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

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

Chronic testicular Chlamydia muridarum infection impairs mouse fertility and offspring development

With approximately 131 million new genital tract infections occurring each year, Chlamydia is the most common sexually transmitted bacterial pathogen worldwide. Male and female infections occur at similar rates and both cause serious pathological sequelae. Despite this, the impact of chlamydial infection on male fertility has long been debated, and the effects of paternal chlamydial infection on offspring development are unknown. Using a male mouse chronic infection model, we show that chlamydial infection persists in the testes, adversely affecting the testicular environment. Infection increased leukocyte infiltration, disrupted the blood:testis barrier and reduced spermiogenic cell numbers and seminiferous tubule volume. Sperm from infected mice had decreased motility, increased abnormal morphology, decreased zona-binding capacity, and increased DNA damage. Serum anti-sperm antibodies were also increased. When both acutely and chronically infected male mice were bred with healthy female mice, 16.7% of pups displayed developmental abnormalities. Female offspring of chronically infected sires had smaller reproductive tracts than offspring of noninfected sires. The male pups of infected sires displayed delayed testicular development, with abnormalities in sperm vitality, motility, and sperm-oocyte binding evident at sexual maturity. These data suggest that chronic testicular Chlamydia infection can contribute to male infertility, which may have an intergenerational impact on sperm quality

United in Separation? Lozi Secessionism in Zambia and Namibia

Secessionism perseveres as a complex political phenomenon in Africa, yet often a more in-depth analysis is overshadowed by the aspirational simplicity of pursuing a new state. Using historical and contemporary approaches, this edited volume offers the most exhaustive collection of empirical studies of African secessionism to date. The respected expert contributors put salient and lesser known cases into comparative perspective, covering Biafra, Katanga, Eritrea and South Sudan alongside Barotseland, Cabinda, and the Comoros, among others. Suggesting that African secessionism can be understood through the categories of aspiration, grievance, performance, and disenchantment, the book's analytical framework promises to be a building block for future studies of the topic

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