The first international workshop on the role and impact of mathematics in medicine: a collective account

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for inter- disciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining

Overgeneral autobiological memory in women: association with childhood abuse and history of depression in a community sample

Objective. Numerous studies have reported elevated levels of overgeneral autobiographical memory among depressed patients and also among those previously exposed to a traumatic event. No previous study has examined their joint association with overgeneral memory in a community sample, nor examined whether the associations are with both juvenile- and adult-onset depression. Methods. The current study examined the relative importance of exposure to childhood abuse and neglect in overgeneral memory of women with and without a history of major depressive disorder (MDD). Autobiographical memory test together with standardized interviews of childhood experiences and MDD were assessed in a risk-stratified community sample of 103 women aged 25–37. Results. Overgenerality in memory was associated with recalled childhood sexual abuse (CSA) but not other adversities. A history of CSA was predictive of overgeneral memory bias even in the absence of MDD. Our analyses indicated no significant association between a history of MDD and overgeneral memory in women who reported no CSA. However, overgeneral memory was increased in women who reported CSA and MDD with a significant difference found in relation to positive cues, the highest scores being seen among those with adult rather than juvenile-onset depression. Conclusions. The findings highlight the significance of CSA in predicting overgeneral memory, differential response in relation to positive and negative cue memories, and point to a specific role in the development of depression for overgeneral memory following CSA.

Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Indirect population dynamic benefits of altered life-history trade-offs in response to egg harvesting

Variations in demographic rates due to differential resource allocation between individuals are important considerations in the development of accurate population dynamic models. Systematic harvesting can alter age structure and/or reduce population density, conferring indirect positive benefits on the source population as a result of a consequent redistribution of resources between the remaining individuals. Independently of effects mediated through changes in density and competition, demographic rates can also be influenced by within-individual competition for resources. Harvesting dependent life stages can reduce an individual's current reproductive costs, allowing increased investment in its future fecundity and survival. Although such changes in demographic rates are well known, there has been little exploration of the potential impact on population dynamics. We use empirical data collected from a successfully reintroduced population of the Mauritius kestrel Falco punctatus to explore the population consequences of manipulating reproductive effort through harvesting. Consequent increases in an individual's future fecundity and survival allow source populations to withstand longer and more intensive harvesting regimes without being exposed to an increase in extinction risk, increasing maximum sustainable yields. These effects may also buffer populations against the impacts of stochastic events, but directional shifts in environmental conditions that increase reproductive costs may have detrimental population-level effects.

Evolutionary history of vegetative reproduction in Porpidia s. l. (lichen-forming ascomycota)

The evolutionary history of gains and losses of vegetative reproductive propagules (soredia) in Porpidia s.l., a group of lichen-forming ascomycetes, was clarified using Bayesian Markov chain Monte Carlo (MCMC) approaches to monophyly tests and a combined MCMC and maximum likelihood approach to ancestral character state reconstructions. The MCMC framework provided confidence estimates for the reconstructions of relationships and ancestral character states, which formed the basis for tests of evolutionary hypotheses. Monophyly tests rejected all hypotheses that predicted any clustering of reproductive modes in extant taxa. In addition, a nearest-neighbor statistic could not reject the hypothesis that the vegetative reproductive mode is randomly distributed throughout the group. These results show that transitions between presence and absence of the vegetative reproductive mode within Porpidia s.l. occurred several times and independently of each other. Likelihood reconstructions of ancestral character states at selected nodes suggest that - contrary to previous thought - the ancestor to Porpidia s.l. already possessed the vegetative reproductive mode. Furthermore, transition rates are reconstructed asymmetrically with the vegetative reproductive mode being gained at a much lower rate than it is lost. A cautious note has to be added, because a simulation study showed that the ancestral character state reconstructions were highly dependent on taxon sampling. However, our central conclusions, particularly the higher rate of change from vegetative reproductive mode present to absent than vice versa within Porpidia s.l., were found to be broadly independent of taxon sampling. [Ancestral character state reconstructions; Ascomycota, Bayesian inference; hypothesis testing; likelihood; MCMC; Porpidia; reproductive systems]