How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Governors and directors: Competing models of corporate governance

Why do we use the term ‘corporate governance’ rather than ‘corporate direction’? Early British joint stock companies were normally managed by a single ‘governor’. The ‘court of governors’ or ‘board of directors’ emerged slowly as the ruling body for companies. By the nineteenth century, however, companies were typically run by directors while not-for-profit entities such as hospitals, schools and charitable bodies had governors. The nineteenth century saw steady refinement of the roles of company directors, often in response to corporate scandals, with a gradual change from the notion of the director as a ‘representative shareholder’ to the directors being seen collectively as ‘representatives of the shareholders’. Governors in not-for-profit entities, however, were regarded as having broader responsibilities. The term ‘governance’ itself suggests that corporate boards should be studied as ‘political’ entities rather than merely through economic lenses such as agency theory

Biomass burning fuel consumption rates: a field measurement database

Landscape fires show large variability in the amount of biomass or fuel consumed per unit area burned. Fuel consumption (FC) depends on the biomass available to burn and the fraction of the biomass that is actually combusted, and can be combined with estimates of area burned to assess emissions. While burned area can be detected from space and estimates are becoming more reliable due to improved algorithms and sensors, FC is usually modeled or taken selectively from the literature. We compiled the peerreviewed literature on FC for various biomes and fuel categories to understand FC and its variability better, and to provide a database that can be used to constrain biogeochemical models with fire modules. We compiled in total 77 studies covering 11 biomes including savanna (15 studies, average FC of 4.6 t DM (dry matter) ha 1 with a standard deviation of 2.2),tropical forest (n = 19, FC = 126 +/- 77),temperate forest (n = 12, FC = 58 +/- 72),boreal forest (n = 16, FC = 35 +/- 24),pasture (n = 4, FC = 28 +/- 9.3),shifting cultivation (n = 2, FC = 23, with a range of 4.0-43),crop residue (n = 4, FC = 6.5 +/- 9.0),chaparral (n = 3, FC = 27 +/- 19),tropical peatland (n = 4, FC = 314 +/- 196),boreal peatland (n = 2, FC = 42 [42-43]),and tundra (n = 1, FC = 40). Within biomes the regional variability in the number of measurements was sometimes large, with e. g. only three measurement locations in boreal Russia and 35 sites in North America. Substantial regional differences in FC were found within the defined biomes: for example, FC of temperate pine forests in the USA was 37% lower than Australian forests dominated by eucalypt trees. Besides showing the differences between biomes, FC estimates were also grouped into different fuel classes. Our results highlight the large variability in FC, not only between biomes but also within biomes and fuel classes. This implies that substantial uncertainties are associated with using biome-averaged values to represent FC for whole biomes. Comparing the compiled FC values with co-located Global Fire Emissions Database version 3 (GFED3) FC indicates that modeling studies that aim to represent variability in FC also within biomes, still require improvements as they have difficulty in representing the dynamics governing FC

Degradation of communal rangelands in South Africa: towards an improved understanding to inform policy

In South Africa, the relative extent of range degradation under freehold compared to communal tenure has been strongly debated. We present a perspective on the processes that drive rangeland degradation on land under communal tenure. Our findings are based on literature as well as extensive field work on both old communal lands and ‘released’ areas, where freehold farms have been transferred to communal ownership. We discuss the patterns of degradation that have accompanied communal stewardship and make recommendations on the direction policy should follow to prevent further degradation and mediate rehabilitation of existing degraded land.Keywords: communal rangelands, land degradation, rehabilitation, social systemsAfrican Journal of Range & Forage Science 2013, 30(1&2): 57–6

Victimisation in the lives of lesbian-identified women in South Africa : implications for clinical assessment and treatment

Few clinical studies have examined victimisation in the lives of lesbian women in South Africa and whether there are distinct implications for psychological treatment. This paper presents the assessment and treatment of a lesbian-identified South African survivor of childhood sexual abuse who, as an adult, was raped and later gang raped. Her victimisation in adulthood represented ‘corrective rape’ motivated by the prejudiced assumption that the sexuality of lesbian women is pathological and should be ‘corrected’ through rape. This paper lends insights into the role of heterosexism in shaping vulnerability to victimisation and the process of recovery. It provides recommendations for work with sexual minority clients and highlights the implications when there is an absence of safety and support in the external environment

Facilitation or Competition? Tree Effects on Grass Biomass across a Precipitation Gradient

