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.     

Internalized Other Interviewing in Relational Therapy: Three Discursive Approaches to Understanding its Use and Outcomes

For over 20 years, family therapist Karl Tomm has been engaging families and couples with a therapeutic intervention he calls Internalized Other Interviewing (IOI). The IOI (cf. Emmerson‐Whyte, 2010; Hurley, 2006) entails interviewing clients, from the personal experiences of partners and family members as an internalized other. The IOI is based on the idea that through dialogues over time, one can internalize a sense of one's conversational partner responsiveness in reliably anticipated ways. Anyone who has thought in a conversation with a family member or partner, “Oh there s/he goes again,” or anticipates next words before they leave the other's mouth, has a sense of what we are calling an internalized other. For Tomm, the internalized anticipations partners and family members may have offers entry points into new dialogues with therapeutic potential—particularly, when their actual dialogues get stuck in dispreferred patterns.     

Assessing Risk‐Based Upper Limits of Melamine Migration from Food Containers

Melamine contamination of food has become a major food safety issue because of incidents of infant disease caused by exposure to this chemical. This study was aimed at establishing a safety limit in Taiwan for the degree of melamine migration from food containers. Health risk assessment was performed for three exposure groups (preschool children, individuals who dine out, and elderly residents of nursing homes). Selected values of tolerable daily intake (TDI) for melamine were used to calculate the reference migration concentration limit (RMCL) or reference specific migration limit (RSML) for melamine food containers. The only existing values of these limits for international standards today are 1.2 mg/L (0.2 mg/dm²) in China and 30 mg/L (5 mg/dm²) in the European Union. The factors used in the calculations included the specific surface area of food containers, daily food consumption rate, body weight, TDI, and the percentile of the population protected at a given migration concentration limit (MCL). The results indicate that children are indeed at higher risk of melamine exposure at toxic levels than are other groups and that the 95th percentile of MCL (specific surface area = 5) for children aged 1–6 years should be the RMCL (0.07 mg/dm²) for protecting the sensitive and general population.     

ECONOMIC DETERMINANTS OF THE TIMING OF PREFERENTIAL TRADE AGREEMENT FORMATIONS AND ENLARGEMENTS

Preferential trade agreements (PTAs) have proliferated over the past 60 years. While a small number of recent studies have examined empirically the economic determinants of the likelihood of a pair of countries having a PTA, this study explains empirically the timing of all PTA formations and enlargements from 1950 through 2006 using duration analysis. Our main and novel goal is to predict (in‐ and out‐of‐sample) a substantive share of these 1,560 PTA events using a parsimonious model with mainly economic variables, taking selection dynamics into account. Our analysis reveals that we can predict correctly in‐sample the actual year of entry into force for 26% of the 1,560 bilateral PTA formations/enlargements in the period 1950–2006 among 10,518 pairings of 146 countries using only a few economic and political variables. Moreover, we can predict correctly in‐sample 57% of these PTA events within a 10‐year window leading up to the event using this model. The model also performs well out‐of‐sample for the near term (82%), but not if the out‐of‐sample period is very long. We conclude with an evaluation of the model's ability to predict the timing of the North American Free Trade Agreement, the European Union's formation and enlargements, and the model's ten most likely post‐2006 PTA events. (JEL F14, F15)     

Racial Group Comparisons of Conceptualizations of Rap Music Constructs: A Cross-racial Validity Study of the Rap Music Attitude and Perception Scale

Interpretations and perceptions of the effects and content of rap music lyrics have been given considerable attention in the literature in recent years, yet few assessment tools have been developed that can produce reliable and valid inferences about these views. One exception is the Rap-music Attitude and Perception (RAP) Scale. This study examined the cross-racial effects on attitudes toward and perceptions of rap music using a sample of 1,254 college students. A cross-sectional survey design was used to gather these data. Three specific hypotheses were tested and were supported or partially supported. Alpha reliabilities for the full scale and for each of the three sub-scales were good for black and white students separately. Criterion validity for these groups was also good. Finally, tests of factorial equivalence suggested that the factor structure of the RAP was equivalent across racial groups. The RAP is a tool with strong psychometric properties and can be used by practitioners and researchers working with black and white subgroups. Directions for future research on the utility of the RAP are forwarded.     

Beyond Contact? Policy approaches to work with families of looked after children in four European countries

In England, placement within the looked after system is not viewed as a desirable long‐term solution for most children, and policy has prioritised continued contact with parents, and swift return home, wherever possible. This review examines policy approaches to work with families of looked after children in England and in three other European countries: Denmark, France and the Netherlands, aiming to identify areas for shared learning in relation to this challenging area of policy and practice. The research highlights relationships between care populations and policy understandings of the purpose of work with families, including understandings of children's and/or parents’ rights.     

Dose‐Response Models Incorporating Aerosol Size Dependency for Francisella tularensis

The effect of bioaerosol size was incorporated into predictive dose‐response models for the effects of inhaled aerosols of Francisella tularensis (the causative agent of tularemia) on rhesus monkeys and guinea pigs with bioaerosol diameters ranging between 1.0 and 24 μm. Aerosol‐size‐dependent models were formulated as modification of the exponential and β‐Poisson dose‐response models and model parameters were estimated using maximum likelihood methods and multiple data sets of quantal dose‐response data for which aerosol sizes of inhaled doses were known. Analysis of F. tularensis dose‐response data was best fit by an exponential dose‐response model with a power function including the particle diameter size substituting for the rate parameter k scaling the applied dose. There were differences in the pathogen's aerosol‐size‐dependence equation and models that better represent the observed dose‐response results than the estimate derived from applying the model developed by the International Commission on Radiological Protection (ICRP, 1994) that relies on differential regional lung deposition for human particle exposure.