Jason Fox - Academia.edu (original) (raw)

Papers by Jason Fox

We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension d ... more We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension d for all d ≥ 4 (see Theorem 2.13). These examples result from applying CAT(0)/CAT(−1) filling constructions (based on singular doubly warped products) to finite volume hyperbolic manifolds with toral cusps.

Israel Journal of Mathematics, 2008

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a ... more We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev. As an application, we prove a group-theoretic analog of the Gromov-Thurston 2π Theorem in the context of relatively hyperbolic groups.

Geometry & Topology, 2005

If G is a group, a pseudocharacter f : G → R is a function which is "almost" a homomorphism. If G... more If G is a group, a pseudocharacter f : G → R is a function which is "almost" a homomorphism. If G admits a nontrivial pseudocharacter f , we define the space of ends of G relative to f and show that if the space of ends is complicated enough, then G contains a nonabelian free group. We also construct a quasiaction by G on a tree whose space of ends contains the space of ends of G relative to f . This construction gives rise to examples of "exotic" quasi-actions on trees.

In particular, we obtain information about the simplicial volumes of some 4--dimensional homology... more In particular, we obtain information about the simplicial volumes of some 4--dimensional homology spheres described by Ratcliffe and Tschantz, answering a question of Belegradek and establishing the existence of 4--dimensional homology spheres with positive simplicial volume.

Intertextuality refers to the meaning(s) inherent in and created by the ways texts exist in relat... more Intertextuality refers to the meaning(s) inherent in and created by the ways texts exist in relation to one another, the reader, and the world that contextualizes them.

Journal of Athletic Training, 2008

Context: Inversion ankle sprains can lead to a chronic condition called functional ankle instabil... more Context: Inversion ankle sprains can lead to a chronic condition called functional ankle instability (FAI). Limited research has been reported regarding isokinetic measures for the plantar flexors and dorsiflexors of the ankle.

This paper describes our initial steps to develop new visualization concepts that can generate in... more This paper describes our initial steps to develop new visualization concepts that can generate insight and understanding from National Airspace System (NAS) simulation data. The capacity of the United States' National Airspace System (NAS) must at least double to handle the projected increase in passenger demand by 2025. To address this challenge, new capacity-enhancing concepts are being developed. These concepts are tested and evaluated on a NAS simulation tool called the Airspace Concept Evaluation System (ACES). Concept developers need improved visualization techniques to better understand ACES simulation outputs, and thereby comprehend the strengths, weaknesses and effects of their capacityincreasing concepts. Examining ACES outputs is a nontrivial task. ACES simulates the entire NAS and generates an enormous amount of data. A single simulation run can include over 60,000 flight segments and output tens of gigabytes of data. Traditional approaches for displaying these outputs fall short of what concept developers need. Existing visualization techniques are straightforward geographic plots of aircraft or their related metrics (density, environmental impact, delay, etc.), which are often overwhelming and not illuminating. For example, drawing 10,000 aircraft at their true locations over the continental United States results in a density that is too high for observers to understand the situation and extract useful information. The contribution of this paper is in describing new visualization concepts for this problem domain, where our visualizations do not rely primarily upon plotting data at their true geographic coordinates. We draw from cognitive science principles, perception, ATM characteristics and information visualization techniques to synthesize new approaches for displaying ACES data. Our goal is to enable the user to detect subtle correlations, patterns, trends and relationships that provide insight. We describe our general strategies and approaches, including the results of asking concept developers what specific questions they wanted a visualization tool to answer. Then we present eight new visualization concepts that reveal different aspects of the NAS simulation data, with preliminary implementations of three concepts. Future work includes evaluation on more datasets. A measure of success will be the ability of these new visualization modes to enable users to see subtle but important patterns, trends, correlations, features, and relationships that they could not previously see by any previous means. The goal is to generate insight and allow observers to find important characteristics that they did not even know to look for initially. This paper has contributed eight new visualization concepts aimed at generating insight from simulations of the NAS. The goal is to aid future ATM concept developers in designing and evaluating their capacity-enhancing concepts. Traffic Flow Management (TFM) might be another user group that would be interested in these concepts. To truly demonstrate that our visualization concepts can help developers in these tasks, these concepts need to be further implemented and evaluated, especially on a variety of ACES datasets generated by the VAMS concept developers.

