Robert Root | Lafayette College (original) (raw)

Papers by Robert Root

Numeracy, 2019

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social... more The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation offer nuanced views of the nature and importance of quantitative literacy. Its use in a writing seminar connecting quantitative literacy and social justice is described.

2007 IEEE Symposium on Artificial Life, 2007

This paper describes the use of both robotic and digital organisms to help in the study and under... more This paper describes the use of both robotic and digital organisms to help in the study and understanding of the evolution of biological structures. Our premise in this paper is that simulations using robotic and digital organisms are an effective methodology for studying how some features evolved in swimming fish. Experiments with the artificial organisms allow us to evaluate the hypothesis that backbones evolved in fish in part because they result in higher velocity, acceleration and maneuverability. The use of both robotic and digital organisms provides the ability to (1) use computers to efficiently explore a very large search space of possibilities, (2) validate (using the robotic organisms) that the digital models accurately reflect the physical constraints of the environment.

Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology, 2002

Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends li... more Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends like a homogenous, continuous beam in all species except tuna. This simple beam-like behavior is surprising because the underlying tendon structure, muscle structure and behavior are complex. Given this incongruence, our goal was to understand the mechanical role of various myoseptal tendons. We modeled a pumpkinseed sunfish, Lepomis gibbosus, using experimentally-derived physical and mechanical attributes, swimming from rest with steady muscle activity. Axially oriented muscle-tendons, transverse and axial myoseptal tendons, as suggested by current morphological knowledge, interacted to replicate the force and moment distribution. Dynamic stiffness and damping associated with muscle activation, realistic muscle force generation, and force distribution following tendon geometry were incorporated. The vertebral column consisted of 11 rigid vertebrae connected by joints that restricted bending to the lateral plane and endowed the body with its passive viscoelasticity. In reaction to the acceleration of the body in an inviscid fluid and its internal transmission of moment via the vertebral column, the model predicted the kinematic response. Varying only tendon geometry and stiffness, four different simulations were run. Simulations with only intrasegmental tendons produced unstable axial and lateral tail forces and body motions. Only the simulation that included both intra-and intersegmental tendons, muscle-enhanced segment stiffness, and a stiffened caudal joint produced stable and large lateral and axial forces at the tail. Thus this model predicts that axial tendons function within a myomere to (1) convert axial force to moment (moment transduction), (2) transmit axial forces between adjacent myosepta (segment coupling), and, intersegmentally, to (3) distribute axial forces (force entrainment), and (4) stiffen joints in bending (flexural stiffening). The fact that all four functions are needed to produce the most realistic swimming motions suggests that axial tendons are essential to the simple beam-like behavior of fish.

Niederman, Derrick, and Boyum, David. What the Numbers Say: A Field Guide to Mastering Our Numeri... more Niederman, Derrick, and Boyum, David. What the Numbers Say: A Field Guide to Mastering Our Numerical World. (New York: Broadway Books/Random House, 2003). 288 pp. Hardcover, ISBN 978-0-7679-0998-3. Paperback, 978-0-7679-0999-0. Available as an eBook. Blastland, Michael, and Dilnot, Andrew. The Numbers Game: The Commonsense Guide to Understanding Numbers in the News, in Politics and in Life. (New York: Gotham Books/Penguin, 2009). 192 pp. Hardcover, ISBN 978-1-5924-0423-0. Paperback, ISBN 978-1-5924-0485-8. Available as an eBook. Popular books on quantitative literacy need to be easy to read, reasonably comprehensive in scope, and include examples that are thought-provoking and memorable. In contrast to textbooks, popular books can dispense with exercises and structure, and instead offer an informal voice and an inviting style. In this genre John Allen Paulos’ Innumeracy is widely regarded as a classic. However, Paulos\u27 book is out of date, and it takes a whimsical approach to man...

Numeracy, 2020

We propose a relationship between sensory modality, numerical formatting, and performance on a su... more We propose a relationship between sensory modality, numerical formatting, and performance on a survey simulating healthcare decision-making. We examine the current literature on aural health literacy, and specifically aural literacy coupled with health numeracy. We then create a survey instrument called the Bhala test for this purpose and demonstrate that it is moderately internally consistent and provides results that correlate with the NUMi assessment, a widely accepted measure of health numeracy. The quantitative information provided in the Bhala test has two treatments, percentage and natural frequency formats, in an effort to determine which format is easier for subjects to use in decision-making. The Bhala test is administered to a convenience sample of Mechanical Turk workers in a randomized comparative structure. The results do not support the hypothesis that numerical formatting affects subjects' ability to make healthcare decisions. By comparing these results to previous studies on numerical formatting, we provide evidence to support the notion that sensory modality is an essential component of numeracy, and that aural numeracy should be considered separately from print numeracy.

