Irregular speech rate dissociates auditory cortical entrainment, evoked responses, and frontal alpha

The entrainment of slow rhythmic auditory cortical activity to the temporal regularities in speech is considered to be a central mechanism underlying auditory perception. Previous work has shown that entrainment is reduced when the quality of the acoustic input is degraded, but has also linked rhythmic activity at similar time scales to the encoding of temporal expectations. To understand these bottom-up and top-down contributions to rhythmic entrainment, we manipulated the temporal predictive structure of speech by parametrically altering the distribution of pauses between syllables or words, thereby rendering the local speech rate irregular while preserving intelligibility and the envelope fluctuations of the acoustic signal. Recording EEG activity in human participants, we found that this manipulation did not alter neural processes reflecting the encoding of individual sound transients, such as evoked potentials. However, the manipulation significantly reduced the fidelity of auditory delta (but not theta) band entrainment to the speech envelope. It also reduced left frontal alpha power and this alpha reduction was predictive of the reduced delta entrainment across participants. Our results show that rhythmic auditory entrainment in delta and theta bands reflect functionally distinct processes. Furthermore, they reveal that delta entrainment is under top-down control and likely reflects prefrontal processes that are sensitive to acoustical regularities rather than the bottom-up encoding of acoustic features

Predicting Sense Of Community in a Historic Latino/Latina Neighborhood Undergoing Gentrification

Neighborhoods with generational Mexican American populations may have high levels of block Social Cohesion and neighborhood Sense of Community. Streetcar-focused development via federal and local investment often spurs gentrification in neighborhoods with ethnic concentrations, which shifts neighborhood demographics towards more White and higher income households. The new residential and business investment in the neighborhood often has an impact on existing neighborhood social dynamics. This study includes mixed methods resident survey data of long term and newer residents. The qualitative data analysis informs quantitative data analysis in order to better understand resident descriptions of the impact of neighborhood streetcar focused gentrification on social factors in a generational Latino/Latina neighborhood at one point in time just before the streetcar opening. Specifically the study seeks to: (a) provide a description of generational and new resident experiences with block Social Cohesion and neighborhood Sense of Community; (b) determine differences (between Latino/Latina households and those with children present and other study participants) in block Social Cohesion, neighborhood Sense of Community, and Involvement in Neighborhood and Voluntary Associations; and (c) determine what factors predict neighborhood Sense of Community. The study highlights the Latino/Latina residents’ maintenance of a strong ethnic identity, generational neighborhood based social ties, and ongoing involvement in neighborhood schools and religious traditions that contribute to a strong neighborhood Sense of Community. Newer residents report being drawn to and supporting the maintenance of the neighborhood Sense of Community

Just Mathematics: Getting Started Teaching Postsecondary Math for Social Justice

Following the summer 2020 civil rights movement and increasing attention to the intersections of mathematics with politics and power, many math educators have reported a desire to implement an antiracist pedagogy and to examine the intersections of their subject with issues of equity, inclusion, and social justice. Many resources exist for K-12 math educators interested in incorporating social justice into their curricula, but resources are comparatively scarce for college and university instructors (though this is changing quickly!). We discuss why one may want to teach mathematics for social justice, how to begin to implement issues of social justice into postsecondary math courses, and publicly available social justice materials for postsecondary math courses

Penrose Limit and String Theories on Various Brane Backgrounds

We investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p,q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly solved by the spheroidal wave functions.Comment: 41 pages, Latex, minor correction

Root asymptotics of spectral polynomials for the Lame operator

The study of polynomial solutions to the classical Lam\'e equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr\"odinger equation with finite gap potential given by the Weierstrass $\wp$-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.Comment: final version, to appear in Commun. Math. Phys.; 13 pages, 3 figures, LaTeX2

Leadership

The EYFS offers leadership challenges within ECEC which are profound and challenging, but not wholly unique to the sector. In other words, there are common features of leadership that apply to all phases of education, but it is recognised that there are specific issues relating to ECEC. This chapter explores those challenges to help identify responses which are appropriate to the sector. The chapter begins by exploring the complexity of ECEC provision in England to identify leadership and management responsibilities within the system. The key role is identified as the formal leader of settings with more than one employee. Differences between leadership and management are discussed, as is leadership as a set of social behaviours. This definition, which extends the simple measure of accountability for formal managers, allows for the exploration of shared or collective leadership approaches to creating and sustaining effective learning environments as well as ensuring the safety and welfare of young children. The discussion then moves towards identifying organisational structures and behaviours which support such ambitions. Issues specific to the sector, such as multi-agency working and a heavily gendered workforce, are explored in the context of leadership theories to guide practitioners as to their role. The chapter closes with some practical tips as to how to move beyond the notion of single accountable executive towards collective and connective leadership within each setting. This chapter aims to to: • Explore issues about leadership in relation to ECEC; • Discuss different styles of leadership and reflect on the core values that underpin ECEC; • Discuss leadership in settings in relation to contributing factors that correspond to the share value system

The Gambier Mapping

We propose a discrete form for an equation due to Gambier and which belongs to the class of the fifty second order equations that possess the Painleve property. In the continuous case, the solutions of the Gambier equation is obtained through a system of Riccati equations. The same holds true in the discrete case also. We use the singularity confinement criterion in order to study the integrability of this new mapping.Comment: PlainTe