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We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate bilevel-infeasible solutions using a second-order-cone-based cut-generating procedure. We propose DC separation strategies and consider several approaches for removing redundant disjunctions and normalization. Using these DCs, we propose a branch-and-cut algorithm for the problem class we study, and a cutting-plane method for the problem variant with only binary variables. We present an extensive computational study on a diverse set of instances, including instances with binary and with integer variables, and instances with a single and with multiple linking constraints. Our computational study demonstrates that the proposed enhancements of our solution approaches are effective for improving the performance. Moreover, both of our approaches outperform a state-of-the-art generic solver for mixed-integer bilevel linear programs that is able to solve a linearized version of our binary instances. [ABSTRACT FROM AUTHOR]

Purpose: This study was intended to investigate a small-scale School-based Motivational Interviewing (SBMI) pilot with first-year college students. This approach honors student autonomy, supports self-determination and has the potential to impact educational outcomes in higher education. Motivational Interviewing (MI) is an evidence based conversational skill set, defined as "a collaborative conversational style for strengthening a person's own motivation and commitment to change" (Miller and Rollnick, 2013, p. 12). Student perceptions of satisfaction with the faculty-student mentoring intervention were sought. Relational aspects of MI (partnership, empathy and alliance) were also explored. Design/methodology/approach: A mixed-method approach was used for the SBMI study, focused on college students with recent academic setbacks (N = 19). Findings: The intervention was deployed with high levels of MI technical fidelity and relational quality. Participants reported high satisfaction with the intervention. The relational aspects and participant perceived alliance with their faculty were highly correlated across the intervention, adding to the discussion of the mechanisms of MI that contribute to its effectiveness. Research limitations/implications: This work is formative, yet at this point is not generalizable given the scope of the study. Practical implications: Findings are encouraging for further development of this innovative pedagogical approach. Possible future applications of research are provided. Social implications: Discussed herein, SBMI has the potential to meet the needs of traditionally underrepresented student groups. Originality/value: The reported study is the initial portion of a larger intervention development project. [ABSTRACT FROM AUTHOR]

MINLO (mixed-integer nonlinear optimization) formulations of the disjunction between the origin and a polytope via a binary indicator variable have broad applicability in nonlinear combinatorial optimization, for modeling a fixed cost c associated with carrying out a set of d activities and a convex variable cost function f associated with the levels of the activities. The perspective relaxation is often used to solve such models to optimality in a branch-and-bound context, especially in the context in which f is univariate (e.g., in Markowitz-style portfolio optimization). But such a relaxation typically requires conic solvers and are typically not compatible with general-purpose NLP software which can accommodate additional classes of constraints. This motivates the study of weaker relaxations to investigate when simpler relaxations may be adequate. Comparing the volume (i.e., Lebesgue measure) of the relaxations as means of comparing them, we lift some of the results related to univariate functions f to the multivariate case. Along the way, we survey, connect and extend relevant results on integration over a simplex, some of which we concretely employ, and others of which can be used for further exploration on our main subject. [ABSTRACT FROM AUTHOR]

High school students in accelerated curricula tend to report higher level of perceived stress compared to general education students, but often receive limited school support (Conger et al., 2021). This study explored student experiences of a targeted intervention using Motivational Interviewing (Motivation, Assessment, and Planning; MAP) compared to an Action Planning (AP) intervention through a randomized, within-subject design. Twenty ninth grade students enrolled in one advanced placement class who exhibited emotional and/or academic risks mid-year were assigned to initially receive either MAP or AP, and the other intervention second. Data collection occurred immediately after and approximately one month following each meeting. Wilcoxon Signed-Rank test showed statistically significant increase in student-reported importance to change (S = 35.5, N = 20, p = 0.04) after MAP compared to AP, but with questionable clinical significance of small differences. Although there is a significant statistical difference in interventionist-reported therapeutic alliance (S = 95, N = 20, p < 0.001) favoring MAP, students reported similar increase in therapeutic alliance (S = −18.5, N = 20, p = 0.03) after both conditions. Students also reported similar increase in confidence to change (S = 1, N = 20, p = 0.99) and progress toward goals (S = −18, N = 20, p = 0.04) after experiencing both interventions. Findings from this study suggest that both MAP and AP have the potential to improve students' perceived importance and confidence to change, therapeutic alliance, and goal attainment. Qualitative analyses of written and verbal data provided support for high acceptability of both MAP and AP. The current study sheds light on the impact and acceptability of two targeted interventions appropriate for high school students in advanced placement classes. [ABSTRACT FROM AUTHOR]