Savanna ecosystems are dominated by two distinct plant life forms, grasses and trees, but the interactions between them are poorly understood. Here, we quantified the effects of isolated savanna trees on grass biomass as a function of distance from the base of the tree and tree height, across a precipitation gradient in the Kruger National Park, South Africa. Our results suggest that mean annual precipitation (MAP) mediates the nature of tree-grass interactions in these ecosystems, with the impact of trees on grass biomass shifting qualitatively between 550 and 737 mm MAP. Tree effects on grass biomass were facilitative in drier sites (MAP≤550 mm), with higher grass biomass observed beneath tree canopies than outside. In contrast, at the wettest site (MAP = 737 mm), grass biomass did not differ significantly beneath and outside tree canopies. Within this overall precipitation-driven pattern, tree height had positive effect on sub-canopy grass biomass at some sites, but these effects were weak and not consistent across the rainfall gradient. For a more synthetic understanding of tree-grass interactions in savannas, future studies should focus on isolating the different mechanisms by which trees influence grass biomass, both positively and negatively, and elucidate how their relative strengths change over broad environmental gradients. © 2013 Moustakas et al

APENAS UNA PARTE DE NEGRO. Valores socio-raciales y accionar político de las élites de «color quebrado» en Jamaica, Venezuela, y las Antillas Francesas (siglos XVIII y XIX)

This essay compares the socio-racial prejudices and egalitarian aspirations of “mixedblood” elites of Jamaica, Venezuela , and the French Antilles . The aim is to show how these factors affected the political activities of the members of that sector, especially during the revolutionary period and the abolitionist era. We argue that their activities had contradictory consequences fostering both the perpetuation and the downfall of discriminatory regimes established during the colonial era.Este ensayo analiza comparativamente los prejuicios socio-raciales y las aspiraciones igualitarias de las élites de «color quebrado» de Jamaica, Venezuela, y las Antillas Francesas. El objetivo es mostrar cómo esos factores incidieron sobre la actividad política de los miembros de ese sector, sobre todo durante el período revolucionario y la era abolicionista. Sostenemos que dicha actividad tuvo consecuencias opuestas, incidiendo tanto sobre la perpetuación como sobre el fin de los regímenes discriminatorios instaurados durante la época colonial

“A Hideous Torture on Himself”: Madness and Self-Mutilation in Victorian Literature

This paper suggests that late nineteenth-century definitions of self-mutilation, a new category of psychiatric symptomatology, were heavily influenced by the use of selfinjury as a rhetorical device in the novel, for the literary text held a high status in Victorian psychology. In exploring Dimmesdale’s “self-mutilation” in The Scarlet Letter in conjunction with psychiatric case histories, the paper indicates a number of common techniques and themes in literary and psychiatric texts. As well as illuminating key elements of nineteenth-century conceptions of the self, and the relation of mind and body through ideas of madness, this exploration also serves to highlight the social commentary implicit in many Victorian medical texts. Late nineteenth-century England, like mid-century New England, required the individual to help himself and, simultaneously, others; personal charity and individual philanthropy were encouraged, while state intervention was often presented as dubious. In both novel and psychiatric text, self-mutilation is thus presented as the ultimate act of selfish preoccupation, particularly in cases on the “borderlands” of insanity

Fire regimes and variability in aboveground woody biomass in miombo woodland

This study combined a process-based ecosystem model with a fire regime model to understand the effect of changes in fire regime and climate pattern on woody plants of miombo woodland in African savanna. Miombo woodland covers wide areas in Africa and is subject to frequent anthropogenic fires. The model was developed based on observations of tree topkill rates in individual tree size classes for fire intensity and resprouting. Using current and near-future climate patterns, the model simulated the dynamics of miombo woodland for various fire return intervals and grass cover fractions, allowing fire intensity to be estimated. There was a significant relationship between aboveground woody biomass and long-term fire regimes. An abrupt increase in fire intensity and/or fire frequency applied as a model forcing led to reduced long-term average aboveground woody biomass and mean tree size. Fire intensity increased with increasing living grass biomass (which provides increased flammable fuel), thereby affecting the relationship between fire regime and tree size, creating a demographic bottleneck on the route to tree maturity. For the current fire regime in miombo woodland, with a fire return interval of about 1.6-3 years, the model-predicted fire intensity lower than 930-1700 kW m-1 is necessary to maintain today's aboveground woody biomass under current climate conditions. Future climate change was predicted to have a significant positive effect on woody plants in miombo woodland associated with elevated CO2 concentration and warming, allowing woody plants to survive more effectively against periodic fires