Methods of tropical optimization in rating alternatives based on pairwise comparisons

We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained solution when it is not unique. Provided the approximation problem yields a set of score vectors, rather than a unique (up to a constant factor) one, we find those vectors in the set, which least and most differentiate between the alternatives with the highest and lowest scores, and thus can be representative of the entire solution.Comment: 9 pages, presented at the Annual Intern. Conf. of the German Operations Research Society (GOR), Helmut Schmidt University Hamburg, Germany, August 30 - September 2, 201

Activating Generalized Fuzzy Implications from Galois Connections

This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept Analysis, can be interpreted as fuzzy incidents. Thus knowledge processing, discovery, exploration and visualization as well as data mining are new research areas for fuzzy implications as they are areas where Formal Concept Analysis has a niche.F.J. Valverde-Albacete—was partially supported by EU FP7 project LiMoSINe, (contract 288024). C. Peláez-Moreno—was partially supported by the Spanish Government-CICYT project 2011-268007/TEC.Publicad

Reverse Engineering Time Discrete Finite Dynamical Systems: A Feasible Undertaking?

With the advent of high-throughput profiling methods, interest in reverse engineering the structure and dynamics of biochemical networks is high. Recently an algorithm for reverse engineering of biochemical networks was developed by Laubenbacher and Stigler. It is a top-down approach using time discrete dynamical systems. One of its key steps includes the choice of a term order, a technicality imposed by the use of Gröbner-bases calculations. The aim of this paper is to identify minimal requirements on data sets to be used with this algorithm and to characterize optimal data sets. We found minimal requirements on a data set based on how many terms the functions to be reverse engineered display. Furthermore, we identified optimal data sets, which we characterized using a geometric property called “general position”. Moreover, we developed a constructive method to generate optimal data sets, provided a codimensional condition is fulfilled. In addition, we present a generalization of their algorithm that does not depend on the choice of a term order. For this method we derived a formula for the probability of finding the correct model, provided the data set used is optimal. We analyzed the asymptotic behavior of the probability formula for a growing number of variables n (i.e. interacting chemicals). Unfortunately, this formula converges to zero as fast as , where and . Therefore, even if an optimal data set is used and the restrictions in using term orders are overcome, the reverse engineering problem remains unfeasible, unless prodigious amounts of data are available. Such large data sets are experimentally impossible to generate with today's technologies

A Grassmann algebra for matroids

We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a tropical linear space is its Plucker vector, which we view as a tensor, and a tropical linear space is recovered from its Plucker vector as the kernel of the corresponding wedge multiplication map. We prove that an arbitrary d-tensor satisfies the tropical Plucker relations (valuated exchange axiom) if and only if the d-th wedge power of the kernel of wedge-multiplication is free of rank one. This provides a new cryptomorphism for valuated matroids, including ordinary matroids as a special case

A school-based intervention to reduce overweight and inactivity in children aged 6–12 years: study design of a randomized controlled trial

Background Effective interventions to prevent overweight and obesity in children are urgently needed especially in inner-city neighbourhoods where prevalence of overweight and inactivity among primary school children is high. A school based intervention was developed aiming at the reduction of overweight and inactivity in these children by addressing both behavioural and environmental determinants. Methods/design The main components of the intervention (Lekker Fit!) are the re-establishment of a professional physical education teacher; three (instead of two) PE classes per week; additional sport and play activities outside school hours; fitness testing; classroom education on healthy nutrition, active living and healthy lifestyle choices; and the involvement of parents. The effectiveness of the intervention is evaluated through a cluster randomized controlled trial in 20 primary schools among grades 3 through 8 (6–12 year olds). Primary outcome measures are BMI, waist circumference and fitness. Secondary outcome measures are assessed in a subgroup of grade 6–8 pupils (9–12 year olds) through classroom questionnaires and constitute of nutrition and physical activity behaviours and behavioural determinants. Multilevel regression analyses are used to study differences in outcomes between children in the intervention schools and in control schools, taking clustering of children within schools into account. Discussion Hypotheses are that the intervention results in a lower prevalence of children being overweight and an improved mean fitness score, in comparison with a control group where the intervention is not implemented. The results of our study will contribute to the discussion on the role of physical education and physical activity in the school curriculum. Trial registration [ISRCTN84383524

