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Articles 1 - 9 of 9
Full-Text Articles in Applied Mathematics
Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk
Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk
Department of Mathematics: Faculty Publications
One quarter of veterans returning from the 1990–1991 Persian Gulf War have developed Gulf War Illness (GWI) with chronic pain, fatigue, cognitive and gastrointestinal dysfunction. Exertion leads to characteristic, delayed onset exacerbations that are not relieved by sleep. We have modeled exertional exhaustion by comparing magnetic resonance images from before and after submaximal exercise. One third of the 27 GWI participants had brain stem atrophy and developed postural tachycardia after exercise (START: Stress Test Activated Reversible Tachycardia). The remainder activated basal ganglia and anterior insulae during a cognitive task (STOPP: Stress Test Originated Phantom Perception). Here, the role of attention …
Intermediate C∗-Algebras Of Cartan Embeddings, Jonathan H. Brown, Ruy Exel, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff
Intermediate C∗-Algebras Of Cartan Embeddings, Jonathan H. Brown, Ruy Exel, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff
Department of Mathematics: Faculty Publications
Let A be a C*-algebra and let D be a Cartan subalgebra of A. We study the following question: if B is a C*-algebra such that D B A, is D a Cartan subalgebra of B? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A onto B, and the case when A is nuclear and D is a C*-diagonal of A. In both cases there is a one-to-one correspondence between the intermediate C*-algebras B, and a class of open subgroupoids of the groupoid G, where ! G is the twist …
A “Rule-Of-Five” Framework For Models And Modeling To Unify Mathematicians And Biologists And Improve Student Learning, C. Diaz Eaton, H. C. Highlander, K. D. Dahlquist, G. Ledder, M.D. Lamar, R.C. Schugart
A “Rule-Of-Five” Framework For Models And Modeling To Unify Mathematicians And Biologists And Improve Student Learning, C. Diaz Eaton, H. C. Highlander, K. D. Dahlquist, G. Ledder, M.D. Lamar, R.C. Schugart
Department of Mathematics: Faculty Publications
Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the “Rule-of-Four,” initially used in calculus reform efforts, to a “Rule-of-Five” framework for models and modeling that is inclusive of varying disciplinary definitions of each. This unifying framework allows us to both build on strengths that each discipline and its students bring, but also identify gaps in modeling activities practiced by each discipline. We also discuss benefits to student learning and interdisciplinary collaboration.
Predicting Impacts Of Chemicals From Organisms To Ecosystem Service Delivery: A Case Study Of Insecticide Impacts On A Freshwater Lake, Nika Galic, Chris J. Salice, Bjorn Birnir, Randall J.F. Bruins, Virginie Ducrot, Henriette I. Jager, Andrew Kanarek, Roberto Pastorok, Richard Rebarber, Pernille Thorbek, Valery E. Forbes
Predicting Impacts Of Chemicals From Organisms To Ecosystem Service Delivery: A Case Study Of Insecticide Impacts On A Freshwater Lake, Nika Galic, Chris J. Salice, Bjorn Birnir, Randall J.F. Bruins, Virginie Ducrot, Henriette I. Jager, Andrew Kanarek, Roberto Pastorok, Richard Rebarber, Pernille Thorbek, Valery E. Forbes
Department of Mathematics: Faculty Publications
Assessing and managing risks of anthropogenic activities to ecological systems is necessary to ensure sustained delivery of ecosystem services for future generations. Ecological models provide a means of quantitatively linking measured risk assessment end points with protection goals, by integrating potential chemical effects with species life history, ecological interactions, environmental drivers and other potential stressors. Here we demonstrate how an ecosystem modeling approach can be used to quantify insecticide-induced impacts on ecosystem services provided by a lake from toxicity data for organism-level endpoints. We used a publicly available aquatic ecosystem model AQUATOX that integrates environmental fate of chemicals and their …
Determinants Of Incidence And Hessian Matrices Arising From The Vector Space Lattice, Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe
Determinants Of Incidence And Hessian Matrices Arising From The Vector Space Lattice, Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe
