There will be a strong increase in the number of people affected by most movement disorders between 2010 and 2050. This increase will mostly depend on the future aging of populations in terms of their age structure and future life expectancy.

One challenging problem in biology is to understand the mechanism of DNA packing in a confined volume such as a cell. It is known that confined circular DNA is often knotted and hence the topology of the extracted (and relaxed) circular DNA can be used as a probe of the DNA packing mechanism. However, in order to properly estimate the topological properties of the confined circular DNA structures using mathematical models, it is necessary to generate large ensembles of simulated closed chains (i.e., polygons) of equal edge lengths that are confined in a volume such as a sphere of certain fixed radius. Finding efficient algorithms that properly sample the space of such confined equilateral random polygons is a difficult problem. In this paper we propose a method that generates confined equilateral random polygons based on their probability distribution. This method requires the creation of a large database initially. However, once the database has been created, a confined equilateral random polygon of length n can be generated in linear time in terms of n. The errors introduced by the method can be controlled and reduced by the refinement of the database. Furthermore, our numerical simulations indicate that these errors are unbiased and tend to cancel each other in a long polygon.

So far all calculations of the number of demented people are based on rates from meta-analyses, mean rates of meta-analyses or spatial analyses. This article presents age- and gender-specific prevalence and incidence rates of dementia that are based on a large sample of the German Sick Funds (Stichprobendaten von Versicherten der gesetzlichen Krankenversicherung (GKV)) with 2.3 million people from the year 2002. Prevalence rates increase from 0.8% and 0.6% for 60-64 year old men and women to 30% and 43% for men and women aged 100 or older, respectively. Incidence rates increase from 0.18 and 0.14 cases per 100 person-years for 60-64-year old men and women to 9.9 and 10.9 for over 95 year old men and women, respectively. Our results confirm rates from earlier studies on the basis of meta-analyses. Regional differences show for the first time that higher prevalence rates exist for East German women and men above age 85. In 2007 about 1.07 million moderately or severely demented people live in Germany of which about 244 000 are incident cases when we extrapolate our rates to the population of this year.

In this paper we continue our earlier studies [5, 6] on the generation methods of random equilateral polygons confined in a sphere. The first half of the paper is concerned with the generation of confined equilateral random walks. We show that if the selection of a vertex is uniform subject to the position of its previous vertex and the confining condition, then the distributions of the vertices are not uniform, although there exists a distribution such that if the initial vertex is selected following this distribution, then all vertices of the random walk follow this same distribution. Thus in order to generate a confined equilateral random walk, the selection of a vertex cannot be uniform subject to the position of its previous vertex and the confining condition. We provide a simple algorithm capable of generating confined equilateral random walks whose vertex distribution is almost uniform in the confinement sphere. In the second half of the paper we show that any process generating confined equilateral random walks can be turned into a process generating confined equilateral random polygons with the property that the vertex distribution of the polygons approaches the vertex distribution of the walks as the polygons get longer and longer. In our earlier studies, the starting point of the confined polygon is fixed at the center of the sphere. The new approach here allows us to move the the starting point of the confined polygon off the center of the sphere.

In this paper we continue our earlier studies (Diao et al 2011

This paper analyses the influence of relevant variables (age, sex, marital status, health, income, education and children) on the risk of belonging to one of the four main types of household in which old European people live nowadays: alone, with partner, with others, in a collective household. Nine countries with different social and political contexts are compared by using different data sources. These socio-demographic characteristics play the same role in all countries except for the influence of childlessness and of gender, but the geographical heterogeneity of the living arrangements remains partly unexplained due to currently inadequate comparative data sources for Europe. This research paper is part of the Future Elderly Living Conditions in Europe project (FELICIE, 5th Framework Programme of the European Community for Research, Quality of Life), which covers nine European countries. The goal of the project is to forecast up to 2030 the types of households in which people aged 75+ will live and their future care needs on the basis of the determinants of living conditions: age, sex, marital status, health, number of children and financial situation.

It is well known that genomic materials (long DNA chains) of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes but the general DNA packing mechanism remains an unsolved problem. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. For example, in the case of (mutant) bacteriophage P4, DNA molecules packed inside the bacteriophage head are considered to be circular since the two sticky ends of the DNA are close to each other. The DNAs extracted from the capsid without separating the two ends can thus preserve the topology of the (circular) DNAs. It turns out that the circular DNAs extracted from bacteriophage P4 are non-trivially knotted with very high probability and with a bias toward chiral knots. In order to study this problem using a systematic approach based on mathematical modeling, one needs to introduce a DNA packing model under extreme volume confinement condition and test whether such a model can produce the kind of knot spectrum observed in the experiments. In this paper we introduce and study a model of equilateral random polygons con_ned in a sphere. This model is not meant to generate polygons that model DNA packed in a virus head directly. Instead, the average topological characteristics of this model may serve as benchmark data for totally randomly packed circular DNAs. The difference between the biologically observed topological characteristics and our benchmark data might reveal the bias of DNA packed in the viral capsids and possibly lead to a better understanding of the DNA packing mechanism, at least for the bacteriophage DNA. The purpose of this paper is to provide information about the knot spectrum of equilateral random polygons under such a spherical confinement with length and confinement ratios in a range comparable to circular DNAs packed inside bacteriophage heads.

An introductory programming course ofers students problem solving analysis and design experience as well as exposure to the basic tenets of algorithmic thinking. Unfortunately, most introductory programming courses tend to concentrate on the syntax of a programming language (such as Basic, Pascal, e++, Java, etc.) at the expense of problem solving activities.The Flowchart Interpreter (FLINT) program supports problem solving activities while utilizing minimal-syntax flowcharts as visual representations of problem solving algorithms. FLINT provides the immediate feedback of an interpreted language as well as tools for simulation designed for use by novice programmers. This paper discusses the motivation for FLNT, including an analysis of the problems of typical introductory programming courses. An experimental study confirming the utility of flowcharts for introductory programming students is presented. Finally, the FLINT system is described in terms of its use by beginning programmers.