The influence of learning on evolution: a mathematical framework.

The Baldwin effect can be observed if phenotypic learning influences the evolutionary fitness of individuals, which can in turn accelerate or decelerate evolutionary change. Evidence for both learning-induced acceleration and deceleration can be found in the literature. Although the results for both outcomes were supported by specific mathematical or simulation models, no general predictions have been achieved so far. Here we propose a general framework to predict whether evolution benefits from learning or not. It is formulated in terms of the gain function, which quantifies the proportional change of fitness due to learning depending on the genotype value. With an inductive proof we show that a positive gain-function derivative implies that learning accelerates evolution, and a negative one implies deceleration under the condition that the population is distributed on a monotonic part of the fitness landscape. We show that the gain-function framework explains the results of several specific simulation models. We also use the gain-function framework to shed some light on the results of a recent biological experiment with fruit flies.

Pharmaceutical and Industrial Traits in Genetically Modified Crops: Co-existence with Conventional Agriculture, August 2006

This paper discusses the implications of using genetically modified crops to biomanufacture pharmaceuticals and industrial compounds from the perspective of their co-existence with conventional agriculture. Such plant-made pharmaceuticals and plantmade industrial products rely on exciting scientific and technological breakthroughs and promise new opportunities for the agricultural sector, but they also entail novel risks. The management of the externalities and of the possible unintended economic effects that arise in this context is critical and poses difficult questions for regulators.

The existence of nursing in caring for terminally ills’life: a phenomenological study

By taking care of cancer patients in their process of end of life, nursing experience situations of suffering before the anguish of others. This study aimed to understand the meaning and significance attributed by the nurses from the palliative care cancer hospital. This is a phenomenological research, grounded in Heidegger’s thinking, performed with 13 nurses, who work at Oncology hospitalward, through semi-structured interviews, which were analyzed according to the steps recommended by Josgrilberg. From understanding the statementsof the subjects, two ontological themesemerged: Feeling satisfaction and love in the care offered and Feeling anger and inabilitytowards terminally ill patients.We inferred that working in Oncology Ward is something rewarding for these professionals, but it entails physical and mental suffering, from feeling helpless before the death-dying process. Thus, we showedthat nursing professionals need to be recognized as human beings and as such, also deserving of care.

Affect-related synesthesias: A prospective view on their existence, expression and underlying mechanisms

The literature on developmental synaesthesia has seen numerous sensory combinations, with surprisingly few reports on synaesthesias involving affect. On the one hand, emotion, or more broadly affect, might be of minor importance to the synaesthetic experience (e.g. Sinke et al., 2012). On the other hand, predictions on how affect could be relevant to the synaesthetic experience remain to be formulated, in particular those that are driven by emotion theories. In this theoretical paper, we hypothesize that a priori studies on synaesthesia involving affect will observe the following. Firstly, the synaesthetic experience is not merely about discrete emotion processing or overall valence (positive, negative) but is determined by or even altered through cognitive appraisal processes. Secondly, the synaesthetic experience changes temporarily on a quantitative level according to i) the affective appraisal of the inducing stimulus or ii) the current affective state of the individual. These hypotheses are inferred from previous theoretical and empirical accounts on synaesthesia (including the few examples involving affect), different emotion theories, crossmodal processing accounts in synaesthetes and nonsynaesthetes, and the presumed stability of the synaesthetic experience. We hope that the current review will succeed in launching a new series of studies on "affective synaesthesias". We particularly hope that such studies will apply the same creativity in experimental paradigms as we have seen and still see when assessing and evaluating "traditional" synaesthesias.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

Traité de l'existence et des attributs de Dieu (Nouvelle édition, accompagnée de notes et précédée d'une introduction et d'une analyse des chapitres, par M. Alph. Aulard,...) / par Fénelon

[Traité de l'existence de Dieu (français). 1878]

Traité de l'existence et des attributs de Dieu ; suivi de Lettres sur divers sujets de métaphysique et de religion / par Fénelon,...

[Traité de l'existence de Dieu (français). 1878]

The daily market for funds in Europe: Mathematical appendix

This paper includes the derivations of the main expressions in the paper ``The Daily Market for Funds in Europe: Has Something Changed With the EMU?'' by G. Pérez Quirós and H. Rodríguez Mendizábal.

Análisis del comportamiento de los resultados en 'full' y 'direct costing'

In this paper we perform a mathematical analyse of profits and losses indirect and full costing. They are compared in different situations, mainlythe utilisation of productive capacity and the existence of beginninginventories. Direct costing was conceived as a system of cost accountingwhich would show profits as a function of sales. In full costing profitsdepend on available combinations of sales, production, costs of beginninginventories, etc., and information displayed in financial statements displayappears incongruent. Differences in profits with full and direct costingincrease when full costing allocates fixed costs according to normalproduction, in some cases differences, and financial statements would showmore incongruent performance. It is concluded about the importance thatprofit and loss statement expresses profits in both costing systems.

Existence of sparsely supported correlated equilibria

We show that every finite N-player normal form game possesses a correlated equilibrium with a precise lower bound on the number of outcomes to which it assigns zero probability. In particular, the largest games with a unique fully supported correlated equilibrium are two-player games; moreover, the lower bound grows exponentially in the number of players N.

Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study.

BACKGROUND: New HIV infections in men who have sex with men (MSM) have increased in Switzerland since 2000 despite combination antiretroviral therapy (cART). The objectives of this mathematical modelling study were: to describe the dynamics of the HIV epidemic in MSM in Switzerland using national data; to explore the effects of hypothetical prevention scenarios; and to conduct a multivariate sensitivity analysis. METHODOLOGY/PRINCIPAL FINDINGS: The model describes HIV transmission, progression and the effects of cART using differential equations. The model was fitted to Swiss HIV and AIDS surveillance data and twelve unknown parameters were estimated. Predicted numbers of diagnosed HIV infections and AIDS cases fitted the observed data well. By the end of 2010, an estimated 13.5% (95% CI 12.5, 14.6%) of all HIV-infected MSM were undiagnosed and accounted for 81.8% (95% CI 81.1, 82.4%) of new HIV infections. The transmission rate was at its lowest from 1995-1999, with a nadir of 46 incident HIV infections in 1999, but increased from 2000. The estimated number of new infections continued to increase to more than 250 in 2010, although the reproduction number was still below the epidemic threshold. Prevention scenarios included temporary reductions in risk behaviour, annual test and treat, and reduction in risk behaviour to levels observed earlier in the epidemic. These led to predicted reductions in new infections from 2 to 26% by 2020. Parameters related to disease progression and relative infectiousness at different HIV stages had the greatest influence on estimates of the net transmission rate. CONCLUSIONS/SIGNIFICANCE: The model outputs suggest that the increase in HIV transmission amongst MSM in Switzerland is the result of continuing risky sexual behaviour, particularly by those unaware of their infection status. Long term reductions in the incidence of HIV infection in MSM in Switzerland will require increased and sustained uptake of effective interventions.

Constraints and non-existence of rational expectations equilibria

In this article we show that in the presence of trading constraints, such as short sale constraints, the standard definition of a Rational Expectations Equilibrium allows for equilibrium prices that reveal information unknown to any active trader in the market. We propose a new definition of the Rational Expectations Equilibrium that incorporates a stronger measurability condition than measurability with respect to the join of the information sets of the agents and give an example of non-existence of equilibrium. The example is robust to perturbations on the data of the economy and the introduction of new assets.