Community-Based Projects in Applied Statistics: Using Service-Learning to Enhance Student Understanding

Community-Based Projects in Applied Statistics: Using Service-Learning to Enhance Student Understanding

Computational and mathematical modeling of the effects of tailbeat frequency and flexural stiffness in swimming fish

Zoology, 2014

Artificial Life, 2009. …, Jan 1, 2009

To test adaptation hypotheses about the evolution of animals, we need information about the behav... more To test adaptation hypotheses about the evolution of animals, we need information about the behavior of phenotypically-variable individuals in a specific environment. To model behavior of ancient fish-like vertebrates, we previously combined evolutionary robotics and software simulations to create autonomous biomimetic swimmers in a simple aquatic environment competing and foraging for a single source of food. This system allowed us to test the hypothesis that selection for improved forage navigation drove the evolution of stiffer tails. In this paper, we extend our framework to evaluate more complex environments and hypotheses. Specifically, we test the hypothesis that predatorprey dynamics and the need for effective foraging strategies, operating simultaneously, were key selection pressures driving the evolution of morphological and sensory traits in early, fishlike vertebrates. Three evolvable traits were chosen because of

2009 IEEE Symposium on Artificial Life, 2009

To test adaptation hypotheses about the evolution of animals, we need information about the behav... more To test adaptation hypotheses about the evolution of animals, we need information about the behavior of phenotypically-variable individuals in a specific environment. To model behavior of ancient fish-like vertebrates, we previously combined evolutionary robotics and software simulations to create autonomous biomimetic swimmers in a simple aquatic environment competing and foraging for a single source of food. This system allowed us to test the hypothesis that selection for improved forage navigation drove the evolution of stiffer tails. In this paper, we extend our framework to evaluate more complex environments and hypotheses. Specifically, we test the hypothesis that predator/prey dynamics and the need for effective foraging strategies, operating simultaneously, were key selection pressures driving the evolution of morphological and sensory traits in early, fishlike vertebrates. Three evolvable traits were chosen because of their importance in propulsion and predator avoidance: (1) the number of vertebrae in the axial skeleton, (2) the trailing edge span of the caudal fin, and (3) the sensitivity of the sensory lateral line. To produce variable offspring, we used a genetic algorithm that rewarded parents with high fitness, allowing them to mate randomly and combine their mutated gametes. Offspring were then instantiated as autonomous embodied robots, the prey. These prey were chased by a non-evolving autonomous predator. Both kinds of robots were surface swimmers. The prey used a control architecture based on that of living fish: a two-layer subsumption architecture with
predator escape over-riding steady swimming during foraging. The performance of six different prey robots in each generation was judged with a relative fitness function that rewarded a combination of high speed, rapid escape acceleration, escape responses, and the ability to stay away from the predator while at the same time staying close to the food source. This approach, which we call biomimetic evolutionary analysis, shows promise for investigators seeking new ways to test evolutionary hypotheses about biological systems.

To understand the mechanical behavior of fast-starting fish, we modeled the pumpkinseed sunfish, ... more To understand the mechanical behavior of fast-starting fish, we modeled the pumpkinseed sunfish, Lepomis gibbosus, as a longitudinally-loaded beam that behaves as an elastic column eccentrically-loaded by lateral musculature. Since bending moments are a function of the shape of the body, we used real sunfish to determine, (1) from cross-sections, the effective moment arm of the lateral musculature, and, (2) from high speed video, the points about which the body bends. Since electromyography of faststarting fish revealed simultaneous activation of both sides of the lateral musculature in stage 1 of a Ctype start, we used this pattern to model the internal forces from which the reactive loads were determined. The model predicts that fast-starting sunfish produce a standing wave of bending moment posteriorly that then becomes a traveling wave of bending moment moving caudally from the anterior region. At the time of the standing moment wave, the body reaches its maximal effective flexural stiffness and, as a result, would be able to rapidly transmit bending moments along the body axis.

Annotated Bibliography on Fair Division and Social Justice

Boundary value problems for degenerate von Kármán equations

This article presents regularity results that admit a weak formulation for degenerate von Kármán ... more This article presents regularity results that admit a weak formulation for degenerate von Kármán boundary value problems modeling the deformation of clamped plates that lose stiffness in one direction. These boundary value problems are derived in the author’s companion article [ibid. 57, 19-36 (1999; Zbl 1025.74018)]. The equations are a fourth-order elliptic-parabolic system of weakly coupled nonlinear equations. The article includes the weak formulation and a brief description of the appropriate existence results for the formulation.

