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Your search keyword '"Hill, Kaitlin"' showing total 23 results
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23 results on '"Hill, Kaitlin"'

1. Most probable transition paths in piecewise-smooth stochastic differential equations

Author

Hill, Kaitlin, Zanetell, Jessica, and Gemmer, John A

Subjects
Mathematics - Dynamical Systems, Mathematics - Probability, 37H10, 37J45
Abstract

We develop a path integral framework for determining most probable paths in a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin-Wentzell theory of large deviations to cases where the system is piecewise-smooth and may be non-autonomous. In particular, we consider an $n-$dimensional system with a switching manifold in the drift that forms an $(n-1)-$dimensional hyperplane and investigate noise-induced transitions between metastable states on either side of the switching manifold. To do this, we mollify the drift and use $\Gamma-$convergence to derive an appropriate rate functional for the system in the piecewise-smooth limit. The resulting functional consists of the standard Freidlin-Wentzell rate functional, with an additional contribution due to times when the most probable path slides in a crossing region of the switching manifold. We explore implications of the derived functional through two case studies, which exhibit notable phenomena such as non-unique most probable paths and noise-induced sliding in a crossing region., Comment: 38 pages, 9 figures

Published
2021
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2. Mathematical model of gender bias and homophily in professional hierarchies

Author

Clifton, Sara M., Hill, Kaitlin, Karamchandani, Avinash J., Autry, Eric A., McMahon, Patrick, and Sun, Grace

Subjects
Physics - Physics and Society, Computer Science - Social and Information Networks
Abstract

Women have become better represented in business, academia, and government over time, yet a dearth of women at the highest levels of leadership remains. Sociologists have attributed the leaky progression of women through professional hierarchies to various cultural and psychological factors, such as self-segregation and bias. Here, we present a minimal mathematical model that reveals the relative role that bias and homophily (self-seeking) may play in the ascension of women through professional hierarchies. Unlike previous models, our novel model predicts that gender parity is not inevitable, and deliberate intervention may be required to achieve gender balance in several fields. To validate the model, we analyze a new database of gender fractionation over time for 16 professional hierarchies. We quantify the degree of homophily and bias in each professional hierarchy, and we propose specific interventions to achieve gender parity more quickly.

Published
2019
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3. Heat conduction through permafrost and its potential for explosive behavior

Author

Hill, Kaitlin and McGehee, Richard

Subjects
Physics - Geophysics
Abstract

The recent widespread thaw of permafrost has led to observations of explosive gas emissions, which expel ice and soil debris and leave behind large craters. This phenomenon appears to be caused by a buildup of pressure from below the permafrost, possibly due to gas released as permafrost melts, followed by a sudden emission of gas through the surface. Although there have been some studies modeling the processes involved in crater formation using computationally complex models, we propose that these explosive events can be attributed to a simple heat diffusion-based process. Under certain boundary conditions and parameters, this may be sufficient to describe the explosive behavior observed. We demonstrate this effect by linearly increasing surface temperature from average monthly values (1961-1990) at an example latitude, which causes more dramatic melting from below the permafrost than above. This may lead to a buildup of gas pressure, if the permafrost is both continuous and has a high ice saturation, and has the potential for sudden gas release., Comment: 5 pages, 1 figure

Published
2018

5. Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo

Author

Hill, Kaitlin, Abbot, Dorian S., and Silber, Mary

Subjects
Mathematics - Dynamical Systems, Physics - Atmospheric and Oceanic Physics, 49J52, 37N05 (Primary), 37B55, 37G15 (Secondary)
Abstract

As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcation behavior of certain Arctic energy balance models have been shown to be sensitive to how ice-albedo feedback is parameterized. We analyze an Arctic energy balance model in the limit as a smoothing parameter associated with ice-albedo feedback tends to zero, which introduces a discontinuity boundary to the dynamical systems model. Our analysis provides a case study where we use the system in this limit to guide the investigation of bifurcation behavior of the original albedo-smoothed system. In this case study, we demonstrate that certain qualitative bifurcation behaviors of the albedo-smoothed system can have counterparts in the limit with no albedo smoothing. We use this perspective to systematically explore the parameter space of the model. For example, we uncover parameter sets for which the largest transition, with increasing greenhouse gases, is from a perennially ice-covered Arctic to a seasonally ice-free state, an unusual bifurcation scenario that persists even when albedo-smoothing is reintroduced. This analysis provides an alternative perspective on how parameters of the model affect bifurcation behavior. We expect our approach, which exploits the width of repelling sliding intervals for understanding the hysteresis loops, would carry over to other positive feedback systems with a similar natural piecewise-smooth limit, and when the feedback strength is likewise modulated with seasons or other periodic forcing., Comment: 29 pages, 12 figures, 2 tables

