The genus spectrum of a hyperbolic 3-manifold

In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the commensurability class. In addition, we show that any finite volume hyperbolic 3-manifold has many pairs of non-isometric finite covers with identical spectra. Forgetting multiplicities, we can also construct pairs where the volume ratio is unbounded

Absolute profinite rigidity and hyperbolic geometry

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group $\mathrm{PSL}(2,\mathbb{Z}[\omega])$ with $\omega^2+\omega+1=0$ is rigid in this sense. Other examples include the non-uniform lattice of minimal co-volume in $\mathrm{PSL}(2,\mathbb{C})$ and the fundamental group of the Weeks manifold (the closed hyperbolic $3$-manifold of minimal volume).Comment: v2: 35 pages. Final version. To appear in the Annals of Mathematics, Vol. 192, no. 3, November 202

Collisions at infinity in hyperbolic manifolds

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and Sisto

Modeling the impact of vaccination control strategies on a foot and mouth disease outbreak in the Central United States

The central United States (U.S.) has a large livestock population including cattle, swine, sheep and goats. Simulation models were developed to assess the impact of livestock herd types and vaccination on foot and mouth disease (FMD) outbreaks using the North American Animal Disease Spread Model. In this study, potential FMD virus outbreaks in the central region of the U.S. were simulated to compare different vaccination strategies to a depopulation only scenario. Based on data from the U.S. Department of Agriculture National Agricultural Statistics Service, a simulated population of 151,620 livestock operations characterized by latitude and longitude, production type, and herd size was generated. For the simulations, a single 17,000 head feedlot was selected as the initial latently infected herd in an otherwise susceptible population. Direct and indirect contact rates between herds were based on survey data of livestock producers in Kansas and Colorado. Control methods included ring vaccination around infected herds. Feedlots ≥3000 head were either the only production type that was vaccinated or were assigned the highest vaccination priority. Simulated vaccination scenarios included low and high vaccine capacity, vaccination zones of 10 km or 50 km around detected infected premises, and vaccination trigger of 10 or 100 detected infected herds. Probability of transmission following indirect contact, movement controls and contact rate parameters were considered uncertain and so were the subjects of sensitivity analysis. All vaccination scenarios decreased number of herds depopulated but not all decreased outbreak duration. Increased size of the vaccination zone during an outbreak decreased the length of the outbreak and number of herds destroyed. Increased size of the vaccination zone primarily resulted in vaccinating feedlots ≥3000 head across a larger area. Increasing the vaccination capacity had a smaller impact on the outbreak and may not be feasible if vaccine production and delivery is limited. The ability to vaccinate all the production types surrounding an infected herd did not appear as beneficial as priority vaccination of feedlot production types that have high numbers of indirect contacts. Outbreak duration, number of herds depopulated and the effectiveness of vaccination were sensitive to indirect contact transmission probability and movement restrictions. The results of this study will provide information about the impacts of disease control protocols which may be useful in choosing the optimal control methods to meet the goals of rapid effective control and eradication

Probabilistic computer model of optimal runway turnoffs

Landing delays are currently a problem at major air carrier airports and many forecasters agree that airport congestion will get worse by the end of the century. It is anticipated that some types of delays can be reduced by an efficient optimal runway exist system allowing increased approach volumes necessary at congested airports. A computerized Probabilistic Runway Turnoff Model which locates exits and defines path geometry for a selected maximum occupancy time appropriate for each TERPS aircraft category is defined. The model includes an algorithm for lateral ride comfort limits

Motivation of Shoulder Surgery Patients for Rehabilitation

International Journal of Exercise Science 10(2): 234-245, 2017 Motivation can be a valuable construct during physical rehabilitation. Rehabilitation can be uncomfortable and painful, testing patients’ rehabilitation motivation and continued participation. Maintaining motivation throughout rehabilitation is important for patients to return to optimal joint motion and daily functioning. The purpose of this research project was to examine rehabilitation motivation after shoulder surgery (rotator cuff repairs, slap repairs, biceps tenodesis, acromioplasty, distal clavicle excision or combination). Persons who underwent shoulder surgery (December 2014 – April 2015) voluntarily participated in the study. The Self Regulation Questionnaire was used to assess patients’ self-regulation and motivation. Surveys were administered to participants during rehabilitation at appointments with the physician. This study revealed significant changes to participants’ self-regulation throughout the 16-week post shoulder surgical rehabilitation process. Significant increases were discovered when looking at patients’ attention to goals and employing strategies to meet those goals. Other main areas of increase included problem solving, planning rehabilitation outside of therapy and coping with challenging times in rehabilitation. Data allows researchers and health care professionals to evaluate the dynamics of motivation fluctuation during rehabilitation. In addition, data will allow researchers to identify areas of motivational concern to implement motivation techniques in order to aid patients through rehabilitation

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat