In Search of a Match: A Guide for Helping Students Make Informed College Choices

This guide is designed for counselors, teachers, and advisers who work with high school students from low-income families and students who are the first in their families to pursue a college education. It offers strategies for helping these students identify, consider, and enroll in "match" colleges -- that is, selective colleges that are a good fit for students based on their academic profiles, financial considerations, and personal needs. Many of the suggestions in this guide are based on insights and lessons learned from the College Match Program, a pilot program that MDRC codeveloped with several partners and implemented in Chicago and New York City to address the problem of "undermatching," or what happens when capable high school students enroll in colleges for which they are academically overqualified or do not apply to college at all. The key lessons of the College Match Program, which are reflected in this guide, are that students are willing to apply to selective colleges when:* They learn about the range of options available to them.* They engage in the planning process early enough to meet college and financial aid deadlines.* They receive guidance, support, and encouragement at all stages.Informed by those key lessons, the guide tracks the many steps in the college search, application, and selection process, suggesting ways to incorporate a match focus at each stage: creating a match culture, identifying match colleges, applying to match colleges, assessing the costs of various college options, selecting a college, and enrolling in college. Because many students question their ability to succeed academically or fit in socially at a selective college, and because they may hesitate to enroll even when they receive good advice and encouragement, the guide offers tips and strategies to help students build the confidence they need to pursue the best college education available to them. Each section also suggests tools and resources in the form of websites and printed materials that counselors, advisers, and students can use, as well as case studies to illustrate the experiences of College Match participants throughout the process

Community structure in industrial SAT instances

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. It is believed that most of these successful techniques exploit the underlying structure of industrial instances. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. Representing SAT instances as graphs, we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver, and observe that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. Motivated by this observation, we finally present an application that exploits the community structure to detect relevant learned clauses, and we show that detecting these clauses results in an improvement on the performance of the SAT solver. Empirically, we observe that this improves the performance of several SAT solvers on industrial SAT formulas, especially on satisfiable instances.Peer ReviewedPostprint (published version

The Fractal Dimension of SAT Formulas

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental testing process. Recently, there have been some attempts to analyze the structure of these formulas in terms of complex networks, with the long-term aim of explaining the success of these SAT solving techniques, and possibly improving them. We study the fractal dimension of SAT formulas, and show that most industrial families of formulas are self-similar, with a small fractal dimension. We also show that this dimension is not affected by the addition of learnt clauses. We explore how the dimension of a formula, together with other graph properties can be used to characterize SAT instances. Finally, we give empirical evidence that these graph properties can be used in state-of-the-art portfolios.Comment: 20 pages, 11 Postscript figure

Community Structure in Industrial SAT Instances

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental process. It is believed that these techniques exploit the underlying structure of industrial instances. However, there are few works trying to exactly characterize the main features of this structure. The research community on complex networks has developed techniques of analysis and algorithms to study real-world graphs that can be used by the SAT community. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, inspired by the results on complex networks, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. In our analysis, we represent SAT instances as graphs, and we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erd\"os-R\'enyi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver. In particular, we use the community structure to detect that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. This is, learned clauses tend to contain variables of distinct communities