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.

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.

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.

Lessons learned after 2 full scale disaster exercises in a Swiss pediatric hospital

Introduction: Following a disaster, up to 50% of mass casualties are children. The number of disaster increases worldwide, including in Switzerland. Following national order, the mapping of the various risks of disaster in Switzerland will be completed by the end of 2012. Pre-hospital disaster drills and plans are well established and regularly tested. In-hospital disaster plans are much less frequently tested, if only available. Pediatric in-hospital full scale disaster exercises have never been reported in Switzerland. Based on our local constraints, we set up and evaluated a disaster plan during two full scale exercises. Methods: In a university hospital treating more than 35 000 pediatric emergencies per year, two exercises involving mock victims of a disaster aged 9 to 14 years old were successively set up over a period of 3 years. The exercises were planned during the day, without modification of the normal emergency room activities. The hospital staff was informed and trained in advance. Variables such as the alarm timing and transmission, triage set-up and function, special disaster medical records utilization, communication and victims' identification were assessed. Family members participated in the second exercise. An evaluation team observed and record exercises activities, identifying strength and weaknesses. Results: On two separate occasions, a total of 44 mock patients participated, were triaged, admitted and treated in the hospital according to usual standards of care. Alarm transmission was not appropriate during the first exercise. Triage overload occurred on one occasion. In-hospital communication needed readjustment. Identification and in-hospital tracking of the children remained problematic. Hospital employees showed great enthusiasm and stressed the positive effect of full scale exercises on their knowledge of the hospital disaster plan. Conclusions: Performing real life disaster exercises in a pediatric hospital was very beneficial. The disaster plan was adapted to local needs and updated accordingly. An alarm transmission protocol was elaborated and tested. Triage set-up was adapted and tested. A hospital identification plan for injured children was created and tested. Full scale hospital exercises evaluating disaster plans revealed several weaknesses in the system. Practice readjustments based on local experience were made. A tested pediatric disaster plan adapted to local constraints could minimize chaos, optimize care and support in the event of a real disaster. Children's identification and family reunification following a disaster remains a challenge.

Evaluating solutions to process, view and listen mathematical formula within an accessible context

Proves de conversió de fòrmules matemàtiques des d'editors de text ofimàtics i des de Làtex. Visionat en HTML i MathML. El millor resultat s'aconsegueix amb MSWord+MathType i IE+MathPlayer.

Long-term fertilizer field trials: comparison of three mathematical response models

Selostus: Lannoituksen pitkäaikaiset kenttäkokeet: kolmen matemaattisen mallin vertailu

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Conceptual framework for strengthening exercises to prevent hamstring strains

High-speed running accounts for the majority of hamstring strains in many sports. The terminal swing phase is believed to be the most hazardous as the hamstrings are undergoing an active lengthening contraction in a long muscle length position. Prevention-based strength training mainly focuses on eccentric exercises. However, it appears crucial to integrate other parameters than the contraction type. Therefore, the aim of this study is to present a conceptual framework based on six key parameters (contraction type, load, range of motion, angular velocity, uni-/bilateral exercises, kinetic chain) for the hamstring's strength exercise for strain prevention. Based on the biomechanical parameters of sprinting, it is proposed to use high-load eccentric contractions. The movement should be performed at a slow to moderate angular velocity and focused at the knee joint, while the hip is kept in a large flexion position in order to reach a greater elongation stress of the hamstrings than in the terminal swing phase. In this way, we believe that, during sprinting, athletes would be better trained to brake the knee extension effectively in the whole range of motion without overstretch of the hamstrings. Finally, based on its functional application, unilateral open kinetic chain should be preferred.

Memorial exercises in honor of William Boyd Allison : in Hall of House of Representatives, State Capitol, Des Moines, Iowa, Tuesday, September 8, 1908

Program of the memorial in honor of William Boyd Allison, senior Senator of the State of Iowa, who died at his home in Dubuque, Iowa, August 4, 1908. It includes full text of remarks presented at the memorial by dignitaries in attendance.

Case studies and mathematical models of ecological speciation. 1. Cichlids in a crater lake.

A recent study of a pair of sympatric species of cichlids in Lake Apoyo in Nicaragua is viewed as providing probably one of the most convincing examples of sympatric speciation to date. Here, we describe and study a stochastic, individual-based, explicit genetic model tailored for this cichlid system. Our results show that relatively rapid (<20,000 generations) colonization of a new ecological niche and (sympatric or parapatric) speciation via local adaptation and divergence in habitat and mating preferences are theoretically plausible if: (i) the number of loci underlying the traits controlling local adaptation, and habitat and mating preferences is small; (ii) the strength of selection for local adaptation is intermediate; (iii) the carrying capacity of the population is intermediate; and (iv) the effects of the loci influencing nonrandom mating are strong. We discuss patterns and timescales of ecological speciation identified by our model, and we highlight important parameters and features that need to be studied empirically to provide information that can be used to improve the biological realism and power of mathematical models of ecological speciation.