A fundamental NP-hard combinatorial-optimization in the area of statistical designs is the maximum-entropy sampling problem (MESP), which seeks to maximize Shannon's "differential entropy" over all subsets of a prespecified cardinality from a set of n Gaussian random variables. This problem has applications in many areas, such as the redesign of environmental-monitoring networks. Most algorithms for exact solution of MESP are branch-and-bound based, and one of the best upper bounds is based on Anstrecher's recent concave "linx relaxation" of differential entropy. A key paradigm for improving bounds is by "masking" the covariance of the random variables with a correlation matrix. The main result establishes that in the best case, the linx bound can be improved by an amount that is at least linear in n by masking. These and other recent results on the hot topic of MESP are leading to practical algorithms for exact solution of meaningful design problems in applied areas such as environmental statistics. The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-s principal submatrix of a given order n covariance matrix C. Exact algorithms are based on a branch-and-bound framework. The problem has wide applicability in spatial statistics and in particular in environmental monitoring. Probably the best upper bound for the maximum empirically is Anstreicher's scaled "linx" bound. An earlier methodology for potentially improving any upper-bounding method is by masking, that is, applying the bounding method to C ∘ M , where M is any correlation matrix. We establish that the linx bound can be improved via masking by an amount that is at least linear in n, even when optimal scaling parameters are used. We also extend an earlier result that the linx bound is convex in the logarithm of a scaling parameter, making a full characterization of its behavior and providing an efficient means of calculating its limiting behavior in all cases. Funding: J. Lee was supported by the Air Force Office of Scientific Research [Grant FA9550-19-1-0175]. M. Fampa was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 303898/2016-0 and 434683/2018-3]. [ABSTRACT FROM AUTHOR]

We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that the DDF problem is NP-hard and has no constant-factor polynomial-time approximation algorithm unless P = NP. Therefore, to solve the DDF problem effectively, we propose two convex integer-programming formulations and investigate their corresponding complementary and Lagrangian-dual problems. Leveraging the concavity of the objective functions in the two proposed convex integer-programming formulations, we design an exact algorithm, aimed at solving the DDF problem to optimality. We further derive a family of submodular valid inequalities and optimality cuts, which can significantly enhance the algorithm performance. We also develop scalable randomized-sampling and local-search algorithms with provable performance guarantees. Finally, we test our algorithms using real-world data on the new phasor-measurement-units placement problem for modern power grids, considering the existing conventional sensors. Our numerical study demonstrates the efficiency of our exact algorithm and the scalability and high-quality outputs of our approximation algorithms. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: Y. Li and W. Xie were supported in part by Division of Civil, Mechanical and Manufacturing Innovation [Grant 2046414] and Division of Computing and Communication Foundations [Grant 2246417]. J. Lee was supported in part by Air Force Office of Scientific Research [Grants FA9550-19-1-0175 and FA9550-22-1-0172]. M. Fampa was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 305444/2019-0 and 434683/2018-3]. F. Qiu and R. Yao were supported in part by the U.S. Department of Energy Advanced Grid Modeling Program under [Grant DE-OE0000875]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2022.0235. [ABSTRACT FROM AUTHOR]

The investigation of combinatorial diameters of polyhedra is a classical topic in linear programming due to its connection with the possibility of an efficient pivot rule for the simplex method. We are interested in the diameters of polyhedra formed from the so-called parallel or series connection of oriented matroids. Oriented matroids are the natural way to connect representable matroid theory with the combinatorics of linear programming, and these connections are fundamental operations for the construction of more complicated matroids from elementary matroid blocks. We prove that, for polyhedra whose combinatorial diameter satisfies the Hirsch-conjecture bound regardless of the right-hand sides in a standard-form description, the diameters of their parallel or series connections remain small in the Hirsch-conjecture bound. These results are a substantial step toward devising a diameter bound for all polyhedra defined through totally unimodular matrices based on Seymour's famous decomposition theorem. Our proof techniques and results exhibit a number of interesting features. While the parallel connection leads to a bound that adds just a constant, for the series connection one has to linearly take into account the maximal value in a specific coordinate of any vertex. Our proofs also require a careful treatment of non-revisiting edge walks in degenerate polyhedra as well as the construction of edge walks that may take a "detour" to facets that satisfy the non-revisiting conjecture when the underlying polyhedron may not. [ABSTRACT FROM AUTHOR]

