One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n_i numbers with n_i lying in a given range. The goal is to maximize a Schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n₁,..., n_p) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape. This research is partially supported by ROC National Science grant NSC 92-2115-M-009-014.     

Moving in or Breaking Up? The Role of Distance in the Development of Romantic Relationships

Most romantic relationships start with a living apart together (LAT) phase during which the partners live in two separate households. Over time, a couple might decide to move in together, to separate, or to remain together while maintaining their nonresidential status. This study investigates the competing risks that partners in a LAT relationship will experience the transition to coresidence or to separation. We consider the amount of time LAT partners have to travel to see each other to be a key determinant of relationship development. For our statistical analyses, we use seven waves of the German Family Panel Pairfam (2008/2009–2014/2015) and analyze couples in the age group 20–40 years. We distinguish between short-distance relationships (the partners have to travel less than one hour) and long-distance relationships (the partners have to travel one hour or more). Estimating a competing risks model, we find that couples in long-distance relationships are more likely to separate than those living in close proximity. By contrast, the probability of experiencing a transition to coresidence is lower for LAT couples in long-distance than for those in short-distance relationships. Interaction analyses reveal that distance seems to be irrelevant for the relationship development of couples with two nonemployed (unemployed, in education or other inactive) partners.     

Investigating Possible Effects of Ethnicity and Age on Gambling as an Escape

Previous research has shown that there are a number of risk factors for disordered and problem gambling, including an individual’s ethnicity and age. Endorsing gambling as an escape has also been shown to contribute to and maintain disordered gambling. The present study examined potential interactions between ethnicity and age as they relate to disordered gambling, as well as if ethnicity and age would be predictors of endorsing gambling as an escape. Three hundred fifteen adults from the United States completed measures relating to gambling. Participants were grouped into ethnic categories of Caucasian and non-Caucasian, and age groups of 18–25, 26–35, 36–55, and 56 years old and above. Non-Caucasians reported more gambling problems than Caucasians. A significant interaction was found between ethnicity and age for 36–55 year olds. Overall, participants were more likely to gamble for positive than negative reinforcement. However, only gambling as an escape was a significant predictor of disordered gambling. Implications and limitations are discussed with the thought that these results are informative to practitioners treating disordered gambling.     

Comparison of Modes of Administration and Response Options in the Assessment of Subjective Health Using the First Question of SF-36

To compare two modes of administration (self-administered; by interviewer) and two response options format (using words; images of “facial-expressions”) of the first question of SF-36 (Q1SF-36), and to test its validity. We included 825 participants (20–90 years). Q1SF-36, using words or images, was included in a global questionnaire interview and at the end participants filled the SF-36. The agreement was tested by weighted kappa coefficients (WKappa). Classification Trees were used in the calibration of Q1SF-36 responses, with the physical (PDSF36) and mental dimensions of SF-36. Polyserial correlation coefficients and areas under the ROC curves (AUC) were used for validation. After categorization, using PDSF36 classification trees, the WKappa were 0.770 (self-administered vs. interviewer), 0.569 (self-administered vs. facial-expressions) and 0.566 (interviewer vs. facial-expressions). The WKappa between the PDSF36 and the modes (self-administered, interviewer and facial-expressions) were 0.784, 0.713 and 0.579 and the corresponding polyserial correlation coefficients were 0.784, 0.713 and 0.579. A good discriminatory power was found comparing the modes with the PDSF36 (AUC = 0.907, 0.923 and 0.827), but not with mental dimension (AUC = 0.538, 0.501 and 0.629). The Q1SF-36, by self-administration or interviewer, may be a valid alternative for assessment of subjective physical health, but not mental health.