On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.

Progress report from the strategic sanctuary for the destruction of free will

Progress Report from the Strategic Sanctuary for the Destruction of Free Will presents a new work combining film, music and installation that juxtaposes the setting of the institution with the aesthetics of psychedelia.Progress Report from the Strategic Sanctuary for the Destruction of Free Will is an installation, film and sound work that takes over the gallery. Using plain white card, it distorts the structure of the gallery’s architecture, producing a paranoid shrunken space. Inside this space, performers in cardboard costumes re-enact abstracted, broken gestures drawn from video documentation of acid trips, psychedelic dancing, rehab sessions and radical psychotherapy workshops. Progress Report from the Strategic Sanctuary for the Destruction of Free Will has been formed through Pil and Galia Kollectiv’s research into the anti-psychiatry movement, their interests in counter cultural movements and their studies around biopolitics and the proliferation of societal medication. In 1958, having had a life changing experience with LSD, former alcoholic Charles Dederich founded Synanon, a drug rehabilitation program based on residential care and an aggressive form of group therapy called ‘The Game’. The organisation gradually evolved into a controversial alternative community, described in a critical pamphlet as creating Strategic Sanctuaries for the Destruction of Free Will, “a subversive program for mixing delinquents and lefties”. In 1984, anti-psychiatrist R. D. Laing described tranquillizers as chemical straight jackets. With our growing understanding of the plasticity of the brain and the potential to shape it, the tension between liberation and control in the struggle over the mind continues to define our relationship to labour, culture and production. Interrogating these ideas, the exhibition poses the question of whether a collective body can overcome the solipsism of the incommunicable experience of the individual mind.

e-Leadership through strategic alignment: an empirical study of small and medium sized enterprises in the digital age

Small and medium sized enterprises (SMEs) play an important role in the European economy. A critical challenge faced by SME leaders, as a consequence of the continuing digital technology revolution, is how to optimally align business strategy with digital technology to fully leverage the potential offered by these technologies in pursuit of longevity and growth. There is a paucity of empirical research examining how e-leadership in SMEs drives successful alignment between business strategy and digital technology fostering longevity and growth. To address this gap, in this paper we develop an empirically derived e-leadership model. Initially we develop a theoretical model of e-leadership drawing on strategic alignment theory. This provides a theoretical foundation on how SMEs can harness digital technology in support of their business strategy enabling sustainable growth. An in-depth empirical study was undertaken interviewing 42 successful European SME leaders to validate, advance and substantiate our theoretically driven model. The outcome of the two stage process – inductive development of a theoretically driven e-leadership model and deductive advancement to develop a complete model through in-depth interviews with successful European SME leaders – is an e-leadership model with specific constructs fostering effective strategic alignment. The resulting diagnostic model enables SME decision makers to exercise effective e-leadership by creating productive alignment between business strategy and digital technology improving longevity and growth prospects.

Relational architecture and relational capability: organisational levers to support strategic supplier relationships

The resource based view of strategy suggests that competitiveness in part derives from a firms ability to collaborate with a subset of its supply network to co-create highly valued products and services. This relational capability relies on a foundational intra and inter-organisational architecture, the manifestation of strategic, people, and process decisions facilitating the interface between the firm and its strategic suppliers. Using covariance-based structural equation modelling we examine the relationships between internal and external features of relational architecture, and their relationship with relational capability and relational quality. This is undertaken on data collected by mail survey. We find significant relationships between both internal and external relational architecture and relational capability and between relational capability and relational quality. Novel constructs for internal and external elements of relational architecture are specified to demonstrate their positive influence on relational capability and relationship quality.

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function lambda(t), t >= 0, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel-Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright (C) 2009 John Wiley & Sons, Ltd.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

Protecting clean critical points by local disorder correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics. Copyright (C) EPLA, 2011

Newton`s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton`s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.