The time of graph bootstrap percolation

Graph bootstrap percolation, introduced by Bollob\'as in 1968, is a cellular automaton defined as follows. Given a "small" graph $H$ and a "large" graph $G = G_0 \subseteq K_n$, in consecutive steps we obtain $G_{t+1}$ from $G_t$ by adding to it all new edges $e$ such that $G_t \cup e$ contains a new copy of $H$. We say that $G$ percolates if for some $t \geq 0$, we have $G_t = K_n$. For $H = K_r$, the question about the size of the smallest percolating graphs was independently answered by Alon, Frankl and Kalai in the 1980's. Recently, Balogh, Bollob\'as and Morris considered graph bootstrap percolation for $G = G(n,p)$ and studied the critical probability $p_c(n,K_r)$, for the event that the graph percolates with high probability. In this paper, using the same setup, we determine, up to a logarithmic factor, the critical probability for percolation by time $t$ for all $1 \leq t \leq C \log\log n$.Comment: 18 pages, 3 figure

Purposiveness, Intelligibility and Kant's Scepticism: Reconsidering Ng's Account of Hegel's Response to Kant

Hegel's integration of the concept of Life in the Logic has long been disputed and rejected by many scholars. The most common objection was that it seemed counterintuitive to integrate an empirical phenomenon such as Life into a Logic that, in fact, ought to present an immanent development of pure concepts. Hegel was often accused of bringing empirical considerations into his Logic in order to develop his logical account of Life. Consequently, there has been a great discussion about the question as to whether a Logic is an appropriate place for this concept—a discussion that did not occur with respect to other categories in Hegel's Logic. Now, in contemporary literature on Hegel, there is a surge of genuine interest in Hegel's logical account of Life, accompanied by the insight that the concept of Life plays an important and indispensable role in Hegel's philosophy. However, what this role is precisely is a controversial issue

Photosensitive disorders in HIV

Photosensitive disorders are common, affecting up to 5% of HIV-positive patients. HIV itself induces photosensitivity but photoaggravated drug reactions, porphyria cutanea tarda and nutritional disorders such as pellagra are also more common in patients with HIV. In South Africa, actinic lichenoid leukomelanoderma of HIV is a unique photosensitive disorder which is associated with advanced HIV. It is important to be able to recognise these conditions and withdraw photosensitising medications wherever possible

Mechanism, External Purposiveness, and Object Individuation: from Mechanism to Teleology in Hegel's Science of Logic

This article is an investigation into Hegel's claim that teleology is the truth of mechanism, which Hegel puts forward in the objectivity section in the Science of Logic. Contrary to most accounts of this section of the Logic, I make a case for a reading of Hegel's conception of external purposiveness according to which the latter makes a positive contribution to the structural development of the concepts of the Logic. I argue that external purposiveness plays a major role in understanding the Hegelian claim of teleology as the truth of mechanism. More specifically, I argue that structures of external purposiveness provide the conditions for the individuation of mechanical objects

Antecedents Influencing Rugby Migration In South Africa

This study set out to determine the most important antecedents influencing the decision of players at the top five South African rugby unions to play overseas. A literature review was conducted in order to establish the theory base for the study. A survey, utilizing a self-administered questionnaire, of players at the top five South African rugby unions was conducted to determine the antecedents influencing the migration decision. The study noted financial reasons as the main antecedent in the decision to migrate. Based on players opinions, any strategy devised by the rugby unions to address the problem of player migration would have to focus on a number of facets rather than on one single area of concern

Spatiotemporal modeling of schistosomiasis in Ghana: linking remote sensing data to infectious disease

More than 90% of the worldwide schistosomiasis burden falls on sub-Saharan Africa. Control efforts are often based on infrequent, small-scale health surveys, which are expensive and logistically difficult to conduct. The use of satellite imagery to predictively model infectious disease transmission has great potential for public health applications. The transmission of schistosomiasis, a disease acquired from contact with contaminated surface water, requires specific environmental conditions to sustain freshwater snails. If a connection between schistosomiasis and remotely sensed environmental variables can be established, then cost effective and current disease risk predictions can be made available. Schistosomiasis transmission has unknown seasonality, and the disease is difficult to study due to a long lag between infection and clinical symptoms. To overcome these challenges, we employed a comprehensive 15-year time-series built from remote sensing feeds, which is the longest environmental dataset to be used in the application of remote sensing to schistosomiasis. The following environmental variables will be used in the model: accumulated precipitation, land surface temperature, vegetative growth indices, and climate zones created from a novel climate regionalization technique. This technique, improves upon the conventional Köppen-Geiger method, which has been the primary climate classification system in use the past 100 years. These predictor variables will be regressed against 8 years of national health data in Ghana, the largest health dataset of its kind to be used in this context, and acquired from freely available satellite imagery data. A benefit of remote sensing processing is that it only requires training and time in terms of resources. The results of a fixed effects model can be used to develop a decision support framework to design treatment schemes and direct scarce resources to areas with the highest risk of infection. This framework can be applied to diseases sensitive to climate or to locations where remote sensing would be better suited than health surveys.Published versio

