Search

Recent developments in particle physics have revealed deep connections between scattering amplitudes and tropical geometry. At the heart of this relationship are the chirotropical Grassmannian $\text{Trop}^\chi \text{G}(k,n)$ and chirotropical Dressian $\text{Dr}^\chi(k,n)$, polyhedral fans built from uniform realizable chirotopes that encode the combinatorial structure of generalized Feynman diagrams. We prove that $\text{Trop}^\chi \text{G}(3,n) = \text{Dr}^\chi(3,n)$ for $n = 6,7,8$, and develop algorithms to compute these objects from their rays modulo lineality. Using these algorithms, we compute all chirotropical Grassmannians $\text{Trop}^\chi \text{G}(3,n)$ for $n = 6,7,8$ across all isomorphism classes of chirotopes. We prove that each chirotopal configuration space $X^\chi(3,6)$ is diffeomorphic to a polytope with an associated canonical logarithmic differential form. Finally, we show that the equality between chirotropical Grassmannian and Dressian fails for $(k,n) = (4,8)$., Comment: 13 pages, 2 figures

Research has established the vital role administrators play in the success and sustainability of high-quality early childhood care and education (ECEC) programs. However, many center-based program administrators assume their leadership roles by being promoted from a teaching position. Consequently, while they may assume their administrative role with a strong background in teaching young children, they often lack the specific education, specialized training, and experience needed to successfully lead and sustain a high-quality ECEC program. Adult learning theory, as well as research across many workforce sectors, including early childhood education highlights the need to align professional development opportunities with career development stages. This Research Brief provides an in-depth profile of the largest career development stage group: the proficient administrator. Building on the established characterization of proficient administrators as those who shift from struggling to juggling responsibilities, focus on improving their efficiency and effectiveness, and fit into the "conscious competence" learning stage, this study examines their perceived alignment between current and ideal work experiences, career origins, current role perceptions, levels of self-efficacy, and mastery of critical leadership competencies.

Home visiting connects expectant parents, new caregivers, and their young children with a support person, called a home visitor. The home visitor meets regularly with the family, develops a relationship with them, and supports them to achieve their goals and meet their needs. To reach the thousands of additional families who could benefit from home visiting, we must increase support for culturally relevant and family-centered models. A new report -- "Community-Based Home Visiting: Fidelity to Families, Commitment to Outcomes" -- delves into the unique strengths and challenges of community-based home visiting models, whose design and measures of success intentionally center the perspectives of the families and communities they serve. These models are often developed by those with experience with the unique cultures, strengths, and solutions of he community they live in and aim to serve. This report summarizes themes from listening sessions with 30+ community-based home visiting models from across the country. It offers policy and funding recommendations that would improve support for these models and therefore families' access to home visiting that best meets their goals. [Additional support was provided by the National Home Visiting Coalition Steering Committee.]

The Shaping Futures Together agenda highlights policies and investments that families and practitioners say will ensure all children thrive. This playbook provides recommended policy and research strategies that Start Early believes will help to realize those priorities. Each section includes legislative and administrative policy recommendations and research questions specific to each of the following priorities: (1) healthy births & thriving families; (2) positive early learning & development; (3) effective, valued & well-compensated workforce; and (4) strong, sustainable & equitable early childhood ecosystem.

The Alaska Performance Scholarship (APS) rewards students who strive to excel in high school and continue their education in degree and certificate programs in Alaska. This report covers the high school, postsecondary, Alaska residency, and workforce outcomes of the APS program between Fall 2011-2023. [This report was prepared by Resource Data, Inc.]

The decomposition of oceanic flow into its balanced and unbalanced motions carries theoretical and practical significance for the oceanographic community. These two motions have distinct dynamical characteristics and affect the transport of tracers differently from one another. The launch of Surface Water and Ocean Topography (SWOT) satellite provides a prime opportunity to diagnose the surface balanced and unbalanced motions on a global scale at an unprecedented spatial resolution. Here, we apply dynamic-mode decomposition (DMD), a linear-algebraic data-driven method, to a tidally-forced numerical simulation and one-day-repeat SWOT observations of sea-surface height (SSH) in the Gulf Stream extension. DMD is able to separate out the spatial modes associated with sub-inertial periods from super-inertial periods. The sub-inertial modes of DMD can be used to extract geostrophically balanced motions from SSH fields, which have an imprint of internal tides and gravity waves. We utilize the statistical relation between relative vorticity and strain rate as the metric to gauge the extraction of geostrophy.

