Topological finiteness properties of monoids. Part 1: Foundations

We initiate the study of higher dimensional topological finiteness properties of monoids. This is done by developing the theory of monoids acting on CW complexes. For this we establish the foundations of $M$-equivariant homotopy theory where $M$ is a discrete monoid. For projective $M$-CW complexes we prove several fundamental results such as the homotopy extension and lifting property, which we use to prove the $M$-equivariant Whitehead theorems. We define a left equivariant classifying space as a contractible projective $M$-CW complex. We prove that such a space is unique up to $M$-homotopy equivalence and give a canonical model for such a space via the nerve of the right Cayley graph category of the monoid. The topological finiteness conditions left-$\mathrm{F}_n$ and left geometric dimension are then defined for monoids in terms of existence of a left equivariant classifying space satisfying appropriate finiteness properties. We also introduce the bilateral notion of $M$-equivariant classifying space, proving uniqueness and giving a canonical model via the nerve of the two-sided Cayley graph category, and we define the associated finiteness properties bi-$\mathrm{F}_n$ and geometric dimension. We explore the connections between all of the these topological finiteness properties and several well-studied homological finiteness properties of monoids which are important in the theory of string rewriting systems, including $\mathrm{FP}_n$, cohomological dimension, and Hochschild cohomological dimension. We also develop the corresponding theory of $M$-equivariant collapsing schemes (that is, $M$-equivariant discrete Morse theory), and among other things apply it to give topological proofs of results of Anick, Squier and Kobayashi that monoids which admit presentations by complete rewriting systems are left-, right- and bi-$\mathrm{FP}_\infty$.Comment: 59 pages, 1 figur

Query Complexity of Derivative-Free Optimization

This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and those with access to only function evaluations. However, there are situations in which DFO is unavoidable, and for such situations we propose a new DFO algorithm that is proved to be near optimal for the class of strongly convex objective functions. A distinctive feature of the algorithm is that it uses only Boolean-valued function comparisons, rather than function evaluations. This makes the algorithm useful in an even wider range of applications, such as optimization based on paired comparisons from human subjects, for example. We also show that regardless of whether DFO is based on noisy function evaluations or Boolean-valued function comparisons, the convergence rate is the same

Buprestidae, Cerambycidae, and Scolytidae Associated with Successive Stages of \u3ci\u3eAgrilus Bilineatus\u3c/i\u3e (Coleoptera: Buprestidae) Infestation of Oaks in Wisconsin

The species of Buprestidae, Cerambycidae, and Scolytidae found in association with Agrilus bilineatus (Weber) in declining oaks, Quercus spp., in Wisconsin, were Chrysobothris femorata (Olivier) and Dicerca sp. (Buprestidae); Amniscus macula (Say),Cyrtaphorus verrucosus (Olivier), Euderces picipes (Fabricius), Graphisurus fasciatus (DeGeer), Neodytus acuminatus (Fabricius), Sarosesthes fulminans (Fabricius), and Xylotrechus colonus (Fabricius) (Cerambycidae); and Monarthrum fasciatum (Say), Monarthrum mali (Fitch), Pseudopityophthorus minutissimus (Zimmerman), and Xylaterinus politus (Say) (Scolytidae). In general, weakened oaks were first attacked by A. bilineatus. and at times that same year by C. femorata. G. fasdalus, and P. minutissimus. Infestation by M.fasciatum, M. mali, and X. politus began the season following first attack by A. bilineatus. With the exception of A. bilineatus, the above mentioned Buprestidae and Cerambycidae appeared to preferentially infest dead wood, often those portions that had died the previous season

CHANGES IN RETAIL FOOD DELIVERY: SIGNALS FOR PRODUCERS, PROCESSORS AND DISTRIBUTORS

This paper contains two chapters related to changes in retail food delivery and sales. The first discusses trends in consumer demographics and lifestyles and how these continue to drive changes in the way food is prepared and delivered to consumers. Retail stores are responding with new formats: providing more ready to eat foods; more convenient store layouts; lower prices and better service in niche markets across the country. Their demands send signals up the food chain to processors and producers that alter their production and inventory decisions. Electronic information technology speeds these changes and leads to more efficient operation with, allegedly, better service for consumers. The second chapter discusses how advances in information technology affect not only the internal business operations in food firms throughout the food supply chain but also how the product flows and how businesses link their processes together. The reengineering of the food supply chain by way of an industry-wide initiative called "efficient consumer response" (ECR) is explained and analyzed for its motivations and implementation, thus far. The many facets of ECR such as product replenishment and promotion are discussed. Lessons learned from ECR include that it is possible to accommodate the coexistence of firms of various sizes and types, and that the role of trade associations in facilitating industry-wide changes is vital and impressive.Agribusiness, Industrial Organization,

Design and Control of Motion Compensation Cardiac Catheters

Robotic cardiac catheters have the potential to revolutionize heart surgery by extending minimally invasive techniques to complex surgical repairs inside the heart. However, catheter technologies are currently unable to track fast tissue motion, which is required to perform delicate procedures inside a beating heart. This paper proposes an actuated catheter tool that compensated for the motion of heart structures like the mitral valve apparatus by servoing a catheter guidewire inside a flexible sheath. We examine design and operation parameters that affect performance and establish that friction and backlash limit the tracking performance of the catheter system. Based on the results of these experiments and a model of the backlash behavior, we propose and implement compensation methods to improve trajectory tracking performance. The catheter system is evaluated with 3D ultrasound guidance in simulate in vivo conditions. the results demonstrate that with mechanical and control system design improvements, a robotic catheter system can accurately track the fast motion of the human mitral valve.Engineering and Applied Science