Renal function in children with congenital neurogenic bladder

AIMS: Preservation of renal function in children with congenital neurogenic bladder is an important goal of treatment for the disease. This study analyzed the evolution of renal function in patients with congenital neurogenic bladder. METHODS: We reviewed the records of 58 pediatric patients with respect to the following attributes: gender, age, etiology of neurogenic bladder, reason for referral, medical/surgical management, episodes of treated urinary tract infections, urodynamics, DMSA scintigraphy, weight, height, blood pressure, glomerular filtration rate, microalbuminuria and metabolic acidosis. Statistical analysis was performed, adopting the 5% significance level. RESULTS: The mean age at presentation was 4.2 ± 3.5 years. Myelomeningocele was the most frequent etiology (71.4%). Recurrent urinary tract infection was the reason for referral in 82.8% of the patients. Recurrent urinary tract infections were diagnosed in 84.5% of the patients initially; 83.7% of those patients experienced improvement during follow-up. The initial mean glomerular filtration rate was 146.7 ± 70.1 mL/1.73 m²/min, and the final mean was 193.6 ± 93.6 mL/1.73 m²/min, p = 0.0004. Microalbuminuria was diagnosed in 54.1% of the patients initially and in 69% in the final evaluation. Metabolic acidosis was present in 19% of the patients initially and in 32.8% in the final assessment. CONCLUSIONS: Patient referral to a pediatric nephrologist was late. A reduction in the number of urinary tract infections was observed with adequate treatment, but microalbuminuria and metabolic acidosis occurred frequently despite adequate management

Kinder über Kindermuseen: eine empirische Studie zu Qualitätskriterien

"Kindermuseen wollen mit ihren Angeboten Kinder ansprechen und ihnen vielfältige Erfahrungen ermöglichen. Doch es sind die Erwachsenen, die entscheiden, welche Inhalte, Methoden und Vermittlungsformen für die Kinder im Kontext der Museumsarbeit die richtigen sind. Mit der vorliegenden Studie wurden Kinder nach ihren Einschätzungen der Kindermuseen befragt. 405 Schüler im Alter von sechs bis zehn Jahren füllten nach einem Besuch in einem von vier Kindermuseen einen Satzergänzungstest zu ihren Erlebnissen aus. Es zeigte sich z.B., dass die Kinder es schätzen, selbstständig etwas zu tun und sich kreativ zu beschäftigen. Aus den Antworten wurden Qualitätskriterien für die pädagogische Arbeit in Kindermuseen - aus der Perspektive von Kindern - entwickelt." (Autorenreferat)"Children's museums target children with their exhibitions and offer a multifaced array of experiences, but adults are the ones who decide on the content and its presentation. In this study, children were asked about exhibitions they had visited. 405 elementary school children between 6 and 10 years of age filled out a small questionnaire about their experiences in one of four children's museums. Results indicated that children enjoy being active, doing things on their own, and engaging in creative activities. Criteria for the quality of children's museums were derived from the children's answers." (author's abstract

Growth and mortality of the exploited mangrove crab Ucides cordatus (Ucididae) in N-Brazil.

Reliable estimates of growth and mortality parameters are crucial for understanding how populations of exploited species may respond to shifts in fishing pressure. Results of previous studies on growth of the ecologically and economically important mangrove crab Ucides cordatus in Brazil differ strongly and age estimates for minimum legal capture size (60 mm carapace width) range between less than 1 and 6–10 years. These discrepancies are probably due to inherent problems of the applied methods, namely laboratory based observations and cohort-analyses. The present paper takes a new approach by measuring individual growth increments of U. cordatus in situ. Crabs were measured, tagged, released into 100 m² field enclosures and periodically recaptured. There was no indication of an enclosure effect and 209 growth increments were obtained from specimens measuring 20.5 to 89.5 mm in carapace width (CW). For improving the size coverage of the von Bertalanffy growth curve, first instar juveniles were reared in the laboratory up to an age of six months. Their average percent size increase (PI) was 22.57 ± 6.75% during biweekly measurements, resulting in a CW of 7.8 to 11.5 mm after six months. Average PI of the enclosure crabs ranged between 10.87 ± 1.17% (indiv. 80 mm CW) per moult and two large females had moulted without growing. Growth analysis revealed a larger asymptotic size in males than in females (89 mm versus 72 mm) while the growth parameter K of the von Bertalanffy growth function (VBGF) was lower in males (0.17 versus 0.25), resulting in similar growth performance of the two sexes (males: 1.16; females: 1.10). Age at legal minimum capture size estimated by the inversed VBGF was 6.13 years in males and 7.38 years in females, corroborating the mid to upper range of earlier growth estimates. Mortality parameters (Z, M and F) were calculated using length converted catch curves. Z in males was higher than in females (0.69 versus 0.49), as expected from the male-biased fishery. M, F and the exploitation rate E were estimated for three different scenarios taking into account the uncertainty of the age/size of functional maturity. Our study provides key information for the sustainable management of the U. cordatus fishery and confirms that the species is relatively slow growing and long-lived (> 10 years), suggesting a high vulnerability to overfishing