Piecewise Convex Curves and their Integral Representation

2000 Mathematics Subject Classification: 52A10.

ARCS collaboration tools

The Australian Research Collaboration Service (ARCS) has been supporting a wide range of Collaboration Services and Tools which have been allowing researchers, groups and research communities to share ideas and collaborate across organisational boundaries.----- This talk will give an introduction to a number of exciting technologies which are now available. Focus will be on two main areas of Video Collaboration Tools, allowing researchers to talk face-to-face and share data in real-time, and Web Collaboration Tools, allowing researchers to share information and ideas with other like-minded researchers irrespective of distance or organisational structure. A number of examples will also be shown of how these technologies have been used with in various research communities.----- A brief introduction will be given to a number of services which ARCS is now operating and/or supporting such as:--- * EVO – A video conferencing application, which is particularly suited to desktop or low bandwidth applications.--- * AccessGrid – An open source video conferencing and collaboration tool kit, which is great for room to room meetings.--- * Sakai – An online collaboration and learning environment, support teaching and learning, ad hoc group collaboration, support for portfolios and research collaboration.--- * Plone – A ready-to-run content management system, that provides you with a system for managing web content that is ideal for project groups, communities, web sites, extranets and intranets.--- * Wikis – A way to easily create, edit, and link pages together, to create collaborative websites.

ARCS collaboration tools and support workshop

Registration fees for this workshop are being met by ARCS. There is no cost to attend; however space is limited.----- The Australian Research Collaboration Service (ARCS) has been supporting a wide range of Collaboration Services and Tools which have been allowing researchers, groups and research communities to share ideas and collaborate across organisational boundaries.----- This workshop will give an introduction into a number of web based and real-time collaboration tools and services which researchers may find useful for day-to-day collaboration with members of a research team located within an institution or across institutions. Attendees will be shown how a number of these tools work with strong emphasis placed on how these tools can help facilitate communication and collaboration. Attendees will have the opportunity to try out a number of examples themselves, and interact with the workshop staff to discuss how their own use cases could benefit from the tools and services which can be provided.----- Outline: A hands on introduction will be given to a number of services which ARCS is now operating and/or supporting such as:--- * EVO – A video conferencing environment, which is particularly suited to desktop or low bandwidth applications.--- * AccessGrid – An open source video conferencing and collaboration tool kit, which is great for room to room meetings.--- * Sakai – An online collaboration and learning environment, support teaching and learning, ad hoc group collaboration, support for portfolios and research collaboration.--- * Plone and Drupal – A ready-to-run content management system, that provides you with a system for managing web content that is ideal for project groups, communities, web sites, extranets and intranets.--- * Wikis – A way to easily create, edit, and link pages together, to create collaborative websites.

Soundness of workflow nets with reset arcs

Petri nets are often used to model and analyze workflows. Many workflow languages have been mapped onto Petri nets in order to provide formal semantics or to verify correctness properties. Typically, the so-called Workflow nets are used to model and analyze workflows and variants of the classical soundness property are used as a correctness notion. Since many workflow languages have cancelation features, a mapping to workflow nets is not always possible. Therefore, it is interesting to consider workflow nets with reset arcs. Unfortunately, soundness is undecidable for workflow nets with reset arcs. In this paper, we provide a proof and insights into the theoretical limits of workflow verification.

Optimal strategies and minimax lower bounds for online convex games

A number of learning problems can be cast as an Online Convex Game: on each round, a learner makes a prediction x from a convex set, the environment plays a loss function f, and the learner’s long-term goal is to minimize regret. Algorithms have been proposed by Zinkevich, when f is assumed to be convex, and Hazan et al., when f is assumed to be strongly convex, that have provably low regret. We consider these two settings and analyze such games from a minimax perspective, proving minimax strategies and lower bounds in each case. These results prove that the existing algorithms are essentially optimal.

Cryptanalysis of the convex hull click human identification protocol

Recently, a convex hull-based human identification protocol was proposed by Sobrado and Birget, whose steps can be performed by humans without additional aid. The main part of the protocol involves the user mentally forming a convex hull of secret icons in a set of graphical icons and then clicking randomly within this convex hull. While some rudimentary security issues of this protocol have been discussed, a comprehensive security analysis has been lacking. In this paper, we analyze the security of this convex hull-based protocol. In particular, we show two probabilistic attacks that reveal the user’s secret after the observation of only a handful of authentication sessions. These attacks can be efficiently implemented as their time and space complexities are considerably less than brute force attack. We show that while the first attack can be mitigated through appropriately chosen values of system parameters, the second attack succeeds with a non-negligible probability even with large system parameter values that cross the threshold of usability.

Cryptanalysis of the convex hull click human identification protocol

Recently a convex hull based human identification protocol was proposed by Sobrado and Birget, whose steps can be performed by humans without additional aid. The main part of the protocol involves the user mentally forming a convex hull of secret icons in a set of graphical icons and then clicking randomly within this convex hull. In this paper we show two efficient probabilistic attacks on this protocol which reveal the user’s secret after the observation of only a handful of authentication sessions. We show that while the first attack can be mitigated through appropriately chosen values of system parameters, the second attack succeeds with a non-negligible probability even with large system parameter values which cross the threshold of usability.

Matching image sets via adaptive multi convex hull

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image set. Existing multi-model approaches extract local models by clustering each image set individually only once, with fixed clusters used for matching with various image sets. This may not be optimal for discrimination, as undesirable environmental conditions (eg. illumination and pose variations) may result in the two closest clusters representing different characteristics of an object (eg. frontal face being compared to non-frontal face). To address the above problem, we propose a novel approach to enhance nearest points based methods by integrating affine/convex hull classification with an adapted multi-model approach. We first extract multiple local convex hulls from a query image set via maximum margin clustering to diminish the artificial variations and constrain the noise in local convex hulls. We then propose adaptive reference clustering (ARC) to constrain the clustering of each gallery image set by forcing the clusters to have resemblance to the clusters in the query image set. By applying ARC, noisy clusters in the query set can be discarded. Experiments on Honda, MoBo and ETH-80 datasets show that the proposed method outperforms single model approaches and other recent techniques, such as Sparse Approximated Nearest Points, Mutual Subspace Method and Manifold Discriminant Analysis.

Separable spatiotemporal priors for convex reconstruction of time-varying 3D point clouds

Reconstructing 3D motion data is highly under-constrained due to several common sources of data loss during measurement, such as projection, occlusion, or miscorrespondence. We present a statistical model of 3D motion data, based on the Kronecker structure of the spatiotemporal covariance of natural motion, as a prior on 3D motion. This prior is expressed as a matrix normal distribution, composed of separable and compact row and column covariances. We relate the marginals of the distribution to the shape, trajectory, and shape-trajectory models of prior art. When the marginal shape distribution is not available from training data, we show how placing a hierarchical prior over shapes results in a convex MAP solution in terms of the trace-norm. The matrix normal distribution, fit to a single sequence, outperforms state-of-the-art methods at reconstructing 3D motion data in the presence of significant data loss, while providing covariance estimates of the imputed points.

A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.