On secure multi-party computation in black-box groups

We study the natural problem of secure n-party computation (in the passive, computationally unbounded attack model) of the n-product function f G (x 1,...,x n ) = x 1 ·x 2 ⋯ x n in an arbitrary finite group (G,·), where the input of party P i is x i  ∈ G for i = 1,...,n. For flexibility, we are interested in protocols for f G which require only black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our results are as follows. First, on the negative side, we show that if (G,·) is non-abelian and n ≥ 4, then no ⌈n/2⌉-private protocol for computing f G exists. Second, on the positive side, we initiate an approach for construction of black-box protocols for f G based on k-of-k threshold secret sharing schemes, which are efficiently implementable over any black-box group G. We reduce the problem of constructing such protocols to a combinatorial colouring problem in planar graphs. We then give two constructions for such graph colourings. Our first colouring construction gives a protocol with optimal collusion resistance t < n/2, but has exponential communication complexity O(n*2t+1^2/t) group elements (this construction easily extends to general adversary structures). Our second probabilistic colouring construction gives a protocol with (close to optimal) collusion resistance t < n/μ for a graph-related constant μ ≤ 2.948, and has efficient communication complexity O(n*t^2) group elements. Furthermore, we believe that our results can be improved by further study of the associated combinatorial problems.

On-line estimation of Allan variance parameters

A new online method is presented for estimation of the angular random walk and rate random walk coefficients of IMU (inertial measurement unit) gyros and accelerometers. The online method proposes a state space model and proposes parameter estimators for quantities previously measured from off-line data techniques such as the Allan variance graph. Allan variance graphs have large off-line computational effort and data storage requirements. The technique proposed here requires no data storage and computational effort of O(100) calculations per data sample.

Anomaly detection in online social networks : using data-mining techniques and fuzzy logic

This research is a step forward in improving the accuracy of detecting anomaly in a data graph representing connectivity between people in an online social network. The proposed hybrid methods are based on fuzzy machine learning techniques utilising different types of structural input features. The methods are presented within a multi-layered framework which provides the full requirements needed for finding anomalies in data graphs generated from online social networks, including data modelling and analysis, labelling, and evaluation.

Developing young students’ meta-representational competence through integrated mathematics and science investigations

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.

Structuring representations of continuous data through investigations in grade 1

The study of data modelling with elementary students involves the analysis of a developmental process beginning with children’s investigations of meaningful contexts: visualising, structuring, and representing data and displaying data in simple graphs (English, 2012; Lehrer & Schauble, 2005; Makar, Bakker, & Ben-Zvi, 2011). A 3-year longitudinal study investigated young children’s data modelling, integrating mathematical and scientific investigations. One aspect of this study involved a researcher-led teaching experiment with 21 mathematically able Grade 1 students. The study aimed to describe explicit developmental features of students’ representations of continuous data...

A subexponential construction of graph coloring for multiparty computation

We show the first deterministic construction of an unconditionally secure multiparty computation (MPC) protocol in the passive adversarial model over black-box non-Abelian groups which is both optimal (secure against an adversary who possesses any tgraphs. More specifically, following the result of Desmedt et al. (2012) that the problem of MPC over non-Abelian groups can be reduced to finding a t-reliable n-coloring of planar graphs, we show the construction of such a graph which allows a path from the input nodes to the output nodes when any t-party subset is in the possession of the adversary. Unlike the deterministic constructions from Desmedt et al. (2012) our construction has subexponential complexity and is optimal at the same time, i.e., it is secure for any t

Optimisation algorithms for microarray biclustering

In providing simultaneous information on expression profiles for thousands of genes, microarray technologies have, in recent years, been largely used to investigate mechanisms of gene expression. Clustering and classification of such data can, indeed, highlight patterns and provide insight on biological processes. A common approach is to consider genes and samples of microarray datasets as nodes in a bipartite graphs, where edges are weighted e.g. based on the expression levels. In this paper, using a previously-evaluated weighting scheme, we focus on search algorithms and evaluate, in the context of biclustering, several variations of Genetic Algorithms. We also introduce a new heuristic “Propagate”, which consists in recursively evaluating neighbour solutions with one more or one less active conditions. The results obtained on three well-known datasets show that, for a given weighting scheme,optimal or near-optimal solutions can be identified.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

Producing the NAPLAN Machine: A Schizoanalytic Cartography

Everything revolves around desiring-machines and the production of desire… Schizoanalysis merely asks what are the machinic, social and technical indices on a socius that open to desiring-machines (Deleuze & Guattari, 1983, pp. 380-381). Achievement tests like NAPLAN are fairly recent, yet common, education policy initiatives in much of the Western world. They intersect with, use and change pre-existing logics of education, teaching and learning. There has been much written about the form and function of these tests, the ‘stakes’ involved and the effects of their practice. This paper adopts a different “angle of vision” to ask what ‘opens’ education to these regimes of testing(Roy, 2008)? This paper builds on previous analyses of NAPLAN as a modulating machine, or a machine characterised by the increased intensity of connections and couplings. One affect can be “an existential disquiet” as “disciplinary subjects attempt to force coherence onto a disintegrating narrative of self”(Thompson & Cook, 2012, p. 576). Desire operates at all levels of the education assemblage, however our argument is that achievement testing manifests desire as ‘lack’; seen in the desire for improved results, the desire for increased control, the desire for freedom, the desire for acceptance to name a few. For Deleuze and Guattari desire is irreducible to lack, instead desire is productive. As a productive assemblage, education machines operationalise and produce through desire; “Desire is a machine, and the object of the desire is another machine connected to it”(Deleuze & Guattari, 1983, p. 26). This intersection is complexified by the strata at which they occur, the molar and molecular connections and flows they make possible. Our argument is that when attention is paid to the macro and micro connections, the machines built and disassembled as a result of high-stakes testing, a map is constructed that outlines possibilities, desires and blockages within the education assemblage. This schizoanalytic cartography suggests a new analysis of these ‘axioms’ of testing and accountability. It follows the flows and disruptions made possible as different or altered connections are made and as new machines are brought online. Thinking of education machinically requires recognising that “every machine functions as a break in the flow in relation to the machine to which it is connected, but at the same time is also a flow itself, or the production of flow, in relation to the machine connected to it”(Deleuze & Guattari, 1983, p. 37). Through its potential to map desire, desire-production and the production of desire within those assemblages that have come to dominate our understanding of what is possible, Deleuze and Guattari’s method of schizoanalysis provides a provocative lens for grappling with the question of what one can do, and what lines of flight are possible.

