Zeta measures and Thermodynamic Formalism for temperature zero

We address the analysis of the following problem: given a real H\"older potential $f$ defined on the Bernoulli space and $\mu_f$ its equilibrium state, it is known that this shift-invariant probability can be weakly approximated by probabilities in periodic orbits associated to certain zeta functions. Given a H\"older function $f>0$ and a value $s$ such that $0<s<1$, we can associate a shift-invariant probability $\nu_{s}$ such that for each continuous function $k$ we have $$\int k d\nu_{s}=\frac{\sum_{n=1}^{\infty}\sum_{x\in Fix_{n}}e^{sf^{n}(x)-nP(f)}\frac{k^{n}(x)}{n}}{\sum_{n=1}^{\infty}\sum_{x\in Fix_{n}}e^{sf^{n}(x)-nP(f)}},$$ where $P(f)$ is the pressure of $f$, $Fix_n$ is the set of solutions of $\sigma^n(x)=x$, for any $n\in \mathbb{N}$, and $f^{n}(x) = f(x) + f(\sigma(x)) + f(\sigma^2(x))+... + f(\sigma^{n-1} (x)).$ We call $\nu_{s}$ a zeta probability for $f$ and $s$. It is known that $\nu_s \to \mu_{f}$, when $s \to 1$. We consider for each value $c$ the potential $c f$ and the corresponding equilibrium state $\mu_{c f}$. What happens with $\nu_{s}$ when $c$ goes to infinity and $s$ goes to one? This question is related to the problem of how to approximate the maximizing probability for $f$ by probabilities on periodic orbits. We study this question and also present here the deviation function $I$ and Large Deviation Principle for this limit $c\to \infty, s\to 1$. We will make an assumption: $\lim_{c\to \infty, s\to 1} c(1-s)= L>0$. We do not assume here the maximizing probability for $f$ is unique

Route learning and shortcut performance in adults with intellectual disability: a study with virtual environments

The ability to learn routes though a virtual environment (VE) and to make a novel shortcut between two locations was assessed in 18 adults with intellectual disability and 18 adults without intellectual disability matched on chronological age. Participants explored two routes (A ⇔ B and A ⇔ C) until they reached a learning criterion. Then, they were placed at B and were asked to find the shortest way to C (B ⇔ C, five trials). Participants in both groups could learn the routes, but most of the participants with intellectual disability could not find the shortest route between B and C. However, the results also revealed important individual differences within the intellectual disability group, with some participants exhibiting more efficient wayfinding behaviour than others. Individuals with intellectual disability may differ in the kind of spatial knowledge they extract from the environment and/or in the strategy they use to learn routes

Prevalence and causes of blindness and visual impairment in Muyuka: a rural health district in South West Province, Cameroon.

AIM: To estimate the prevalence and causes of blindness and visual impairment in the population aged 40 years and over in Muyuka, a rural district in the South West Province of Cameroon. METHODS: A multistage cluster random sampling methodology was used to select 20 clusters of 100 people each. In each cluster households were randomly selected and all eligible people had their visual acuity (VA) measured by an ophthalmic nurse. Those with VA <6/18 were examined by an ophthalmologist. RESULTS: 1787 people were examined (response rate 89.3%). The prevalence of binocular blindness was 1.6% (95% CI: 0.8% to 2.4%), 2.2% (1.% to 3.1%) for binocular severe visual impairment, and 6.4% (5.0% to 7.8%) for binocular visual impairment. Cataract was the main cause of blindness (62.1%), severe visual impairment (65.0%), and visual impairment (40.0%). Refractive error was an important cause of severe visual impairment (15.0%) and visual impairment (22.5%). The cataract surgical coverage for people was 55% at the <3/60 level and 33% at the <6/60 level. 64.3% of eyes operated for cataract had poor visual outcome (presenting VA<6/60). CONCLUSIONS: Strategies should be developed to make cataract services affordable and accessible to the population in the rural areas. There is an urgent need to improve the outcome of cataract surgery. Refractive error services should be provided at the community level

Large Deviations for Quantum Spin probabilities at temperature zero

We consider certain self-adjoint observables for the KMS state associated to the Hamiltonian $H= \sigma^x \otimes \sigma^x$ over the quantum spin lattice $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes ...$. For a fixed observable of the form $L \otimes L \otimes L \otimes ...$, where $L:\mathbb{C}^2 \to \mathbb{C}^2$, and for the zero temperature limit one can get a naturally defined stationary probability $\mu$ on the Bernoulli space $\{1,2\}^\mathbb{N}$. This probability is ergodic but it is not mixing for the shift map. It is not a Gibbs state for a continuous normalized potential but its Jacobian assume only two values almost everywhere. Anyway, for such probability $\mu$ we can show that a Large Deviation Principle is true for a certain class of functions. The result is derived by showing the explicit form of the free energy which is differentiable

Varietal selection by growers in central Cameroon

The diet of the inhabitants of the forested regions of Cameroon is based on starch, part of which comes from plantains (Dury et al. 2002). An increase in production using new techniques is necessary in order to meet the challenge of providing food security for the country (Temple 2000). Varietal improvement contributes to these changes, but although the objectives pursued when creating varieties are known (Auboiron et al. 1998), the lack of research on farmers' knowledge and their expertise of the existing varietal potential is deplorable (CRDI 2001). A study of these farmer's knowledge would be a useful contribution to the improvement of production systems by the introduction of new varieties. The present study is concerned with local knowledge of the different plantain varieties and the factors which determine the choice of varieties by the growers. (Résumé d'auteur

Sélection variétale par des producteurs du Centre du Cameroun

Le régime alimentaire dans les régions forestières du Cameroun est basé sur les amylacées, dont fait partie la banane plantain (Dury et al. 2002). L'accroissement de la production par des changements techniques est nécessaire pour répondre aux enjeux de la sécurité alimentaire du pays (Temple 2000). L'amélioration variétale contribue à ces changements, mais si les objectifs poursuivis dans la création variétale sont connus (Auboiron et al. 1998), on déplore l'insuffisance de recherches sur les savoirs des agriculteurs et de leur maîtrise du potentiel variétal existant (CRDI 2001). Un examen du savoir de ces agriculteurs paraît utile pour contribuer à l'amélioration des systèmes de production par l'introduction de nouvelles variétés. La présente étude porte sur les connaissances locales sur les différentes variétés de plantain et les déterminants du choix des variétés par les producteurs. (Résumé d'auteur