Our national survey of the early intervention (EI) and early childhood special education (ECSE) workforce highlights key strengths and concerns. Workers find their roles rewarding, appreciate making a difference for children and families, and are well-qualified, with most holding at least a bachelor's degree. However, the workforce lacks diversity, which may not reflect the children served, and nearly all workers are female, while more boys receive EI and ECSE services. High-stress levels, large caseloads, inadequate support, and poor compensation are significant issues. Addressing these challenges through better training, support, and innovative solutions is essential to retain and attract qualified professionals, ensuring children and families receive the necessary services without delays. [Funding for this report was provided by Early Childhood Personnel Center at the University of Connecticut.]

One in five college students, or 22 percent, are parents. They are highly motivated students and earn grades on par with or better than their childless peers. However, child care challenges often lead student parents to leave school or workforce training without completing; shift from full-time to part-time schooling or programming; and miss, arrive late to, or leave early from school or work training. In Georgia, women, single parents, parents with an annual household income under $50,000 (particularly in South Georgia, where families' median household incomes are lower), and parents under age 30 are most likely to report long-term employment or educational disruptions due to child care issues, blocking their path to fulfilling their educational goals and pursuing economic mobility. Parents' inability to access consistent, reliable, and affordable child care is one of their biggest barriers to reaching these goals. Nearly one in five applicants to the Childcare and Parent Services (CAPS) program, administered through the Georgia Department of Early Care and Learning (DECAL), identify as students; in May 2022, CAPS established student parents as a priority group for their program. Since then, more than 16,000 student parents have applied for CAPS. Yet only 42 percent of those applicants were approved for a subsidy. DECAL established the CAPS Student Parent 2Gen Pilot program to test a strategy to better serve their student parent priority group at three technical college sites. This brief summarizes the theory of change behind DECAL's 2Gen Pilot and Child Trends' plans for evaluating the pilot. It was created in conjunction with DECAL, using funding from DECAL.

Finite dimensional simple modules of quantum affine algebras of type A correspond to semistandard Young tableaux of rectangular shapes. In this paper, we classify all prime modules corresponding to 2-column semistandard Young tableaux. Moreover, we give a conjectural sufficient condition for a module corresponding to a tableau with more than two columns to be prime., Comment: This is a part of the original file arXiv:2303.05618v3. The original file arXiv:2303.05618v3 is splited into two parts. The other part of the original file arXiv:2303.05618v3 has the title: Tropical Geometry, Quantum Affine Algebras, and Scattering Amplitudes

We consider a rotating non-hydrostatic flow with arbitrary stratification and argue that 1) the appropriate form of potential vorticity (PV) for this system is in terms of isopycnal deviation and 2) the decomposition into energetically orthogonal solutions is fundamentally a PV-inversion. The new closed-form expression for available potential vorticity (APV) is expressed in terms of isopycnal deviation, following the ideas in Wagner & Young (2015). This form of APV linearizes to quasigeostrophic PV (QGPV) after discarding the nonlinear stretching term and a height nonlinearity, the latter of which is not present in constant stratification. This formulation leads to positive definite definitions of potential enstrophy and total energy expressed in terms of isopycnal deviation, from which the quadratic versions emerge at lowest order. It is exactly these quantities diagonalized by the linear eigenmodes. Internal-gravity waves, geostrophic motions, inertial oscillations, and a mean density anomaly form the energetically and enstrophically orthogonal constituents of flow. The complete state of the fluid can be represented in terms of these physically realizeable modes and determined from the derived projection operators using the horizontal velocity and density anomaly. The projection of the fluid state onto the non-hydrostatic wave modes, reveals that one must first account for the PV portion of the flow before recovering the wave solutions. We apply the physical insights of the decomposition to a mesoscale eddy showing how strict adherence to adiabatic rearrangement places strong constraints on the vertical structure of such eddies, including a skew towards stronger cyclonic eddies in the upper water-column. Finally, the expression for APV is shown to reproduce the height nonlinearity of shallow-water PV, a well know feature that breaks the cyclone-anticyclone symmetry in QGPV.

