Heterogeneity in Family Life Course Patterns and Intra-Cohort Wealth Disparities in Late Working Age

Considering soaring wealth inequalities in older age, this research addresses the relationship between family life courses and widening wealth differences between individuals as they age. We holistically examine how childbearing and marital histories are associated with personal wealth at ages 50–59 for Western Germans born between 1943 and 1967. We propose that deviations from culturally and institutionally-supported family patterns, or the stratified access to them, associate with differential wealth accumulation over time and can explain wealth inequalities at older ages. Using longitudinal data from the German Socio-Economic Panel Study (SOEP, v34, waves 2002–2017), we first identified typical family trajectory patterns between ages 16 and 50 with multichannel sequence analysis and cluster analysis. We then modelled personal wealth ranks at ages 50–59 as a function of family patterns. Results showed that deviations from the standard family pattern (i.e. stable marriage with, on average, two children) were mostly associated with lower wealth ranks at older age, controlling for childhood characteristics that partly predict selection into family patterns and baseline wealth. We found higher wealth penalties for greater deviation and lower penalties for moderate deviation from the standard family pattern. Addressing entire family trajectories, our research extended and nuanced our knowledge of the role of earlier family behaviour for later economic wellbeing. By using personal-level rather than household-level wealth data, we were able to identify substantial gender differences in the study associations. Our research also recognised the importance of combining marital and childbearing histories to assess wealth inequalities.

Quasi-Popular Matchings, Optimality, and Extended Formulations

Let [Formula: see text] be an instance of the stable marriage problem in which every vertex ranks its neighbors in a strict order of preference. A matching [Formula: see text] in [Formula: see text] is popular if [Formula: see text] does not lose a head-to-head election against any matching. Popular matchings generalize stable matchings. Unfortunately, when there are edge costs, to find or even approximate up to any factor a popular matching of minimum cost is NP-hard. Let [Formula: see text] be the cost of a min-cost popular matching. Our goal is to efficiently compute a matching of cost at most [Formula: see text] by paying the price of mildly relaxing popularity. Our main positive results are two bicriteria algorithms that find in polynomial time a “quasi-popular” matching of cost at most [Formula: see text]. Moreover, one of the algorithms finds a quasi-popular matching of cost at most that of a min-cost popular fractional matching, which could be much smaller than [Formula: see text]. Key to the other algorithm is a polynomial-size extended formulation for an integral polytope sandwiched between the popular and quasi-popular matching polytopes. We complement these results by showing that it is NP-hard to find a quasi-popular matching of minimum cost and that both the popular and quasi-popular matching polytopes have near-exponential extension complexity.

Exploiting Two-Level Information Entropy across Social Networks for User Identification

As the popularity of online social networks has grown, more and more users now hold multiple virtual accounts at the same time. Under these circumstances, identifying multiple social accounts belonging to the same user across different social networks is of great importance for many applications, such as user recommendation, personalized services, and information fusion. In this paper, we mainly aggregate user profile information and user behavior information, then measures and analyzes the attributes contained in these two types of information to implement across social networks user identification. Moreover, as different user attributes have different effects on user identification, this paper therefore proposes a two-level information entropy-based weight assignment method (TIW) to weigh each attribute. Finally, we combine the scoring formula with the bidirectional stable marriage matching algorithm to achieve optimal user account matching and thereby obtain the final matching pairs. Experimental results demonstrate that the proposed two-level information entropy method yields excellent performance in terms of precision rate, recall rate, F -measure ( F 1 ), and area under curve (AUC).

Bribery and Control in Stable Marriage

We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several manipulation goals. For instance, one goal is to make sure that a given pair of agents is matched in a stable solution, and this may be achieved by the manipulative action of reordering some agents' preference lists. We present a comprehensive study of the computational complexity of all problems arising in this way. We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard cases, focusing on the natural parameter "budget" (that is, the number of manipulative actions one is allowed to perform), we also conduct a parameterized complexity analysis and encounter mostly parameterized hardness results.