Chronological categorization and decomposition of customer loads

The majority of distribution utilities do not have accurate information on the constituents of their loads. This information is very useful in managing and planning the network, adequately and economically. Customer loads are normally categorized in three main sectors: 1) residential; 2) industrial; and 3) commercial. In this paper, penalized least-squares regression and Euclidean distance methods are developed for this application to identify and quantify the makeup of a feeder load with unknown sectors/subsectors. This process is done on a monthly basis to account for seasonal and other load changes. The error between the actual and estimated load profiles are used as a benchmark of accuracy. This approach has shown to be accurate in identifying customer types in unknown load profiles, and is used in cross-validation of the results and initial assumptions.

Kernel analysis on Grassmann manifolds for action recognition

Modelling video sequences by subspaces has recently shown promise for recognising human actions. Subspaces are able to accommodate the effects of various image variations and can capture the dynamic properties of actions. Subspaces form a non-Euclidean and curved Riemannian manifold known as a Grassmann manifold. Inference on manifold spaces usually is achieved by embedding the manifolds in higher dimensional Euclidean spaces. In this paper, we instead propose to embed the Grassmann manifolds into reproducing kernel Hilbert spaces and then tackle the problem of discriminant analysis on such manifolds. To achieve efficient machinery, we propose graph-based local discriminant analysis that utilises within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, respectively. Experiments on KTH, UCF Sports, and Ballet datasets show that the proposed approach obtains marked improvements in discrimination accuracy in comparison to several state-of-the-art methods, such as the kernel version of affine hull image-set distance, tensor canonical correlation analysis, spatial-temporal words and hierarchy of discriminative space-time neighbourhood features.

Planar difference functions

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.

Mutually unbiased bases as submodules and subspaces

Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with projective and affine planes. We propose a connection with higher dimensional projective geometries and projective Hjelmslev geometries. We show that this proposed geometric structure is present in several constructions of MUBs.

Repeating patterns : strategies to assist young students to generalise the mathematical structure

This paper focuses on very young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5-10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns.

Modelling the information seeking user by the decision they make

The article focuses on how the information seeker makes decisions about relevance. It will employ a novel decision theory based on quantum probabilities. This direction derives from mounting research within the field of cognitive science showing that decision theory based on quantum probabilities is superior to modelling human judgements than standard probability models [2, 1]. By quantum probabilities, we mean decision event space is modelled as vector space rather than the usual Boolean algebra of sets. In this way,incompatible perspectives around a decision can be modelled leading to an interference term which modifies the law of total probability. The interference term is crucial in modifying the probability judgements made by current probabilistic systems so they align better with human judgement. The goal of this article is thus to model the information seeker user as a decision maker. For this purpose, signal detection models will be sketched which are in principle applicable in a wide variety of information seeking scenarios.

A family of Alltop functions that are EA-inequivalent to the cubic function

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (\emph{IEEE Trans. Inf. Theory} 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these sequences were optimal with respect to the known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases (MUBs), a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called \emph{Alltop functions}. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs.

Pre-crash and non-crash traffic flow trends analysis on motorways

Crashes that occur on motorways contribute to a significant proportion (40-50%) of non-recurrent motorway congestions. Hence, reducing the frequency of crashes assists in addressing congestion issues (Meyer, 2008). Crash likelihood estimation studies commonly focus on traffic conditions in a short time window around the time of a crash while longer-term pre-crash traffic flow trends are neglected. In this paper we will show, through data mining techniques that a relationship between pre-crash traffic flow patterns and crash occurrence on motorways exists. We will compare them with normal traffic trends and show this knowledge has the potential to improve the accuracy of existing models and opens the path for new development approaches. The data for the analysis was extracted from records collected between 2007 and 2009 on the Shibuya and Shinjuku lines of the Tokyo Metropolitan Expressway in Japan. The dataset includes a total of 824 rear-end and sideswipe crashes that have been matched with crashes corresponding to traffic flow data using an incident detection algorithm. Traffic trends (traffic speed time series) revealed that crashes can be clustered with regards to the dominant traffic patterns prior to the crash. Using the K-Means clustering method with Euclidean distance function allowed the crashes to be clustered. Then, normal situation data was extracted based on the time distribution of crashes and were clustered to compare with the “high risk” clusters. Five major trends have been found in the clustering results for both high risk and normal conditions. The study discovered traffic regimes had differences in the speed trends. Based on these findings, crash likelihood estimation models can be fine-tuned based on the monitored traffic conditions with a sliding window of 30 minutes to increase accuracy of the results and minimize false alarms.

