Joyal's Suspension Functor on Θ\Theta and Kan's Combinatorial Spectra

In [Joyal] where the category $\Theta$ is first defined it is noted that the dimensional shift on $\Theta$ suggests an elegant presentation of the unreduced suspension on cellular sets. In this note we prove that the reduced suspension associated to that presentation is left Quillen with respect to the Cisinski model category structure presenting the $\left(\infty,1\right)$-category of pointed spaces and enjoys the correct universal property. More, we go on to describe how, in forthcoming work, inspired by the combinatorial spectra described in [Kan], this suspension functor entails a description of spectra which echoes the weaker form of the homotopy hypothesis, we describe the development of a presentation of spectra as locally finite weak $\mathbf{Z}$-groupoids

Optimal Decentralized State-Feedback Control with Sparsity and Delays

This work presents the solution to a class of decentralized linear quadratic state-feedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into independent subproblems that are solved using dynamic programming. The approach presented herein both unifies and generalizes many existing results

Breast Self-Examination Teaching for Women in Chemical Dependency Programs

Fifty-two women from 5 chemical dependency programs participated in a 1 hour health education program teaching breast self-examination using breast models. Tactile skills and general information about breast cancer and breast self-examination were presented. The program was evaluated for its ability to teach this high risk population. Nine true/false questions and lump detection skills were evaluated using_a pretest/posttest non-experimental design. A level of significance for the true/false questions was set at .01, and for lump detection skills it was set at .05. Dependent t tests was used to statistically analyze the data. Participants improved their general knowledge about breast cancer and self-examination as a result of this program (p \u3c.01). Lump detection skills also improved (p \u3c.05). This study indicates health education programs are of value and can potentially decrease the survival discrepancy for breast cancer for a specific high risk population

Optimal Control for LQG Systems on Graphs---Part I: Structural Results

In this two-part paper, we identify a broad class of decentralized output-feedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among subsystems and the inter-controller communication is characterized by the same directed graph. Furthermore, this graph is assumed to be a multitree, that is, its transitive reduction can have at most one directed path connecting each pair of nodes. In this first part, we derive sufficient statistics that may be used to aggregate each controller's growing available information. Each controller must estimate the states of the subsystems that it affects (its descendants) as well as the subsystems that it observes (its ancestors). The optimal control action for a controller is a linear function of the estimate it computes as well as the estimates computed by all of its ancestors. Moreover, these state estimates may be updated recursively, much like a Kalman filter

Optimal Control of Two-Player Systems with Output Feedback

In this article, we consider a fundamental decentralized optimal control problem, which we call the two-player problem. Two subsystems are interconnected in a nested information pattern, and output feedback controllers must be designed for each subsystem. Several special cases of this architecture have previously been solved, such as the state-feedback case or the case where the dynamics of both systems are decoupled. In this paper, we present a detailed solution to the general case. The structure of the optimal decentralized controller is reminiscent of that of the optimal centralized controller; each player must estimate the state of the system given their available information and apply static control policies to these estimates to compute the optimal controller. The previously solved cases benefit from a separation between estimation and control which allows one to compute the control and estimation gains separately. This feature is not present in general, and some of the gains must be solved for simultaneously. We show that computing the required coupled estimation and control gains amounts to solving a small system of linear equations