Many developed economies face declining fertility rates and aging populations, driven significantly by the rising prevalence of childless households. This paper extends a simple overlapping generations (OLG) model to examine how this trend affects household utility. By assuming heterogeneous preferences for child-rearing, the model treats the proportion of childless households as endogenous, determined by utility maximization. The analysis reveals that an increase in childlessness generally exerts a negative impact on overall household utility. Furthermore, the study evaluates childcare support policies, balancing the distortionary effects of higher taxes against the benefits of reduced rearing costs and enhanced social security from a larger future workforce. Numerical simulations suggest that while most households favor the introduction of childcare support, their preferred tax rates vary significantly. These findings highlight the complex trade-offs in policy design when addressing demographic shifts through fiscal interventions.
This article argues that Jane Addams developed a distinctive peace theory drawing on Herbert Spencer and Giuseppe Mazzini in response to gendered war discourse. Spencer's typology of militaristic and industrial societies influenced Addams's critique of American militarism, while Mazzini's vision of concentric circles of ethical obligation influenced her positive vision. Contrasting with William James's famous moral alternatives to war, Addams distanced herself from masculine heroism, establishing discourse centered on human needs. Her "new humanitarianism," rooted in Hull-House experiences and Mazzini-inspired ethics of nurture, offered an ethical alternative to militarism. During WWI, Addams strategically adjusted her rhetoric to the women's peace movement, emphasizing women's sensibilities and expanding her ethics based on universal needs like improving "the standard of life" and advocating for international food relief. Addams's creative intellectual synthesis of Spencer and Mazzini and her strategic adaptation to gendered audiences made indispensable contributions to her distinctive political theory.
We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing K-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined through the Ginsparg-Wilson relation, which is restricted to flat tori in even dimensions, our formulation offers several key advantages: 1) It can be applied straightforwardly to the Atiyah-Patodi-Singer index for manifolds with boundary. 2) The boundary can be curved, allowing for the inclusion of gravitational background effects. 3) The mod-2 index in both even and odd dimensions can be defined as a natural extension of the same formulation. In this talk, we present the mathematical proof and provide numerical evidence supporting the formulation.
We discuss complex Farey graphs for the Euclidean imaginary quadratic number fields ℚ(√(-d)), d∈{1, 2, 3, 7, 11}. We study hyperbolic versions of A. Schmidt's Farey polygons living in 3-dimensional hyperbolic space ℍ^3. Using these Farey polygons we recover tessellations of the hyperbolic plane ℍ^2 that are defined by the action of the Hecke groups H_4 and H_6 and have been studied earlier by I. Short and M. Walker. Moreover, hyperbolic Farey polygons allow us to define polyhedra that induce Farey tessellations of ℍ^3 by the action of certain Bianchi groups. Using complex Farey graphs we consider geodesic complex continued fraction expansions. Our method provides a different and more general approach as the one from the discussion by M. Hockman.
Gender differences in childhood play have long been recognized, yet few studies have examined how these early play tendencies relate to autistic spectrum disorder (ASD)-related traits later in life, particularly from a developmental perspective that links early experiences with adult cognitive characteristics. The present study explored gender differences in play styles and their associations with ASD-related cognitive characteristics using both quantitative and text-mining approaches. Participants were 135 young adults (52 males and 83 females, aged 18-29 years) who completed the Autism-Spectrum Quotient (AQ), Empathy Quotient (EQ), and Systemizing Quotient (SQ), and provided open-ended descriptions of memorable play experiences from early childhood. Quantitative analyses showed that males scored significantly higher on the AQ and SQ, whereas females scored higher on the EQ and reported more frequent engagement in social and cooperative play. Regression analyses further indicated that stronger systemizing tendencies and lower levels of social play were associated with higher ASD-related traits, particularly among males. Text-mining analyses of a subsample (19 males, 23 females) yielded consistent results: males most often recalled competitive and rule-based play (e.g., games, competition, sports), while females described imaginative, cooperative, and socially interactive play (e.g., friends, pretend play, drawing). Together, these findings suggest that gender differences in play reflect underlying empathizing-systemizing cognitive orientations, highlighting the developmental significance of childhood play experiences in relation to ASD-related traits.