Perspectives on Reconceptualizing Early Mathematics Learning

This introductory section provides an overview of the different perspectives on reconceptualizing early mathematics learning. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualizing the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed. Although these themes are diffused throughout the chapters, we restrict our introduction to the core focus of each of the chapters.

Crunch time : how did the students perform?

Two newspaper numbers games based on simple arithmetic relationships are discussed. One is rather trivial, but very useful as an introduction to the second, whose potential to give students of elementary algebra practice in semi ad-hoc reasoning and to build general arithmetic reasoning skills was explored theoretically in an earlier paper. Preliminary results on the effectiveness of this general approach are presented, with student performance and feedback on an assignment task and formal examination included, and recommendations for future work.

Control of an underactuated-slender-hull unmanned underwater vehicle using Port-Hamiltonian theory

This paper presents a control design for tracking of attitude and speed of an underactuated slender-hull unmanned underwater vehicle (UUV). The control design is based on Port-Hamiltonian theory. The target dynamics (desired dynamic response) is shaped with particular attention to the target mass matrix so that the influence of the unactuated dynamics on the controlled system is suppressed. This results in achievable dynamics independent of uncontrolled states. Throughout the design, insight of the physical phenomena involved is used to propose the desired target dynamics. The performance of the design is demonstrated through simulation with a high-fidelity model.

Random projections on manifolds of symmetric positive definite matrices for image classification

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account manifold geometry is typically done via (1) embedding the manifolds in tangent spaces, or (2) embedding into Reproducing Kernel Hilbert Spaces (RKHS). While embedding into tangent spaces allows the use of existing Euclidean-based learning algorithms, manifold shape is only approximated which can cause loss of discriminatory information. The RKHS approach retains more of the manifold structure, but may require non-trivial effort to kernelise Euclidean-based learning algorithms. In contrast to the above approaches, in this paper we offer a novel solution that allows SPD matrices to be used with unmodified Euclidean-based learning algorithms, with the true manifold shape well-preserved. Specifically, we propose to project SPD matrices using a set of random projection hyperplanes over RKHS into a random projection space, which leads to representing each matrix as a vector of projection coefficients. Experiments on face recognition, person re-identification and texture classification show that the proposed approach outperforms several recent methods, such as Tensor Sparse Coding, Histogram Plus Epitome, Riemannian Locality Preserving Projection and Relational Divergence Classification.

Dictionary learning and sparse coding on Grassmann manifolds : an extrinsic solution

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis.

Multi-shot person re-identification via relational stein divergence

Person re-identification is particularly challenging due to significant appearance changes across separate camera views. In order to re-identify people, a representative human signature should effectively handle differences in illumination, pose and camera parameters. While general appearance-based methods are modelled in Euclidean spaces, it has been argued that some applications in image and video analysis are better modelled via non-Euclidean manifold geometry. To this end, recent approaches represent images as covariance matrices, and interpret such matrices as points on Riemannian manifolds. As direct classification on such manifolds can be difficult, in this paper we propose to represent each manifold point as a vector of similarities to class representers, via a recently introduced form of Bregman matrix divergence known as the Stein divergence. This is followed by using a discriminative mapping of similarity vectors for final classification. The use of similarity vectors is in contrast to the traditional approach of embedding manifolds into tangent spaces, which can suffer from representing the manifold structure inaccurately. Comparative evaluations on benchmark ETHZ and iLIDS datasets for the person re-identification task show that the proposed approach obtains better performance than recent techniques such as Histogram Plus Epitome, Partial Least Squares, and Symmetry-Driven Accumulation of Local Features.

The Number Crunch game : a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.