Symplectic modular symmetry in heterotic string vacua: flavor, CP, and R-symmetries

We examine a common origin of four-dimensional flavor, CP, and U(1)R symmetries in the context of heterotic string theory with standard embedding. We find that flavor and U(1)R symmetries are unified into the Sp(2h + 2, ℂ) modular symmetries of Calabi-Yau threefolds with h being the number of moduli fields. Together with the $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP CP symmetry, they are enhanced to GSp(2h + 2, ℂ) ≃ Sp(2h + 2, ℂ) ⋊ $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP generalized symplectic modular symmetry. We exemplify the S3, S4, T′, S9 non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and ℤ2, S4 flavor symmetries on three-parameter examples of Calabi-Yau threefolds. Thus, non-trivial flavor symmetries appear in not only the exact orbifold limit but also a certain class of Calabi-Yau three-folds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

Best Graph Type to Compare Discrete Groups: Bar, Dot, and Tally

Different graph types might differ in group comparison due to differences in underlying graph schemas. Thus, this study examined whether graph schemas are based on perceptual features (i.e., each graph has a specific schema) or common invariant structures (i.e., graphs share several common schemas), and which graphic type (bar vs. dot vs. tally) is the best to compare discrete groups. Three experiments were conducted using the mixing-costs paradigm. Participants received graphs with quantities for three groups in randomized positions and were given the task of comparing two groups. The results suggested that graph schemas are based on a common invariant structure. Tally charts mixed either with bar graphs or with dot graphs showed mixing costs. Yet, bar and dot graphs showed no mixing costs when paired together. Tally charts were the more efficient format for group comparison compared to bar graphs. Moreover, processing time increased when the position difference of compared groups was increased.

The Tangled Bank

Why are there so many kinds of organisms, and why do they cluster into discrete groups associated with particular locales? These and other ecological questions find answers in the expansive version of evolution that is presently emerging. Heredity, variation, natural selection, and adaptation are rooted in the level of genes, but incorporate features that grow out of the many tiers of biological organization. The communitarian view of life complements the one focused on the individual organism, and requires us to reexamine the meaning of both organism and individual. It embraces broad-gauge phenomena such as nutrient cycles, and gave birth to Gaia: the vision of Earth as a self-regulating system that has kept our planet hospitable to life for nearly 4 billion years.

Chebyshev polynomials and inequalities for Kleinian groups

The principal character of a representation of the free group of rank two into [Formula: see text] is a triple of complex numbers that determines an irreducible representation uniquely up to conjugacy. It is a central problem in the geometry of discrete groups and low dimensional topology to determine when such a triple represents a discrete group which is not virtually abelian, that is, a Kleinian group. A classical necessary condition is Jørgensen’s inequality. Here, we use certain shifted Chebyshev polynomials and trace identities to determine new families of such inequalities, some of which are best possible. The use of these polynomials also shows how we can identify the principal character of some important subgroups from that of the group itself.

KMS states on crossed products by abelian groups

We provide a general description of the KMS states for flows whose fixed point algebra satisfies a certain regularity condition. This is then applied to crossed products by discrete groups, and in particular to certain flows on crossed products by discrete abelian groups where the methods can be combined with spectral analysis for abelian automorphism groups.

Craniometric Variation in a Regional Sample from Antioquia, Medellín, Colombia

Population affinity estimation is frequently assessed from measurements of the cranium. Traditional models place individuals into discrete groups―such as Hispanic―that often encompass very diverse populations. Current research, including this study, challenges these assumptions using more refined population affinity estimation analyses. We examine craniometric data for a sample of individuals from different regions in Antioquia, Colombia. We first assessed the sample to understand intraregional variation in cranial shape as a function of birthplace or a culturally constructed social group label. Then, pooling the Colombian data, we compare cranial variation with global contemporary and prehistoric groups. Results did not indicate significant intraregional variation in Antioquia; classification models performed poorly (28.6% for birthplace and 36.6% for social group). When compared to other groups (American Black, American White, Asian, modern Hispanic, and prehistoric Native American), our model correctly classified 75.5% of the samples. We further refined the model by separating the pooled Hispanic sample into Mexican and Guatemalan samples, which produced a correct classification rate of 74.4%. These results indicate significant differences in cranial form among groups commonly united under the classification “Hispanic” and bolster the addition of a refined approach to population affinity estimation using craniometric data.

Project-Think and the Fragmentation and Defragmentation of Civil Society in Egypt, Palestine, and Turkey

By drawing from authors’ fieldwork in Egypt, Palestine, and Turkey, this article critically examines perceptions of project-think among civic organizations in the Middle East. As a managerial rationality, project-think has four key components: (a) a prioritization of discrete needs and discrete groups, (b) an orientation toward funding, (c) a focus on short-term and measurable results, and (d) the positioning of nongovernmental organizations (NGOs) as career ladders. Through unpacking these four components, we find that project-think is perceived to contribute to the fragmentation of civil society by fracturing social issues, dividing the NGO sector, isolating organizational energy, and complicating relations between groups. Simultaneously, we demonstrate that, civic actors use various strategies to circumvent the perceived impacts of fragmentation. By mapping these intertwined meanings and experiences of fragmentation and defragmentation, this study contributes to debates concerning the political effects of managerialism among civil society in the Global South.

Examples of Calabi-Yau threefolds with small Hodge numbers

We observe some suitable examples of Calabi-Yau threefolds for heterotic superstring compactifications. It is reasonable to seek CY threefolds with Euler characteristic equals ±6 because of generation’s number. Hosotani mechanism for violations of the gauge group by the Wilson loops requires such CY space has a non-trivial fundamental group. These spaces can be obtained by factoring the complete intersection Calabi-Yau spaces by the free action of some discrete group. Also we shortly discuss cases when discrete groups act with fixed point sets.

An Exploration of the Heterogeneous Nature of Reading Comprehension Development in First Grade: The Impact of Word and Meaning Skills

This exploratory study builds upon extant reading development studies by identifying discrete groups based on reading comprehension trajectories across first grade. The main goal of this study was to enhance the field’s understanding of early reading comprehension development and its underlying subcomponent skills, with the intent of better understanding the development of comprehension in students who display risk for reading difficulties and disabilities. A sample of first-grade readers ( N = 314) were assessed at three timepoints across the first-grade year. These data were utilized to derive empirical latent classes based on reading comprehension performance across the first-grade year. Reading subcomponent skill assessments (phonological awareness, word reading, decoding, linguistic comprehension, and reading fluency), measured in the fall of first grade, were compared across latent classes to examine how they related to growth across the first-grade year. Results suggest that there were four distinct latent classes with differential reading comprehension development, each of which could also be distinguished by the subskill assessments. These findings are presented within the context of the broader reading research base and implications for practice are discussed.