In this study, water-based precursor solutions with citric acid as the chelating agent were prepared, and the effect of the pH of the precursor solutions on the morphology and microstructure of the Li1.3Al0.3Ti1.7(PO4)3 (LATP) coating layer was investigated. A clear precursor solution was prepared and its colour changed depending on the pH of the solution, suggesting that citric acid effectively formed chelate complexes composed of Li, Al, Ti and P ions. The scanning electron microscopy and energy-dispersive X-ray spectroscopy mapping analyses showed that a low pH resulted in a homogeneous LATP coating layer with a fine particle size and less dense morphology. When the pH value was increased, dense and enhanced surface coverage was obtained, whereas an inhomogeneous atomic distribution was confirmed in the LATP coating. The LATP-coated LiCoO2 (LCO) cathode exhibited enhanced specific capacity retention compared to that of the pristine LCO cathode. [ABSTRACT FROM AUTHOR]

We study integer-valued matrices with bounded determinants. Such matrices appear in the theory of integer programs (IPs) with bounded determinants. For example, an IP can be solved in strongly polynomial time if the constraint matrix is bimodular: that is, the determinants are bounded in absolute value by two. Determinants are also used to bound the ℓ 1 distance between IP solutions and solutions of its linear relaxation. One of the first to quantify the complexity of IPs with bounded determinants was Heller, who identified the maximum number of differing columns in a totally unimodular matrix. Each extension of Heller's bound to general determinants has been superpolynomial in the determinants or the number of equations. We provide the first column bound that is polynomial in both values. For integer programs with box constraints, our result gives the first ℓ 1 distance bound that is polynomial in the determinants and the number of equations. Our result can also be used to derive a bound on the height of Graver basis elements that is polynomial in the determinants and the number of equations. Furthermore, we show a tight bound on the number of differing columns in a bimodular matrix; this is the first tight bound since Heller. Our analysis reveals combinatorial properties of bimodular IPs that may be of independent interest. Funding: J. Lee was supported in part by the Office of Naval Research [Grant N00014-21-1-2135] and the Air Force Office of Scientific Research [Grant FA9550-19-1-0175]. J. Paat was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant [Grant RGPIN-2021-02475]. [ABSTRACT FROM AUTHOR]

As companies have come to terms with the fact that their brand names and imagery have connections to America’s racist history, they have publicly announced their commitments to shed their ignominious trademarks. But, unlike a physical monument, a trademark cannot be destroyed or removed. Under the prevailing doctrine, abandoned trademarks return to the public domain, free for another company to claim and use—even if it may capitalize on the mark’s recognition as a symbol of oppression. This puts companies that wish to sever their ties with their racist trademarks in an intractable situation: either they make good on their commitments and risk losing their ability to prevent others from adopting the marks, or they try to use the marks or their vestiges in limited ways that may avoid abandonment. This dilemma is heightened because the abandonment doctrine has been applied inconsistently by courts, precisely because some judges wish to avoid the dramatic consequences that result from deeming a trademark abandoned. This Article makes three contributions to the discourses on trademark law and race and the law, revealing how the law has erected barriers to companies that wish to engage in efforts to ameliorate the harm caused by their use of racist trademarks. First, this Article explains how trademark law has contributed to the proliferation of harmful racial and ethnic stereotypes and identifies the limits on the tools that can be employed to curb the use of such symbols. Second, this Article comprehensively describes the trademark abandonment doctrine, bringing to light the distinctions that courts have tacitly drawn between express and implied abandonment, the flaws in the current doctrine, and the perverse incentives it creates for companies that wish to shed their racist trademarks. Third, this Article illustrates how trademark law and systems can be reformed to promote antiracist efforts while simultaneously rectifying problems that affect a broader group of trademark holders. [ABSTRACT FROM AUTHOR]

Based on a factorization of an input covariance matrix, we define a mild generalization of an upper bound of Nikolov and of Li and Xie for the NP-hard constrained maximum-entropy sampling problem (CMESP). We demonstrate that this factorization bound is invariant under scaling and independent of the particular factorization chosen. We give a variable-fixing methodology that could be used in a branch-and-bound scheme based on the factorization bound for exact solution of CMESP, and we demonstrate that its ability to fix is independent of the factorization chosen. We report on successful experiments with a commercial nonlinear programming solver. We further demonstrate that the known "mixing" technique can be successfully used to combine the factorization bound with the factorization bound of the complementary CMESP and with the "linx bound" of Anstreicher. History: Andrea Lodi, area editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 305444/2019-0 and 434683/2018-3] and the Air Force Office of Scientific Research [Grant A9550-19-1-0175]. [ABSTRACT FROM AUTHOR]