Published
2015
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6. Persistence of Saddle Behavior in the Nonsmooth Limit of Smooth Dynamical Systems

Author

Leifeld, Julie, Hill, Kaitlin, and Roberts, Andrew

Subjects
Mathematics - Dynamical Systems, 37
Abstract

Models such as those involving abrupt changes in the Earth's reflectivity due to ice melt and formation often use nonlinear terms (e.g., hyperbolic tangent) to model the transition between two states. For various reasons, these models are often approximated by "simplified" discontinuous piecewise-linear systems that are obtained by letting the length of the transition region limit to zero. The smooth versions of these models may exhibit equilibrium solutions that are destroyed as parameter changes transition the models from smooth to nonsmooth. Using one such model as motivation, we explore the persistence of local behavior around saddle equilibria under these transitions. We find sufficient conditions under which smooth models with saddle equilibria can become nonsmooth models with "zombie saddle" behavior, and analogues of stable and unstable manifolds persist.

Published
2015

20. Proceedings of the 3rd Biennial Conference of the Society for Implementation Research Collaboration (SIRC) 2015: advancing efficient methodologies through community partnerships and team science

Author

Lewis, Cara, primary, Darnell, Doyanne, additional, Kerns, Suzanne, additional, Monroe-DeVita, Maria, additional, Landes, Sara J., additional, Lyon, Aaron R., additional, Stanick, Cameo, additional, Dorsey, Shannon, additional, Locke, Jill, additional, Marriott, Brigid, additional, Puspitasari, Ajeng, additional, Dorsey, Caitlin, additional, Hendricks, Karin, additional, Pierson, Andria, additional, Fizur, Phil, additional, Comtois, Katherine A., additional, Palinkas, Lawrence A., additional, Chamberlain, Patricia, additional, Aarons, Gregory A., additional, Green, Amy E., additional, Ehrhart, Mark. G., additional, Trott, Elise M., additional, Willging, Cathleen E., additional, Fernandez, Maria E., additional, Woolf, Nicholas H., additional, Liang, Shuting Lily, additional, Heredia, Natalia I., additional, Kegler, Michelle, additional, Risendal, Betsy, additional, Dwyer, Andrea, additional, Young, Vicki, additional, Campbell, Dayna, additional, Carvalho, Michelle, additional, Kellar-Guenther, Yvonne, additional, Damschroder, Laura J., additional, Lowery, Julie C., additional, Ono, Sarah S., additional, Carlson, Kathleen F., additional, Cottrell, Erika K., additional, O’Neil, Maya E., additional, Lovejoy, Travis L., additional, Arch, Joanna J., additional, Mitchell, Jill L., additional, Lewis, Cara C., additional, Marriott, Brigid R., additional, Scott, Kelli, additional, Coldiron, Jennifer Schurer, additional, Bruns, Eric J., additional, Hook, Alyssa N., additional, Graham, Benjamin C., additional, Jordan, Katelin, additional, Hanson, Rochelle F., additional, Moreland, Angela, additional, Saunders, Benjamin E., additional, Resnick, Heidi S., additional, Stirman, Shannon Wiltsey, additional, Gutner, Cassidy A., additional, Gamarra, Jennifer, additional, Vogt, Dawne, additional, Suvak, Michael, additional, Wachen, Jennifer Schuster, additional, Dondanville, Katherine, additional, Yarvis, Jeffrey S., additional, Mintz, Jim, additional, Peterson, Alan L., additional, Borah, Elisa V., additional, Litz, Brett T., additional, Molino, Alma, additional, McCaughan, Stacey Young, additional, Resick, Patricia A., additional, Pandhi, Nancy, additional, Jacobson, Nora, additional, Serrano, Neftali, additional, Hernandez, Armando, additional, Schreiter, Elizabeth Zeidler-, additional, Wietfeldt, Natalie, additional, Karp, Zaher, additional, Pullmann, Michael D., additional, Lucenko, Barbara, additional, Pavelle, Bridget, additional, Uomoto, Jacqueline