A derivation of degenerate von Kármán equations for strongly anisotropic plates

Grant title: MANEUVERABILITY AND PERFORMANCE VERSATILITY IN SWIMMING FISH

2009 IEEE Symposium on Artificial Life, 2009

To test adaptation hypotheses about the evolution of animals, we need information about the behav... more To test adaptation hypotheses about the evolution of animals, we need information about the behavior of phenotypically-variable individuals in a specific environment. To model behavior of ancient fish-like vertebrates, we previously combined evolutionary robotics and software simulations to create autonomous biomimetic swimmers in a simple aquatic environment competing and foraging for a single source of food. This system allowed us to test the hypothesis that selection for improved forage navigation drove the evolution of stiffer tails. In this paper, we extend our framework to evaluate more complex environments and hypotheses. Specifically, we test the hypothesis that predatorprey dynamics and the need for effective foraging strategies, operating simultaneously, were key selection pressures driving the evolution of morphological and sensory traits in early, fishlike vertebrates. Three evolvable traits were chosen because of

Boundary value problems for degenerate elliptic-parabolic equations of the fourth order

Transactions of the American Mathematical Society, 1991

Numeracy, 2010

192 pp. Hardcover, ISBN 978-1-5924-0423-0. Paperback, ISBN 978-1-5924-0485-8. Available as an eBook.

Journal of Mathematical Analysis and Applications, 1991

Equilibrium of a Radially Symmetric Inhomogeneous Plate Under Tension and Load

Journal of Applied Mechanics, 1997

ABSTRACT This paper studies a mathematical model for small deflections of a radially symmetric st... more ABSTRACT This paper studies a mathematical model for small deflections of a radially symmetric strongly inhomogeneous elastic plate under a normal load and tension in the center plane. The type of inhomogeneity studied occurs in injection molded plastics. The model consists of a Dirichlet boundary value problem for a linear fourth-order ordinary differential equation. A general expression is derived for physically reasonable solutions under relatively broad restrictions on the inhomogeneity and load. The solutions are analyzed and interpreted in terms of their physical significance.

Numeracy, 2019

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social... more The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation offer nuanced views of the nature and importance of quantitative literacy. Its use in a writing seminar connecting quantitative literacy and social justice is described.

2007 IEEE Symposium on Artificial Life, 2007

This paper describes the use of both robotic and digital organisms to help in the study and under... more This paper describes the use of both robotic and digital organisms to help in the study and understanding of the evolution of biological structures. Our premise in this paper is that simulations using robotic and digital organisms are an effective methodology for studying how some features evolved in swimming fish. Experiments with the artificial organisms allow us to evaluate the hypothesis that backbones evolved in fish in part because they result in higher velocity, acceleration and maneuverability. The use of both robotic and digital organisms provides the ability to (1) use computers to efficiently explore a very large search space of possibilities, (2) validate (using the robotic organisms) that the digital models accurately reflect the physical constraints of the environment.

Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology, 2002

Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends li... more Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends like a homogenous, continuous beam in all species except tuna. This simple beam-like behavior is surprising because the underlying tendon structure, muscle structure and behavior are complex. Given this incongruence, our goal was to understand the mechanical role of various myoseptal tendons. We modeled a pumpkinseed sunfish, Lepomis gibbosus, using experimentally-derived physical and mechanical attributes, swimming from rest with steady muscle activity. Axially oriented muscle-tendons, transverse and axial myoseptal tendons, as suggested by current morphological knowledge, interacted to replicate the force and moment distribution. Dynamic stiffness and damping associated with muscle activation, realistic muscle force generation, and force distribution following tendon geometry were incorporated. The vertebral column consisted of 11 rigid vertebrae connected by joints that restricted bending to the lateral plane and endowed the body with its passive viscoelasticity. In reaction to the acceleration of the body in an inviscid fluid and its internal transmission of moment via the vertebral column, the model predicted the kinematic response. Varying only tendon geometry and stiffness, four different simulations were run. Simulations with only intrasegmental tendons produced unstable axial and lateral tail forces and body motions. Only the simulation that included both intra-and intersegmental tendons, muscle-enhanced segment stiffness, and a stiffened caudal joint produced stable and large lateral and axial forces at the tail. Thus this model predicts that axial tendons function within a myomere to (1) convert axial force to moment (moment transduction), (2) transmit axial forces between adjacent myosepta (segment coupling), and, intersegmentally, to (3) distribute axial forces (force entrainment), and (4) stiffen joints in bending (flexural stiffening). The fact that all four functions are needed to produce the most realistic swimming motions suggests that axial tendons are essential to the simple beam-like behavior of fish.