Department of Mathematics: Faculty Publications
Let V = ni= o VI bethe lattice of subspaces of the n-dimensional vector space over the finite field Fq, and let A be the graded Gorenstein algebra defined over Q which has V as a Q basis. Let F be the Macaulay dual generator for A. We explicitly compute the Hessian determinant j 2F= Xi Xj j, evaluated at the point X1 = X2 = ... = XN = 1, and relate it to the determinant of the incidence matrix between V1 and Vn-1. Our exploration is motivated by the fact that both of these matrices naturally …
Associated Primes And Syzygies Of Linked Modules, Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi, Arash Sadeghi, Ryo Takahaski
Associated Primes And Syzygies Of Linked Modules, Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi, Arash Sadeghi, Ryo Takahaski
Department of Mathematics: Faculty Publications
Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local ring R, if a Cohen-Macaulay R-module M of grade g is linked to an R-module N by a Gorenstein ideal c, such that AssR(M)\AssR(N) = ;, then M R N is isomorphic to direct sum of copies of R=a, where a is a Gorenstein ideal of R of grade g + 1. We give a criterion for the depth of a local ring (R;m; k) in terms of the homological dimensions of the modules linked to the syzygies of the residue eld k. As a …
A Doubly Nonlocal Laplace Operator And Its Connection To The Classical Laplacian, Petronela Radu, Kelseys Wells
A Doubly Nonlocal Laplace Operator And Its Connection To The Classical Laplacian, Petronela Radu, Kelseys Wells
Department of Mathematics: Faculty Publications
In this paper, motivated by the state-based peridynamic frame- work, we introduce a new nonlocal Laplacian that exhibits double nonlocality through the use of iterated integral operators. The operator introduces addi- tional degrees of exibility that can allow for better representation of physical phenomena at different scales and in materials with different properties. We study mathematical properties of this state-based Laplacian, including connec- tions with other nonlocal and local counterparts. Finally, we obtain explicit rates of convergence for this doubly nonlocal operator to the classical Laplacian as the radii for the horizons of interaction kernels shrink to zero.
Intermediate Cell States In Epithelial-To-Mesenchymal Transition, Yutong Sha, Daniel Haensel, Guadalupe Gutierrez, Huijing Du, Xing Dai, Qing Nie
Intermediate Cell States In Epithelial-To-Mesenchymal Transition, Yutong Sha, Daniel Haensel, Guadalupe Gutierrez, Huijing Du, Xing Dai, Qing Nie
Department of Mathematics: Faculty Publications
The transition of epithelial cells into a mesenchymal state (epithelial-to-mesenchymal transition or EMT) is a highly dynamic process implicated in various biological processes. During EMT, cells do not necessarily exist in ‘pure’ epithelial or mesenchymal states. There are cells with mixed (or hybrid) features of the two, which are termed as the intermediate cell states (ICSs). While the exact functions of ICS remain elusive, together with EMT it appears to play important roles in embryogenesis, tissue development, and pathological processes such as cancer metastasis. Recent single cell experiments and advanced mathematical modeling have improved our capability in identifying ICS and …
Persistence Metrics For A River Population In A Two-Dimensional Benthic-Drift Model, Yu Jin, Qihua Huang, Julia Blackburn, Mark A. Lewis
Persistence Metrics For A River Population In A Two-Dimensional Benthic-Drift Model, Yu Jin, Qihua Huang, Julia Blackburn, Mark A. Lewis
Department of Mathematics: Faculty Publications
The study of population persistence in river ecosystems is key for understanding population dynamics, invasions, and instream flow needs. In this paper, we extend theories of persistence measures for population models in one-dimensional rivers to a benthic-drift model in two-dimensional depth- averaged rivers. We define the fundamental niche and the source and sink metric, and establish the net reproductive rate R0 to determine global persistence of a population in a spatially heterogeneous two-dimensional river. We then couple the benthic-drift model into the two-dimensional computational river model, River2D, to study the growth and persistence of a population and its source …