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As part of the Snowmass'21 community planning excercise, the Advanced Accelerator Concepts (AAC) community proposed future linear colliders with center-of-mass energies up to 15 TeV and luminosities up to 50$\times10^{34}$ cm$^{-2}$s$^{-1}$ in a compact footprint. In addition to being compact, these machines must also be energy efficient. We identify two challenges that must be addressed in the design of these machines. First, the Beam Delivery System (BDS) must not add significant length to the accelerator complex. Second, beam parameters must be chosen to mitigate beamstrahlung effects and maximize the luminosity-per-power of the machine. In this paper, we review advances in plasma lens technology that will help to reduce the length of the BDS system and we detail new Particle-in-Cell simulation studies that will provide insight into beamstrahlung mitigation techniques. We apply our analysis to both $e^+e^-$ and $\gamma\gamma$ colliders.

C$^3$ is an opportunity to realize an e$^+$e$^-$ collider for the study of the Higgs boson at $\sqrt{s} = 250$ GeV, with a well defined upgrade path to 550 GeV while staying on the same short facility footprint. C$^3$ is based on a fundamentally new approach to normal conducting linear accelerators that achieves both high gradient and high efficiency at relatively low cost. Given the advanced state of linear collider designs, the key system that requires technical maturation for C$^3$ is the main linac. This white paper presents the staged approach towards a facility to demonstrate C$^3$ technology with both Direct (source and main linac) and Parallel (beam delivery, damping ring, ancillary component) R&D. The white paper also includes discussion on the approach for technology industrialization, related HEP R&D activities that are enabled by C$^3$ R&D, infrastructure requirements and siting options., Comment: contribution to Snowmass 2021

This panel examines research on early education from two research practice partnerships, the Baltimore Education Research Consortium (BERC) with Baltimore City Schools and Johns Hopkins University in Baltimore, Maryland, and the Stanford-SFUSD Partnership with San Francisco Unified School District (SFUSD) and Stanford University in San Francisco, California. First, it explores how BERC convened the Early Education Data Collaborative (EEDC), a collection of Baltimore agencies that provide services to children from birth through the early elementary years whose goal is to understand how different pathways to kindergarten may be associated with kindergarten readiness and later learning outcomes. Second, it explores a line of research by a Stanford University professor and her team of doctoral students working with SFUSD's early education department. The Stanford team worked with SFUSD to establish and test a new Pre-Kindergarten (Pre-K) early literacy assessment aligned to K-12 measures, and also established a kindergarten readiness indicator that has been used by SFUSD over the past three years. The Baltimore sample included 11,897 kindergarten students across two cohorts with matched program and birth records. The San Francisco Transitional Kindergarten study examines literacy outcomes, as measured by the Fountas and Pinnell Benchmark Assessment System, of Kindergarteners enrolled in SFUSD in the 2013-2014 and 2014-2015 school years. The sample contains 6,174 students, 5% of which (309 students) had enrolled in the TK program. Another 17% (1,051 students) attended the district's Pre-K program. The remainder of the students had the option to attend a Pre-K program offered by San Francisco. Both studies examine the use of longitudinal data sets from large urban school districts with robust early education programs. The Baltimore study provides an analysis comparing kindergarten readiness measures for the three most common pathways to kindergarten: Baltimore City Schools Pre-K, Baltimore City Head Start, and both programs. Preliminary results from the first cohort of students from the Baltimore study show when the mother's background and the circumstances of the child's birth are accounted for (Model 2), students with prior experience in only Head Start are more likely to be ready for kindergarten than students who did not attend either program (odds ratio: 1.260; 95% CI: 1.016, 1.563). When the mother's background and the circumstances of the child's birth are accounted for (Model 2), children who attended both Head Start and BCPS Pre-K are nearly four times as likely to be identified as ready for kindergarten as children from neither program (odds ratio: 3.904; 95% CI: 3.058, 4.983). Children who attended only BCPS Pre-K were three times as likely to be ready for kindergarten than children who attended neither program (odds ratio: 3.314; 95% CI: 2.744, 4.009) when family background is taken into account. Preliminary results from the SFUSD Transitional Kindergarten (TK) study indicate that the program may have increased fall student literacy outcomes. Fall results, however, indicate that TK students are not more likely to be able to read books. Four data tables are appended.