We study mixed-integer nonlinear optimization (MINLO) formulations of the disjunction x ∈ { 0 } ∪ [ ℓ , u ] , where z is a binary indicator for x ∈ [ ℓ , u ] ( 0 ≤ ℓ < u ), and y "captures" f(x), which is assumed to be convex and positive on its domain [ ℓ , u ] , but otherwise y = 0 when x = 0 . This model is very useful in nonlinear combinatorial optimization, where there is a fixed cost c for operating an activity at level x in the operating range [ ℓ , u ] , and then, there is a further (convex) variable cost f(x). So the overall cost is c z + f (x) . In applied situations, there can be N 4-tuples (f , ℓ , u , c) , and associated (x, y, z), and so, the combinatorial nature of the problem is that for any of the 2 N choices of the binary z-variables, the non-convexity associated with each of the (f , ℓ , u) goes away. We study relaxations related to the perspective transformation of a natural piecewise-linear under-estimator of f, obtained by choosing linearization points for f. Using 3-d volume (in (x, y, z)) as a measure of the tightness of a convex relaxation, we investigate relaxation quality as a function of f, ℓ , u, and the linearization points chosen. We make a detailed investigation for convex power functions f (x) : = x p , p > 1 . [ABSTRACT FROM AUTHOR]

We study MINLO (mixed-integer nonlinear optimization) formulations of the disjunction x ∈ { 0 } ∪ [ l , u ] , where z is a binary indicator of x ∈ [ l , u ] ( u > ℓ > 0 ), and y "captures" f(x), which is assumed to be convex on its domain [l, u], but otherwise y = 0 when x = 0 . This model is useful when activities have operating ranges, we pay a fixed cost for carrying out each activity, and costs on the levels of activities are convex. Using volume as a measure to compare convex bodies, we investigate a variety of continuous relaxations of this model, one of which is the convex-hull, achieved via the "perspective reformulation" inequality y ≥ z f (x / z) . We compare this to various weaker relaxations, studying when they may be considered as viable alternatives. In the important special case when f (x) : = x p , for p > 1 , relaxations utilizing the inequality y z q ≥ x p , for q ∈ [ 0 , p - 1 ] , are higher-dimensional power-cone representable, and hence tractable in theory. One well-known concrete application (with f (x) : = x 2 ) is mean-variance optimization (in the style of Markowitz), and we carry out some experiments to illustrate our theory on this application. [ABSTRACT FROM AUTHOR]

Disruptive behavior disorders in childhood are increasingly pervasive and associated with numerous, negative long-term outcomes. The current study examined whether adding a brief, home-visitation intervention to an existing, multi-component (child and teacher) intervention, would improve social-emotional and behavioral outcomes for young children with challenging behavior in home and school settings who required intensive support. A total of 379 teacher-parent-student triads were screened for elevated levels of behavioral risk in school and home settings and then randomly assigned to school only intervention (i.e., teacher and student components), home only intervention (i.e., parent), both combined, or business-as-usual control conditions. We examined baseline and posttest outcomes across prosocial behavior, problem behavior, and academic domains. The results demonstrated substantial support for the teacher and child-focused condition and combined conditions, and modest support for the parent-focused condition. The study advances the literature by increasing the knowledge base related to these interventions implemented alone and in combination. [ABSTRACT FROM AUTHOR]

The well-known M-P (Moore-Penrose) pseudoinverse is used in several linear-algebra applications; for example, to compute least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given matrix is sparse, its M-P pseudoinverse can be completely dense, potentially leading to high computational burden and numerical difficulties, especially when we are dealing with high-dimensional matrices. The M-P pseudoinverse is uniquely characterized by four properties, but not all of them need to be satisfied for some applications. In this context, Fampa and Lee (Oper. Res. Lett., 46:605–610, 2018) and Xu et al. (SIAM J. Optim., to appear) propose local-search procedures to construct sparse block-structured generalized inverses that satisfy only some of the M-P properties. (Vector) 1-norm minimization is used to induce sparsity and to keep the magnitude of the entries under control, and theoretical results limit the distance between the 1-norm of the solution of the local searches and the minimum 1-norm of generalized inverses with corresponding properties. We have implemented several local-search procedures based on results presented in these two papers and make here an experimental analysis of them, considering their application to randomly generated matrices of varied dimensions, ranks, and densities. Further, we carried out a case study on a real-world data set. [ABSTRACT FROM AUTHOR]