Validation of the Comprehensive Feeding Practices Questionnaire with parents of 10-to-12-year-olds

Abstract Background: There is a lack of validated instruments for quantifying feeding behavior among parents of older children and adolescents. The Comprehensive Feeding Practices Questionnaire (CFPQ) is a self-report measure to assess multiple parental feeding practices. The CFPQ is originally designed for use with parents of children ranging in age from about 2 to 8 years. It is previously validated with American and French parents of children within this age range. The aim of the present study was to adapt and test the validity of this measure with parents of older children (10-to-12-year-olds) in a Norwegian setting. Methods: A sample of 963 parents of 10-to-12-year-olds completed a Norwegian, slightly adapted version of the CFPQ. Scale analyses were performed to test the validity of the instrument in our sample. Results: Although a few problematic items and scales were revealed, scale analyses showed that the psychometric properties of the slightly adapted, Norwegian version of the CFPQ were surprisingly similar to those of the original CFPQ. Conclusions: Our results indicated that the CFPQ, with some small modifications, is a valid tool for measuring multiple parental feeding practices with parents of 10-to12-year-olds

Prenatal Hypoxic-Ischemic Insult Changes the Distribution and Number of NADPH-Diaphorase Cells in the Cerebellum

Astrogliosis, oligodendroglial death and motor deficits have been observed in the offspring of female rats that had their uterine arteries clamped at the 18th gestational day. Since nitric oxide has important roles in several inflammatory and developmental events, here we evaluated NADPH-diaphorase (NADPH-d) distribution in the cerebellum of rats submitted to this hypoxia-ischemia (HI) model. At postnatal (P) day 9, Purkinje cells of SHAM and non-manipulated (NM) animals showed NADPH-d+ labeling both in the cell body and dendritic arborization in folia 1 to 8, while HI animals presented a weaker labeling in both cellular structures. NADPH-d+ labeling in the molecular (ML), and in both the external and internal granular layer, was unaffected by HI at this age. At P23, labeling in Purkinje cells was absent in all three groups. Ectopic NADPH-d+ cells in the ML of folia 1 to 4 and folium 10 were present exclusively in HI animals. This labeling pattern was maintained up to P90 in folium 10. In the cerebellar white matter (WM), at P9 and P23, microglial (ED1+) NADPH-d+ cells, were observed in all groups. At P23, only HI animals presented NADPH-d labeling in the cell body and processes of reactive astrocytes (GFAP+). At P9 and P23, the number of NADPH-d+ cells in the WM was higher in HI animals than in SHAM and NM ones. At P45 and at P90 no NADPH-d+ cells were observed in the WM of the three groups. Our results indicate that HI insults lead to long-lasting alterations in nitric oxide synthase expression in the cerebellum. Such alterations in cerebellar differentiation might explain, at least in part, the motor deficits that are commonly observed in this model

Foreign policy and globalization theory: The case of Israel

Since the early 1990s, international relations has witnessed a stimulating debate on globalization. This debate laid the foundations for globalization theory (GT), providing the tools for an empirical examination of the globalization of multiple activities: from politics and organized violence, to finance, trade and production, through culture and environmental degradation. However, examination of what appear to be the best-known works on globalization reveals that foreign policy has been virtually excluded from GT. In this context, based on what is described here as a synergistic transformationalist approach (STA) to globalization, I provide a critique of GT. The critique is geared towards examining why foreign policy hitherto has been overlooked by contemporary GT. I expose the problems this generates and address them by exploring how STA enables GT to incorporate foreign policy. I use the case of Israel heuristically to elicit how incorporating foreign policy into GT may provide a better understanding of the relationship between foreign policy and globalization. Three themes are highlighted: the role of foreign policy in inducing and reproducing globalization; determining the mutually constitutive relationship between globalization and the state; and shaping the interfacing between international politics and globalization