Niederman, Derrick, and Boyum, David. What the Numbers Say: A Field Guide to Mastering Our Numeri... more Niederman, Derrick, and Boyum, David. What the Numbers Say: A Field Guide to Mastering Our Numerical World. (New York: Broadway Books/Random House, 2003). 288 pp. Hardcover, ISBN 978-0-7679-0998-3. Paperback, 978-0-7679-0999-0. Available as an eBook. Blastland, Michael, and Dilnot, Andrew. The Numbers Game: The Commonsense Guide to Understanding Numbers in the News, in Politics and in Life. (New York: Gotham Books/Penguin, 2009). 192 pp. Hardcover, ISBN 978-1-5924-0423-0. Paperback, ISBN 978-1-5924-0485-8. Available as an eBook. Popular books on quantitative literacy need to be easy to read, reasonably comprehensive in scope, and include examples that are thought-provoking and memorable. In contrast to textbooks, popular books can dispense with exercises and structure, and instead offer an informal voice and an inviting style. In this genre John Allen Paulos’ Innumeracy is widely regarded as a classic. However, Paulos\u27 book is out of date, and it takes a whimsical approach to man...

Numeracy, 2020

We propose a relationship between sensory modality, numerical formatting, and performance on a su... more We propose a relationship between sensory modality, numerical formatting, and performance on a survey simulating healthcare decision-making. We examine the current literature on aural health literacy, and specifically aural literacy coupled with health numeracy. We then create a survey instrument called the Bhala test for this purpose and demonstrate that it is moderately internally consistent and provides results that correlate with the NUMi assessment, a widely accepted measure of health numeracy. The quantitative information provided in the Bhala test has two treatments, percentage and natural frequency formats, in an effort to determine which format is easier for subjects to use in decision-making. The Bhala test is administered to a convenience sample of Mechanical Turk workers in a randomized comparative structure. The results do not support the hypothesis that numerical formatting affects subjects' ability to make healthcare decisions. By comparing these results to previous studies on numerical formatting, we provide evidence to support the notion that sensory modality is an essential component of numeracy, and that aural numeracy should be considered separately from print numeracy.

Community-Based Projects in Applied Statistics: Using Service-Learning to Enhance Student Understanding

Community-Based Projects in Applied Statistics: Using Service-Learning to Enhance Student Understanding

Computational and mathematical modeling of the effects of tailbeat frequency and flexural stiffness in swimming fish

Zoology, 2014

Artificial Life, 2009. …, Jan 1, 2009

To test adaptation hypotheses about the evolution of animals, we need information about the behav... more To test adaptation hypotheses about the evolution of animals, we need information about the behavior of phenotypically-variable individuals in a specific environment. To model behavior of ancient fish-like vertebrates, we previously combined evolutionary robotics and software simulations to create autonomous biomimetic swimmers in a simple aquatic environment competing and foraging for a single source of food. This system allowed us to test the hypothesis that selection for improved forage navigation drove the evolution of stiffer tails. In this paper, we extend our framework to evaluate more complex environments and hypotheses. Specifically, we test the hypothesis that predatorprey dynamics and the need for effective foraging strategies, operating simultaneously, were key selection pressures driving the evolution of morphological and sensory traits in early, fishlike vertebrates. Three evolvable traits were chosen because of

