2-Rainbow domination number of Cartesian products: C_{n}\square C_{3} and C_{n}\square C_{5}

A function \(f:V(G)\rightarrow \mathcal P (\{1,\ldots ,k\})\) is called a \(k\) -rainbow dominating function of \(G\) (for short \(kRDF\) of \(G)\) if \( \bigcup \nolimits _{u\in N(v)}f(u)=\{1,\ldots ,k\},\) for each vertex \( v\in V(G)\) with \(f(v)=\varnothing .\) By \(w(f)\) we mean \(\sum _{v\in V(G)}\left|f(v)\right|\) and we call it the weight of \(f\) in \(G.\) The minimum weight of a \( kRDF\) of \(G\) is called the \(k\) -rainbow domination number of \(G\) and it is denoted by \(\gamma _{rk}(G).\) We investigate the \(2\) -rainbow domination number of Cartesian products of cycles. We give the exact value of the \(2\) -rainbow domination number of \(C_{n}\square C_{3}\) and we give the estimation of this number with respect to \(C_{n}\square C_{5},\) \((n\ge 3).\) Additionally, for \(n=3,4,5,6,\) we show that \(\gamma _{r2}(C_{n}\square C_{5})=2n.\)      

On parallel policies for ranking and selection problems

In this paper we develop and test experimental methodologies for selection of the best alternative among a discrete number of available treatments. We consider a scenario where a researcher sequentially decides which treatments are assigned to experimental units. This problem is particularly challenging if a single measurement of the response to a treatment is time-consuming and there is a limited time for experimentation. This time can be decreased if it is possible to perform measurements in parallel. In this work we propose and discuss asynchronous extensions of two well-known Ranking & Selection policies, namely, Optimal Computing Budget Allocation (OCBA) and Knowledge Gradient (KG) policy. Our extensions (Asynchronous Optimal Computing Budget Allocation (AOCBA) and Asynchronous Knowledge Gradient (AKG), respectively) allow for parallel asynchronous allocation of measurements. Additionally, since the standard KG method is sequential (it can only allocate one experiment at a time) we propose a parallel synchronous extension of KG policy – Synchronous Knowledge Gradient (SKG). Computer simulations of our algorithms indicate that our parallel KG-based policies (AKG, SKG) outperform the standard OCBA method as well as AOCBA, if the number of evaluated alternatives is small or the computing/experimental budget is limited. For experimentations with large budgets and big sets of alternatives, both the OCBA and AOCBA policies are more efficient.     

Agent Rationality Behind Network Formation

We search for agent behavior rules which lead to the emergence of social networks that exhibit empirically observed phenomena: small-world property, scale-free degree distribution and stability in time. We assume that agents form and sever links using a cost-benefit analysis. Agents receive benefit from own links and from links that their friends form. On the other hand, link formation, deletion and keeping is costly. We find that a simple model structure which relies only on convex cost of link upkeep leads to stable networks which exhibit the small-world property.     

Debate on nanotechnology in the Swedish daily press 2004–2009

This work presents the results of an on-going project that explores the media debate on nanotechnology in the Swedish daily press. Based on the analysis of articles published between 2004 and 2009 in two national and two regional Swedish daily broadsheets, it examines frames and themes used, the general tone of the articles as well as the actors active in the debate. Results of the analysis show that a positive tone dominates the Swedish coverage, which is mostly focused on future applications of nanotechnology. However, in the final stage of the studied period, the Swedish press started focus more on potential risks of nanotechnology as well as regulatory questions.     

Insulin resistance,oxidative stress markers and the blood antioxidant system in overweight elderly men

The purpose of the study was to examine in the blood of overweight men aged from 62 to 83 years, the relationships between age and insulin resistance, selected parameters of the oxidative stress, and the antioxidant defense system. The population studied was divided into two groups: the group ‘young-old’ consisted of men aged 62 to 74 years old, and the group ‘old-old’– of men aged between 75 and 83 years. The total antioxidative status (TAS) and concentrations of thiobarbituric acid reactive substances (TBARS) were measured in the blood plasma. In the serum samples, the levels of antibodies against oxidized LDL (oLAB), glucose, total cholesterol, HDL-cholesterol, triglycerides and insulin were measured. Homeostasis Model Assessment of Insulin Resistance (HOMA_IR) was calculated. Concentration of reduced glutathione (GSH) and glutathione peroxidase activity (GPx) were determined in the red blood cells hemolysate. The results of the study did not show significant differences between groups investigated with respect to concentrations of TBARS, TAS, GSH and GPx. However, significantly higher concentrations of glucose and antibodies against oxLDL (p < 0.05) were observed in the group of men over 74 years old in comparison to the group of ‘young-old’ men. It was indicated that the increased insulin resistance and hyperglycemia in elderly men are related to body mass and that they cause intensified oxidative modifications of LDL.     

Books and Publications Received

Manpower developments should be examined against the population background. Population and manpower structure of post-war Europe is the haphazard result of various trends, war losses and tremendous shifts of population. Conditions have been changing rapidly, so that computations regarding the structural changes of populations prior to 1949 are in many cases not significant.

The major pre-war trends in economic structure appear to have continued after the war with the exception of commerce, which has not maintained its previous upward trend.

The present disturbed situation is not a convenient platform for projections of population or of manpower. Anyhow, any speculation as to future developments should be based on the knowledge of the specific conditions obtaining in the various countries. Differences in the economic and social structure, as well as in legislation between the various parts of Europe, no longer warrant a smooth and uniform development in accordance with the pre-war pattern. There are, on the other hand, some features of a prospective rapprochement in the economic and social field between Western and Eastern Europe.