Pensions modelling

Valuable insights into the problem of how to fund defined benefitpension schemes can be obtained by analysis using the standardBlack–Scholes/Merton option pricing model, consideringthe pension fund finances jointly with those of the sponsoringcompany. The nature of the fund assets and liabilities is completelydifferent, and this lies behind current controversies aboutthe appropriate discount rate, valuation, financial accountingand preferential status for pension fund claimants in insolvency.     

A sequence and structural study of transmembrane helices

A comparison is made between the distribution of residue preferences, three dimensional nearest neighbour contacts, preferred rotamers, helix-helix crossover angles and peptide bond angles in three sets of proteins: a non-redundant set of accurately determined globular protein structures, a set of four-helix bundle structures and a set of membrane protein structures. Residue preferences for the latter two sets may reflect overall helix stabilising propensities but may also highlight differences arising out of the contrasting nature of the solvent environments in these two cases. The results bear out the expectation that there may be differences between residue type preferences in membrane proteins and in water soluble globular proteins. For example, the -branched residue types valine and isoleucine are considerably more frequently encountered in membrane helices. Likewise, glycine and proline, residue types normally associated with `helix-breaking' propensity are found to be relatively more common in membrane helices. Three dimensional nearest neighbour contacts along the helix, preferred rotamers, and peptide bond angles are very similar in the three sets of proteins as far as can be ascertained within the limits of the relatively low resolution of the membrane proteins dataset. Crossing angles for helices in the membrane protein set resemble the four helix bundle set more than the general non-redundant set, but in contrast to both sets they have smaller crossing angles consistent with the dual requirements for the helices to form a compact structure while having to span the membrane. In addition to the pairwise packing of helices we investigate their global packing and consider the question of helix supercoiling in helix bundle proteins.     

Rational choice based on vague preferences

This paper studies vague preferences. In contrast to the concept of fuzzy preferences, the more general notion of vague preferences does not entail the assumption that the different degrees of preference are completely ordered. It is shown that the more general concept of a vague preference order arises very naturally in the context of aggregating a set of (exact) weak orders. Furthermore, necessary and sufficient conditions for the rationalizability of an exact choice function by means of a vague preference order are given. It turns out that in the general case these conditions are weaker than in the case where the degrees of preference are completely ordered. Consequently, there exist choice functions which are rationalizable by a general vague preference order but which are not rationalizable by a fuzzy preference order, or more generally by any vague preference order which induces a complete ranking of the degrees of preference. Examples of such choice functions are provided.This is a revised version of a discussion paper which was written at the University of Karlsruhe. I am grateful to Georg Bol and an anonymous referee for valuable comments. The research has been made possible by a fellowship of the DFG (Deutsche Forschungsgemeinschaft) which is also gratefully acknowledged.     

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.     

A survey of multicriteria optimization or the vector maximum problem,part I: 1776–1960

In this survey, the history of the subject from 1776 until 1960 is presented. A brief biographical sketch of Vilfredo Pareto is given first. Then, the more or less simultaneous development of the concepts of utility, preference, and welfare theory follows, with results which go back to Hausdorff and Cantor. A brief discussion of the work of Borel and von Neumann as initiators of game theory is included. Each of these areas has developed enough to warrant its own survey; hence, they are reviewed here only insofar as they provide necessary foundations. Thereafter, the concepts of efficiency, vector maximum problem, and Pareto optimality are reviewed in connection with production theory, programming, and economics. The survey is presented within a unified mathematical framework, and the emphasis is on mathematical results, rather than psychological or socio-economic discussion. To enable the reader to draw conclusions without having to obtain each article himself, the results have been presented in somewhat more detail than usual.     

An Intersection Theorem on an Unbounded Set and Its Application to the Fair Allocation Problem

We prove the following theorem. Let m and n be any positive integers with mn, and let be a subset of the n-dimensional Euclidean space ⁿ . For each i=1, . . . , m, there is a class of subsets M _i ^j of ^Tn . Assume that for each i=1, . . . , m, that M _i ^j is nonempty and closed for all i, j, and that there exists a real number B(i, j) such that and its jth component _{xjB(i, j)} imply . Then, there exists a partition of {1, . . . , n} such that for all i and We prove this theorem based upon a generalization of a well-known theorem of Birkhoff and von Neumann. Moreover, we apply this theorem to the fair allocation problem of indivisible objects with money and obtain an existence theorem.     

Community structure and ethnic preferences in school friendship networks

Recently developed concepts and techniques of analyzing complex systems provide new insight into the structure of social networks. Uncovering recurrent preferences and organizational principles in such networks is a key issue to characterize them. We investigate school friendship networks from the Add Health database. Applying threshold analysis, we find that the friendship networks do not form a single connected component through mutual strong nominations within a school, while under weaker conditions such interconnectedness is present. We extract the networks of overlapping communities at the schools (c-networks) and find that they are scale free and disassortative in contrast to the direct friendship networks, which have an exponential degree distribution and are assortative. Based on the network analysis we study the ethnic preferences in friendship selection. The clique percolation method we use reveals that when in minority, the students tend to build more densely interconnected groups of friends. We also find an asymmetry in the behavior of black minorities in a white majority as compared to that of white minorities in a black majority.     

Site Preferences of Hyperfine Impurities in Ni2Al3 Phases

The site occupation of indium solutes in Ni₂Al₃-type compounds was determined using perturbed angular correlation of gamma rays. Measurements were made for compositions on both sides of the stoichiometric composition. Sites were identified through their quadrupole interactions. For transition-metal (TM) rich aluminides and galliumides, indium solutes occupy only one of two inequivalent trivalent-metal sites (Al or Ga). For TM-poor aluminides, indium solutes tend to locate at noncrystallographic sites such as in grain boundaries. For TM-poor galliumides, the solutes occupy nickel sites while close to the stoichiometric composition they also occupy sites on an empty Ni-sublattice. Composition dependences of site preference for indium solutes in Pt₂Al₃ and Ni₂Ga₃ are examined in terms of a recently developed thermodynamic model. This revised version was published online in September 2006 with corrections to the Cover Date.     

群体决策随机偏爱数映射的若干性质

1引言近年来,群体决策在社会选择、福利、经济和军事等领域得到广泛应用,从而其理论研究越来越被人们所重视.20世纪中叶,K.J,Arrow提出了偏爱公理系和不可能性定理,并