A., additional, Negrete, Andrea, additional, Cevasco, Molly, additional, Kerns, Suzanne E. U., additional, Franks, Robert P., additional, Bory, Christopher, additional, Miech, Edward J., additional, Damush, Teresa M., additional, Satterfield, Jason, additional, Satre, Derek, additional, Wamsley, Maria, additional, Yuan, Patrick, additional, O’Sullivan, Patricia, additional, Best, Helen, additional, Velasquez, Susan, additional, Barnett, Miya, additional, Brookman-Frazee, Lauren, additional, Regan, Jennifer, additional, Stadnick, Nicole, additional, Hamilton, Alison, additional, Lau, Anna, additional, Roesch, Scott, additional, Powell, Byron J., additional, Waltz, Thomas J., additional, Chinman, Matthew J., additional, Damschroder, Laura, additional, Smith, Jeffrey L., additional, Matthieu, Monica M., additional, Proctor, Enola K., additional, Kirchner, JoAnn E., additional, Matthieu, Monica J., additional, Rosen, Craig S., additional, Walker, Sarah C., additional, Bishop, Asia S., additional, Lockhart, Mariko, additional, Rodriguez, Allison L., additional, Manfredi, Luisa, additional, Nevedal, Andrea, additional, Rosenthal, Joel, additional, Blonigen, Daniel M., additional, Mauricio, Anne M., additional, Dishion, Thomas D., additional, Rudo-Stern, Jenna, additional, Smith, Justin D., additional, Wolk, Courtney Benjamin, additional, Harker, Colleen, additional, Olsen, Anne, additional, Shingledecker, Travis, additional, Barg, Frances, additional, Mandell, David, additional, Beidas, Rinad S., additional, Hansen, Marissa C., additional, Aranda, Maria P., additional, Torres-Vigil, Isabel, additional, Hartzler, Bryan, additional, Steinfeld, Bradley, additional, Gildred, Tory, additional, Harlin, Zandrea, additional, Shephard, Fredric, additional, Ditty, Matthew S., additional, Doyle, Andrea, additional, Bickel, John A., additional, Cristaudo, Katharine, additional, Fox, Dan, additional, Combs, Sonia, additional, Lischner, David H., additional, Van Dorn, Richard A., additional, Tueller, Stephen J., additional, Hinde, Jesse M., additional, Karuntzos, Georgia T., additional, Peterson, Roselyn, additional, Berliner, Lucy, additional, Murray, Laura K., additional, Botanov, Yevgeny, additional, Kikuta, Beverly, additional, Chen, Tianying, additional, Navarro-Haro, Marivi, additional, DuBose, Anthony, additional, Korslund, Kathryn E., additional, Linehan, Marsha M., additional, Harker, Colleen M., additional, Karp, Elizabeth A., additional, Edmunds, Sarah R., additional, Ibañez, Lisa V., additional, Stone, Wendy L., additional, Andrews, Jack H., additional, Johnides, Benjamin D., additional, Hausman, Estee M., additional, Hawley, Kristin M., additional, Prusaczyk, Beth, additional, Ramsey, Alex, additional, Baumann, Ana, additional, Colditz, Graham, additional, Choy-Brown, Mimi, additional, Meza, Rosemary D., additional, Wiltsey-Stirman, Shannon, additional, Sedlar, Georganna, additional, Lucid, Leah, additional, Zounlome, Nelson, additional, Lewis, Cara, additional, Monson, Candice M., additional, Shields, Norman, additional, Mastlej, Marta, additional, Landy, Meredith SH, additional, Lane, Jeanine, additional, Finn, Natalie K., additional, Torres, Elisa M., additional, Malte, Carol A., additional, Lott, Aline, additional, Saxon, Andrew J., additional, Boyd, Meredith, additional, Pierce, Jennifer D., additional, Lorthios-Guilledroit, Agathe, additional, Richard, Lucie, additional, Filiatrault, Johanne, additional, Hallgren, Kevin, additional, Crotwell, Shirley, additional, Muñoz, Rosa, additional, Gius, Becky, additional, Ladd, Benjamin, additional, McCrady, Barbara, additional, Epstein, Elizabeth, additional, Clapp, John D., additional, Ruderman, Danielle E., additional, Barwick, Melanie, additional, Barac, Raluca, additional, Zlotkin, Stanley, additional, Salim, Laila, additional, Davidson, Marnie, additional, Bunger, Alicia