Results 11 to 20 of about 385,134 (275)
The bottleneck degree of algebraic varieties [PDF]
SIAM Journal on Applied Algebra and Geometry, 2019 A bottleneck of a smooth algebraic variety $X \subset \mathbb{C}^n$ is a pair of distinct points $(x,y) \in X$ such that the Euclidean normal spaces at $x$ and $y$ contain the line spanned by $x$ and $y$.
Di Rocco, Sandra +2 more
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The algebraic degree of semidefinite programming [PDF]
Mathematical Programming, 2008 Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of ...
Nie, Jiawang +2 more
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Maximizing Algebraic Connectivity via Minimum Degree and Maximum Distance
IEEE Access, 2018 Algebraic connectivity, the second smallest eigenvalue of the graph Laplacian matrix, is a fundamental performance measure in various network systems, such as multi-agent networked systems.
Gang Li +3 more
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Homogeneous Algebraic Varieties and Transitivity Degree
Proceedings of the Steklov Institute of Mathematics, 2022 Let $X$ be an algebraic variety such that the group $\text{Aut}(X)$ acts on $X$ transitively. We define the transitivity degree of $X$ as a maximal number $m$ such that the action of $\text{Aut}(X)$ on $X$ is $m$-transitive. If the action of $\text{Aut}(X)$ is $m$-transitive for all $m$, the transitivity degree is infinite.
Arzhantsev, Ivan V. +2 more
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Algebraic Degree of Polynomial Optimization [PDF]
SIAM Journal on Optimization, 2009 Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, %% on these polynomials, we prove that the optimality conditions always hold on optimizers, and the coordinates of optimizers are algebraic functions of the coefficients of the input polynomials.
Nie, Jiawang, Ranestad, Kristian
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It Is Better to Be Semi-Regular When You Have a Low Degree [PDF]
EntropyWe study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity as well as the full spectrum distribution. For an integer d∈3,7,
Theodore Kolokolnikov
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Influence of the Linear Layer on the Algebraic Degree in SP-Networks
IACR Transactions on Symmetric Cryptology, 2022 We consider SPN schemes, i.e., schemes whose non-linear layer is defined as the parallel application of t ≥ 1 independent S-Boxes over F2n and whose linear layer is defined by the multiplication with a (n · t) × (n · t) matrix over F2.
Carlos Cid +5 more
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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On the Degree of Product of Two Algebraic Numbers
Mathematics, 2023 A triplet (a,b,c) of positive integers is said to be product-feasible if there exist algebraic numbers α, β and γ of degrees (over Q) a, b and c, respectively, such that αβγ=1.
Lukas Maciulevičius
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Composition algebras of degree two [PDF]
Proceedings of the Edinburgh Mathematical Society, 1999 Composition algebras in which the subalgebra generated by any element has dimension at most two are classified over fields of characteristic ≠2,3. They include, besides the classical unital composition algebras, some closely related algebras and all the composition algebras with invariant quadratic norm.
Elduque, A., Pérez-Izquierdo, J.M.
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