Projection Theorems Using Effective Dimension

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

Making the Inscrutable, Scrutable: Race and Space in Victoria\u27s Chinatown, 1891

This article analyzes the racial and social structure of Victoria, British Columbia\u27s capital city, in particular its Chinatown neighbourhood. The authors\u27 methodology combines the use of geographical information systems (gis) with discourse analysis, and devise a theoretical framework derived from the ideas of Henri Lefebvre. The authors come to the view that the community was extensively but not exclusively Chinese and a Chinese population that was not confined to Chinatown ; and further that the boundaries of race were not as fixed as they have often been assumed to be. . [IBSSRU - Quotes from original] Reprinted by permission of BC Studie

Asymptotic divergences and strong dichotomy

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

Relationship of Plasma Ghrelin Concentrations with End-Products of Carbohydrate Fermentation for Beef Cattle During a Feeding Interval

Four steers (BW 1281±28.2 lb) were used to determine the relationship of plasma ghrelin concentrations with end-products of carbohydrate fermentation and hormones and metabolites indicative of nutrition status during a 12-h feeding interval. A common high-energy diet was offered at 240% of the intake necessary for BW maintenance (2.4xM) or 80% of the intake necessary for BW maintenance (0.8xM). At initiation of period I, 2 steers were allowed 2.4xM intake, whereas intake for the remaining 2 steers was restricted to 0.8xM. Equal aliquots of feed were offered at 0800 and at 2000 h. On 7, 14, and 21 d following initiation of intake restriction, serial blood samples were collected via indwelling jugular catheter at 15-min intervals through the 12-h feeding interval. Plasma samples were assayed for ghrelin, GH, insulin (INS), and NEFA concentrations. Rumen fluid samples were collected throughout the feeding interval and processed for subsequent analyses of VFA concentrations. Following period I, steers were weighed, dietary treatments were switched between steer groups, intake amounts were recalculated, and sampling period II then was initiated as described for period I. Regardless of amount of DMI, plasma ghrelin and GH concentrations fluctuated as a result of sampling time relative to feeding. Plasma ghrelin concentrations were elevated prior to feeding at 0800 and 2000 h and reached a nadir from 1 and 3 h post-feeding. Although GH was elevated prior to the 0800 h feeding, it was not elevated at 1800 h despite increasing ghrelin concentrations. A tendency for an interaction of dietary treatment by sampling time relative to feeding which indicated an inverse relationship of plasma INS and ghrelin concentrations for cattle in a positive nutrient balance but no relationship between the two hormones when cattle were in negative energy balance. An interaction of dietary treatment by sampling time relative to feeding also resulted for plasma NEFA concentrations. A positive relationship of NEFA and ghrelin concentrations resulted for cattle when energy and protein intake were below the requirement for maintenance of BW. Ruminal VFA concentrations were weakly correlated to plasma ghrelin concentrations. These data are consistent with the hypothesis that, whereas plasma ghrelin concentrations fluctuate with nutritional status of the ruminant animal, the fluctuation is not completely explained by fluctuations in GH, NEFA, INS or ruminal VFA concentrations

Prolonged, Moderate Nutrient Restriction in Beef Cattle Results in Persistently-Elevated Plasma Ghrelin Concentrations

Four steers (BW 1281±28.2 kg) were used in a crossover design to determine the effects of prolonged, moderate energy and protein restriction on plasma ghrelin and GH concentrations. A common high-energy diet was offered at 240% of the intake necessary for BW maintenance (2.4xM) or 80% of the intake necessary for BW maintenance (0.8xM). As a common starting point, all steers were adjusted to 2.4xM during a 23-d pre-trial adaptation period. At initiation of period 1, 2 steers remained at 2.4xM, whereas intake for the remaining 2 steers was restricted to 0.8xM. Feed allotments were offered twice daily in equal aliquots at 0800 and at 2000 h. On 7, 14, and 21 d following initiation of restriction, serial blood samples were collected via indwelling jugular catheter at 15-min intervals throughout a 12-h feeding interval. Following period 1, steers were weighed and intake amounts were recalculated. Dietary treatments were switched between steer groups, 2.4xM intake was established, and sampling period II was initiated as described for period I. Plasma samples were assayed for ghrelin, GH, insulin (INS), and NEFA concentrations. Subsequent to analyses, hormone data were pooled by hour for statistical analyses. The energy and protein restriction resulted in decreased BW for 0.8xM (-108.9 lb) steers compared with 2.4xM (127.9 lb) steers. Body weight loss along with decreased plasma INS concentrations and elevated plasma NEFA and GH concentrations indicate that these steers were in a catabolic state and mobilizing body tissue stores to meet nutrient requirements not met by dietary intake. Plasma ghrelin concentrations also were elevated for the 0.8xM steers compared with those of 2.4xM steers throughout the 21-d treatment period. These data are consistent with the hypothesis that plasma ghrelin concentrations are elevated in cattle throughout a prolonged, moderate energy and protein restriction that result in a catabolic state

Dwelling places and social spaces: Revealing the environments of urban workers in Victoria using historical GIS