The paper describes the applicability and acceptability of a selective intervention—Motivation, Assessment, and Planning (MAP)—for high school students that was developed based on the principles of motivational interviewing (MI) and tailored to the unique needs and strengths of students taking accelerated coursework, specifically Advanced Placement (AP) and International Baccalaureate (IB) classes. In addition to detailing the intervention in terms of MI spirit, processes, and relational and technical skills, we report applicability and acceptability data from a second iteration of MAP implementation in eight AP/IB programs in a Southeastern state during spring 2018. We analyzed quantitative and qualitative acceptability data from 121 high school freshmen (97 from AP and 24 from IB courses), as well as the seven MAP coaches who were trained using the Motivational Interview Training and Assessment System (Frey et al. 2017). To gain perspectives from the intended end users of the refined MAP, 12 school counselors and school psychologists who were not trained in MAP evaluated the intervention and provided qualitative and quantitative data on applicability and acceptability. All three stakeholder groups (students, coaches, and school mental health staff) rated and described the intervention as highly acceptable and appropriate for addressing the social-emotional needs of adolescents in AP/IB classes. [ABSTRACT FROM AUTHOR]

Educational researchers and school-based practitioners are increasingly infusing motivational interviewing (MI) into new and existing intervention protocols to provide support to students, parents, teachers, and school administrators. To date, however, the majority of the research in this area has focused on feasibility of implementation rather than fidelity of implementation. In this manuscript, we will present MI fidelity data from 245 audio-recorded conversations with 113 unique caregivers and 20 coaches, who implemented a school-based, positive parenting intervention. The aggregate fidelity scores across coaches, parents, and sessions provide evidence the training and support procedures were effective in assisting school-based personnel to implement MI with reasonable levels of fidelity in practice settings. Further, results suggest that MI fidelity varied between sessions and coaches and that within-coach variation (e.g., session-level variation in the quality of MI delivered) greatly exceeded between-coach variation. Implications for practice and future research are discussed. [ABSTRACT FROM AUTHOR]

Reviews of the motivational interviewing (MI) training literature demonstrate MI is a nuanced skill set that takes carefully planned didactic training, application of skills in context-specific practice settings, and ongoing support to promote reflective practice and sustained proficiency. Despite the robust knowledge base related to training and how MI works to achieve favorable outcomes, these two literature bases are not well integrated. In an effort to inform and guide future research, we propose the mechanisms of motivational interviewing (MMI) conceptual framework, which expands upon previous work. Specifically, the framework adds training as an ongoing process consistent with Bennett-Levy's (Behav Cogn Psychother 34:57–78, 2006) model of skill development and acquisition to the existing two-path framework that helps us to understand how MI works to achieve its desired effects (Magill et al., J Consult Clin Psychol 82:973–983, 2014). Herein, we describe measures used to evaluate the mechanisms within the four MMI framework links: initial training to competency, competency to proficiency, proficiency to talk about change, and talk about change to behavior change. Next, we synthesize the literature associated with each of the mechanisms of the MMI. We conclude by discussing implications for practice and research. This framework offers a more complete path structure to understand the mechanisms of change associated with MI that could improve our understanding of inconsistent effect sizes observed across prior trials evaluating MI effectiveness. [ABSTRACT FROM AUTHOR]

The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-s principal submatrix of an order-n covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on convex optimization. We present a methodology for "mixing" these bounds to achieve better bounds. [ABSTRACT FROM AUTHOR]

Fundamental in matrix algebra and its applications, a generalized inverse of a real matrix A is a matrix H that satisfies the Moore--Penrose (M--P) property AH A = A. If H also satisfies the additional useful M--P property, H AH = H, it is called a reflexive generalized inverse. Reflexivity is equivalent to minimum rank, so we are particularly interested in reflexive generalized inverses. We consider aspects of symmetry related to the calculation of a sparse reflexive generalized inverse of A. As is common, and following Fampa and Lee [Oper. Res. Lett., 46 (2018), pp. 605-610] for calculating sparse generalized inverses, we use (vector) 1-norm minimization for inducing sparsity and for keeping the magnitude of entries under control. When A is symmetric, we may naturally desire a symmetric H, while generally such a restriction on H may not lead to a 1-norm minimizing reflexive generalized inverse. We investigate a block construction method to produce a symmetric reflexive generalized inverse that is structured and has guaranteed sparsity. We provide a theoretically efficient and practical local-search algorithm to block construct an approximate 1-norm minimizing symmetric reflexive generalized inverse. Another aspect of symmetry that we consider relates to another M--P property: H is ah-symmetric if AH is symmetric. The ah-symmetry property is the key one for solving least-squares problems using H. Here we do not assume that A is symmetric, and we do not impose symmetry on H. We investigate a column block construction method to produce an ah-symmetric reflexive generalized inverse that is structured and has guaranteed sparsity. We provide a theoretically efficient and practical local-search algorithm to column block construct an approximate 1-norm minimizing ah-symmetric reflexive generalized inverse. [ABSTRACT FROM AUTHOR]

