Constructive Dimension and Turing Degrees

This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dim_H(S) and constructive packing dimension dim_P(S) is Turing equivalent to a sequence R with dim_H(R) <= (dim_H(S) / dim_P(S)) - epsilon, for arbitrary epsilon > 0. Furthermore, if dim_P(S) > 0, then dim_P(R) >= 1 - epsilon. The reduction thus serves as a *randomness extractor* that increases the algorithmic randomness of S, as measured by constructive dimension. A number of applications of this result shed new light on the constructive dimensions of Turing degrees. A lower bound of dim_H(S) / dim_P(S) is shown to hold for the Turing degree of any sequence S. A new proof is given of a previously-known zero-one law for the constructive packing dimension of Turing degrees. It is also shown that, for any regular sequence S (that is, dim_H(S) = dim_P(S)) such that dim_H(S) > 0, the Turing degree of S has constructive Hausdorff and packing dimension equal to 1. Finally, it is shown that no single Turing reduction can be a universal constructive Hausdorff dimension extractor, and that bounded Turing reductions cannot extract constructive Hausdorff dimension. We also exhibit sequences on which weak truth-table and bounded Turing reductions differ in their ability to extract dimension.Comment: The version of this paper appearing in Theory of Computing Systems, 45(4):740-755, 2009, had an error in the proof of Theorem 2.4, due to insufficient care with the choice of delta. This version modifies that proof to fix the error

Scaled tree fractals do not strictly self-assemble

In this paper, we show that any scaled-up version of any discrete self-similar {\it tree} fractal does not strictly self-assemble, at any temperature, in Winfree's abstract Tile Assembly Model.Comment: 13 pages, 3 figures, Appeared in the Proceedings of UCNC-2014, pp 27-39; Unconventional Computation and Natural Computation - 13th International Conference, UCNC 2014, London, ON, Canada, July 14-18, 2014, Springer Lecture Notes in Computer Science ISBN 978-3-319-08122-

Lines Missing Every Random Point

We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.

Synthesis of spiro quasi[1]catenanes and quasi[1]rotaxanes via a templated backfolding strategy

Due to their well-defined three-dimensional geometry, spiro compounds are widely utilized in drug research. From the central tetrahedral carbon atom, besides the regular structure, an inverted spiro connectivity may be envisioned. Here we disclose the synthesis of this molecule class that we have coined quasi[1]catenanes. Next to their fascinating and aesthetic shape, the higher compactness as compared to regular spiro bicycles is noteworthy. To enable synthetic access to compact entangled multimacrocyclic molecules, we have developed a new strategy. The key element is a template, which is covalently connected to the linear precursors, and spatially directs the sterically congested backfolding macrocyclizations that are required to give quasi[1]catenanes. Similarly, quasi[1]rotaxanes are made

The Importance of Small Fire Refugia in the Central Sierra Nevada, California, USA

Fire refugia – the unburned areas within fire perimeters – are important to the survival of many taxa through fire events and the revegetation of post-fire landscapes. Previous work has shown that species use and benefit from small-scale fire refugia (1 m2 to 1000 m2), but our understanding of where and how fire refugia form is largely limited to the scale of remotely sensed data (i.e., 900 m2 Landsat pixels). To examine the causes and consequences of small fire refugia, we field-mapped all unburned patches ≥1 m2 within a contiguous 25.6 ha forest plot that burned at generally low-to-moderate severity in the 2013 Yosemite Rim Fire, California, USA. Within the Yosemite Forest Dynamics Plot (YFDP), there were 685 unburned patches ≥1 m2, covering a total unburned area of 12,597 m2 (4.9%). Small refugia occurred in all fire severity classifications. Random forest models showed that the proportion of unburned area of 100 m2 grid cells corresponded to pre-fire density and basal area of trees, distance to the nearest stream, and immediate fire mortality, but the relationships were complex and model accuracy was variable. From a pre-fire population of 34,061 total trees ≥1 cm diameter at breast height (1.37 m; DBH) within the plot (1,330 trees ha-1), trees of all five of the most common species and those DBH \u3c30 cm had higher immediate survival rates if their boles were wholly or partially within an unburned patch (P ≤0.001). Trees 1 cm ≤ DBH \u3c10 that survived were located closer to the center of the unburned patch than the edge (mean 1.1 m versus 0.6 m; ANOVA; P ≤0.001). Four-year survival rates for trees 1 cm ≤ DBH \u3c10 cm were 58.8% within small refugia and 2.7% in burned areas (P ≤0.001). Species richness and the Shannon Diversity Index (SDI) were associated with unburned quadrats in NMDS ordinations 3 years post-fire. Burn heterogeneity in mixed-conifer forests likely exists at all scales and small refugia contribute to diversity of forest species and structures. Thus, managers may wish to consider scales from 1-m2 to the landscape when designing fuel reduction prescriptions. The partial predictability of refugia location suggests that further work may lead to predictive models of refugial presence that have considerable potential to preserve ecological function or human habitation in fire-frequent forests

Development of EM-CCD-based X-ray detector for synchrotron applications

A high speed, low noise camera system for crystallography and X-ray imaging applications is developed and successfully demonstrated. By coupling an electron-multiplying (EM)-CCD to a 3:1 fibre-optic taper and a CsI(Tl) scintillator, it was possible to detect hard X-rays. This novel approach to hard X-ray imaging takes advantage of sub-electron equivalent readout noise performance at high pixel readout frequencies of EM-CCD detectors with the increase in the imaging area that is offered through the use of a fibre-optic taper. Compared with the industry state of the art, based on CCD camera systems, a high frame rate for a full-frame readout (50 ms) and a lower readout noise (<1 electron root mean square) across a range of X-ray energies (6–18 keV) were achieved

Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW

Компьютерная томография и магнитно-резонансная томография в диагностике опухолей средостения

Резюме. Проанализированы результаты обследования 95 больных с опухолями средостения (ОС) с использованием рентгенологических методов: компьютерной томографии (КТ), магнитно-резонансной томографии (МРТ). Приведена КТ- и МРТ-семиотика ОС, оценена информативность результатов каждого метода в зависимости от локализации опухоли. На основании полученных данных обоснованы показания к применению и последовательность использования неинвазивных лучевых методов в целях диагностики ОС. В частности, МРТ наиболее показана при локализации опухоли в заднем и передневерхнем отделах средостения, тогда как КТ целесообразнее проводить, если опухоль располагается в переднесреднем, передненижнем или среднем отделах средостения. Ключевые слова: опухоли средостения, рентгенологическое исследование, компьютерная томография, магнитно-резонансная томография, диагностическая эффективность.Summary. The paper reports findings of examination of 95 patients with mediastinum tumors (MS) using the following roentgenologic methods: computed tomography (CT) and magnetic resonance tomography (MRT). CR and MRT semeiology of MS is described and the informative value of each method is assessed in dependence on tumor’s localization. Based on these findings, indications for application of non-invasive radiation methods in examination of mediastinum tumors are developed as well as the sequence of their using. In particular, MRT is especially promising in tumors localized in posterior and antero-superior portions of the mediastinum, while CT is more appropriate in tumors localized in antero-medial, antero-lower or medial portions of the mediastinum. Key Words: mediastinum tumors, roentgenologic examination, computed tomography, magnetic resonance tomography, diagnostic efficiency