Raytheon's TACEC (Terminal Area Capacity Enhancement Concept) proposes to increase airspace capac... more Raytheon's TACEC (Terminal Area Capacity Enhancement Concept) proposes to increase airspace capacity by using closely-spaced formations of arriving and departing aircraft to greatly increase airport capacities. However, a blunder in a tightly-spaced formation could cause a collision with another aircraft or its wake vortices. Therefore, humans need tools and visualization aids to detect and respond to blunders. This paper is the first in a series of experiments to evaluate the ability of different visualization modes to enable detection of lateral blunders. We tested four viewpoints, one warning aid, and three blunder speeds in a within-subjects design. This study had twelve participants. The main result was that changing the viewpoint made a large difference; the cockpit view was by far the worst. Blunder detection varied by speed and was difficult in the presence of noise. Future experiments should use more realistic simulators and pilots as participants.

Satellites represent scarce resources that must be carefully scheduled to maximize their value to... more Satellites represent scarce resources that must be carefully scheduled to maximize their value to service consumers. Near-optimal satellite task scheduling is so computationally difficult that it typically takes several hours to schedule one day’s activities for a set of satellites and tasks. Thus, often a requestor will not know if a task will be scheduled until it is too late to accommodate scheduling failures. This paper presents our experiences creating a fast Analogical Reasoning (AR) system and an even faster Case-Based Reasoner (CBR) that can predict, in less than a millisecond, whether a hypothetical task will be scheduled successfully. Requestors can use the system to refine tasks for maximum schedulability. We report on three increasingly narrow approaches that use domain knowledge to constrain the problem space. We show results that indicate the method can achieve >80% accuracy on the given problem.

We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension d ... more We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension d for all d ≥ 4 (see Theorem 2.13). These examples result from applying CAT(0)/CAT(−1) filling constructions (based on singular doubly warped products) to finite volume hyperbolic manifolds with toral cusps.

Israel Journal of Mathematics, 2008

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a ... more We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev. As an application, we prove a group-theoretic analog of the Gromov-Thurston 2π Theorem in the context of relatively hyperbolic groups.

Geometry & Topology, 2005

If G is a group, a pseudocharacter f : G → R is a function which is "almost" a homomorphism. If G... more If G is a group, a pseudocharacter f : G → R is a function which is "almost" a homomorphism. If G admits a nontrivial pseudocharacter f , we define the space of ends of G relative to f and show that if the space of ends is complicated enough, then G contains a nonabelian free group. We also construct a quasiaction by G on a tree whose space of ends contains the space of ends of G relative to f . This construction gives rise to examples of "exotic" quasi-actions on trees.

In particular, we obtain information about the simplicial volumes of some 4--dimensional homology... more In particular, we obtain information about the simplicial volumes of some 4--dimensional homology spheres described by Ratcliffe and Tschantz, answering a question of Belegradek and establishing the existence of 4--dimensional homology spheres with positive simplicial volume.

Intertextuality refers to the meaning(s) inherent in and created by the ways texts exist in relat... more Intertextuality refers to the meaning(s) inherent in and created by the ways texts exist in relation to one another, the reader, and the world that contextualizes them.

Journal of Athletic Training, 2008

Context: Inversion ankle sprains can lead to a chronic condition called functional ankle instabil... more Context: Inversion ankle sprains can lead to a chronic condition called functional ankle instability (FAI). Limited research has been reported regarding isokinetic measures for the plantar flexors and dorsiflexors of the ankle.

