The 'Dirty Work' of the Lie

The panel "Duplicity/Complicity: Performing and Misperforming Lies" at PSi #15 in Croatia in July 2009 examined the half-truths, hidden assumptions and power relations embedded in every act of performance through an analysis of the way bodies, buildings, personae and communities perform and misperform lies. It was a collection of new academic voices from Australia and Croatia, intersecting and colliding and, at times, outright lying, with each other and with commentary from Alan Read. Inspired by this successful adventure in collaborative academic mis-performance, "The ‘Dirty Work’ of the Lie" takes the challenge set by the Prelude Panel at PSI #15 and subjects the ideas emerging from this panel to "friendly fire" in order to build a multi authored response to 'performance that lies', with reference to the work of A Chorus of Women, disabled artists Bill Shannon, Aaron Williamson and Kathryn Araneillo, US dance performer Ann Liv Young and US theatre and festival director Peter Sellars. In doing so, "The 'Dirty Work' of the Lie" provides a reflexive response to the duplicity inherent in the performances, and also in our own academic analyses. With Alan Read acting as interlocutor, each contributor will creatively respond to a paper presented by another, developing the key intersecting issues that emerged through the formation of the panel. These issues include impression management, self-belief and performers who are 'taken in by their own act', the dirty work of taking others in with an act, the guerrilla dimension of lying, the productivity of the lie, and questions of audience engagement and ethics. As a result, this new paper tests how the 'misperformance' of lies across different cultural sites, be it deliberate or accidental, can become a productive – and, indeed, politicised – aspect of cultural performance, betraying accepted attitudes, ideas and structures of authority and offering alternative visions. Through it’s distinctively multi vocal texture, "The 'Dirty Work' of the Lie" also interrogates the modes of analysis available to us, questioning the 'duplicity' in our reflecting, responding and listening to each other as well as the work.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Sequential development of algebra knowledge : a cognitive analysis

Learning to operate algebraically is a complex process that is dependent upon extending arithmetic knowledge to the more complex concepts of algebra. Current research has shown a gap between arithmetic and algebraic knowledge and suggests a pre-algebraic level as a step between the two knowledge types. This paper examines arithmetic and algebraic knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Results of a longitudinal study designed to investigate students' readiness for algebra are presented. Thirty-three students in Grades 7, 8, and 9 participated. A model for the transition from arithmetic to pre-algebra to algebra is proposed and students' understanding of relevant knowledge is discussed.

RcppArmadillo : accelerating R with high-performance C++ linear algebra

The R statistical environment and language has demonstrated particular strengths for interactive development of statistical algorithms, as well as data modelling and visualisation. Its current implementation has an interpreter at its core which may result in a performance penalty in comparison to directly executing user algorithms in the native machine code of the host CPU. In contrast, the C++ language has no built-in visualisation capabilities, handling of linear algebra or even basic statistical algorithms; however, user programs are converted to high-performance machine code, ahead of execution. A new method avoids possible speed penalties in R by using the Rcpp extension package in conjunction with the Armadillo C++ matrix library. In addition to the inherent performance advantages of compiled code, Armadillo provides an easy-to-use template-based meta-programming framework, allowing the automatic pooling of several linear algebra operations into one, which in turn can lead to further speedups. With the aid of Rcpp and Armadillo, conversion of linear algebra centered algorithms from R to C++ becomes straightforward. The algorithms retains the overall structure as well as readability, all while maintaining a bidirectional link with the host R environment. Empirical timing comparisons of R and C++ implementations of a Kalman filtering algorithm indicate a speedup of several orders of magnitude.

Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

Robust numeric set watermarking : numbers don’t lie

Ever since Cox et. al published their paper, “A Secure, Robust Watermark for Multimedia” in 1996 [6], there has been tremendous progress in multimedia watermarking. The same pattern re-emerged with Agrawal and Kiernan publishing their work “Watermarking Relational Databases” in 2001 [1]. However, little attention has been given to primitive data collections with only a handful works of research known to the authors [11, 10]. This is primarily due to the absence of an attribute that differentiates marked items from unmarked item during insertion and detection process. This paper presents a distribution-independent, watermarking model that is secure against secondary-watermarking in addition to conventional attacks such as data addition, deletion and distortion. The low false positives and high capacity provide additional strength to the scheme. These claims are backed by experimental results provided in the paper.

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.

Multipliers of Sobolev spaces

Let Wm,p denote the Sobolev space of functions on Image n whose distributional derivatives of order up to m lie in Lp(Image n) for 1 less-than-or-equals, slant p less-than-or-equals, slant ∞. When 1 < p < ∞, it is known that the multipliers on Wm,p are the same as those on Lp. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order less-than-or-equals, slant1 whose first order derivatives are also integrable of order less-than-or-equals, slant1, belong to the class of multipliers on Wm,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on Lp, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on Wm,l are necessarily integrable distributions of order less-than-or-equals, slant1 or less-than-or-equals, slant2 accordingly as m is odd or even. We have obtained the multipliers from L1(Image n) into Wm,p, 1 less-than-or-equals, slant p less-than-or-equals, slant ∞, and the multiplier space of Wm,1 is realised as a dual space of certain continuous functions on Image n which vanish at infinity.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

A denotational semantics for the generalized ER model and a simple ER algebra

The recent spurt of research activities in Entity-Relationship Approach to databases calls for a close scrutiny of the semantics of the underlying Entity-Relationship models, data manipulation languages, data definition languages, etc. For reasons well known, it is very desirable and sometimes imperative to give formal description of the semantics. In this paper, we consider a specific ER model, the generalized Entity-Relationship model (without attributes on relationships) and give denotational semantics for the model as well as a simple ER algebra based on the model. Our formalism is based on the Vienna Development Method—the meta language (VDM). We also discuss the salient features of the given semantics in detail and suggest directions for further work.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.