Problems of the randomization test for AB designs

N = 1 designs imply repeated registrations of the behaviour of the same experimental unit and the measurements obtained are often few due to time limitations, while they are also likely to be sequentially dependent. The analytical techniques needed to enhance statistical and clinical decision making have to deal with these problems. Different procedures for analysing data from single-case AB designs are discussed, presenting their main features and revising the results reported by previous studies. Randomization tests represent one of the statistical methods that seemed to perform well in terms of controlling false alarm rates. In the experimental part of the study a new simulation approach is used to test the performance of randomization tests and the results suggest that the technique is not always robust against the violation of the independence assumption. Moreover, sensitivity proved to be generally unacceptably low for series lengths equal to 30 and 40. Considering the evidence available, there does not seem to be an optimal technique for single-case data analysis

Percolation of spatially constrained Erdos-R enyi networks with degree correlations

Motivated by experiments on activity in neuronal cultures [J. Soriano, M. Rodr ́ıguez Mart́ınez, T. Tlusty, and E. Moses, Proc. Natl. Acad. Sci. 105, 13758 (2008)], we investigate the percolation transition and critical exponents of spatially embedded Erd̋os-Ŕenyi networks with degree correlations. In our model networks, nodes are randomly distributed in a two-dimensional spatial domain, and the connection probability depends on Euclidian link length by a power law as well as on the degrees of linked nodes. Generally, spatial constraints lead to higher percolation thresholds in the sense that more links are needed to achieve global connectivity. However, degree correlations favor or do not favor percolation depending on the connectivity rules. We employ two construction methods to introduce degree correlations. In the first one, nodes stay homogeneously distributed and are connected via a distance- and degree-dependent probability. We observe that assortativity in the resulting network leads to a decrease of the percolation threshold. In the second construction methods, nodes are first spatially segregated depending on their degree and afterwards connected with a distance-dependent probability. In this segregated model, we find a threshold increase that accompanies the rising assortativity. Additionally, when the network is constructed in a disassortative way, we observe that this property has little effect on the percolation transition.

Giant monopole energies from a constrained relativistic mean-field approach

Background:Average energies of nuclear collective modes may be efficiently and accurately computed using a nonrelativistic constrained approach without reliance on a random phase approximation (RPA). Purpose: To extend the constrained approach to the relativistic domain and to establish its impact on the calibration of energy density functionals. Methods: Relativistic RPA calculations of the giant monopole resonance (GMR) are compared against the predictions of the corresponding constrained approach using two accurately calibrated energy density functionals. Results: We find excellent agreement at the 2% level or better between the predictions of the relativistic RPA and the corresponding constrained approach for magic (or semimagic) nuclei ranging from 16 O to 208 Pb. Conclusions: An efficient and accurate method is proposed for incorporating nuclear collective excitations into the calibration of future energy density functionals.

Assessing positive mental health in people with chronic physical health problems: correlations with socio-demographic variables and physical health status

Background: A holistic perspective on health implies giving careful consideration to the relationship between physical and mental health. In this regard the present study sought to determine the level of Positive Mental Health (PMH) among people with chronic physical health problems, and to examine the relationship between the observed levels of PMH and both physical health status and socio-demographic variables. Methods: The study was based on the Multifactor Model of Positive Mental Health (Lluch, 1999), which comprises six factors: Personal Satisfaction (F1), Prosocial Attitude (F2), Self-control (F3), Autonomy (F4), Problem-solving and Self-actualization (F5), and Interpersonal Relationship Skills (F6). The sample comprised 259 adults with chronic physical health problems who were recruited through a primary care center in the province of Barcelona (Spain). Positive mental health was assessed by means of the Positive Mental Health Questionnaire (Lluch, 1999). Results: Levels of PMH differed, either on the global scale or on specific factors, in relation to the following variables: age: global PMH scores decreased with age (r=-0.129; p=0.038); b) gender: men scored higher on F1 (t=2.203; p=0.028) and F4 (t=3.182; p=0.002), while women scored higher on F2 (t -3.086; p=0.002) and F6 (t=-2.744; p=0.007); c) number of health conditions: the fewer the number of health problems the higher the PMH score on F5 (r=-0.146; p=0.019); d) daily medication: polymedication patients had lower PMH scores, both globally and on various factors; e) use of analgesics: occasional use of painkillers was associated with higher PMH scores on F1 (t=-2.811; p=0.006). There were no significant differences in global PMH scores according to the type of chronic health condition. The only significant difference in the analysis by factors was that patients with hypertension obtained lower PMH scores on the factor Autonomy (t=2.165; p=0.032). Conclusions: Most people with chronic physical health problems have medium or high levels of PMH. The variables that adversely affect PMH are old age, polypharmacy and frequent consumption of analgesics. The type of health problem does not influence the levels of PMH. Much more extensive studies with samples without chronic pathology are now required in order to be able to draw more robust conclusions.

