91 research outputs found

    Results on the Dimension Spectra of Planar Lines

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    In this paper we investigate the (effective) dimension spectra of lines in the Euclidean plane. The dimension spectrum of a line L_{a,b}, sp(L), with slope a and intercept b is the set of all effective dimensions of the points (x, ax + b) on L. It has been recently shown that, for every a and b with effective dimension less than 1, the dimension spectrum of L_{a,b} contains an interval. Our first main theorem shows that this holds for every line. Moreover, when the effective dimension of a and b is at least 1, sp(L) contains a unit interval. Our second main theorem gives lower bounds on the dimension spectra of lines. In particular, we show that for every alpha in [0,1], with the exception of a set of Hausdorff dimension at most alpha, the effective dimension of (x, ax + b) is at least alpha + dim(a,b)/2. As a consequence of this theorem, using a recent characterization of Hausdorff dimension using effective dimension, we give a new proof of a result by Molter and Rela on the Hausdorff dimension of Furstenberg sets

    Review of \u3ci\u3eEvery Twelve Seconds: Industrialized Slaughter and the Politics of Sight. \u3c/i\u3eBy Timothy Pachirat.

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    In June 2004, political scientist Timothy Pachirat went to work on the killfloor of an unnamed beef slaughterhouse in Omaha, Nebraska. He started out as a liver hanger in the cooler. There carcasses hang before being sent to the fabrication floor where hundreds of handheld knives and saws reinvent chilled half-carcasses as steaks, rounds, and roasts that are then boxed and shipped to distributors and retailers around the world. For four days he worked in the chutes, driving cattle to the knocking box to be stunned, as required by the Humane Slaughter Act, before being turned into meat. Then for three months he was in QC (quality control), which afforded him access to the entire kill floor. In December, when asked by a USDA inspector to blow the whistle on food safety violations, he explained that he was actually an undercover ethnographer. The next day Pachirat quit his job, but stayed in Omaha for another 18 months conducting, on a much less grueling schedule, participant-observation research and interviews with community and union organizers, slaughterhouse workers, USDA inspectors, cattle ranchers, and small-slaughterhouse operators. Sadly, this later research does not appear in his account

    Review of \u3ci\u3eEvery Twelve Seconds: Industrialized Slaughter and the Politics of Sight. \u3c/i\u3eBy Timothy Pachirat.

    Get PDF
    In June 2004, political scientist Timothy Pachirat went to work on the killfloor of an unnamed beef slaughterhouse in Omaha, Nebraska. He started out as a liver hanger in the cooler. There carcasses hang before being sent to the fabrication floor where hundreds of handheld knives and saws reinvent chilled half-carcasses as steaks, rounds, and roasts that are then boxed and shipped to distributors and retailers around the world. For four days he worked in the chutes, driving cattle to the knocking box to be stunned, as required by the Humane Slaughter Act, before being turned into meat. Then for three months he was in QC (quality control), which afforded him access to the entire kill floor. In December, when asked by a USDA inspector to blow the whistle on food safety violations, he explained that he was actually an undercover ethnographer. The next day Pachirat quit his job, but stayed in Omaha for another 18 months conducting, on a much less grueling schedule, participant-observation research and interviews with community and union organizers, slaughterhouse workers, USDA inspectors, cattle ranchers, and small-slaughterhouse operators. Sadly, this later research does not appear in his account

    Polynomial Space Randomness in Analysis

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    We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko\u27s framework for polynomial space computability in R^n to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem characterizes weakly pspace random points. That is, a point x is weakly pspace random if and only if the Lebesgue differentiation theorem holds for a point x for every pspace L_1-computable function

    Semicomputable Points in Euclidean Spaces

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    We introduce the notion of a semicomputable point in R^n, defined as a point having left-c.e. projections. We study the range of such a point, which is the set of directions on which its projections are left-c.e., and is a convex cone. We provide a thorough study of these notions, proving along the way new results on the computability of convex sets. We prove realization results, by identifying computability properties of convex cones that make them ranges of semicomputable points. We give two applications of the theory. The first one provides a better understanding of the Solovay derivatives. The second one is the investigation of left-c.e. quadratic polynomials. We show that this is, in fact, a particular case of the general theory of semicomputable points

    Projection Theorems Using Effective Dimension

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    In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrand\u27s projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal. We use Kolmogorov complexity to give two new results on the Hausdorff and packing dimensions of orthogonal projections onto lines. The first shows that the conclusion of Marstrand\u27s theorem holds whenever the Hausdorff and packing dimensions agree on the set E, even if E is not analytic. Our second result gives a lower bound on the packing dimension of projections of arbitrary sets. Finally, we give a new proof of Marstrand\u27s theorem using the theory of computing

    Phosphorylation of cardiac troponin by guanosine 3':5'-monophosphate-dependent protein kinase.

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    Journal ArticleHomogeneous cGMP-dependent protein kinase catalyzes the rapid incorporation of phosphate, specifically into the inhibitory subunit of purified cardiac troponin with a maximal incorporation of 1 mol of phosphate/mol of troponin. When troponin was incubated in the presence of both cGMP- and cAMP-dependent protein kinases, a maximal incorporation of 1 mol of phosphate/mol of troponin was observed which suggested phosphorylation of the same site by the two kinases. Both cyclic nucleotide-dependent kinases had similar Km values for troponin, but the Vmax value for the phosphorylation reaction catalyzed by cAMP-dependent protein kinase was 12-fold greater than the value obtained for cGMP-dependent protein kinase

    Cows, Pigs, Corporations, and Anthropologists

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    Don Stull is professor emeritus of anthropology at the University of Kansas, where he taught from 1975 to 2015. He has been editor-in-chief of Human Organization, president of the Society for Applied Anthropology, and a recipient of the SfAA’s Sol Tax Distinguished Service Award. In 2001 he was presented with the key to Garden City, Kansas, and made an honorary citizen in recognition of the value of his work to this community

    Asymptotic divergences and strong dichotomy

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    The Schnorr-Stimm dichotomy theorem [31] concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet S. The theorem asserts that, for any such sequence S, the following two things are true. (1) If S is not normal in the sense of Borel (meaning that every two strings of equal length appear with equal asymptotic frequency in S), then there is a finite-state gambler that wins money at an infinitely-often exponential rate betting on S. (2) If S is normal, then any finite-state gambler betting on S loses money at an exponential rate betting on S. In this paper we use the Kullback-Leibler divergence to formulate the lower asymptotic divergence div(S||a) of a probability measure a on S from a sequence S over S and the upper asymptotic divergence Div(S||a) of a from S in such a way that a sequence S is a-normal (meaning that every string w has asymptotic frequency a(w) in S) if and only if Div(S||a) = 0. We also use the Kullback-Leibler divergence to quantify the total risk RiskG(w) that a finite-state gambler G takes when betting along a prefix w of S. Our main theorem is a strong dichotomy theorem that uses the above notions to quantify the exponential rates of winning and losing on the two sides of the Schnorr-Stimm dichotomy theorem (with the latter routinely extended from normality to a-normality). Modulo asymptotic caveats in the paper, our strong dichotomy theorem says that the following two things hold for prefixes w of S. (10) The infinitely-often exponential rate of winning in 1 is 2Div(S||a)|w| . (20) The exponential rate of loss in 2 is 2-RiskG(w) . We also use (10) to show that 1 - Div(S||a)/c, where c = log(1/mina¿S a(a)), is an upper bound on the finite-state a-dimension of S and prove the dual fact that 1 - div(S||a)/c is an upper bound on the finite-state strong a-dimension of S
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