Generating a smallest binary tree by proper selection of the longest edges to bisect in a unit simplex refinement

In several areas like global optimization using branch-and-bound methods for mixture design, the unit n-simplex is refined by longest edge bisection (LEB). This process provides a binary search tree. For \(n>2\), simplices appearing during the refinement process can have more than one longest edge (LE). The size of the resulting binary tree depends on the specific sequence of bisected longest edges. The questions are how to calculate the size of one of the smallest binary trees generated by LEB and how to find the corresponding sequence of LEs to bisect, which can be represented by a set of LE indices. Algorithms answering these questions are presented here. We focus on sets of LE indices that are repeated at a level of the binary tree. A set of LEs was presented in Aparicio et al. (Informatica 26(1):17–32, 2015), for \(n=3\). An additional question is whether this set is the best one under the so-called \(m_k\)-valid condition.     

Maximum cardinality neighbourly sets in quadrilateral free graphs

Neighbourly set of a graph is a subset of edges which either share an end point or are joined by an edge of that graph. The maximum cardinality neighbourly set problem is known to be NP-complete for general graphs. Mahdian (Discret Appl Math 118:239–248, 2002) proved that it is in polynomial time for quadrilateral-free graphs and proposed an \(O(n^{11})\) algorithm for the same, here n is the number of vertices in the graph, (along with a note that by a straightforward but lengthy argument it can be proved to be solvable in \(O(n^5)\) running time). In this paper we propose an \(O(n^2)\) time algorithm for finding a maximum cardinality neighbourly set in a quadrilateral-free graph.     

Fast parallel $$\alpha $$-stable distribution function evaluation and parameter estimation using OpenCL in GPGPUs

\(\alpha \)-Stable distributions are a family of probability distributions found to be suitable to model many complex processes and phenomena in several research fields, such as medicine, physics, finance and networking, among others. However, the lack of closed expressions makes their evaluation analytically intractable, and alternative approaches are computationally expensive. Existing numerical programs are not fast enough for certain applications and do not make use of the parallel power of general purpose graphic processing units. In this paper, we develop novel parallel algorithms for the probability density function and cumulative distribution function—including a parallel Gauss–Kronrod quadrature—, quantile function, random number generator and maximum likelihood estimation of \(\alpha \)-stable distributions using OpenCL, achieving significant speedups and precision in all cases. Thanks to the use of OpenCL, we also evaluate the results of our library with different GPU architectures.     

A Bayesian sequential design with binary outcome

Several researchers have proposed solutions to control type I error rate in sequential designs. The use of Bayesian sequential design becomes more common; however, these designs are subject to inflation of the type I error rate. We propose a Bayesian sequential design for binary outcome using an alpha‐spending function to control the overall type I error rate. Algorithms are presented for calculating critical values and power for the proposed designs. We also propose a new stopping rule for futility. Sensitivity analysis is implemented for assessing the effects of varying the parameters of the prior distribution and maximum total sample size on critical values. Alpha‐spending functions are compared using power and actual sample size through simulations. Further simulations show that, when total sample size is fixed, the proposed design has greater power than the traditional Bayesian sequential design, which sets equal stopping bounds at all interim analyses. We also find that the proposed design with the new stopping for futility rule results in greater power and can stop earlier with a smaller actual sample size, compared with the traditional stopping rule for futility when all other conditions are held constant. Finally, we apply the proposed method to a real data set and compare the results with traditional designs.     

Colorful Disclosures: Identifying Identity-Based Differences and Enhancing Critical Consciousness in Supervision

ABSTRACT

Managing microaggressions and marginalizing experiences while negotiating the ongoing oppression that occurs in micro, mezzo, and macro settings can be particularly challenging for clinicians of color. Thus, supervision with clinicians of color must include affirmation, empowerment, and exploration of the intracultural/intercultural dynamics inherent in the treatment-providing process and clinical supervision. Through case studies, autoethnographic studies of our supervision experiences, and interviews with supervisors and supervisees, we reflect on how axes of identity, including race, power, and privilege, inform practitioners’ clinical lenses and affect their vulnerability in treatment and the clinical supervision dyad. Special attention is placed on the clinical supervisor–clinician–client triad (the triple process) and the interpersonal dynamics of cultural sensitivity, cultural humility, and authentic responsiveness that supervisors aim to model and cultivate in the supervisory relationship. In addition to sustaining clinical growth for clinicians of color, adding this level of complexity to supervision supports equity in direct clinical practice, enhancing efficacy outcomes for clients and communities. Recommendations and pedagogical strategies are offered to support supervisors in initiating difficult dialogues and shifting the paradigm to promote this transformational perspective.     

Illuminating the Phenomenological Challenges of Cross-Cultural Supervision

ABSTRACT

The authors discuss transference enactments that occur during cross-cultural supervision. Previous research has shown that few mental health professionals willingly talk about race during supervision and that White supervisees experience significant difficulty when directly engaged in discussions about race. They introduce a new phenomenon, “stereotypical” transference enactments, as a means for understanding the countertransference Black female clinical supervisors experience during clinical supervision of White supervisees. The findings indicated that effective cross-cultural supervision should address the intersectionality of race and gender to enhance the development of multicultural clinical skills. The clinical and educational challenges are discussed by using two case vignettes.     

Increasing Competency,Self-Confidence,and Connectedness Among Foster Care Alumni Entering a 4-Year University: Findings from an Early-Start Program

Research shows that few foster care alumni enroll and complete post-secondary education. For those who do enroll, many experience challenges associated with academic and social adjustment and are at risk of dropping out. Many college-based programs are being developed and are available to foster care alumni to support them during their post-secondary education. This study used pre-tests, post-tests, and journal entries of seventeen participants to evaluate a strengths-based, resilience-oriented early-start program for newly enrolled students at a large public university that provides knowledge about the institution, resources (e.g., tutoring), and social support necessary for foster care alumni to make a smooth transition into college life and to increase short and long-term student success. Quantitative and qualitative findings indicate that students who participated in the early-start program showed increased confidence and competency in academic and social adjustment. Findings also showed personal growth (e.g., building resiliency) and an increased connectedness among students who participated in the program. Study findings can inform the development of new on-campus support programs and help enhance existing programming. Future research should address short and long-term outcomes and experiences of students who are former foster youth who have participated in on-campus support programs.     

Reports of Conferences,Institutes, and Seminars

This installment of "Serials Spoken Here" covers events that transpired between late September and late October 2008. Reported herein are two Webinars, one on ONIX for Serials, the other on SUSHI, and two conferences: the eighty-fourth annual Meeting of the Potomac Technical Processing Librarians and the New England Library Association's Annual Conference.     

Integrated methodology for multiple systems estimation and record linkage using a missing data formulation

There are now three essentially separate literatures on the topics of multiple systems estimation, record linkage, and missing data. But in practice the three are intimately intertwined. For example, record linkage involving multiple data sources for human populations is often carried out with the expressed goal of developing a merged database for multiple system estimation (MSE). Similarly, one way to view both the record linkage and MSE problems is as ones involving the estimation of missing data. This presentation highlights the technical nature of these interrelationships and provides a preliminary effort at their integration.