Genetic origin of the relationship between parental negativity and behavior problems from early childhood to adolescence: A longitudinal genetically sensitive study.

Little is known about how genetic and environmental factors contribute to the association between parental negativity and behavior problems from early childhood to adolescence. The current study fitted a cross-lagged model in a sample consisting of 4,075 twin pairs to explore (a) the role of genetic and environmental factors in the relationship between parental negativity and behavior problems from age 4 to age 12, (b) whether parent-driven and child-driven processes independently explain the association, and (c) whether there are sex differences in this relationship. Both phenotypes showed substantial genetic influence at both ages. The concurrent overlap between them was mainly accounted for by genetic factors. Causal pathways representing stability of the phenotypes and parent-driven and child-driven effects significantly and independently account for the association. Significant but slight differences were found between males and females for parent-driven effects. These results were highly similar when general cognitive ability was added as a covariate. In summary, the longitudinal association between parental negativity and behavior problems seems to be bidirectional and mainly accounted for by genetic factors. Furthermore, child-driven effects were mainly genetically mediated, and parent-driven effects were a function of both genetic and shared-environmental factors.

Some optimization and decision problems in proportional reinsurance

Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function (Gerber & Shiu, 1998) is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs.

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

Approximation to the theory of affinities to manage the problems of the groupping process

New economic and enterprise needs have increased the interest and utility of the methods of the grouping process based on the theory of uncertainty. A fuzzy grouping (clustering) process is a key phase of knowledge acquisition and reduction complexity regarding different groups of objects. Here, we considered some elements of the theory of affinities and uncertain pretopology that form a significant support tool for a fuzzy clustering process. A Galois lattice is introduced in order to provide a clearer vision of the results. We made an homogeneous grouping process of the economic regions of Russian Federation and Ukraine. The obtained results gave us a large panorama of a regional economic situation of two countries as well as the key guidelines for the decision-making. The mathematical method is very sensible to any changes the regional economy can have. We gave an alternative method of the grouping process under uncertainty.

Enjoying cooperative games: The R package GameTheory

This paper focuses on cooperative games with transferable utility. We propose the computation of two solutions, the Shapley value for n agents and the nucleolus with a maximum of four agents. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud and the random arrival rules. Keywords: Cooperative game, Shapley value, nucleolus, claims problem, claims rule, bankruptcy.

Similar problems, different solutions: Comparing refuse collection in the Netherlands and Spain

Local public service provision can vary greatly because of differences in institutional arrangements, public service markets, and national traditions regarding government intervention. In this paper we compare the procedures adopted by the local governments of the Netherlands and Spain in arranging for the provision of solid waste collection. We find that Spain faces a consolidation problem, opting more frequently to implement policies of privatization and cooperation, at the expense of competition. By contrast, the Netherlands has, on average, larger municipalities, resorting somewhat less to privatization and cooperation, and more to competition. The two options - cooperation and competition - have their merits when striving to strike a balance between transaction costs and scale economies. The choices made in organizational reform seem to be related to several factors, among which the nature of the political system and the size of municipalities appear to be relevant.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

¿Para qué sirven los problemas en la clase de matemáticas? = What is the use of problems in Mathematics lessons?

The results obtained in several yield tests, at an international level (mainly the famous PISA 2003 report, by the OCDE), have raised a multiplicity of performances in order to improve the students' yield regarding problem solving. In this article we set a clear guideline on how problems should be used in Mathematics lessons, not for obtaining better scores in the yield tests but for improving the development of Mathematical thinking in students. From this perspective, the author analyses, through eight reflections, how the concept of problem, transmitted both in the school and from society, influences the students