We efficiently treat bilinear forms in the context of global optimization, by applying McCormick convexification and by extending an approach of Saxena et al. (Math Prog Ser B 124(1–2):383–411, 2010) for symmetric quadratic forms to bilinear forms. A key application of our work is in treating "structural convexity" in a symmetric quadratic form. [ABSTRACT FROM AUTHOR]

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. We also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size. Summary of Contribution: Chance-constrained programs are in general NP-hard but widely used in practice for lowering the risk of undesirable outcomes during decision making under uncertainty. Assuming finite scenarios of uncertain parameter, chance-constrained programs can be reformulated as mixed-integer linear programs with binary variables representing whether or not the constraints are satisfied in corresponding scenarios. A useful quantile bound for solving chance-constrained programs can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. In this paper, we develop algorithms for optimally and heuristically grouping scenarios to tighten the quantile bounds. We aim to improve both the computation and solution quality of a variety of chance-constrained programs formulated for different Operations Research problems. [ABSTRACT FROM AUTHOR]

Disruptive behavior problems frequently emerge in the preschool years and are associated with numerous, long-term negative outcomes, including comorbid disorders. First Step is a psychosocial early intervention with substantial empirical evidence supporting its efficacy among young children. The present study reports on a validation study of the revised and updated First Step early intervention, called First Step Next, conducted within four preschool settings. One hundred sixty students at risk for school failure, and their teachers, were randomized to intervention and control conditions. Results indicated coach and teacher adherence to implementing the core components of the program was excellent. Teachers and parents had high satisfaction ratings. For the three First Step Next prosocial domains, Hedges' g effect sizes (ESs) ranged from 0.34 to 0.91. For the problem behavior domain, children who received the First Step Next intervention had significant reductions in teacher- and parent-reported problem behavior as compared to children randomized to the control condition. For the problem behavior domain, Hedges' g ESs ranged from 0.33 to 0.63, again favoring the intervention condition. All of the domains were statistically significant. This study builds on the evidence base supporting the First Step intervention in preschool settings. [ABSTRACT FROM AUTHOR]

This article explores how aspects of posthuman theory, and in particular diffraction as theorised by Haraway and then Barad, can be used by theatre makers to develop the practice of being and making in company at this current moment in time. I begin with an analysis of the ways stories (including stories within plays) are shared in the rehearsal room. When framed as a diffractive practice that allows for the 'iterative (re)configuring', difference can be foregrounded both as a radical dramaturgy, and a process tool for collaborating, creating and developing performance material—new ways of being together. Donna Haraway, in Staying with the Trouble, references an essay by Ursula K. Le Guin, who calls for the need for new kinds of stories, that gather many strands together by a process of exploring the potential connections between all things: explorations of multiples and difference rather than egos and individualism. Here, I consider diffraction in the context of the work of Flute Theatre where Kelly Hunter MBE has developed a dramaturgical process for using Shakespeare's later plays when working with children with severe autism and their families. This diffractive dramaturgy explores the way we audience / perform work for each other. Subjectivity and objectivity for example, are experienced differently when explored from the point of view that all matter is entangled. There is the potential for a dramaturgy of agential cuts that manifest as a kaleidoscope of intra-actions and material manifestations: a myriad of entwined textures diffracted through and with the participants own experience and context. This is a new experimental, experiential landscape, where we feel for and towards (in a tentacular way) a collaborative making process that tilts the optic away from traditional expectations. It is a multi-perspective way of working; a posthuman process that finds form in difference. [ABSTRACT FROM AUTHOR]

We introduce the generalized constrained maximum-entropy sampling problem (GCMESP) as a common generalization of the ordinary constrained maximum-entropy sampling problem (CMESP) and the constrained D-optimality problem (CDOPTP). Exact algorithms for both CMESP and CDOPTP are based on branch-and-bound methods. We extend a spectral upper-bounding method for the CMESP to the GCMESP. [ABSTRACT FROM AUTHOR]