The Pacific Northwest underwent rapid economic growth in the late 19th century and cities on both sides of the Canada/US border burgeoned. The building boom was sustained by a large cohort of tradesmen and skilled labourers who lived in modest cabins, tenement blocks, boarding houses, and residential hotels. Most of these urban wageworkers were unmarried. They left few records of their experiences outside the job site or union hall. In this case study of Victoria, British Columbia circa 1891, we deployed a historical geographical information system (HGIS) to reconstitute the urban residential and social space of about 2,000 otherwise elusive working men. Our research framework combines qualitative methods that are familiar to historians and quantitative methods favoured by geospatial researchers. By integrating both qualitative and quantitative data, we are able to represent the multiple spatial conditions experienced by Victoria’s wageworkers in the early 1890s. In the process, we repopulated the city and reconstructed a largely vanished urban landscape. A primary objective of the essay is to demonstrate how gis can be used as a research tool and new epistemology in the field of labour history

Plasma Ghrelin Concentrations of Beef Cattle Consuming a Similar Amount of Dietary Energy Supplied by Different Ingredients

Previous research demonstrated that restricting nutrient intake by decreasing DMI of a high-grain diet increased plasma ghrelin concentrations. Objectives of this experiment were to determine 1) whether dietary ingredient composition influenced plasma ghrelin concentrations when energy intake was similar, and 2) whether relationships existed between plasma ghrelin concentrations and plasma insulin, NEFA, and GH concentrations or end-products of carbohydrate fermentation in the rumen. Five steers (1290 ± 39.9 lb) were used in a crossover design with dietary treatments of 50% hay-50% concentrate (HAY) offered at an amount that would meet the steer’s NEm requirement plus supply an additional 3.5 Mcal of NEg daily, or a diet composed of 10% hay-90% concentrate but limit-fed to achieve an energy intake similar to that of the HAY steers (LFC). Feed was offered in equal aliquots twice daily. Period I: on d 21 following initiation of the dietary treatment, serial blood samples were collected via indwelling jugular catheter at 15-min intervals, and rumen fluid samples were collected hourly throughout a 12-h feeding interval. Following period I, steers were weighed, dietary treatments were switched between steer groups, and intake amounts were recalculated on the basis of period I ending BW. Period II adaptation and sampling was repeated as described for period 1. Plasma samples were assayed for ghrelin, insulin, GH, and NEFA concentrations. Rumen fluid was assayed for VFA concentrations and pH. Net energy for gain was similar between treatment groups (3.5 ± 0.04 Mcal NEg/d). However, a higher DMI was required by HAY steers compared with LFC steers (20.7 vs. 15.9 ± 0.13 lb) to achieve the same energy intake. Plasma ghrelin concentrations were similar for HAY and LFC steers (115 vs. 107 ± 3.3 pg/mL) despite differences in DMI and ingredient composition. Plasma GH, NEFA, and insulin concentrations also were similar regardless of dietary ingredient composition. Strong correlations between plasma ghrelin concentrations and other hormones and metabolites or end-products of carbohydrate fermentation did not result. These data are consistent with the hypothesis that ingredient composition and quantity of DMI do not influence plasma ghrelin concentrations of steers when energy intake is similar and steers are in positive energy balance

Growth and predation activity at deep-sea hydrothermal vents along the Galápagos Rift

Growth rates of unclassified mussels collected from hydrothermal vents on the Pacific Ocean (2500 m) are among the highest recorded for deep-sea species. Mature mussels have mean growth rates of about 1 cm yr-1 which are comparable to growth rates of shallow water mussels...

Use of 25-hydroxyvitamin D3 and vitamin E to improve tenderness of beef from the longissimus dorsi of heifers

The objective of this trial was to determine whether a single bolus of 25-hydroxyvitamin D3 (25-OH D3), vitamin E, or a combination of the 2 would improve the tenderness of steaks from the LM of beef heifers. Forty-eight Angus crossbred heifers were allotted randomly to 8 pens. Six heifers were in each pen, and there were 2 pens per treatment. The 4 treatments included control (no 25-OH D3 or vitamin E); 25-OH D3 (500 mg of 25-OH D3 administered as a one-time oral bolus 7 d before slaughter); vitamin E (1,000 IU of vitamin E administered daily as a top-dress for 104 d before slaughter); or combination (500 mg of 25-OH D3administered as a one-time oral bolus 7 d before slaughter and 1,000 IU of vitamin E administered daily as a top-dress for 104 d before slaughter). Blood samples were obtained on the day that heifers were allotted to treatments, on the day 25-OH D3 was administered, and on the day before slaughter. Plasma calcium concentration was increased when 25-OH D3 was administered with or without vitamin E (P \u3c 0.007). In LM, calcium concentration tended to increase (P = 0.10) when 25-OH D3 was administered alone but not when 25-OH D3 was administered with vitamin E. Concentrations of 25-OH D3 and 1,25-dihydroxyvitamin D3 in plasma were increased when 25-OH D3 was administered with or without vitamin E (P \u3c 0.001). Steaks from heifers treated with 25-OH D3or vitamin E, but not both, tended to have lower Warner-Bratzler shear force than steaks in the control group at 14 d postmortem (P = 0.08). Postmortem protein degradation as measured by Western blot of the 30-kDa degradation product of troponin-T was increased with all treatments after 3 d postmortem (P ≤ 0.07), but not at 7 or 14 d postmortem. Unexpectedly, the use of 500 mg of 25-OH D3 fed as an oral bolus 7 d before slaughter or 1,000 IU of vitamin E administered daily for 104 d before slaughter alone, but not in combination, effectively decreased Warner-Bratzler shear force