Variations, approximation, and low regularity in one dimension

We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general of the form of a standard Lipschitz "variation". Part of this investigation, but of interest in its own right, is an example of a nowhere locally Lipschitz minimizer which serves as a counter-example to any putative Tonelli partial regularity statement. Under these low assumptions we find it nonetheless remains possible to derive necessary conditions for minimizers, in terms of approximate continuity and equality of the one-sided derivatives.Comment: v3, 60 pages. To appear in CoVPDE. Minor cosmetic correction

Defining fitness in an uncertain world

The recently elucidated definition of fitness employed by Fisher in his fundamental theorem of natural selection is combined with reproductive values as appropriately defined in the context of both random environments and continuing fluctuations in the distribution over classes in a class-structured population. We obtain astonishingly simple results, generalisations of the Price Equation and the fundamental theorem, that show natural selection acting only through the arithmetic expectation of fitness over all uncertainties, in contrast to previous studies with fluctuating demography, in which natural selection looks rather complicated. Furthermore, our setting permits each class to have its characteristic ploidy, thus covering haploidy, diploidy and haplodiploidy at the same time; and allows arbitrary classes, including continuous variables such as condition. The simplicity is achieved by focussing just on the effects of natural selection on genotype frequencies: while other causes are present in the model, and the effect of natural selection is assessed in their presence, these causes will have their own further effects on genoytpe frequencies that are not assessed here. Also, Fisher’s uses of reproductive value are shown to have two ambivalences, and a new axiomatic foundation for reproductive value is endorsed. The results continue the formal darwinism project, and extend support for the individual-as-maximising-agent analogy to finite populations with random environments and fluctuating class-distributions. The model may also lead to improved ways to measure fitness in real populations

Generating power and controversy: Understanding Tanzania’s independent power projects

Initially conceived of within the broader context of power sector reform in the late 1980s and early 1990s, Independent Power Projects (IPPs) were intended to relieve state utilities of the burden of financing new plants, bring quick, quality power and reduce costs for end-users. Although IPPs have indeed contributed to generation capacity in Tanzania, much of the power that resulted from investments has been supplied neither quickly nor cheaply. Embarking on power sector reform in the early 1990s, Tanzania made IPPs a pillar of its reform strategy. Presently, Songas and IPTL, the country’s two IPPs are helping to reduce load shedding. However, these projects have not been without controversy. One of Tanzania’s IPPs was taken to international arbitration over a dispute related to construction costs. The state electric utility, Tanzania Electric Supply Company Limited (TANESCO), currently pays more than 50% of its current revenue towards combined fuel and capacity charges for the IPPs. Capacity charges for the country’s two IPPs are equivalent to approximately one percent of GDP. The Government of Tanzania (GoT) is intervening to assist TANESCO with its monthly IPP payments at present. With twenty-year Power Purchase Agreements (PPAs) between IPPs and TANESCO, these costs are expected to continue, albeit with some modifications due to refinancing, fuel conversion and further development of the natural gas market. This paper provides a detailed summary of how and why IPPs developed in Tanzania as well as their impact to date. Development outcomes, namely the extent to which the host country is benefiting from reliable, affordable power and investment outcomes, the degree to which investors have made favourable returns and been able to expand market share, are analysed in turn. IPPs offer more than a decade of experiences in private sector investment in developing countries and a detailed understanding of them may be the key to unlocking and sustaining future power investment

Defining fitness in an uncertain world

The recently elucidated definition of fitness employed by Fisher in his fundamental theorem of natural selection is combined with reproductive values as appropriately defined in the context of both random environments and continuing fluctuations in the distribution over classes in a class-structured population. We obtain astonishingly simple results, generalisations of the Price Equation and the fundamental theorem, that show natural selection acting only through the arithmetic expectation of fitness over all uncertainties, in contrast to previous studies with fluctuating demography, in which natural selection looks rather complicated. Furthermore, our setting permits each class to have its characteristic ploidy, thus covering haploidy, diploidy and haplodiploidy at the same time; and allows arbitrary classes, including continuous variables such as condition. The simplicity is achieved by focussing just on the effects of natural selection on genotype frequencies: while other causes are present in the model, and the effect of natural selection is assessed in their presence, these causes will have their own further effects on genoytpe frequencies that are not assessed here. Also, Fisher’s uses of reproductive value are shown to have two ambivalences, and a new axiomatic foundation for reproductive value is endorsed. The results continue the formal darwinism project, and extend support for the individual-as-maximising-agent analogy to finite populations with random environments and fluctuating class-distributions. The model may also lead to improved ways to measure fitness in real populations

Generating power and controversy: Understanding Tanzania’s independent power projects

Initially conceived of within the broader context of power sector reform in the late 1980s and early 1990s, Independent Power Projects (IPPs) were intended to relieve state utilities of the burden of financing new plants, bring quick, quality power and reduce costs for end-users. Although IPPs have indeed contributed to generation capacity in Tanzania, much of the power that resulted from investments has been supplied neither quickly nor cheaply. Embarking on power sector reform in the early 1990s, Tanzania made IPPs a pillar of its reform strategy. Presently, Songas and IPTL, the country’s two IPPs are helping to reduce load shedding. However, these projects have not been without controversy. One of Tanzania’s IPPs was taken to international arbitration over a dispute related to construction costs. The state electric utility, Tanzania Electric Supply Company Limited (TANESCO), currently pays more than 50% of its current revenue towards combined fuel and capacity charges for the IPPs. Capacity charges for the country’s two IPPs are equivalent to approximately one percent of GDP. The Government of Tanzania (GoT) is intervening to assist TANESCO with its monthly IPP payments at present. With twenty-year Power Purchase Agreements (PPAs) between IPPs and TANESCO, these costs are expected to continue, albeit with some modifications due to refinancing, fuel conversion and further development of the natural gas market. This paper provides a detailed summary of how and why IPPs developed in Tanzania as well as their impact to date. Development outcomes, namely the extent to which the host country is benefiting from reliable, affordable power and investment outcomes, the degree to which investors have made favourable returns and been able to expand market share, are analysed in turn. IPPs offer more than a decade of experiences in private sector investment in developing countries and a detailed understanding of them may be the key to unlocking and sustaining future power investment

Foundations of a mathematical theory of darwinism.

This paper pursues the 'formal darwinism' project of Grafen, whose aim is to construct formal links between dynamics of gene frequencies and optimization programmes, in very abstract settings with general implications for biologically relevant situations. A major outcome is the definition, within wide assumptions, of the ubiquitous but problematic concept of 'fitness'. This paper is the first to present the project for mathematicians. Within the framework of overlapping generations in discrete time and no social interactions, the current model shows links between fitness maximization and gene frequency change in a class-structured population, with individual-level uncertainty but no uncertainty in the class projection operator, where individuals are permitted to observe and condition their behaviour on arbitrary parts of the uncertainty. The results hold with arbitrary numbers of loci and alleles, arbitrary dominance and epistasis, and make no assumptions about linkage, linkage disequilibrium or mating system. An explicit derivation is given of Fisher's Fundamental Theorem of Natural Selection in its full generality