Assessing the Early Impact of School of One: Evidence from Three School-Wide Pilots

For more than 150 years, education has been organized around classrooms in which one teacher attempts to meet the needs of a large group of students who have a wide range of prior experiences, knowledge, and ways of learning. This structure makes it exceedingly difficult to ensure that all students meet the same standards of performance. School of One (SO1) is an innovative, technology-enhanced math program that seeks to "meet students where they are," by creating individual learning plans, offering multiple teaching strategies, and using daily assessments to monitor progress and adapt lessons as needed. This report evaluates SO1's impact on students' state test scores during the first year of school-wide implementation in three New York City middle schools. It also presents exploratory analysis examining whether exposure to more SO1 material, or mastery of SO1 skills, is associated with improved math performance. Given the early stage of the program's development, the authors caution that the evaluation should not be interpreted as a definitive assessment of SO1's effectiveness. Rather, the findings provide a preliminary assessment of SO1's initial impact on students' math achievement and offer insights that may contribute to the program's development and inform future research

High Density Preheating Effects on Q-ball Decays and MSSM Inflation

Non-perturbative preheating decay of post-inflationary condensates often results in a high density, low momenta, non-thermal gas. In the case where the non-perturbative classical evolution also leads to Q-balls, this effect shields them from instant dissociation, and may radically change the thermal history of the universe. For example, in a large class of inflationary scenarios, motivated by the MSSM and its embedding in string theory, the reheat temperature changes by a multiplicative factor of $10^{12}$.Comment: 4 page

Constraining Modular Inflation in the MSSM from Giant Q-Ball Formation

We discuss constraints on which flat directions can have large vacuum expectation values (VEVs) after inflation. We show that only flat directions which are not charged under B-L and develop positive pressure due to renormalization group effects can have large VEVs of order \Mp. For example, within the MSSM only the $H_uH_d$ flat direction is found to be viable. This strongly constrains the embedding of a broad class of inflationary models in the MSSM or some other supersymmetric extension of the SM. For flat directions with negative pressure, the condensate fragments into very large Q-balls which we call Q-giants. We discuss the formation, evolution and reheating of these Q-giants and show that they decay too late. The analysis requires taking into account new phases of the flat directions, which have been overlooked in the formation and dynamics of the Q-balls. These constraints may be ameliorated by invoking a short period of thermal inflation. The latter, however, is viable in a very narrow window of parameter space and requires fine tuning.Comment: 40 pages, 3 figure

Efficient algorithms for optimization problems involving semi-algebraic range searching

We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that they involve a `growth parameter' $r$ and a semi-algebraic predicate $\Pi(o,o';r)$ of constant complexity on pairs of input objects, which depends on $r$ and is monotone in $r$. One then defines a graph $G(r)$ whose edges are all the pairs $(o,o')$ for which $\Pi(o,o';r)$ is true, and seeks the smallest value of $r$ for which some monotone property holds for $G(r)$. Problems that fit into this context include (i) the reverse shortest path problem in unit-disk graphs, recently studied by Wang and Zhao, (ii) the same problem for weighted unit-disk graphs, with a decision procedure recently provided by Wang and Xue, (iii) extensions of these problems to three and higher dimensions, (iv) the discrete Fr\'echet distance with one-sided shortcuts in higher dimensions, extending the study by Ben Avraham et al., (v) perfect matchings in intersection graphs: given, e.g., a set of fat ellipses of roughly the same size, find the smallest value $r$ such that if we expand each of the ellipses by $r$, the resulting intersection graph contains a perfect matching, (vi) generalized distance selection problems: given, e.g., a set of disjoint segments, find the $k$'th smallest distance among the pairwise distances determined by the segments, for a given (sufficiently small but superlinear) parameter $k$, and (vii) the maximum-height independent towers problem, in which we want to erect vertical towers of maximum height over a 1.5-dimensional terrain so that no pair of tower tips are mutually visible. We obtain significantly improved solutions for problems (i), (ii) and (vi), and new efficient solutions to the other problems.Comment: Significantly generalized and with additional applications. Notice the change in titl