Bargaining over the division of a shrinking pie: An axiomatic approach

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).     

Investigating and ordering Quadrilaterals and their analogies in space—problem fields with various aspects

Problem fields with one or two generating problems and possibilities of varying existing problems give a good chance for self-activities of students and can be used for reaching different general aims. In this paper some topics concerning quadrilaterals will be presented. I hope they will animate teachers for more problem orientation in mathematics education. First we will reflect about different types of convex and non-convex quadrilaterals and possibilities of ordering them. Then we focus on middle-quadrilaterals and types of quadrilaterals with special middle-quadrilaterals as well as their logical ordering. Finally we investigate the analogies in space to the parallelogram and its sub-types and order them in the “house of parallelepipeds”.     

The Shapley value for cooperative games under precedence constraints

Cooperative games are considered where only those coalitions of players are feasible that respect a given precedence structure on the set of players. Strengthening the classical symmetry axiom, we obtain three axioms that give rise to a unique Shapley value in this model. The Shapley value is seen to reflect the expected marginal contribution of a player to a feasible random coalition, which allows us to evaluate the Shapley value nondeterministically. We show that every exact algorithm for the Shapley value requires an exponential number of operations already in the classical case and that even restriction to simple games is #P-hard in general. Furthermore, we outline how the multi-choice cooperative games of Hsiao and Raghavan can be treated in our context, which leads to a Shapley value that does not depend on pre-assigned weights. Finally, the relationship between the Shapley value and the permission value of Gilles, Owen and van den Brink is discussed. Both refer to formally similar models of cooperative games but reflect complementary interpretations of the precedence constraints and thus give rise to fundamentally different solution concepts.     

Medicinal Organometallic Chemistry: Designing Metal Arene Complexes as Anticancer Agents

The field of medicinal inorganic chemistry is rapidly advancing. In particular organometallic complexes have much potential as therapeutic and diagnostic agents. The carbon‐bound and other ligands allow the thermodynamic and kinetic reactivity of the metal ion to be controlled and also provide a scaffold for functionalization. The establishment of structure–activity relationships and elucidation of the speciation of complexes under conditions relevant to drug testing and formulation are crucial for the further development of promising medicinal applications of organometallic complexes. Specific examples involving the design of ruthenium and osmium arene complexes as anticancer agents are discussed.     

Genetically Encoded Bioluminescent Indicator for ERK2 Dimer in Living Cells

In this study, a genetically encoded bioluminescent indicator for ERK2 dimer was developed with the split Renilla luciferase complementation method, in which the formation of ERK2 dimer induces a spontaneous emission of bioluminescence in living cells. In response to extracellular stimuli, such as epidermal growth factor (EGF) or 17β‐estradiol (E2), extracellular signal‐regulated kinase 2 (ERK2) is phosphorylated by its upstream kinase MEK, and also phosphorylates its substrates in various regions of the cell, including the nucleus. Phosphorylated ERK2 is led to form its dimer, thereby transporting itself into the nucleus. We demonstrated with the indicator that stimulation with EGF or E2 induces the formation of ERK2 dimer in living MCF‐7 cells. The dynamics of this dimer formation was examined and discussed.