C., additional, Robertson, Hillary A., additional, Botsko, Christopher, additional, Smith, Brandy N., additional, Trent, Lindsay R., additional, Harned, Melanie S., additional, Ivanoff, André, additional, Garcia, Antonio R., additional, Kim, Minseop, additional, Snowden, Lonnie, additional, Landsverk, John, additional, Sweetland, Annika C., additional, Fernandes, Maria Jose, additional, Santos, Edilson, additional, Duarte, Cristiane, additional, Kritski, Afrânio, additional, Krawczyk, Noa, additional, Nelligan, Caitlin, additional, Wainberg, Milton L., additional, Sommerfeld, David H., additional, Chi, Benjamin, additional, Ezeanolue, Echezona, additional, Sturke, Rachel, additional, Kline, Lydia, additional, Guay, Laura, additional, Siberry, George, additional, Bennett, Ian M., additional, Beidas, Rinad, additional, Gold, Rachel, additional, Mao, Johnny, additional, Powers, Diane, additional, Vredevoogd, Mindy, additional, Unutzer, Jurgen, additional, Schroeder, Jennifer, additional, Volpe, Lane, additional, Steffen, Julie, additional, Pullmann, Michael D, additional, Jungbluth, Nathaniel, additional, Thompson, Kelly, additional, Segell, Eliza, additional, McGee-Vincent, Pearl, additional, Liu, Nancy, additional, Walser, Robyn, additional, Runnals, Jennifer, additional, Shaw, R. Keith, additional, Rosen, Craig, additional, Schmidt, Janet, additional, Calhoun, Patrick, additional, Varkovitzky, Ruth L., additional, Drahota, Amy, additional, Martinez, Jonathan I., additional, Brikho, Brigitte, additional, Meza, Rosemary, additional, Stahmer, Aubyn C., additional, Williamson, Anna, additional, Rubin, Ronnie M., additional, Hurford, Matthew O., additional, Weaver, Shawna L., additional, Mandell, David S., additional, Evans, Arthur C., additional, Stewart, Rebecca E., additional, Matlin, Samantha L., additional, Weaver, Shawna, additional, Hadley, Trevor R., additional, Gerke, Donald R., additional, Lewis, Ericka M., additional, McWilliam, Jenna, additional, Brown, Jacquie, additional, Tucker, Michelle, additional, Conte, Kathleen P, additional, Melvin, Abigail, additional, Liu, Freda, additional, Kotte, Amelia, additional, Hill, Kaitlin A., additional, Mah, Albert C., additional, Korathu-Larson, Priya A., additional, Au, Janelle R., additional, Izmirian, Sonia, additional, Keir, Scott, additional, Nakamura, Brad J., additional, Higa-McMillan, Charmaine K., additional, Cooper, Brittany Rhoades, additional, Funaiole, Angie, additional, Dizon, Eleanor, additional, Hawkins, Eric J., additional, Hagedorn, Hildi J., additional, Berger, Douglas, additional, Frank, Anissa, additional, Achtmeyer, Carol E., additional, Mariano, Anthony J., additional, Wolitzky-Taylor, Kate, additional, Rawson, Richard, additional, Ries, Richard, additional, Roy-Byrne, Peter, additional, Craske, Michelle, additional, Simmons, Dena, additional, Torrente, Catalina, additional, Nathanson, Lori, additional, Carroll, Grace, additional, Brown, Kimbree, additional, Ramos, Karina, additional, Thornton, Nicole, additional, Dishion, Thomas J., additional, Stormshak, Elizabeth A., additional, Shaw, Daniel S., additional, Wilson, Melvin N., additional, Tiderington, Emmy, additional, Smith, Bikki Tran, additional, Padgett, Deborah K., additional, Ray, Marilyn L., additional, Wandersman, Abraham, additional, Lamont, Andrea, additional, Hannah, Gordon, additional, Alia, Kassandra A., additional, Saldana, Lisa, additional, Schaper, Holle, additional, Campbell, Mark, additional, Shapiro, Valerie B., additional, Kim, B.K. Elizabeth, additional, Fleming, Jennifer L., additional, LeBuffe, Paul A., additional, Comtois, Katherine Anne, additional, Weiner, Bryan J., additional, and Halko, Heather, additional

Published
2016
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