Bilinear Forms on the Dirichlet Space

Let $\mathcal{D}$ be the classical Dirichlet space, the Hilbert space of holomorphic functions on the disk. Given a holomorphic symbol function $b$ we define the associated Hankel type bilinear form, initially for polynomials f and g, by $T_{b}(f,g):= _{\mathcal{D}}$, where we are looking at the inner product in the space $\mathcal{D}$. We let the norm of $T_{b}$ denotes its norm as a bilinear map from $\mathcal{D}\times\mathcal{D}$ to the complex numbers. We say a function $b$ is in the space $\mathcal{X}$ if the measure $d\mu_{b}:=| b^{\prime}(z)| ^{2}dA$ is a Carleson measure for $\mathcal{D}$ and norm $\mathcal{X}$ by $$\Vert b\Vert_{\mathcal{X}}:=| b(0)| +\Vert | b^{\prime}(z)| ^{2}dA\Vert_{CM(\mathcal{D})}^{1/2}.$$ Our main result is $T_{b}$ is bounded if and only if $b\in\mathcal{X}$ and $$\Vert T_{b}\Vert_{\mathcal{D\times D}}\approx\Vert b\Vert_{\mathcal{X}}.$$Comment: v1: 29 page

The Dirichlet space: A Survey

In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we focus mainly on certain function theoretic properties of the Dirichlet space and omit covering the interesting connections between this space and operator theory. The results discussed in this survey show what is known about the Dirichlet space and compares it with the related results for the Hardy space.Comment: 35 pages, typoes corrected, some open problems adde

Reviving Knowledges through Play and Resistance: The Case of Navajo Conceptions of Space

The authors explore a possible cause of epistemicidal predispositions of the dominant Eurocentric curricula. They posit that one way to determine a plausible contributing factor of this increasing devastation is to consider epistemicide through the lens of intellectual development. To do this, the authors examine parallel patterns of behavior in the domains of developmental and cognitive psychology. The authors then discuss an alternative framework to the Western conception of space within formal K-12 education by presenting the Navajo conception of space and play. Throughout the paper, the authors argue that all students—and especially those living in poverty in commercially constructed, large urban areas—deserve, and need, an educational framework that expands rather than constricts their schema of space and facilitates their agency to renew and regenerate their environment

Introduction to Confronting Teacher Preparation Epistemicide: Art, Poetry, and Teacher Resistance

In this special issue, we present different perspectives from a documentary project on curricular epistemicide. We view curriculum epistemicide —the annihilation of curriculum—as an embodied process. It limits ways of knowing, questioning, and envisioning the world, and it constricts multiplicity and erases identity and culture. Authors within this volume responded to two requests: 1) they examined some form of epistemicide; and 2) they did not reinforce current systems of power and inequity. Throughout the issue, poetry and photography weave through theoretical papers and empirical studies. A range of methodologies are considered within the articles

Confronting Curriculum Epistemicide: A Conversation with Editors Dan Ness & Rick Sawyer

As an entree into the Special Issue Confronting Curriculum Epistemicide , NWJTE co-editor Maika Yeigh talk with editors Daniel Ness and Richard Sawyer to learn about their inspiration and goals of the Special Issue

Biologically Inspired Feedback Design for Drosophila Flight

We use a biologically motivated model of the Drosophila's flight mechanics and sensor processing to design a feedback control scheme to regulate forward flight. The model used for insect flight is the grand unified fly (GUF) [3] simulation consisting of rigid body kinematics, aerodynamic forces and moments, sensory systems, and a 3D environment model. We seek to design a control algorithm that will convert the sensory signals into proper wing beat commands to regulate forward flight. Modulating the wing beat frequency and mean stroke angle produces changes in the flight envelope. The sensory signals consist of estimates of rotational velocity from the haltere organs and translational velocity estimates from visual elementary motion detectors (EMD's) and matched retinal velocity filters. The controller is designed based on a longitudinal model of the flight dynamics. Feedforward commands are generated based on a desired forward velocity. The dynamics are linearized around this operating point and a feedback controller designed to correct deviations from the operating point. The control algorithm is implemented in the GUF simulator and achieves the desired tracking of the forward reference velocities and exhibits biologically realistic responses

Flying Drosophila stabilize their vision-based velocity controller by sensing wind with their antennae

Flies and other insects use vision to regulate their groundspeed in flight, enabling them to fly in varying wind conditions. Compared with mechanosensory modalities, however, vision requires a long processing delay (~100 ms) that might introduce instability if operated at high gain. Flies also sense air motion with their antennae, but how this is used in flight control is unknown. We manipulated the antennal function of fruit flies by ablating their aristae, forcing them to rely on vision alone to regulate groundspeed. Arista-ablated flies in flight exhibited significantly greater groundspeed variability than intact flies. We then subjected them to a series of controlled impulsive wind gusts delivered by an air piston and experimentally manipulated antennae and visual feedback. The results show that an antenna-mediated response alters wing motion to cause flies to accelerate in the same direction as the gust. This response opposes flying into a headwind, but flies regularly fly upwind. To resolve this discrepancy, we obtained a dynamic model of the fly’s velocity regulator by fitting parameters of candidate models to our experimental data. The model suggests that the groundspeed variability of arista-ablated flies is the result of unstable feedback oscillations caused by the delay and high gain of visual feedback. The antenna response drives active damping with a shorter delay (~20 ms) to stabilize this regulator, in exchange for increasing the effect of rapid wind disturbances. This provides insight into flies’ multimodal sensory feedback architecture and constitutes a previously unknown role for the antennae

Statistical and machine learning methods evaluated for incorporating soil and weather into corn nitrogen recommendations

Nitrogen (N) fertilizer recommendation tools could be improved for estimating corn (Zea mays L.) N needs by incorporating site-specific soil and weather information. However, an evaluation of analytical methods is needed to determine the success of incorporating this information. The objectives of this research were to evaluate statistical and machine learning (ML) algorithms for utilizing soil and weather information for improving corn N recommendation tools. Eight algorithms [stepwise, ridge regression, least absolute shrinkage and selection operator (Lasso), elastic net regression, principal component regression (PCR), partial least squares regression (PLSR), decision tree, and random forest] were evaluated using a dataset containing measured soil and weather variables from a regional database. The performance was evaluated based on how well these algorithms predicted corn economically optimal N rates (EONR) from 49 sites in the U.S. Midwest. Multiple algorithm modeling scenarios were examined with and without adjustment for multicollinearity and inclusion of two-way interaction terms to identify the soil and weather variables that could improve three dissimilar N recommendation tools. Results showed the out-of-sample root-mean-square error (RMSE) for the decision tree and some random forest modeling scenarios were better than the stepwise or ridge regression, but not significantly different than any other algorithm. The best ML algorithm for adjusting N recommendation tools was the random forest approach (r2 increased between 0.72 and 0.84 and the RMSE decreased between 41 and 94 kg N ha−1). However, the ML algorithm that best adjusted tools while using a minimal amount of variables was the decision tree. This method was simple, needing only one or two variables (regardless of modeling scenario) and provided moderate improvement as r2 values increased between 0.15 and 0.51 and RMSE decreased between 16 and 66 kg N ha−1. Using ML algorithms to adjust N recommendation tools with soil and weather information shows promising results for better N management in the U.S. Midwest