269 research outputs found

    The Role of Response Bias in Perceptual Learning

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    Sensory judgments improve with practice. Such perceptual learning is often thought to reflect an increase in perceptual sensitivity. However, it may also represent a decrease in response bias, with unpracticed observers acting in part on a priori hunches rather than sensory evidence. To examine whether this is the case, 55 observers practiced making a basic auditory judgment (yes/no amplitude-modulation detection or forced-choice frequency/amplitude discrimination) over multiple days. With all tasks, bias was present initially, but decreased with practice. Notably, this was the case even on supposedly “bias-free,” 2-alternative forced-choice, tasks. In those tasks, observers did not favor the same response throughout (stationary bias), but did favor whichever response had been correct on previous trials (nonstationary bias). Means of correcting for bias are described. When applied, these showed that at least 13% of perceptual learning on a forced-choice task was due to reduction in bias. In other situations, changes in bias were shown to obscure the true extent of learning, with changes in estimated sensitivity increasing once bias was corrected for. The possible causes of bias and the implications for our understanding of perceptual learning are discussed

    Multiple self-splicing introns in the 16S rRNA genes of giant sulfur bacteria

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    The gene encoding the small subunit rRNA serves as a prominent tool for the phylogenetic analysis and classification of Bacteria and Archaea owing to its high degree of conservation and its fundamental function in living organisms. Here we show that the 16S rRNA genes of not-yet-cultivated large sulfur bacteria, among them the largest known bacterium Thiomargarita namibiensis, regularly contain numerous self-splicing introns of variable length. The 16S rRNA genes can thus be enlarged to up to 3.5 kb. Remarkably, introns have never been identified in bacterial 16S rRNA genes before, although they are the most frequently sequenced genes today. This may be caused in part by a bias during the PCR amplification step that discriminates against longer homologs, as we show experimentally. Such length heterogeneity of 16S rRNA genes has so far never been considered when constructing 16S rRNA-based clone libraries, even though an elongation of rRNA genes due to intervening sequences has been reported previously. The detection of elongated 16S rRNA genes has profound implications for common methods in molecular ecology and may cause systematic biases in several techniques. In this study, catalyzed reporter deposition–fluorescence in situ hybridization on both ribosomes and rRNA precursor molecules as well as in vitro splicing experiments were performed and confirmed self-splicing of the introns. Accordingly, the introns do not inhibit the formation of functional ribosomes

    Stochastic stability at the boundary of expanding maps

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    We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit measures for a model of the intermittent map and obtain stochastic stability for some values of the parameter. The physical measures are obtained as zero-noise limits which are shown to satisfy Pesin?s Entropy Formula

    Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems

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    We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.Comment: To appear in Journal of Statistical Physic

    The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

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    We consider an Euclidean supersymmetric field theory in Z3Z^3 given by a supersymmetric Ί4\Phi^4 perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) L\'evy random walk in Z3Z^3. The Green's function depends on the L\'evy-Khintchine parameter α=3+Ï”2\alpha={3+\epsilon\over 2} with 0<α<20<\alpha<2. For α=32\alpha ={3\over 2} the Ί4\Phi^{4} interaction is marginal. We prove for α−32=Ï”2>0\alpha-{3\over 2}={\epsilon\over 2}>0 sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding L\'evy walk in Z3Z^3 is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding L\'evy walk in Z3Z^3.Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition of norms involving fermions to ensure uniqueness. 2. change in the definition of lattice blocks and lattice polymer activities. 3. Some proofs have been reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos corrected.This is the version to appear in Journal of Statistical Physic

    Infinitely Many Stochastically Stable Attractors

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    Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the basins of attraction of each attractor covers Lebesgue almost all points of M. We prove that the time averages of almost all orbits under random perturbations are given by a finite number of probability measures. Moreover these probability measures are close to the probability measures supported by the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure

    Convergence of random zeros on complex manifolds

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    We show that the zeros of random sequences of Gaussian systems of polynomials of increasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular, the normalized distribution of zeros of systems of m polynomials of degree N, orthonormalized on a regular compact subset K of C^m, almost surely converge to the equilibrium measure on K as the degree N goes to infinity.Comment: 16 page

    Correlations between zeros of a random polynomial

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    We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval (−1,1)(-1,1) are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random polynomial.Comment: 31 pages, 2 figures; a revised version of the J. Stat. Phys. pape
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