A Topological Separation Condition for Fractal Attractors

We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundant on every level. In general this separation condition is weaker than the strong open set condition and is not equivalent to the weak separation property. We prove that this separation condition is equivalent to the strong Markov property (see definition below). We also show that the set of $N$-tuples of contractive homeomorphisms, which are non-redundant on every level, is a $G_\delta$ set in the topology of pointwise convergence of every component mapping with an additional requirement that the supremum of contraction coefficients of mappings be strictly less than one. We give several sufficient conditions for this separation property. For every fixed $N$-tuple of $d\times d$ invertible contraction matrices from a certain class, we obtain density results for $N$-tuples of fixed points which define $N$-tuples of mappings non-redundant on every level.Comment: 19 page

Matrix Big Brunch

Following the holographic description of linear dilaton null Cosmologies with a Big Bang in terms of Matrix String Theory put forward by Craps, Sethi and Verlinde, we propose an extended background describing a Universe including both Big Bang and Big Crunch singularities. This belongs to a class of exact string backgrounds and is perturbative in the string coupling far away from the singularities, both of which can be resolved using Matrix String Theory. We provide a simple theory capable of describing the complete evolution of this closed Universe.Comment: 15 pages, no figures. References adde

What is the value of a standard?

Standards play a critical role in the procurement of defence, and other, systems. Choosing the most appropriate standard is important but has become more topical given the UK Ministry of Defence policy of “as civilian as possible, as military as necessary”. Whereas historically managers might have selected from classes of defence standards, this choice set is now increased to include civil standards. We develop a model that has been commissioned by the UK Defence Standardisation whose responsibilities include supporting project teams on the selection of standards. Our model is based on an extension of Bayesian Belief Networks, called an Influence Diagram, which allows decisions and consequences to be represented as well as uncertain-ties. We have developed an initial model for a real case to assess the feasibility and use. We outline the con-text of the defence procurement project in our case study and describe the reasoning underpinning the model structure. We have found that it is possible to develop a simple model that captures the views of multiple stakeholders and informs a reasoned choice about the value of alternative standards

Balanced scorecard design and performance impacts: some Australian evidence

consideration to the use of performance measurement systems, notably the Balanced Scorecard (BSC). However, there has been limited empirical investigation into the particular benefits that result from the use of the BSC (Ittner and Larcker, 1998). This study empirically examines how the BSC has been applied in practice and whether different BSC designs result in varying performance outcomes. Data is from a cross sectional survey, which provided a sample of 92 Australian firms using BSC. It is hypothesised that the BSC provides greater benefits when 1) cause and effect logic is used between measures 2) nonfinancial measures are tied to compensation and 3) implemented at multiple levels within the organisation. Results support the first proposition, although cause and effect logic appears to be more important if the BSC is tied to compensation. These results are discussed, and implications for practice and future research are presented

PCR for the detection of pathogens in neonatal early onset sepsis.

BACKGROUND: A large proportion of neonates are treated for presumed bacterial sepsis with broad spectrum antibiotics even though their blood cultures subsequently show no growth. This study aimed to investigate PCR-based methods to identify pathogens not detected by conventional culture. METHODS: Whole blood samples of 208 neonates with suspected early onset sepsis were tested using a panel of multiplexed bacterial PCRs targeting Streptococcus pneumoniae, Streptococcus agalactiae (GBS), Staphylococcus aureus, Streptococcus pyogenes (GAS), Enterobacteriaceae, Enterococcus faecalis, Enterococcus faecium, Ureaplasma parvum, Ureaplasma urealyticum, Mycoplasma hominis and Mycoplasma genitalium, a 16S rRNA gene broad-range PCR and a multiplexed PCR for Candida spp. RESULTS: Two-hundred and eight samples were processed. In five of those samples, organisms were detected by conventional culture; all of those were also identified by PCR. PCR detected bacteria in 91 (45%) of the 203 samples that did not show bacterial growth in culture. S. aureus, Enterobacteriaceae and S. pneumoniae were the most frequently detected pathogens. A higher bacterial load detected by PCR was correlated positively with the number of clinical signs at presentation. CONCLUSION: Real-time PCR has the potential to be a valuable additional tool for the diagnosis of neonatal sepsis

Pseudo-Automorphisms of positive entropy on the blowups of products of projective spaces

We use a concise method to construct pseudo-automorphisms f_n of the first dynamical degree d_1(f_n) > 1 on the blowups of the projective n-space for all n > 1 and more generally on the blowups of products of projective spaces. These f_n, for n = 3 have positive entropy, and for n > 3 seem to be the first examples of pseudo-automorphisms with d_1(f_n) > 1 (and of non-product type) on rational varieties of higher dimensions.Comment: Mathematische Annalen (to appear

Modeling the emergence of universality in color naming patterns

The empirical evidence that human color categorization exhibits some universal patterns beyond superficial discrepancies across different cultures is a major breakthrough in cognitive science. As observed in the World Color Survey (WCS), indeed, any two groups of individuals develop quite different categorization patterns, but some universal properties can be identified by a statistical analysis over a large number of populations. Here, we reproduce the WCS in a numerical model in which different populations develop independently their own categorization systems by playing elementary language games. We find that a simple perceptual constraint shared by all humans, namely the human Just Noticeable Difference (JND), is sufficient to trigger the emergence of universal patterns that unconstrained cultural interaction fails to produce. We test the results of our experiment against real data by performing the same statistical analysis proposed to quantify the universal tendencies shown in the WCS [Kay P and Regier T. (2003) Proc. Natl. Acad. Sci. USA 100: 9085-9089], and obtain an excellent quantitative agreement. This work confirms that synthetic modeling has nowadays reached the maturity to contribute significantly to the ongoing debate in cognitive science.Comment: Supplementery Information available here http://www.pnas.org/content/107/6/2403/suppl/DCSupplementa

Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds

We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient conditions for existence of Green currents in codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and Theorem 5.3 are adde

Eigenfunctions of the Laplacian and associated Ruelle operator

Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk \DD and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue $\lambda=-s(1-s)$, where $s={1/2}+ it$, admits an integral representation by a distribution \dd_{f,s} (the Helgason distribution) which is equivariant by $\Gamma$ and supported at infinity \partial\DD=\SS^1. The geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the so-called Bowen-Series transformation. Let $\ll_s$ be the complex Ruelle transfer operator associated to the jacobian $-s\ln |T'|$. M. Pollicott showed that \dd_{f,s} is an eigenfunction of the dual operator $\ll_s^*$ for the eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic eigenfunction $\psi_{f,s}$ of $\ll_s$ for the eigenvalue 1, given by an integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}} \dd_{f,s} (d\eta), \noindent where $J(\xi,\eta)$ is a $\{0,1\}$-valued piecewise constant function whose definition depends upon the geometry of the Dirichlet fundamental domain representing the surface \DD/\Gamma