Combining Globally Rigid Frameworks

Here it is shown how to combine two generically globally rigid bar frameworks in $d$-space to get another generically globally rigid framework. The construction is to identify $d+1$ vertices from each of the frameworks and erase one of the edges that they have in common.Comment: 14 page

Frameworks, Symmetry and Rigidity

Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.Comment: 5 Figures. Replaces Dec. 2008 version. To appear in IJCG

The Social Value of Mortality Risk Reduction: VSL vs. The Social Welfare Function Approach

We examine how different welfarist frameworks evaluate the social value of mortality risk reduction. These frameworks include classical, distributively unweighted cost–benefit analysis—i.e., the “value per statistical life” (VSL) approach—and various social welfare functions (SWFs). The SWFs are either utilitarian or prioritarian, applied to policy choice under risk in either an “ex post” or “ex ante” manner. We examine the conditions on individual utility and on the SWF under which these frameworks display sensitivity to wealth and to baseline risk. Moreover, we discuss whether these frameworks satisfy related properties that have received some attention in the literature, namely equal value of risk reduction, preference for risk equity, and catastrophe aversion. We show that the particular manner in which VSL ranks risk-reduction measures is not necessarily shared by other welfarist frameworks

On the Relative Expressiveness of Argumentation Frameworks, Normal Logic Programs and Abstract Dialectical Frameworks

We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional signature using only atoms from that signature. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Electronic chemical potentials of porous metal-organic frameworks

The binding energy of an electron in a material is a fundamental characteristic, which determines a wealth of important chemical and physical properties. For metal-organic frameworks this quantity is hitherto unknown. We present a general approach for determining the vacuum level of porous metal-organic frameworks and apply it to obtain the first ionisation energy for six prototype materials including zeolitic, covalent and ionic frameworks. This approach for valence band alignment can explain observations relating to the electrochemical, optical and electrical properties of porous frameworks