We supply proofs for a few key results concerning smoothing square roots and model strengthening for a mixed-integer nonlinear-optimization formulation of the the Euclidean Steiner tree problem. [ABSTRACT FROM AUTHOR]

We demonstrate that an earlier semidefinite-programming relaxation for the kissing-number problem cannot provide good upper bounds. Furthermore, we show the existence of an optimal solution for this relaxation that cannot be used as a basis for establishing a good lower bound. [ABSTRACT FROM AUTHOR]

High school students in accelerated classes face heightened school-related stressors but have access to few specialized supports. This article describes the development and initial application of the Motivation, Assessment, and Planning (MAP) intervention, developed to meet the needs of freshmen in Advanced Placement (AP) and International Baccalaureate (IB) curricula. MAP is grounded in motivational interviewing and designed to evoke behavior change following one to two individual meetings with a coach. This study used a multimethod, multisource approach to evaluate the applicability and acceptability of MAP as a Tier 2 support for 9th-grade students completing AP/IB coursework. Quantitative and qualitative acceptability data from 49 AP/IB students, 7 coaches, and 3 potential end-users of MAP were examined. Results indicate MAP was perceived as an acceptable intervention for addressing the social–emotional needs of high-achieving students taking AP/IB classes. Findings and directions for further research of MAP are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we report the fabrication of photoenhanced polarization mode separated fiber Bragg gratings (FBGs) in polarization maintaining (PM) fibers using IR femtosecond laser illumination. The separation of the Bragg resonant wavelengths between the two polarization modes is as large as 1.78 nm due to the photoenhanced birefringence effect generated by the strong ultrashort laser pulses. This large polarization mode separation solves one of the major problems of the conventional PM Bragg gratings (i.e., the narrow spacing or even the partial spectral overlap between spectra of the two polarization eigenmodes) and substantially enhances the multiparameter sensing capability of FBGs by offering a wider sensing range and higher discrimination. Furthermore, the high thermal stability of FBGs (up to 1000 °C for silica fibers) inscribed by IR femtosecond lasers provides for multiparameter sensing in harsh, high temperature environments. [ABSTRACT FROM AUTHOR]

We present several mathematical-optimization formulations for a problem that commonly occurs in geometry processing and specifically in the design of so-called smooth direction fields on surfaces. This problem has direct applications in 3D shape parameterization, texture mapping, and shape design via rough concept sketches, among many others. A key challenge in this setting is to design a set of unit-norm directions, on a given surface, that satisfy some prescribed constraints and vary smoothly. This naturally leads to mixed-integer optimization formulations, because the smoothness needs to be formulated with respect to angle-valued variables, which to compare one needs to fix the discrete jump between nearby points. Previous works have primarily attacked this problem via a greedy ad-hoc strategy with a specialized solver. We demonstrate how the problem can be cast in a standard mathematical-optimization form, and we suggest several relaxations that are especially adapted to modern mathematical-optimization solvers. [ABSTRACT FROM AUTHOR]

An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G=(V,E) and (ii) edge-weights c:V2→R+ on a complete undirected graph. The objective is to find a subset S⊆V of vertices satisfying some graph-based constraint in G that maximizes the weight ∑u∈S,v∉Scuv of edges in the cut (S,V\S). The types of graph constraints we can handle include independent set, vertex cover, dominating set and connectivity. Our main results are for the case when G is a graph with bounded treewidth, where we obtain a 12-approximation algorithm. Our algorithm uses an LP relaxation based on the Sherali-Adams hierarchy. It can handle any graph constraint for which there is a dynamic program of a specific form. Using known decomposition results, these imply essentially the same approximation ratio for GCMC under constraints such as independent set, dominating set and connectivity on a planar graph G. [ABSTRACT FROM AUTHOR]

In Speakman and Lee (Math Oper Res 42(4):1230-1253, 2017), we analytically developed the idea of using volume as a measure for comparing relaxations in the context of spatial branch-and-bound. Specifically, for trilinear monomials, we analytically compared the three possible “double-McCormick relaxations” with the tight convex-hull relaxation. Here, again using volume as a measure, for the convex-hull relaxation of trilinear monomials, we establish simple rules for determining the optimal branching variable and optimal branching point. Additionally, we compare our results with current software practice. [ABSTRACT FROM AUTHOR]

We report a logical error in our article that turns out to be fatal for the main result. The error lies in Lemma 3 for the case of a 3-sum, that is [ABSTRACT FROM AUTHOR]