Minimal kinematics identifies likelihood degenerations where the critical points are given by rational formulas. These rest on the Horn uniformization of Kapranov-Huh. We characterize all choices of minimal kinematics on the moduli space $\mathcal{M}_{0,n}$. These choices are motivated by the CHY model in physics and they are represented combinatorially by 2-trees. We compute 2-tree amplitudes, and we explore extensions to non-planar on-shell diagrams, here identified with the hypertrees of Castravet-Tevelev., Comment: 18 pages

This study utilizes data gathered from a nationwide survey of preschool educators in the United States to examine the prevalence of teaching practices associated with academic-focused rather than play-based approaches. The research delves into how these practices vary across different types of preschool programs, including publicly funded, such as state and locally funded public preschools, federally funded Head Start programs, and private preschools predominantly funded through fees. The analysis also considers various program features influenced by public policies, such as teacher qualifications and classroom characteristics. While the main objective is descriptive--to understand the extent of practice differences across auspices--the study also aims to shed light on potential reasons behind these differences, albeit with a recognition of limitations in establishing causality.

Water is essential for life. The brain, heart, kidneys, and lungs require continued hydration to function, and our bodies need water for digestion, nutrient absorption, blood distribution, and so much more. While water comprises around 60% of the adult body, 75% of infants' bodies are water. Children also drink more water per pound of body weight than adults, with infants consuming the most, whether through formula prepared with water or through breast milk. Because our bodies need a near-constant supply of water, the availability and quality of water are critical parts of the environment that shape child development. This is particularly true during the prenatal and early childhood periods when bodies are especially sensitive to outside influences. However, in the U.S., the systems that were once widely presumed to produce nearly universal, clean, affordable, and trustworthy water have serious gaps and challenges. Additionally, freshwater supplies are being threatened by droughts, overuse, and contamination, exacerbated by climate change. Inequities in access to clean water are the result of decisions that we have made as communities, states, and a nation. New decisions can reverse these inequities and provide all people with access to clean drinking water, with profound effects on the health and well-being of our children. This working paper from the Early Childhood Scientific Council on Equity and the Environment explores how water affects children's health, learning, and behavior, and how ensuring access to safe drinking water is necessary to support the healthy development of all children. It offers specific strategies to address disparities in access to clean water and resources to take action in your community.

The preschool landscape is complex, consisting of several publicly funded programs supported by federal, state, and local funds. Included in this landscape is Head Start, a critical early childhood education (ECE) program that serves--in every state and territory--young children in families with incomes at or below the federal poverty line, families experiencing homelessness, families receiving assistance like Temporary Assistance for Needy Families (TANF) or Supplemental Security Income (SSI), families of children with disabilities, and children who are in the foster care system. Comprehensive data on Head Start programs are available nationally but can be challenging to integrate with other preschool and K-12 data, in part because the data typically flow from local Head Start grantees up to the federal Office of Head Start (OHS), bypassing the state. However, without the inclusion of Head Start data, researchers, policymakers, and preschool administrators are unable to answer key questions about the experiences of those being served or understand which children and families are served in states with Head Start and state pre-kindergarten (pre-K). To better understand the ways Head Start data are being accessed, analyzed, and used with other preschool data at the state level, the Early Childhood Data Collaborative (ECDC) at Child Trends conducted a survey of Head Start State Collaboration Offices (HSCOs). HSCOs play a role coordinating Head Start systems at the state level with other early childhood programs, and they are well positioned to understand the data collection efforts within a state. The primary goal of the survey was to better understand the types of Head Start data that HSCOs can access and how these data are used, disaggregated, and linked with other early childhood and K-12 data; in addition, the survey aimed to understand data-related supports and infrastructure.

Our updated brief reports that while the number of states allowing FCC participation remained unchanged from 2019-2020 to 2022-2023, there were notable shifts in participation within states. The enrollment of children in FCC settings saw significant increases, with some states experiencing substantial growth. However, concerns regarding the quality of these settings and the learning outcomes for children persist, highlighting the need for further research and support as states expand their pre-K programs to include more FCC settings.