Four lectures on Euler integrals by Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, Simon Telen

“…Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.…”
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Linearizability problem of persistent centers by Matej Mencinger, Brigita Ferčec, Wilker Fernandes, Regilene Oliveira

“…Using the methods and algorithms of computational algebra we characterize the planar cubic differential system having linearizable persistent and linearizable weakly persistent centers at the origin.…”
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Taylor Collocation Method for Nonlinear System of SecondOrder Boundary Value Problems by Elçin Gökmen, Mehmet Sezer

“…All numerical computations have been performed on the computer algebraic system Maple 9.…”
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Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections by Janko Böhm, Alessandro Georgoudis, Kasper J. Larsen, Hans Schönemann, Yang Zhang

“…Utilizing modern computational algebraic geometry techniques, this new method successfully trims traditional IBP systems dramatically to much simpler integral-relation systems on unitarity cuts. …”
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Algebraic Statistics in Practice: Applications to Networks by Casanellas, Marta, Petrović, Sonja, Uhler, Caroline

“…Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra, and computational algebra), geometry, and combinatorics to provide insight into knotty problems in mathematical statistics. …”
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Algebraic Statistics in Practice: Applications to Networks by Casanellas, Marta, Petrović, Sonja, Uhler, Caroline

“…Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra, and computational algebra), geometry, and combinatorics to provide insight into knotty problems in mathematical statistics. …”
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Efficient calculation of all steady states in large-scale overlapping generations models by Monireh Riahi, Felix Kuebler, Abdolali Basiri, Sajjad Rahmany

“…The characterization of steady states coincides with a geometrical representation of the algebraic variety of a polynomial ideal, and, in principle, one can apply computational algebraic geometry methods to solve the problem. …”
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Algebraic systems biology: a case study for the Wnt pathway by Gross, E, Harrington, H, Rosen, Z, Sturmfels, B

“…We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.…”

Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE by Yunfeng Jiang, Yang Zhang

“…Abstract In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. …”
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Pushforwards via scattering equations with applications to positive geometries by Tomasz Łukowski, Robert Moerman, Jonah Stalknecht

“…Our results use techniques from computational algebraic geometry, including companion matrices and the global duality of residues, and they extend the application of similar results for rational functions to rational differential forms.…”
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IMPLEMENTATION OF ROOT FINDING ALGORITHM OF MINIMUM PHASE FILTER USING VHDL by Zainab Noori Ghanim, Buthaina Mosa Omran, Malathe Salah Al-Deen

“… Root-finding is an oldest classical problem, which is still an important research topic, due to its impact on computational algebra and geometry. In communications systems, when the impulse response of the channel is minimum phase the state of equalization algorithm is reduced and the spectral efficiency will improved. …”
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Multivariate central limit theorems for random clique complexes by Temčinas, T, Nanda, V, Reinert, G

“…<p>Motivated by open problems in applied and computational algebraic topology, we establish multivariate normal approximation theorems for three random vectors which arise organically in the study of random clique complexes. …”

Decomposing the parameter space of biological networks via a numerical discriminant approach by Harrington, H, Mehta, D, Byrne, H, Hauenstein, J

“…Rather than simply determining the number and stability of steady-states at distinct points in parameter space, we decompose the parameter space into finitely many regions, the number and structure of the steady-state solutions being consistent within each distinct region. From a computational algebraic viewpoint, the boundary of these regions is contained in the discriminant locus. …”

Modeling of Some Classes of Extended Oscillators: Simulations, Algorithms, Generating Chaos, and Open Problems by Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev, Vesselin Kyurkchiev, Asen Rahnev

“…One of the main goals of the study is to share the difficulties that researchers (who are not necessarily professional mathematicians) encounter in using contemporary computer algebraic systems (CASs) for scientific research to examine in detail the dynamics of modifications of classical and newer models that are emerging in the literature (for the large values of the parameters of the models). …”
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Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas by Yuanyuan Liu, Jalil Manafian, Gurpreet Singh, Naief Alabed Alkader, Kottakkaran Sooppy Nisar

“…This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. …”
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Analysis of isogrid reinforced cylindrical vessels in the case of axially symmetric buckling by Stefan HOTHAZIE, Camelia MUNTEANU, Mihaela NASTASE, Radu BIBIRE

“…The analytical algorithm is then implemented in a computed algebra system, which will quickly compute approximate values for the buckling factor and mass of the structure.…”
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Quasi-cyclic codes by Güneri, Cem, Ling, San, Özkaya, Buket

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Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach by Cifuentes, Diego Fernando, Parrilo, Pablo A

“…In this paper, we begin the study of how to exploit chordal structure in computational algebraic geometry---in particular, for solving polynomial systems. …”
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Joining and decomposing reaction networks by Gross, E, Harrington, H, Meshkat, N, Shiu, A

“…Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.…”

Joining and decomposing reaction networks by Gross, E, Harrington, H, Meshkat, N, Shiu, A

“…Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.…”