Hypergeometric solutions to Schr\"odinger equations for the quantum Painlev\'e equations

We consider Schr\"odinger equations for the quantum Painlev\'e equations. We present hypergeometric solutions of the Schr\"odinger equations for the quantum Painlev\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\"odinger equations for the quantum Painlev\'e equations and those of the KZ equation or the confluent KZ equations.Comment: 17 pages; Journal of Mathematical Physics (Vol.52, Issue 8) 201

Spontaneous exciton condensation in 1T-TiSe2: a BCS-like approach

Recently strong evidence has been found in favor of a BCS-like condensation of excitons in 1\textit{T}-TiSe$_2$. Theoretical photoemission intensity maps have been generated by the spectral function calculated within the excitonic condensate phase model and set against experimental angle-resolved photoemission spectroscopy data. Here, the calculations in the framework of this model are presented in detail. They represent an extension of the original excitonic insulator phase model of J\'erome \textit{et al.} [Phys. Rev. {\bf 158}, 462 (1967)] to three dimensional and anisotropic band dispersions. A detailed analysis of its properties and further comparison with experiment are also discussedComment: Submitted to PRB, 11 pages, 7 figure

Parental Co‐Construction of 5‐ to 13‐Year‐Olds\u27 Global Self‐Esteem Through Reminiscing About Past Events

The current study explored parental processes associated with children\u27s global self‐esteem development. Eighty 5‐ to 13‐year‐olds and one of their parents provided qualitative and quantitative data through questionnaires, open‐ended questions, and a laboratory‐based reminiscing task. Parents who included more explanations of emotions when writing about the lowest points in their lives were more likely to discuss explanations of emotions experienced in negative past events with their child, which was associated with child attachment security. Attachment was associated with concurrent self‐esteem, which predicted relative increases in self‐esteem 16 months later, on average. Finally, parent support also predicted residual increases in self‐esteem. Findings extend prior research by including younger ages and uncovering a process by which two theoretically relevant parenting behaviors impact self‐esteem development

Integrating Species Traits into Species Pools

Despite decades of research on the species‐pool concept and the recent explosion of interest in trait‐based frameworks in ecology and biogeography, surprisingly little is known about how spatial and temporal changes in species‐pool functional diversity (SPFD) influence biodiversity and the processes underlying community assembly. Current trait‐based frameworks focus primarily on community assembly from a static regional species pool, without considering how spatial or temporal variation in SPFD alters the relative importance of deterministic and stochastic assembly processes. Likewise, species‐pool concepts primarily focus on how the number of species in the species pool influences local biodiversity. However, species pools with similar richness can vary substantially in functional‐trait diversity, which can strongly influence community assembly and biodiversity responses to environmental change. Here, we integrate recent advances in community ecology, trait‐based ecology, and biogeography to provide a more comprehensive framework that explicitly considers how variation in SPFD, among regions and within regions through time, influences the relative importance of community assembly processes and patterns of biodiversity. First, we provide a brief overview of the primary ecological and evolutionary processes that create differences in SPFD among regions and within regions through time. We then illustrate how SPFD may influence fundamental processes of local community assembly (dispersal, ecological drift, niche selection). Higher SPFD may increase the relative importance of deterministic community assembly when greater functional diversity in the species pool increases niche selection across environmental gradients. In contrast, lower SPFD may increase the relative importance of stochastic community assembly when high functional redundancy in the species pool increases the influence of dispersal history or ecological drift. Next, we outline experimental and observational approaches for testing the influence of SPFD on assembly processes and biodiversity. Finally, we highlight applications of this framework for restoration and conservation. This species‐pool functional diversity framework has the potential to advance our understanding of how local‐ and regional‐scale processes jointly influence patterns of biodiversity across biogeographic regions, changes in biodiversity within regions over time, and restoration outcomes and conservation efforts in ecosystems altered by environmental change

Modeling active electrolocation in weakly electric fish

In this paper, we provide a mathematical model for the electrolocation in weakly electric fishes. We first investigate the forward complex conductivity problem and derive the approximate boundary conditions on the skin of the fish. Then we provide a dipole approximation for small targets away from the fish. Based on this approximation, we obtain a non-iterative location search algorithm using multi-frequency measurements. We present numerical experiments to illustrate the performance and the stability of the proposed multi-frequency location search algorithm. Finally, in the case of disk- and ellipse-shaped targets, we provide a method to reconstruct separately the conductivity, the permittivity, and the size of the targets from multi-frequency measurements.Comment: 37 pages, 11 figure

Identification of input-output LPV models

This chapter presents an overview of the available methods for identifying input-output LPV models both in discrete time and continuous time with the main focus on noise modeling issues. First, a least-squares approach and an instrumental variable method are presented for dealing with LPV-ARX models. Then, a refined instrumental variable approach is discussed to address more sophisticated noise models like Box-Jenkins in the LPV context. This latter approach is also introduced in continuous time and efficient solutions are proposed for both the problem of time-derivative approximation and the issue of continuous-time modeling of the noise

Direct identification of continuous-time LPV models

Controllers in the linear parameter-varying (LPV) framework are commonly designed in continuous time (CT) requiring accurate and low-order CT models of the system. Nonetheless, most of the methods dedicated to the identification of LPV systems are addressed in the discrete-time setting. In practice when discretizing models which are naturally expressed in CT, the dependency on the scheduling variables becomes non-trivial and over-parameterized. Consequently, direct identification of CT-LPV systems in an input-output setting is investigated. To provide consistent model parameter estimates in this setting, a refined instrumental variable approach is proposed. The statistical properties of this approach are demonstrated through a Monte Carlo simulation example

Teacher feedback, writing assignment quality, and third-grade students' revision in lower- and higher-achieving urban schools

The relation of the quality of writing assignments and written instructor responses to student writings to the quality of subsequent student work was investigated in 29 urban third-grade classrooms in 8 schools. Writing assignments were generally of a higher quality in the 4 schools that served primarily middle-class, higher-achieving students, most of whom were white or Asian, versus the 4 schools that served primarily low-income and lower-achieving students, the majority of whom were Latino. Across all classrooms, however, teachers focused on standardizing students' written output, which led to marked improvement in the writing mechanics of students' work. Results of regression analyses indicated that the amount and type of feedback students received predicted a significant, although small, proportion of the variance in the quality of the content, organization, and mechanics of students' final drafts. The quality of the writing assignments predicted a small but significant proportion of the variance in the quality of the content of students' final drafts only. These findings raise questions about the implementation of broad educational policies in classrooms, such as using the writing process approach, and indicate a need for professional development for teachers