- Browse by Author

### Browsing by Author "Mathematical Sciences, School of Science"

Now showing 1 - 10 of 214

###### Results Per Page

###### Sort Options

Item 3D simulation of a viscous flow past a compliant model of arteriovenous-graft annastomosis(Elsevier, 2019-03) Bai, Zengding; Zhu, Luoding; Mathematical Sciences, School of ScienceHemodialysis is a common treatment for end-stage renal-disease patients to manage their renal failure while awaiting kidney transplant. Arteriovenous graft (AVG) is a major vascular access for hemodialysis but often fails due to the thrombosis near the vein-graft anastomosis. Almost all of the existing computational studies involving AVG assume that the vein and graft are rigid. As a first step to include vein/graft flexibility, we consider an ideal vein-AVG anastomosis model and apply the lattice Boltzmann-immersed boundary (LB-IB) framework for fluid-structure-interaction. The framework is extended to the case of non-uniform Lagrangian mesh for complex structure. After verification and validation of the numerical method and its implementation, many simulations are performed to simulate a viscous incompressible flow past the anastomosis model under pulsatile flow condition using various levels of vein elasticity. Our simulation results indicate that vein compliance may lessen flow disturbance and a more compliant vein experiences less wall shear stress (WSS).Item A conclusive theorem on Finsler metrics of sectional flag curvature(arXiv, 2018-12-22) Huang, Libing; Shen, Zhongmin; Mathematical Sciences, School of ScienceIf the flag curvature of a Finsler manifold reduces to sectional curvature, then locally either the Finsler metric is Riemannian, or the flag curvature is isotropic.Item A Literature Review of Similarities Between and Among Patients With Autism Spectrum Disorder and Epilepsy(Springer Nature, 2023-01-18) Assuah, Freda B.; Emanuel, Bryce; Lacasse, Brianna M.; Beggs, John; Lou, Jennie; Motta, Francis C.; Nemzer, Louis R.; Worth, Robert; Cravens, Gary D.; Mathematical Sciences, School of ScienceAutism spectrum disorder (ASD) has been shown to be associated with various other conditions, and most commonly, ASD has been demonstrated to be linked to epilepsy. ASD and epilepsy have been observed to exhibit high rates of comorbidity, even when compared to the co-occurrence of other disorders with similar pathologies. At present, nearly one-half of the individuals diagnosed with ASD also have been diagnosed with comorbid epilepsy. Research suggests that both conditions likely share similarities in their underlying disease pathophysiology, possibly associated with disturbances in the central nervous system (CNS), and may be linked to an imbalance between excitation and inhibition in the brain. Meanwhile, it remains unclear whether one condition is the consequence of the other, as the pathologies of both disorders are commonly linked to many different underlying signal transduction mechanisms. In this review, we aim to investigate the co-occurrence of ASD and epilepsy, with the intent of gaining insights into the similarities in pathophysiology that both conditions present with. Elucidating the underlying disease pathophysiology as a result of both disorders could lead to a better understanding of the underlying mechanism of disease activity that drives co-occurrence, as well as provide insight into the underlying mechanisms of each condition individually.Item An asymptotic expansion for the expected number of real zeros of Kac-Geronimus polynomials(Rocky Mountain Mathematics Consortium, 2021) Aljubran, Hanan; Yattselev, Maxim L.; Mathematical Sciences, School of ScienceLet {φi(z;α)}i=0∞, corresponding to α∈(−1,1), be orthonormal Geronimus polynomials. We study asymptotic behavior of the expected number of real zeros, say 𝔼n(α), of random polynomials Pn(z):= ∑i=0nηiφi(z;α), where η0,…,ηn are i.i.d. standard Gaussian random variables. When α=0, φi(z;0)=zi and Pn(z) are called Kac polynomials. In this case it was shown by Wilkins that 𝔼n(0) admits an asymptotic expansion of the form 𝔼n(0)∼2πlog(n+1)+ ∑p=0∞Ap(n+1)−p (Kac himself obtained the leading term of this expansion). In this work we obtain a similar expansion of 𝔼(α) for α≠0. As it turns out, the leading term of the asymptotics in this case is (1∕π)log(n+1).Item Arithmetic properties of 3-cycles of quadratic maps over Q(Elsevier, 2022-11) Morton, Patrick; Raianu, Serban; Mathematical Sciences, School of ScienceIt is shown that c = -29/16 is the unique rational number of smallest denominator, and the unique rational number of smallest numerator, for which the map fc(x) = x2 + c has a rational periodic point of period 3. Several arithmetic conditions on the set of all such rational numbers c and the rational orbits of fc(x) are proved. A graph on the numerators of the rational 3-periodic points of maps fc is considered which reflects connections between solutions of norm equations from the cubic field of discriminant -23.Item Assessing the hemodynamic contribution of capillaries, arterioles, and collateral arteries to vascular adaptations in arterial insufficiency(Wiley, 2019) Arciero, Julia; Lembcke, Lauren; Franko, Elizabeth; Unthank, Joseph; Mathematical Sciences, School of ScienceObjective