. In this paper, a fix to the scheme is proposed in order to limit the vulnerable time duration to an arbitrarily chosen time span while keeping the forward and backward secrecy of the scheme untouched. Then, the performance analysis for our proposal, Alzaid et al.’s scheme, and Nilsson et al.’s scheme is given.

H-house

The author's approach to the problems associated with building in bushfire prone landscapes comes from 12 years of study of the biophysical and cultural landscapes in the Great Southern Region of Western Australia - research which resulted in the design and construction of the H-house at Bremer Bay. The house was developed using a 'ground up' approach whereby Dr Weir conducted topographical surveys and worked with a local botanist and a bushfire risk consultant to ascertain the level of threat that fire presented to this particular site. The intention from the outset however, was not to design a bushfire resistant house per se, but to develop a design which would place the owners in close proximity to the highly biodiverse heath vegetation of their site. The research aim was to find ways - through architectural design-to link the patterns of usage of the house with other site specific conditions related to the prevailing winds, solar orientation and seasonal change. The H-house has a number of features which increase the level of bushfire safety. These include: Fire rated roller shutters (tested by the CSIRO for ember attack and radiant heat), Fire resistant double glazing (on windows not protected by the shutters), Fibre-cement sheet cladding of the underside of the elevated timber floor structure, Manually operated high pressure sprinkler system on exposed timber decks, A fire refuge (an enlarged laundry, shower area) within the house with a dedicated cabinet for fire fighting equipment) and A low pressure solar powered domestic water supply system.

Uncertainty based MDO of UAS using HAPMOEA

CFD has been successfully used in the optimisation of aerodynamic surfaces using a given set of parameters such as Mach numbers and angle of attack. While carrying out a multidisciplinary design optimisation one deals with situations where the parameters have some uncertain attached. Any optimisation carried out for fixed values of input parameters gives a design which may be totally unacceptable under off-design conditions. The challenge is to develop a robust design procedure which takes into account the fluctuations in the input parameters. In this work, we attempt this using a modified Taguchi approach. This is incorporated into an evolutionary algorithm with many features developed in house. The method is tested for an UCAV design which simultaneously handles aerodynamics, electromagnetics and maneuverability. Results demonstrate that the method has considerable potential.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Exponential asymptotics with multiple stokes lines

When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.

Detection and prevention of distributed denial of services attacks by collaborative effort of software agents, first prototype implementation

Distributed Denial of Services DDoS, attacks has become one of the biggest threats for resources over Internet. Purpose of these attacks is to make servers deny from providing services to legitimate users. These attacks are also used for occupying media bandwidth. Currently intrusion detection systems can just detect the attacks but cannot prevent / track the location of intruders. Some schemes also prevent the attacks by simply discarding attack packets, which saves victim from attack, but still network bandwidth is wasted. In our opinion, DDoS requires a distributed solution to save wastage of resources. The paper, presents a system that helps us not only in detecting such attacks but also helps in tracing and blocking (to save the bandwidth as well) the multiple intruders using Intelligent Software Agents. The system gives dynamic response and can be integrated with the existing network defense systems without disturbing existing Internet model. We have implemented an agent based networking monitoring system in this regard.

A simple and systematic approach to assigning Denavit-Hartenberg Parameters

This paper presents a simple and intuitive approach to determining the kinematic parameters of a serial-link robot in Denavit– Hartenberg (DH) notation. Once a manipulator’s kinematics is parameterized in this form, a large body of standard algorithms and code implementations for kinematics, dynamics, motion planning, and simulation are available. The proposed method has two parts. The first is the “walk through,” a simple procedure that creates a string of elementary translations and rotations, from the user-defined base coordinate to the end-effector. The second step is an algebraic procedure to manipulate this string into a form that can be factorized as link transforms, which can be represented in standard or modified DH notation. The method allows for an arbitrary base and end-effector coordinate system as well as an arbitrary zero joint angle pose. The algebraic procedure is amenable to computer algebra manipulation and a Java program is available as supplementary downloadable material.