Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces

In this paper we show that totally geodesic subspaces determine the commensurability class of a standard arithmetic hyperbolic $n$-orbifold, $n\ge 4$. Many of the results are more general and apply to locally symmetric spaces associated to arithmetic lattices in $\mathbb{R}$-simple Lie groups of type $B_n$ and $D_n$. We use a combination of techniques from algebraic groups and quadratic forms to prove several results about these spaces.Comment: 34 Pages. Corrected typos. Added references. Improved expositio

Analysis and Modeling of a Single-Phased Bifilar-Wound Brushless DG Motor

A single-phase brushless dc motor utilizing a bifilar stator winding and having asymmetrical stator pole faces is investigated. The form of the permanent-magnet component of the stator winding flux linkage is analyzed considering the asymmetry of the stator pole faces. Equations describing the electromechanical dynamics of the motor are then derived along with an expression for the electromagnetic torque. The requirements of the dc-to-ac inverter which drives the motor are determined. Using the expression for electromagnetic torque and inverter characteristics, the form of the so-called static electromagnetic torque is analyzed. The so-called cogging torque is established, and in conjunction with the static electromagnetic torque, used to explain the starting characteristics of the motor. The equations for the electromechanical dynamics are converted into state-model form and two mathematical models of the inverter are developed for use in a computer simulation. This computer simulation is then used to demonstrate steady-state and dynamic operation of the motor

Totally Geodesic Surfaces in Arithmetic Hyperbolic 3-Manifolds

In this talk we will discuss some recent work on the problem of determining the extent to which the geometry of an arithmetic hyperbolic 3-manifold M is determined by the geometric genus spectrum of M (i.e., the set of isometry classes of finite area, properly immersed, totally geodesic surfaces of M, considered up to free homotopy). In particular, we will give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial geometric genus spectrum and analyze the growth of the genera of minimal surfaces across commensurability classes. These results have applications to the study of how Heegard genus grows across commensurability classes

Ordinal Probit Functional Regression Models with Application to Computer-Use Behavior in Rhesus Monkeys

Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, however the exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (\emph{Macaca mulatta}), we introduce the Ordinal Probit Functional Regression Model or OPFRM to perform ordinal function-on-scalar regression. The OPFRM is flexibly formulated to allow for the choice of different basis functions including penalized B-splines, wavelets, and O'Sullivan splines. We demonstrate the operating characteristics of the model in simulation using a variety of underlying covariance patterns showing the model performs reasonably well in estimation under multiple basis functions. We also present and compare two approaches for conducting posterior inference showing that joint credible intervals tend to out perform point-wise credible. Finally, in application, we determine demographic factors associated with the monkeys' computer use over the course of a year and provide a brief analysis of the findings