There is currently a lack of clarity regarding which vascular segments contribute most significantly to flow compensation following a major arterial occlusion. This study uses hemodynamic principles and computational modeling to demonstrate the relative contributions of capillaries, arterioles, and collateral arteries at rest or exercise following an abrupt, total, and sustained femoral arterial occlusion. Methods The vascular network of the simulated rat hindlimb is based on robust measurements of blood flow and pressure in healthy rats from exercise and training studies. The sensitivity of calf blood flow to acute or chronic vascular adaptations in distinct vessel segments is assessed. Results The model demonstrates that decreasing the distal microcirculation resistance has almost no effect on flow compensation, while decreasing collateral arterial resistance is necessary to restore resting calf flow following occlusion. Full restoration of non‐occluded flow is predicted under resting conditions given all chronic adaptations, but only 75% of non‐occluded flow is restored under exercise conditions. Conclusion This computational method establishes the hemodynamic significance of acute and chronic adaptations in the microvasculature and collateral arteries under rest and exercise conditions. Regardless of the metabolic level being simulated, this study consistently shows the dominating significance of collateral vessels following an occlusion.Item An asymptotic expansion for the expected number of real zeros of real random polynomials spanned by OPUC(Elsevier, 2019-01) Aljubran, Hanan; Yattselev, Maxim L.; Mathematical Sciences, School of ScienceLet {φi}∞i=0 be a sequence of orthonormal polynomials on the unit circle with respect to a positive Borel measure μ that is symmetric with respect to conjugation. We study asymptotic behavior of the expected number of real zeros, say En(μ), of random polynomials Pn(z):=∑i=0nηiφi(z), where η0,…,ηn are i.i.d. standard Gaussian random variables. When μ is the acrlength measure such polynomials are called Kac polynomials and it was shown by Wilkins that En(|dξ|) admits an asymptotic expansion of the form En(|dξ|)∼2πlog(n+1)+∑p=0∞Ap(n+1)−p (Kac himself obtained the leading term of this expansion). In this work we generalize the result of Wilkins to the case where μ is absolutely continuous with respect to arclength measure and its Radon-Nikodym derivative extends to a holomorphic non-vanishing function in some neighborhood of the unit circle. In this case En(μ) admits an analogous expansion with coefficients the Ap depending on the measure μ for p≥1 (the leading order term and A0 remain the same).Item Asymptotic normality of quadratic forms with random vectors of increasing dimension(Elsevier, 2018-03) Peng, Hanxiang; Schick, Anton; Mathematical Sciences, School of ScienceThis paper provides sufficient conditions for the asymptotic normality of quadratic forms of averages of random vectors of increasing dimension and improves on conditions found in the literature. Such results are needed in applications of Owen’s empirical likelihood when the number of constraints is allowed to grow with the sample size. Indeed, the results of this paper are already used in Peng and Schick (2013) for this purpose. We also demonstrate how our results can be used to obtain the asymptotic distribution of the empirical likelihood with an increasing number of constraints under contiguous alternatives. In addition, we discuss potential applications of our result. The first example focuses on a chi-square test with an increasing number of cells. The second example treats testing for the equality of the marginal distributions of a bivariate random vector. The third example generalizes a result of Schott (2005) by showing that a standardized version of his test for diagonality of the dispersion matrix of a normal random vector is asymptotically standard normal even if the dimension increases faster than the sample size. Schott’s result requires the dimension and the sample size to be of the same order.Item Asymptotics of bordered Toeplitz determinants and next-to-diagonal Ising correlations(arXiv, 2021) Basor, Estelle; Ehrhardt, Torsten; Gharakhloo, Roozbeh; Its, Alexander; Li, Yuqi; Mathematical Sciences, School of ScienceWe prove the analogue of the strong Szeg{\H o} limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk \cite{YP} for the next-to-diagonal correlations ⟨σ0,0σN−1,N⟩ in the anisotropic square lattice Ising model, we rigorously justify that the next-to-diagonal long-range order is the same as the diagonal and horizontal ones in the low temperature regime. The anisotropy-dependence of the subleading term in the asymptotics of the next-to-diagonal correlations is also established. We use Riemann-Hilbert and operator theory techniques, independently and in parallel, to prove these results.Item Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-Type Weight(Springer, 2020) Barhoumi, Ahmad; Yattselev, Maxim L.; Mathematical Sciences, School of ScienceWe investigate asymptotic behavior of polynomials Qn(z) satisfying non-Hermitian orthogonality relations ∫ΔskQn(s)ρ(s)ds=0,k∈{0,…,n−1}, where Δ:=[−a,a]∪[−ib,ib], a,b>0, and ρ(s) is a Jacobi-type weight.