This paper describes our initial steps to develop new visualization concepts that can generate in... more This paper describes our initial steps to develop new visualization concepts that can generate insight and understanding from National Airspace System (NAS) simulation data. The capacity of the United States' National Airspace System (NAS) must at least double to handle the projected increase in passenger demand by 2025. To address this challenge, new capacity-enhancing concepts are being developed. These concepts are tested and evaluated on a NAS simulation tool called the Airspace Concept Evaluation System (ACES). Concept developers need improved visualization techniques to better understand ACES simulation outputs, and thereby comprehend the strengths, weaknesses and effects of their capacityincreasing concepts. Examining ACES outputs is a nontrivial task. ACES simulates the entire NAS and generates an enormous amount of data. A single simulation run can include over 60,000 flight segments and output tens of gigabytes of data. Traditional approaches for displaying these outputs fall short of what concept developers need. Existing visualization techniques are straightforward geographic plots of aircraft or their related metrics (density, environmental impact, delay, etc.), which are often overwhelming and not illuminating. For example, drawing 10,000 aircraft at their true locations over the continental United States results in a density that is too high for observers to understand the situation and extract useful information. The contribution of this paper is in describing new visualization concepts for this problem domain, where our visualizations do not rely primarily upon plotting data at their true geographic coordinates. We draw from cognitive science principles, perception, ATM characteristics and information visualization techniques to synthesize new approaches for displaying ACES data. Our goal is to enable the user to detect subtle correlations, patterns, trends and relationships that provide insight. We describe our general strategies and approaches, including the results of asking concept developers what specific questions they wanted a visualization tool to answer. Then we present eight new visualization concepts that reveal different aspects of the NAS simulation data, with preliminary implementations of three concepts. Future work includes evaluation on more datasets. A measure of success will be the ability of these new visualization modes to enable users to see subtle but important patterns, trends, correlations, features, and relationships that they could not previously see by any previous means. The goal is to generate insight and allow observers to find important characteristics that they did not even know to look for initially. This paper has contributed eight new visualization concepts aimed at generating insight from simulations of the NAS. The goal is to aid future ATM concept developers in designing and evaluating their capacity-enhancing concepts. Traffic Flow Management (TFM) might be another user group that would be interested in these concepts. To truly demonstrate that our visualization concepts can help developers in these tasks, these concepts need to be further implemented and evaluated, especially on a variety of ACES datasets generated by the VAMS concept developers.

Raytheon's TACEC (Terminal Area Capacity Enhancement Concept) proposes to increase airspace capac... more Raytheon's TACEC (Terminal Area Capacity Enhancement Concept) proposes to increase airspace capacity by using closely-spaced formations of arriving and departing aircraft to greatly increase airport capacities. However, a blunder in a tightly-spaced formation could cause a collision with another aircraft or its wake vortices. Therefore, humans need tools and visualization aids to detect and respond to blunders. This paper is the first in a series of experiments to evaluate the ability of different visualization modes to enable detection of lateral blunders. We tested four viewpoints, one warning aid, and three blunder speeds in a within-subjects design. This study had twelve participants. The main result was that changing the viewpoint made a large difference; the cockpit view was by far the worst. Blunder detection varied by speed and was difficult in the presence of noise. Future experiments should use more realistic simulators and pilots as participants.

Satellites represent scarce resources that must be carefully scheduled to maximize their value to... more Satellites represent scarce resources that must be carefully scheduled to maximize their value to service consumers. Near-optimal satellite task scheduling is so computationally difficult that it typically takes several hours to schedule one day’s activities for a set of satellites and tasks. Thus, often a requestor will not know if a task will be scheduled until it is too late to accommodate scheduling failures. This paper presents our experiences creating a fast Analogical Reasoning (AR) system and an even faster Case-Based Reasoner (CBR) that can predict, in less than a millisecond, whether a hypothetical task will be scheduled successfully. Requestors can use the system to refine tasks for maximum schedulability. We report on three increasingly narrow approaches that use domain knowledge to constrain the problem space. We show results that indicate the method can achieve >80% accuracy on the given problem.