2009 IEEE Symposium on Artificial Life, 2009

To test adaptation hypotheses about the evolution of animals, we need information about the behav... more To test adaptation hypotheses about the evolution of animals, we need information about the behavior of phenotypically-variable individuals in a specific environment. To model behavior of ancient fish-like vertebrates, we previously combined evolutionary robotics and software simulations to create autonomous biomimetic swimmers in a simple aquatic environment competing and foraging for a single source of food. This system allowed us to test the hypothesis that selection for improved forage navigation drove the evolution of stiffer tails. In this paper, we extend our framework to evaluate more complex environments and hypotheses. Specifically, we test the hypothesis that predator/prey dynamics and the need for effective foraging strategies, operating simultaneously, were key selection pressures driving the evolution of morphological and sensory traits in early, fishlike vertebrates. Three evolvable traits were chosen because of their importance in propulsion and predator avoidance: (1) the number of vertebrae in the axial skeleton, (2) the trailing edge span of the caudal fin, and (3) the sensitivity of the sensory lateral line. To produce variable offspring, we used a genetic algorithm that rewarded parents with high fitness, allowing them to mate randomly and combine their mutated gametes. Offspring were then instantiated as autonomous embodied robots, the prey. These prey were chased by a non-evolving autonomous predator. Both kinds of robots were surface swimmers. The prey used a control architecture based on that of living fish: a two-layer subsumption architecture with
predator escape over-riding steady swimming during foraging. The performance of six different prey robots in each generation was judged with a relative fitness function that rewarded a combination of high speed, rapid escape acceleration, escape responses, and the ability to stay away from the predator while at the same time staying close to the food source. This approach, which we call biomimetic evolutionary analysis, shows promise for investigators seeking new ways to test evolutionary hypotheses about biological systems.

To understand the mechanical behavior of fast-starting fish, we modeled the pumpkinseed sunfish, ... more To understand the mechanical behavior of fast-starting fish, we modeled the pumpkinseed sunfish, Lepomis gibbosus, as a longitudinally-loaded beam that behaves as an elastic column eccentrically-loaded by lateral musculature. Since bending moments are a function of the shape of the body, we used real sunfish to determine, (1) from cross-sections, the effective moment arm of the lateral musculature, and, (2) from high speed video, the points about which the body bends. Since electromyography of faststarting fish revealed simultaneous activation of both sides of the lateral musculature in stage 1 of a Ctype start, we used this pattern to model the internal forces from which the reactive loads were determined. The model predicts that fast-starting sunfish produce a standing wave of bending moment posteriorly that then becomes a traveling wave of bending moment moving caudally from the anterior region. At the time of the standing moment wave, the body reaches its maximal effective flexural stiffness and, as a result, would be able to rapidly transmit bending moments along the body axis.

Annotated Bibliography on Fair Division and Social Justice

Boundary value problems for degenerate von Kármán equations

This article presents regularity results that admit a weak formulation for degenerate von Kármán ... more This article presents regularity results that admit a weak formulation for degenerate von Kármán boundary value problems modeling the deformation of clamped plates that lose stiffness in one direction. These boundary value problems are derived in the author’s companion article [ibid. 57, 19-36 (1999; Zbl 1025.74018)]. The equations are a fourth-order elliptic-parabolic system of weakly coupled nonlinear equations. The article includes the weak formulation and a brief description of the appropriate existence results for the formulation.

A derivation of degenerate von Kármán equations for strongly anisotropic plates

Grant title: MANEUVERABILITY AND PERFORMANCE VERSATILITY IN SWIMMING FISH

2009 IEEE Symposium on Artificial Life, 2009

To test adaptation hypotheses about the evolution of animals, we need information about the behav... more To test adaptation hypotheses about the evolution of animals, we need information about the behavior of phenotypically-variable individuals in a specific environment. To model behavior of ancient fish-like vertebrates, we previously combined evolutionary robotics and software simulations to create autonomous biomimetic swimmers in a simple aquatic environment competing and foraging for a single source of food. This system allowed us to test the hypothesis that selection for improved forage navigation drove the evolution of stiffer tails. In this paper, we extend our framework to evaluate more complex environments and hypotheses. Specifically, we test the hypothesis that predatorprey dynamics and the need for effective foraging strategies, operating simultaneously, were key selection pressures driving the evolution of morphological and sensory traits in early, fishlike vertebrates. Three evolvable traits were chosen because of

Boundary value problems for degenerate elliptic-parabolic equations of the fourth order

Transactions of the American Mathematical Society, 1991

Numeracy, 2010

192 pp. Hardcover, ISBN 978-1-5924-0423-0. Paperback, ISBN 978-1-5924-0485-8. Available as an eBook.

Journal of Mathematical Analysis and Applications, 1991

Equilibrium of a Radially Symmetric Inhomogeneous Plate Under Tension and Load

Journal of Applied Mechanics, 1997

ABSTRACT This paper studies a mathematical model for small deflections of a radially symmetric st... more ABSTRACT This paper studies a mathematical model for small deflections of a radially symmetric strongly inhomogeneous elastic plate under a normal load and tension in the center plane. The type of inhomogeneity studied occurs in injection molded plastics. The model consists of a Dirichlet boundary value problem for a linear fourth-order ordinary differential equation. A general expression is derived for physically reasonable solutions under relatively broad restrictions on the inhomogeneity and load. The solutions are analyzed and interpreted in terms of their physical significance.