This is mostly a survey on some mathematical results concerning volumes of polytopes of interest in non-convex optimization. Our motivation is in geometrically comparing relaxations in the context of mixed-integer linear and nonlinear optimization, with the goal of gaining algorithmic and modeling insights. We consider relaxations of: fixed-charge formulations, vertex packing polytopes, boolean-quadric polytopes, and relaxations of graphs of monomials on box domains. Besides surveying the area, we do give a few new results, and we provide many directions for further work. [ABSTRACT FROM AUTHOR]

ABSTRACT Shin, S.; Bae, I., and Lee, J.-I., 2018. Three-dimensional variation of wave transmission around the artificial reefs: experimental and numerical studies. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1011–1015. Coconut Creek (Florida), ISSN 0749-0208. In this study, three-dimensional experiments were conducted to investigate the spatial variation of wave transmission characteristics under the different types and configurations of the artificial reefs. Partially permeable armored by tetrapods and impermeable structures were deployed with the different gaps. Incident wave conditions included both breaking and non-breaking conditions over the structures. Transmitted wave heights in cross-shore and alongshore directions were compared with the empirical formula. The results showed that the wave transmission phenomena were dependent of the structural type, layout, and gap distance. In the case of single structure, as the length of the structure increased, the transmission coefficient decreased. In the case of multiple structures with a gap, the length of the structures and the gap were inversely proportional to the transmission coefficient. [ABSTRACT FROM AUTHOR]

This article describes an ongoing effort to train MSW students to practice motivational interviewing (MI) competently in the context of a university-community field education partnership model. Students in field placement are trained using the Motivational Interviewing Training and Assessment System and participate in a field seminar to hone MI proficiency. Mixed-methods preliminary evaluation data were collected to understand the impact of the training. Results suggest the Motivational Interviewing Training and Assessment System is promising for preparing social work students to use this evidence-supported practice competently. Implications from this practical example are discussed in relation to integrating an evidence-based practice such as MI into the social work curriculum. [ABSTRACT FROM AUTHOR]

Shin, S.; Bae, I., and Lee, J.-I., 2018. Three-dimensional variation of wave transmission around the artificial reefs: experimental and numerical studies. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1011–1015. Coconut Creek (Florida), ISSN 0749-0208. In this study, three-dimensional experiments were conducted to investigate the spatial variation of wave transmission characteristics under the different types and configurations of the artificial reefs. Partially permeable armored by tetrapods and impermeable structures were deployed with the different gaps. Incident wave conditions included both breaking and non-breaking conditions over the structures. Transmitted wave heights in cross-shore and alongshore directions were compared with the empirical formula. The results showed that the wave transmission phenomena were dependent of the structural type, layout, and gap distance. In the case of single structure, as the length of the structure increased, the transmission coefficient decreased. In the case of multiple structures with a gap, the length of the structures and the gap were inversely proportional to the transmission coefficient. [ABSTRACT FROM AUTHOR]

This article describes an ongoing effort to train MSW students to practice motivational interviewing (MI) competently in the context of a university-community field education partnership model. Students in field placement are trained using the Motivational Interviewing Training and Assessment System and participate in a field seminar to hone MI proficiency. Mixed-methods preliminary evaluation data were collected to understand the impact of the training. Results suggest the Motivational Interviewing Training and Assessment System is promising for preparing social work students to use this evidence-supported practice competently. Implications from this practical example are discussed in relation to integrating an evidence-based practice such as MI into the social work curriculum. [ABSTRACT FROM AUTHOR]

When using the standard McCormick inequalities twice to convexify trilinear monomials, as is often the practice in modeling and software, there is a choice of which variables to group first. For the important case in which the domain is a nonnegative box, we calculate the volume of the resulting relaxation, as a function of the bounds defining the box. In this manner, we precisely quantify the strength of the different possible relaxations defined by all three groupings, in addition to the trilinear hull itself. As a by-product, we characterize the best double-McCormick relaxation. We wish to emphasize that, in the context of spatial branch and bound for factorable formulations, our results do not only apply to variables in the input formulation. Our results apply to monomials that involve auxiliary variables as well. So, our results apply to the product of any three (possibly complicated) expressions in a formulation. [ABSTRACT FROM AUTHOR]

In the context of global optimization and mixed-integer non-linear programming, generalizing a technique of D'Ambrosio, Fampa, Lee and Vigerske for handling the square-root function, we develop a virtuous smoothing method, using cubics, aimed at functions having some limited non-smoothness. Our results pertain to root functions ( $$w^p$$ with $$0