Fractal and complex network analyses of protein molecular dynamics

Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal properties of their converted horizontal visibility graphs (HVGs). The energy parameters of protein dynamics we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. The shape of the h(q)h(q) curves from MF-DFA indicates that these time series are multifractal. The numerical values of the exponent h(2)h(2) of MF-DFA show that the series of total energy and potential energy are non-stationary and anti-persistent; the other time series are stationary and persistent apart from series of pressure (with H≈0.5H≈0.5 indicating the absence of long-range correlation). The degree distributions of their converted HVGs show that these networks are exponential. The results of fractal analysis show that fractality exists in these converted HVGs. For each energy, pressure or volume parameter, it is found that the values of h(2)h(2) of MF-DFA on the time series, exponent λλ of the exponential degree distribution and fractal dimension dBdB of their converted HVGs do not change much for different proteins (indicating some universality). We also found that after taking average over all proteins, there is a linear relationship between 〈h(2)〉〈h(2)〉 (from MF-DFA on time series) and 〈dB〉〈dB〉 of the converted HVGs for different energy, pressure and volume.

Potential uses of Bayesian networks as tools for synthesis of systematic reviews of complex interventions

Bayesian networks (BNs) are tools for representing expert knowledge or evidence. They are especially useful for synthesising evidence or belief concerning a complex intervention, assessing the sensitivity of outcomes to different situations or contextual frameworks and framing decision problems that involve alternative types of intervention. Bayesian networks are useful extensions to logic maps when initiating a review or to facilitate synthesis and bridge the gap between evidence acquisition and decision-making. Formal elicitation techniques allow development of BNs on the basis of expert opinion. Such applications are useful alternatives to ‘empty’ reviews, which identify knowledge gaps but fail to support decision-making. Where review evidence exists, it can inform the development of a BN. We illustrate the construction of a BN using a motivating example that demonstrates how BNs can ensure coherence, transparently structure the problem addressed by a complex intervention and assess sensitivity to context, all of which are critical components of robust reviews of complex interventions. We suggest that BNs should be utilised to routinely synthesise reviews of complex interventions or empty reviews where decisions must be made despite poor evidence.

Path algebra for mobile robots

In this paper, we introduce a path algebra well suited for navigation in environments that can be abstracted as topological graphs. From this path algebra, we derive algorithms to reduce routes in such environments. The routes are reduced in the sense that they are shorter (contain fewer edges), but still connect the endpoints of the initial routes. Contrary to planning methods descended from Disjktra’s Shortest Path Algorithm like D , the navigation methods derived from our path algebra do not require any graph representation. We prove that the reduced routes are optimal when the graphs are without cycles. In the case of graphs with cycles, we prove that whatever the length of the initial route, the length of the reduced route is bounded by a constant that only depends on the structure of the environment.

Disorganizing educational tropes: Conceptions of dis/ability and curriculum

A study examined the politics of dis/ability and curriculum. Data were obtained from a review of the new disability studies literature, focusing on the areas of history, sociology, anthropology, and critical legal theory. The results indicate that this new literature challenges popular psychoeducational models that assume disability as an objective medical, individual, and pathological deficiency, effectively restricting the systematic study of dis/ability as relational, external, shifting, and socially constituted. The findings suggest ways in which perceptions of “school problems” have to be adjusted to understand how the constant refiguration of normativities in everyday activities creates perceptions of disability-negative ontologies, generates experiences that incite efforts to modify those perceptions in multiple ways, and produces unintended effects from well-intended approaches that in the end remain irreducible to simplistic definitions for the one “ethical” or “politically correct” strategy.

Borders, belonging, beyond: New curriculum history

For Iain Chambers, understanding the redefinition of social life and hence of social theories is not aided by splitting the analytical register simply between global and local. This is especially problematic if global is taken to mean the dispersal of an already-dominant or privileged version of the local within wider coordinates that ensure the continuation of forms of representation and frames of reference that are familiar and over-exposed. The chapters in New Curriculum History take up the challenge posed by Chambers, collectively confronting the dread of a rationality confronted with what exceeds and slips its grasp. Finding purchase and continually slipping away from the strictures of the taken-for-granted and of fixity, New Curriculum History embodies the dueling reverberations of its non-localizable domains – in some ways, a shaping by its pasts and in others, contributions irreducible to dominant narratives about the field of education and “its” histories...

Hardness of a surface containing uniformly spaced pyramidal asperities

Pyramidal asperities of different apical angle were machined on a flat copper surface. Hardness was estimated from the load-displacement graphs obtained by pressing a spherical rigid indenter onto the asperities. The variation of hardness with apical angle and pitch was recorded with a view to contributing to the development of a general framework for relating measured hardness to the surface roughness.